OOG FILE COPY AD AO 48230

REPORT SAMSO-TR-77-209

Reactive Single Collision Studies with
Metal Atoms or Metal Halides

Chemistry and Physics Laboratory
The Ivan A. Getting Laboratories
The Aerospace Corporation
El Segundo, Calif. 90245

14 November 1977

Interim Report

Prepared for

SPACE AND MISSILE SYSTEMS ORGANIZATION
AIR FORCE SYSTEMS COMMAND
Los Angeles Air Force Station
P.O. Box 92960, Worldway Postal Center
Los Angeles, Calif. 90009

APPROVED FOR PUBLIC RELEASE;
DISTRIBUTION UNLIMITED

This interim report was submitted by The Aerospace Corporation,

El Segundo, CA 90245, under Contract No. F04701-77-C-0078 with the
Space and Missile Systems Organization, Deputy for Advanced Space ^
Programs, P. O. Box 92960, Worldway Postal Center, Los Angeles,

CA 90009 . It was reviewed and approved for The Aerospace Corporation
by S. Siegel, Director, Chemistry and Physics Laboratory. Lieutenant
A. G. Fernandez, SAMSO/YCPT, was the project officer for Advanced
Space Programs.

This report has been reviewed by the Information Office (OI) and is
releasable to the National Technical Information Service (NTIS). At NTIS,
it will be available to the general public, including foreign nations.

This technical report has been reviewed and is approved for publica-
tion. Publication of this report does not constitute Air Force Approval of
the report's findings, or conclusions. It is published only for the exchange
and stimulation of ideas.

SECURITY classification OF THIS PAGE flWl»n Dmim Bnltttd)

I IT JJT^ Tin:

EPORT DOCUMENTATION PAGE

READ INSTRUCTIONS
BEFORE COMPLETING FORM

&EACTIVE ^GLE COLLISION STUDIES WITH METAL

Atoms OR MET AL ^ALiDES. "

78(39 7/1- 10) - 2

7. AUTHORr*;

9. PERFORMING ORGANIZATION NAME AND ADDRESS

The Aerospace Corporation
El Segundo, Calif. 90245 V

It. CONTROLLING OFFICE NAME and ADDRESS >/

Space and Missile Systems Organization /

Air Force Systems Command v ,

Lo 3 Angeles, Calif. 90009

*■ monitoring agency name a ADDRESSCI/ di//«ran( Irom Coninlling OlUct)

16. DISTRIBUTION STATEMENT (ol Ihl* Report)

Approved for public release; distribution unlimited

to. program element, PROJECT, TASK
AREA A WORK UNIT NUMBERS

f/S' IjUj

t5«. DECLASSIFICATION/ DOWNGRADING

schedule

, G

19. KEY WORDS (Cont/nu 0 on roi^oro* «/«f« ti nmcmm^mry and identify by block nuatbor)

y 3 ^

Alkali Atoms

Alkali Halides ^ oh r

Metal Atoms / , n

Reactive Scattering / Zi j

Molecular Beams , V / w 0

20. abstract (Canllnup an nrmrma tida H nacaaamry and Idanllly by ^lock number;

Molecular beam studies at low energy (typically ilOO kj/mole) of reactive scattering of
metal atoms, metal dimers, or metal halides from a variety of halide molecules are reviewed.
Studies of vibrationally inelastic scattering of alkali halides are also reviewed.

DO 1473

(PACSIMILCI

MCURITY CLAttinCAtiON OT THIS FAOC (Whm Oat# Iwtcrw^)

I was fortunate to enter this field practically from its conception as a graduate '

student under Prof. D. R. Herschbach. I was equally fortunate to participate in it to its ,

present stage of maturity because of the dedication of an excellent group of graduate !

students who studied under me at the University of California at Berkeley and Iowa State , |

University: D. D. Parrish, S. M. Lin, C. A. Mims, B. L. Earl, L. C.-H. Loh, L. A. Gundel, jj

j S

C. M. Shollen, R. Behrens, Jr., A. Freedman, and T. P. Parr. I am also indebted to the jj

pi

USAEC and later USERDA for support of this work over a ten year period. l;

!'l

- 1 -

CONTENTS

PREFACE 1

I. Introduction 9

II. The Molecular Beam Approach 13

II. A. Beam Sources 19

II. B. Detection of Scattered Species 16

III. The Variety of Reactive Scattering Measurements 23

III.A. Product Recoil Angle and Energy Distributions 23

III.B. Dependence upon Reactant Quantum States 35

III. C. Dependence upon Product Quantum States 41

IV. Results for Different Chemical Systems 45

IV.A. Scattering of Alkali Halide Molecules 46

IV.B. Reactive Scattering of Alkali Atoms 55

IV. C. Alkali Dimer plus Various Halides 71

V. Closing Remarks 64

REFERENCES 79

i

I-

PRECKDINO page blank-hot niMSD

FIGURES

1. Schematic diagram of a product magnetic deflection slotted
disk velocity analysis apparatus (viewed from above) used to
study reactions of Li atoms with halogen-containing

compounds 115

2. LAB ■* — ►CM coordinate systems velocity vector transfor-
mation diagram for the collision of A and B to give C and D 116

3. LAB angular distributions measured by surface ionization with
a sensitized filament (K + KBr) and desensitized filament (K)

for the scattering of K from HBr 117

4. The upper panel shows three sets (i.e., dash, solid, and dot-dash
curves) of collision-energy-independent product recoil angle and
energy CM distributions which fit (solid curve) the measured
LAB Bal product angular distribution data points from the

Ba + CH^l reaction 118

3 2

5. CM polar contour map of 9 cr/d w9w (assumed energy
independent) for scattering for KI from crossed beams of K and

I2 119

2

6 . Contours show plots of constant LiO (X 77) product flux in the

LAB coordinate system from the LI + NO2 reaction 120

7. Different curves show P(Ep functions obtained by

fitting different 9"^ cr/ 9^ w9w expansion functions
to LiX product LAB recoil velocity spectra measure-
ments for the Li + CH^N02, CCl^^, and CH^I reactions 121

8. LAB angular distributions (normalized to unit peak heights) of
reactively scattered KI or KCl for reactions of K with orientated

(a) CH3I, (b) t-BuI, (c) CHCI3, and (d) CF3I 122

9. The open circles show measured non-reactive scattering of

K from CCl^ transformed into the CM system 123

10. Alkali iodide CM product recoil momentum distributions

normalized to the same peak heights 124

11. Schematic depiction of a possible "double rebound" mechanism

to account for forward KI scattering in the K2 + CH3I reaction 125

-5- prscsdino paos blank-hot PIUOD

I. Introduction

The Bull and Moon (1954) study of the Cs + CCl^ reaction and Taylor and Datz (1955)
study of the K + HBr reaction represent the earliest successful observations of product ?

formation in molecular beam reactive scattering. The subsequent early era of neutral ^

i

molecular beam reactive scattering experiments continued to be dominated by

observations of alkali halide formation in reactions of alkali atoms with compounds

containing halogens because of the sensitivity and selectivity of the hot filament surface

ionization detector. More recently, implementation of advances in vacuum and mass

spectrometry technologies has freed the field of this initial preoccupation with alkali and

alkali halide chemistry and has vastly extended its chemical scope. Nevertheless, studies

of alkali and alkali halide chemistry continue to comprise a significant fraction of the

effort in this field despite the full blossoming of the "non-alkali era". This continuing

interest is partially due to the ability of simple collision models to simulate the observed

reaction features (at least qualitatively) and correlate them with electronic structure for

some of the reaction systems. The conceptual simplicity and directness of the molecular

beam approach continues to make it the most versatile single tool available to the modern :

experimental collision dynamacist who wishes to determine the dependence of the

reaction cross section on detailed parameters (quantum states) of reactant and products. ;

Reactions of alkali atoms continue to provide the chemical arena for the widest ■

\

implementation of the various beam techniques. For this reason, the remainder of this J

chapter is organized so as to first briefly introduce the general beam concept. This is
followed by a discussion of the different types of detailed molecular beam measurements
which have been reported and their current experimental limitations. Particular
experimental studies may be cited here as illustrations. The final section is then devoted

i-

to discussions of the behaviours which have been reported for the different chemical
systems. The emphasis here is on the qualitative reaction features rather than detailed
quantitative numbers because this chapter provides an ideal format for celebrating the
wide variety of reaction mechanisms which are encountered in the alkali and alkali halide
reactions.

It is important to define the scope of the chapter at the outset because of the
enormity of the literature of this field. In general, discussion is confined to relatively
modest (typically <100 kJ/mole) energies in the collision partners and to the absence of
electronic excitation in either reactants or products because these topics are covered in
other chapters. Elastic and rotational inelastic collisions (i.e., "soft" collisions) of the
alkali halides are excluded, whereas vibrational inelastic and reactive collisions of the
alkali halides are included. Elastic and inelastic scattering of alkali atoms are excluded
unless these observations pertain to possible reactions between the same collision
partners. In this regard, "quenching" of glory undulations in the energy dependent total
scattering cross section [e.g., Helbing and Rothe (1968)] are not discussed, and no
attempt was made to insure a complete literature review of studies of the reactive
attenuation of the wide-angle elastic differential cross section. Reactive collisions of
alkali atoms with compounds containing halogens are discussed in detail as are similar
reactions producing alkali oxides, nitrites, cyanides, etc. Reactions of alkali dimers and
of other metal atoms with these same reagents are included in order to assess the extent
to which the chemistry of these species resembles that of the alkali atoms. Related
chemical studies of alkali dimer reactions with hydrogen or alkali atoms and of reactions
of other metals atoms with various oxides are not discussed because it was felt that these
systems are outside of the subject matter encompassed by the title of this volume.

- 10 -

An attempt has been made to cite all relevant experimental studies which appeared
in archival journals through the first quarter of 1977. Theoretical results or unpublished
experimental studies are cited only where they are especially relevant to the discussion.
No attempt has been made to cite all relevant review articles. The following reviews
have proven especially useful in preparing this chapter: Farrar and Lee (1974); Fluendy
and Lawley (1973); Gowenlock, et. 6d. (1976); Greene, et. al. (1966); Greene and Ross
(1968); Grice (1975); Herschbach (1961); Herschbach (1965); Herschbach (1966);
Herschbach (1973); Kinsey (1972); Polanyi (1972); Ross and Greene (1970); Steinfeld and
Kinsey (1970); Toennies (1974); and Zare and Dagdigian (1974).

- 11 -

1

i

1

I

1

[

II. The Molecular Beam Approach

Conceptually, the molecular beam approach is simple and direct. A beam of atoms
or molecules is generated by any of a variety of techniques and allowed to collide with a
second reagent in either a crossed beams or beam plus scattering cell mode of operation;
the scattered species are subsequently detected. Any number of selectors or analyzers
may be inserted between the beam source and detector in order to determine the
dependence of the collision cross section on reactant (E) or product (£') relative
translationeil energies or quantum states of interned motion. The experimental reality is,
of course, that any such selector or analyzer typically represents a significant reduction in
scattered intensity. The essence of molecular beam kinetics is the observation of
scattered species which represent the unreJaxed distribution produced by a single
bimolecular collision process. Experimentally, this is achieved by insuring that the
product of density and time of interaction of the collision partners within the intersection
volume defined by intersecting beams or the scattering cell be sufficiently small that the
probablity of any bimolecular process is low so that two or multiple collision processes are
totally inconsequential. For the same reason, the ambient background pressure must be
sufficiently low that the mean free path within the vacuum chamber exceeds its physical
dimensions. Finally, cryogenic vacuum chamber walls, beam modulation and phase
sensitive detection, and other experimental techniques must be combined in order to
insure that no species which has struck a wall of the vacuum chamber will be recorded as
a scattering event.

The crossed beams and beam plus scattering cell modes of operation are both
acceptable provided that these steps are taken to insure single collision conditions. Beam
plus scattering cell measurements have been common in ion-molecule reaction studies.

- 13 -

PRECEDINS PACK ELANK-NOT PIIMSD

even in determinations of product angular distributions. The majority of studies discussed
here, however, have used the crossed beams mode although scattering cells have been used
quite often in laser induced fluorescence (LIF) studies. It should be noted that resolution
in incident collision energy suffers in the beam plus scattering gas mode of operation. An
extreme example of the influence of this effect was provided by the contrasting
thresholds for change transfer ionization in collisions of alkali atoms with [Rothe and
Fenstermaker (1971)] .

II.A. Beam Sources

Since molecular beam source technology is carefully discussed in chapter 2 of this
volume, only a few relevant points need to be made here. Alkali atom beams have
typically been obtained from two chamber effusive ovens where the temperature of the
first chamber determines the pressure within the source. The second chamber is
maintained at a higher temperature in order to eliminate or at least reduce the alkali
dimer concentration in the beam. The alkali atoms also have a fortunate electronic
structure in that there are no metastable electronic states which can be thermally
populated; this can lead to problems in interpreting results in studies with vapors of some
other metals. Beams of alkali halides and of other metals which may require high
temperature to produce sufficient vapor pressures have often been obtained from single
chamber effusive sources so that the importance of dimer impurities in the beam varies
widely with the chemical system. It is totally inconsequential for the alkaline earths, for
example, because of the weak binding in the dimers. On the other hand, beams of alkali
halides may contain appreciable dimer. The increasing use of nozzle beams, at least with
reactants which have appreciable room temperature vapor pressure, also raises the
problem of possible dimerization or condensation in the expansion process. For example.

- 14 -

Gonzalez Urena et. al (1975) report the observation of K and Rb condensation reactions
with CHgl clusters; similar observations of Br 2 condensation on CI 2 or NH^ clusters are
reported in Behrens et. al (1975). In general, however, this does not appear to have been a
problem in any of the studies reviewed here. Foreman et. al (1972a) have also exploited
this phenomenon of dimerization in a nozzle expansion to produce intense beams of
homonuclear alkali dimers. They made use of the magnetic deflection technique discussed
below to eliminate the residual alkeili atoms from the expanded beam.

The distributions over velocity and internal energy within the beam are important in
the energy balance equation for the scattering process and in the transformation of the
data from the laboratory (LAB) to the center-of-mass (CM) coordinate system. Since this
is discussed in detail in Chapter 2, only a few succinct observations are noted here.
"Effusive" beam sources which are used in scattering studies are seldom at the true
effusive limit so that a thermal velocity distribution is not obtained although the
distribution over internal energy states is probably approximately Boltzman. Deviations
from the Boltzman velocity distribution which are observed are usually small and take the
form of a depletion of the slower particles from the beam [see, for example, Sholeen and
Herm (1976a)] . The cross beam in many of the reactive scattering experiments has been
obtained from a multichannel array source. In this case, deviations from a thermal speed
distribution are somewhat more pronounced [see, for example, Rulis and Bernstein (1972)
and Sholeen and Herm (1976a)] . Vibrational degrees of freedom are probably still
described by the thermal source distribution; there may be minor cooling of rotational
degrees of freedom, although the data on this is scanty at best [Rulis and Bernstein
(1972)] . Rotational and translational temperatures within an expanded nozzle beam are
typical relatively low, and the beam speed distribution is shaply peaked, it is usually a

- 15 -

resonable approximation to assume a thermal distribution over vibrational degrees
characteristic of the source. In the case of alkali dimers from a nozzle expansion,
however, the best available evidence indicates substantial vibrational relaxation as well
[Sinha, et.al. (1973)] , and this introduced slight uncertainty in the interpretation of some
reactive scattering studies with alkali dimers [Whitehead and Grice (1973)].

II.B. Detection of Scattered Species

II.B.l. Surface Ionization Detection

The ionization of alkali atoms at a hot tungsten surface has been known since the
early work of Langmuir [see, for example, Langmuir and Kingdom (1925)] and exploited
as an efficient (sometimes approaching 100%) detector of alkali atoms (M) and alkali
halides (MX) since the early days of molecular beam research [see, for example, Fraser
(1937)]. However, this was not a practical detection technique for molecular beam
studies of chemical reactions until the work of Datz and Taylor (1956) pointed out that Pt
and 12% Pt-8% W alloy surfaces could ionize M with considerably higher efficiencies than
MX and made possible the first crossed beams study of the K + HBr reaction by Taylor and
Datz (1955). Early attempts to study reactions of M with halogen molecules by this
differential surface ionization technique were sometimes erratic, however, until Touw and
Trischka (1963) pointed out that M/MX ionization efficiency ratios were markedly
different on 92% Pt-8% W hot surfaces which had previously been exposed to butane
(desensitized toward MX) versus oxygen (sensitized toward MX). Most molecular beam
studies of reactions of soduim, potassium, rubidium, or cesuim atoms or dimers with
compounds containing halogens have, in fact, employed this simple differential surface
ionization technique, and a representative sample of derived MX scattering distributions

- 16 -

have been confirmed by the independent magnetic deflection technique in Herm, et.al
(1964) and Gordon, et.al . (1968). The MX signal is determined by differential surface
ionization as the difference between signals read on a surface with comparable M and MX
efficiencies (W, Re, sensitized Pt or 92% Pt-8% W) and on a desensitized Pt or 92% Pt-
8% W surface after normalization to equal M sensitivities on the two surfaces. Despite its
wide use, however, there are some problems with the technique which should be noted in
order to better define its limitations. Both M and MX produce an M^ surface ion signal so
that the technique is insensitive to the identity of X. Product channel ratios in reactions
of alkali atoms with interhalogens are still unknown, for example, except for indirect
inferences provided by such studies as Moulton and Herschbach (1966). Desensitized
surfaces also exhibit some sensitivity to MX, and Gillen and Bernstein (1970) demonstrated
that this sensitivity increases with increasing internal excitation of MX. The effect is
small, however, and shouldn't seriously distort product recoil energy measurements.
Because the technique requires the difference of two signals, it cannot be used very close
to the M beam where the non-reactively scattered M greatly exceeds the reactively
scattered MX. For this same reason, it cannot be used to study reactions with very small
total reaction cross sections. Finally, it's chemical scope is limited. Studies of reactions
with some oxidizing gases (e.g., NO 2 ) are impractical because of concurrent sensitization
of the Pt filament [Herm and Herschbach (1970)] . It cannot be used for the study of
reactions of non-alkali metals; it is impractical for the study of Li atom • ■fictions
[Parrish and Herm (1968)] .

il •

I

II.B.l.a Product Magnetic Deflection

Figure 1 shows a schematic diagram of a magnetic deflection-slotted disk velocity-
analysis apparatus which was employed in a study of reactions of Li atoms with NO 2 and a
variety of halogen-containing molecules [Sholeen and Herm (1976a) and (1976b), Sholeen,
et. al. (1976), and Behrens, e^ ah (1976b)]. It is included here as an example of a modern
apparatus for the study of reactive scattering of alkali atoms and, more specifically, to
illustrate the product magnetic deflection technique which was deployed by Parrish and
Herm (1968), (1969), and (1971) in order to circumvent some of the problems of
differential surface ionization. An early molecular beam apparatus for reactive
scattering measurements provided for singly differential measurements in that a product
angular distribution was measured All reported product angular distributions have been
obtained with machines which provided for rotation of the source assembly relative to the
detector assembly, although the new approach of fourier transform doppler spectroscopy
might render this provision unnecessary in some cases in the future [Kinsey (1977)]. In
the particular apparatus shown in Fig. 1, the source assembly was mounted on a platform
j which could be rotated relative to a fixed detector assembly, but the alternate

arrangement is often preferable. The next generation of such machines incorporated one
of the selectors or analyzers discussed in Section III in order to permit doubly differential
measurements. More recently, use of two such devices makes possible triply differential
measurements [e.g., Gillen, e^ ah (1971)]. Figure 1, for example, includes both a slotted
desk velocity selector (SDVS) (J) and inhomogeneous deflecting electromagnet (E). A
mechanical beam chopper (O) with associated light cell (G) and phototransistor (R) for
i phase sensitive detection and an electron multiplier (B) are typical of modern techniques

! deployed to enhance signal-to-noise. A homogeneous electromagnet (C) mass

i

- 18 -

J

,1

spectrometer system was also employed in this particular apparatus in order to separate
the weak Li^ surface ion signal from the copious background due to poteissuim
impurities in the surface ionization filament (A).

In general, an atom or molecule in a magnetic or electric field, jT, will experience an
energy shift, W = W(X). If the field is spatially inhomogeneous, this will produce a force
on the particle given by

F = ^ (1) I

where Hg = " 9W/aX, the effective moment in the direction of the field gradient, is
independent of the field strength only in the case of a first order Zeeman or Stark in-
teraction. A particle moving with a kinetic energy, E, along a coordinate perpendicular to
VX will be displaced at the detector plane by

s" = lx ^^X ^ f"e (2)

in terms of the length of the field (1^^) and distance from the end of the field to the
detector (Ip). Equation (2) is the basis of both magnetic and electric deflection techniques
which are described in a number of monographs on molecular beam experiments [e.g.,

Fraser (1937) or Ramsey (1956)]. In the high field hyperfine Paschen-Bach limit (i.e., ^

A

above a few thousand Gauss), for example, for an alkali atom in the ground state
is approximately + //^, in terms of the Bohr magneton, In a simple deflecting field
such as the conventional "two wire" design [Ramsey (1956)] employed in Fig. 1, thermal
energy alkali atoms may be deflected several mm towards the pole gaps for reasonable

- 19 -

field lengths and easily achieved field gradients, thereby removing them from a well-

_3

collimated beam. On the other hand, » 10 for alkali dimers or alkali halides in

their singlet spin ground electronic states so that these molecules are effectively

undeflected upon traversing the same magnetic field. Thus, Foreman, et. al. (1972a)

employed this technique to prepare a pure beam of alkali dimers (Mg), and a couple of

laboratories have employed it as an alternate surface ionization detection scheme in order

to separate non-reactively scattered M from reactively scattered MX. In addition,

Sholeen and Herm (1976a) managed to confirm the production of both ground state LiO

(X 77) and excited state LiO (A E) from the Li + NO„ reaction because u a u for a

2 ^e — '^o

^ state whereas assumes many values (dependent on the total angular momentum

2

quantum number) which are typical much less than for a 17 state by virtue of strong
coupling of the spin to internal molecular motions.

I1.B.2. Electron Bombardment Ionization-Mass Spectrometer Detection

The extension of molecular beam studies of neutral reactions to include reagents
other than the alkali atoms, dimers, or alkali halides was achieved by the introduction of
an electron bombardment ionizer-mass spectrometer detection system in place of the
conventional surface ionization detector. The reader is referred to Lee, et. al. (1969) for
details of the design of such an appratus. However, a couple of points should be noted.
The surface ionization detector responds to the incident flux. Even the most efficient
electron bombardment ionizers in use as molecular beam detectors have ionization
efficiencies which are orders of magnitude less than unity, however, so that their
detection efficiency varies inversely with the velocity with which a particle traverses the
ionization region. Thus, they measure particle number density rather than flux density.
Flux or number density measurements are equally valid in angular distribution studies, but

- 20 -

the proper detector response function must be included in the subsequent interpretation of
the data. The bond energies of the alkali halide positive ions, MX^, are relatively weak
and vary widely with the particular species under consideration so that electron
bombardment ionization of MX typically produces extensive fragment into + X. Thus,
Sholeen and Herm (1976a) have pointed out that the chemical scope of surface and
electron bombardment ionization detectors complement rather than compete against one
another.

II.B.3. Laser Induced Fluorescence Detection

Laser induced fluorescence has recently proven to be a powerful new molecular
beam detection technique; it is reviewed in Zare and Dagdigian (1974). It can be very
sensitive and provides unparallelled details on reaction energy partitioning by virtue of its
ability to excite individual rovibronic transitions in simple product molecules. Its
chemical scope is, however, generally limited to studies of simple product molecules
which exhibit well-understood electronic transitions in the appropriate spectral range. It
is, for example, an ideal detector for mono-halides or oxides of the alkaline earths. In
contrast, it is less well-suited to studies of the alkali halides whose unpredissociated
excited states are weakly bound and only partially characterized. As presently deployed,
it is also a number density detector. This can lead to some minor ambiuities in
quantitative energy partitioning measurements where the product angular distribution is
unknown, although the seriousness of this problem depends upon the kinematics of the
particular chemical system under study.

-21-

I

III. The Variety of Reactive Scattering Measurements

III.A. Product Recoil Angle and Energy Distributions
III.A.I. The LAB and CM Coordinate Systems

In crossed beams experiments, particles A and B collide in the LAB coordinate

system with velocities and The angular distribution of some scattered particle C '

(which would be the same as A or B in the case of elastic or inelastic scattering) is

typically measured as a function of scattering angle,®, in the plane defined by"v^ andl^.

The kinetic energy of particle motion in the LAB system contains the (dynamically)

2

uninteresting (m^ + m^) C /2 constant of the motion, where m's denote particle masses
and C is the velocity of the center of mass of the collision partners (the centroid vector).
Thus, only the remaining kinetic energy is available to influence the collision dynamics as
relative collision energy.

E =UgV2

in terms of the reactant reduced mass, fx , and relative collision velocity, S = - Vg.

The central data analysis problem in molecular beam kinetics is the transformation
of the measurements from the LAB coordinate systems into the center-of-mass (CM)
coordinate system. The nature of this transformation is illustrated graphically for the
common case of perpendicular interesting beams by the velocity vector transformation
diagram (sometimes denoted a "Newton diagram") shown in Fig. 2 for the A + B — + D
collision which depicts v^, and C originating from the origin of the LAB coordinate
system. This diagram illustrates that scattering of particle C at some angle ® with
velocity "v^ in the LAB would correspond to scattering through an angle 6 with recoil
velocity in the CM.

^ PRSCSDItO PAGE BLAMK-NOT PIlHH)

Several points relevant to typical beam experiments can be made in relation to this
diagram. The second scattered particle (D in Fig. 2) is seldom measured because such
measurements contain no new information conceptually. In practice, measurements of
(fistributions for both particles would provide a refreshing check on the data analysis
(MTOcedure. Since there can be no net linear momentum in the CM system, the dashed lines •
in Fig. 2 indicate that can be calculated from a measurement of Thus, the final
translational energy for the scattered particles is jdso determined by a measurement of
Vq. This in turn determines the total internal excitation of the scattered species, W*, by
the energy balance equation for the scattering process.

E' + W' = E + W+ (4)

where is the exoergicity in the event of a reactive process and primes refer to
scattered species. For any given collision between species in specific quantum states E'
may, of course, assume only discrete values allowed by Eq. (4). Owing to the close spacing
of internal energy levels in C + D and the relatively poor (at best) experimental resolution
in E and E', however, w^, and E' are almost always treated as continuous variables in the
data analysis. The scattering in the CM system must exhibit cylindrical symmetry about ^
because the distribution in impact parameters for the collision possesses this symmetry.
Although no such symmetry exists in general in the LAB distribution owing to distortions
introduced by the transformation Jacobian, this CM symmetry implies that no new
information is conceptually to be obtained by measuring the LAB scattering distribution
out of the plane defined by the intersecting beams. Although such measurements would be
a refreshing experimental check, they are difficult and are seldom attempted. Only a
couple of examples have appeared in the reactive scattering literature for special reasons
re.g., Kwei, et. al. (1970), Gersch and Bernstein (1972). Kinsey, et. al. (1976)1 .

Details of the transformation equations embodied in Fig. 2 are given in Warnock and
Bernstein (1968). Laboratory measurements of the dependence of the scattered intensity
of C on ^ for the collision of two beams with well-defined initial velocities could be
directly inverted to obtain the corresponding scattering distribution in the CM system.
However, such ideal experimental resolution is seldom practical. It has not, for example,
been achieved in any of the studies reviewed in this chapter. In crossed beams studies, it
is generally adequate to regard the directions of beam motion as well defined and to
consider only the distributions over scalar beam speed, i.e. is the number

density of particles within beam A with speeds between v^ and v^ +
number of particles of C scattered per second into LAB solid angles to Q + df2 with
recoil speeds of v^ to v^ + dv^ is given by

1 (®, v^) = K

9

in terms of a detector response function proportionality constant K which

depends on the ionization efficiency and interaction volume defined by the intersecting
beams. Equation (5) is, of course, evaluated in terms of the energy balance Eq. (4) and
trartsformation equations embodied in Fig. 2; the v^ /w^ factor in Eq. (5) is the 3acobian
of this transformation. The corresponding total scattered angular distribution is given

simply by

1 (®) = y I(®, v^) dv^.

i

The object of angiQar distribution measurements in the LAB is, of course, to infer

3 2

the form of the CM differential scattering cross section, 3 <r /9 u, 3 Wq. as a function of

CM recoil speed and solid angle, w , centered on the scattering angle, 6 , defined in

Fig. 2. It may, of course, also depend parametrically on the relative collision energy as

well as internal quantum states of reactants and products. Equations (5) and (6) indicate

that LAB measurements of the distribution in recoil angle and speed, I (O, v^), or just the

total distribution in angle, I (0), contain information on 3 o-/ 3 w 3w^. A broad spectrum

of data analysis procedures has been employed in the literature, ranging from crude

qualitative arguments about the displacement of the I (0) distribution relative to the

angular distribution of C to non-linear least squares fits of polynomial expansions of
3 2

3 0 -/ a w 3w^; these are discussed in the following sections.

The molecular beam technique is ideally suited to the determination of the

dependence on various parameters of relative values of the CM differential scattering
3 2

cross section, 3 o -/3 w 3 w^, the total CM scattered angular distribution,

^CO

3V/3^w = J (3^(r/3^u 3w^)dw^, (7)

the in-plane CM scattered angular distribution,

3(r/3e =27r sine 9^0" /9^w, (8)

or the final product recoil energy probability density distribution.

?(£•)

= |y(9^o-/a^u, 3w^^) (3^(r/3^w 3w^) d^wdw^.

( 3W^,/ 3E'). (9)

- 26 -

However, determination of the absolute differential reactive cross section or total
reaction cross section,

<r = iJi 9Wp)d^wdw^, (10)

is more difficult. In this sense, the molecular beam kinetics approach complements the
conventional kinetics approach which is specifically designed to measure absolute
collisional rate constants. A direct molecular beam determination of absolute cross
sections requires a knowledge of the absolute value of k in Eq. (5); the first example of
such a study for a reaction producing neutral product molecules is the recent report of
Aniansson, eU ah (1974) on the K + RbCl — ► KCl + Rb reaction.

A couple of indirect methods have also been used to infer absolute total reaction
cross sections from molecular beam kinetics studies [reviewed in Steinfeld and Kinsey
(1970)] . One is based on an optical potential model interpretation of the attenuation of
the wide-angle elastic scattering in chemically reactive systems; it is discussed later in
this section. The second method is based upon a comparison of the absolute intensities of
narrow-angle elastic scattering and of reactive scattering in the same chemical systems
as measured in the same apparatus. Since the absolute narrow-angle differential
scattering cross section is known or can be calculated from the long-range electrostatic,
inductive, and dispersive contributions to the pair potential, this method does not require
an absolute measurement of k but does require a knowledge of the relative detection
efficiencies for non-reactive versus reactive scattering. Conceptually, this method should
be able to provide accurate determinations of total reaction cross sections. In practice,
most studies which have employed it have only poorly resolved the shape of ^ <t/ d u>3w^

- 27 -

so that it is difficult to assess the quantitative reliability of the total reaction cross
sections which are reported. Nevertheless, values which have been obtained by this
technique should typically be quantitatively reliable to within a factor of two, and relative
comparisons between related chemical systems should be more reliable.

in.A.2. Product Recoil Angular Distribution Meeisurements

Early reactive scattering studies were largely confined to measurements of product
angular distributions, often with crossed beams which both exhibited thermal speed
distributions. Measurements of this sort are sometimes referred to as "primitive angular
distiributions" in the more recent literature. Figure 3 shows the first product angular
distribution ever reported; it also illustrates the use of the differential surface ionization
technique to study the K + HBr — ► KBr + H reaction. This particular reaction is an
example of a class of reactions involving hydride molecules with special kinematic
constraints which arise because the detected product is much heavier than the undetected
H (or D) product. Thus, the heavy KBr product of this reaction can acquire only relatively
small CM recoil velocity, even for appreciable values of the recoil energy. This

implies that the measured LAB product angular distribution contains practically no
information on the CM differential cross section because the LAB distribution should be
approximately the same as the angular distribution of C for the collisions which lead to
reaction. In their original study, Taylor and Datz (1955) pointed out that this implied that
the shape of the measured LAB product angular distribution usually contained information
on the dependence of the total reaction cross section on relative collision energy, o-(E),
within this approximation of negligble CM recoil speed. This is true because the angular
distribution of C is dependent on (r(E) except in the special case of two thermal beams
with Tg/T^ = mg/m^. Their original collision energy distribution functions were sub-

- 28 -

sequently corrected in Datz, et. ah (1961). Information on the o-(E) dependence for the K
+ HBr [Taylor and Datz (1955), Datz et. ah (1961)], K + HCl [Odiorne and Brooks
(1969)], and Ca, Sr, and Ba + HI [Mims, et.al. (1972)] reactions have been obtained by
this technique, although agreement between measured LAB product angular distributions
and calculated centroid angular distributions has not been good unless corrections were
made for deviations of the actuad beam speed distributions from the ideal thermal
distribution.

Primitive product LAB angular distribution measurements for other reaction systems

where the product mass ratio is not so extreme do provide information on the CM

9^W9^ui3w via the convolution integral [Eq. (6)], although the information content of a

given measurement varies widely with the chemical system. Figure shows a primitive

Bal product angular distribution from the Ba + CH^I reaction reported by Lin, eh ah

(1973b). This is a typical product LAB angular distribution in that it shows a single peak

3 2

with little other structure. It provides information on 9 o-/9 w9w to the extent that it is
broader than and displaced away from the distribution in centroid vectors shown as the
dashed curve in the lower panel of Fig. 4.

All data analyses based on primitive LAB angular distributions alone have had to

3 2

assume an uncoupled CM distribution function, i.e. that d cr/a w9w can be expressed as
some function of recoil angle, 0 , times some function of recoil speed, w. Data analyses
in the very early studies were very qualitative. The preference for backward or forward
scattering in the CM was indicated by a displacement of the LAB product angular
distribution to larger or smaller ® values than the centroid angular distribution. (Unless
otherwise noted, backscattering will refer throughout this chapter to a 0 = 180® event
wherein the metal atom reverses direction as a result of the collision; forward scattering

refers to the opposite limit of 6=0° and no change in metal atom direction. This
definition will be extended later in discussing reactions involving two metal atoms.) In a
similar way, a "characteristic" product recoil energy was estimated from the position of
the peak in the LAB angular distribution and the nominal velocity vector transformation
diagram, although this "characteristic" E' was sometimes misleading because the insidious
effect of the transformation Jacobian was not appreciated in the eaii> work. More
quantitative insight was provided by the introduction of the "single recoil energy
approximation" (SRE) wherein a delta function dependence on CM product recoil speed
was assumed, the transformation Jacobian was included in the LAB — ► CM
transformation, and convolution over beam speed distributions were sometimes included or
rendered unnecessary by the use of a velocity selected beam. The upper panel in Fig. 4
illustrates the real information content of a primitive product LAB angular distribution.
The data can be fit by product recoil energy distributions which vary from the very broad

IS

H to the unrealistically narrow SRE assumption by altering the breadth of the corresponding

i CM product angular distribution. Thus, these measurements typically define the CM

: product angular distribution semi-quantitatively, but the insight into the product recoil

[; energy is more qualitative. In fact, the uncertainty is inferred CM recoil functions may

I

be even worse than is depicted in Fig. 4 for experiments which employ broad beam speed
distributions because the LAB — ► CM transformation is then dependent on the sometimes
uncertain form of (r(E).

Nevetheless, much valuable chemical insight has been and will continue to be
obtained from these primitive LAB angular distribution measurements. The magnitude of
the observed product signal determines the total reaction cross section at least semi-
quantitatively. Differentiation between different possible products which is possible with

-30-

an electron bombardment ionizer-mass filter or laser induced fluorescence detector is

1

!

,i

often interesting. The qualitative or semi-quantitative insight into the CM recoil
functions can be quite interesting, especially in identifying trends within a family of
related reactions. Moreover, these measurements can quantitatively determine
dependences of the CM recoil functions on other parameters such as collision energy in
favorable systems where much is already known about the quantitative form of these CM
recoil functions from other detailed studies. Examples of this quantitative approach are
provided by the recent collisional energy dependent studies of the reactions of Rb + CHjI
[Gonzalez Urena and Bernstein (1974)] , K + CH^I [Rotzoll, et.al. (1975)] , and K + Br 2
[van der Meulen, et.al. (1975)] .

III. A. 3. Product Recoil Velocity Measurements

Resolution of quantitative features of 3^o-/ c? w 9w is much improved when the LAB
distribution in recoil angle and speed is measured by interposing a speed analyzer between
the beam collision volume and detector (e.g.. Fig. 1) . Both slotted desk velocity
selectors (SDVS) and time-of-flight (TOF) analyzers have been used for this purpose. The
reader is referred to other review [e.g., Fluendy and Lawley (1973)] for details of these
devices. In both devices, a slit cut on the circumference of a rotating disk is employed to
transmit scattered particles for a short burst of time. At. The number of particles with a
particular speed v = L/t is determined after an elapsed time t by means of an analyzer
which is situated a distance L from this entrance disk.

In the case of TOF analysis, for example, this analyzer is simply the scattered
intensity detector, and the speed distribution is obtained from the measured distribution in
detector arrival times by

i

-31-

I(v) = l(t)(L/v^). (11)

In practice, the I(v) distribution should be derived by deconvoluting the gate function (At),
detector length, and detector time response function from the measured l(t) function.
One potential disadvantage of this technique is that the L/v^ Jacobian in Eq. (11) causes
the I(t) spectrum to heavily favor high velocity events. However, this is offset by the fact
that the resolution (Av/v = At/t) can be varied during the experiment simply by changing
the analyzer disk rotation frequency. Another advantage of TOP analysis is that the
entire velocity spectrum is scanned so rapidly that slow drifts in beam intensities are
inconsequential. Another disadvantage to the current TOP analysis techniques which are
in use is the low duty factor (typically a few percent) produced by the relatively small
number of slits on the analyzer disk which are used in order to avoid severe "wrap around"
corrections for overlap between fast molecules from one pulse and slow molecules from a
previous pulse. This can be improved by cross-correlating the detector time response with
a random or pseudo-random TOP pulsing function.

In practice, however, the SDVS has proven to be a more attractive alternate method.
Here, the analyzer situated a distance L from the pulsing disk is simply another disk of the
same radius and slit sequence. These disks are affixed to the same rotating shaft, but
corresponding slit are slightly displaced so that only molecules are transmitted which have
the proper velocity to arrive at ."he final slit during the time period when it has rotated
into the open position. Inclusion of intermediate disks to prevent transmission of
I harmonics of the design velocuy permits a duty factor which is only slightly less than 50%

|i [Hostettler and Bernstein (I960)]. Kinsey (1966) describes a geometric procedure for

j!

p locating these intermediate disks, although other schemes have also been employed. Both

- 32 -

SDVS and TOF analyzers should generally be calibrated, often against a known Boltzman
speed distribution; Grosser (1967), however, has described a self-calibrating SDVS. The
SDVS transmitted velocity is directly proportional to the rotational frequency of the
shaft. The resolution, Av/v, is determined by the original design, is independent of v, and
can't be varied during an experiment.

Bernstein and his co-workers have reported an elegant set of studies wherein an
SDVS was employed to prepare a velocity selected beam of alkali atoms and a second
SDVS was used to analyze the reactively scattered alkali halides. The speed distribution
in the unselected cross beam was relatively unimportant because the characteristic speeds
from a room temperature effusive source are generally smaller than the atom speed; it
was, however, included in the data analysis via the convolution integral in Eq. (5). Results
of their studies are cited in Section IV for different chemical systems. As an illustration
of the details which can be resolved, however. Fig. 5 shows a CM contour plot of 9 cr/ a w
8w for the scattering of K1 from crossed beams of K and I 2 which is reported in Gillen, eU
al. (1971). These workers actually determined 3 cr/ 9 w 9w for several E, but the effect
of changing E was small and Fig. 5 shows their composite energy independent map.

However, many of the reported measurements of LAB recoil velocity spectra of

scattered species have employed broad ’’quasi-thermal" speed distributions in both beams.

3 2

This may reduce the resolution attainable in 9 o-/3 w 9w, although the extent of the
" kinematic blurring" implicit in Eq. (5) varies widely with the chemical system. For
example. Fig. 6 shows LAB contours of constant LiO flux from the Li + NOj reaction
which were obtained in the apparatus shown in Fig. 1 by Sholeen and Herm (1976a). Fifty
percent of the centroid vectors which define the origin of the CM coordinate system
terminate within the cross hatched area. This illustrates that the kinematic blurring due

- 33 -

to the broad beam speed distributions is not too severe in this case because the cross
hatched area comprises only a small fraction of the total in-plane LAB recoil velocity
space where appreciable LiO flux was measured.

Most modern experimental measurements use numerical data analysis techniques in

order to correct for the influence of the beam speed distributions on the type of LAB

measurement shown in Fig. 6. Siska (1973), for example, has described a promising

iterative technique for inverting Eq. (5). However, it appears to require a prior smoothing

of the data which makes it difficult to objectively appraise the data's true information

content. Alternately, a number of laboratories have employed a polynomial [e.g., Gillen,

et. al. (1971), Riley and Herschbach (1973), Sholeen and Herm (1976a)] or other

3 2

functional expansion of 9 o/9 w 3w and optimized parameters via a least squares fit of

3 2

Eq. (5) to product LAB recoil velocity measurements. Use of different 9 cr/9 cj9w
expansion functions sometimes provides insight into which CM recoil features are
unequivocally determined by the measurements. For example. Fig. 7 shows the P (E')
curves evaluated in this way by fitting product recoil velocity spectra measured in the
apparatus shown in Fig. 1 for reactions of Li with CH 2 NO 2 , CCl^, and CH^I [Sholeen and
Herm (1976b)]. These results are discussed in Section IV. They are included here to
illustrate that the use of different expansion functions generally provide similar P (E')
functions. However, the uncertainty in the quantitative form of P (E') may still be
significant for the case of an especially unfavorable ratio of the masses of detected and
undetected products (e.g., Li + CH^I — ► Lil + CH^).

t

- 34 -

III.B. Dependence upon Reactant Quantum States

The determination of (r(E) for the case of severe kinematic constraint (i.e., K + HBr
— ►KBr + H and related reactions) with crossed thermal beams was discussed above. i

Beyond this special case, numerous studies have determined the dependence of collision
probability on E by the use of an SDVS on one of the beams or by exploiting the sharp
speed distribution produced by a nozzle or seeded nozzle expansion. In principle a simple
variable temperature effusive source or the ineffectual relaxation of vibrational degrees
of freedom in a nozzle expansion source makes possible a separate assessment of the role
or E and thermally distributed internal reactant states in promoting a particular collision
process. Examples of some of the studies of this sort are provided by Sloane, et. al.

(1972), Freund, eU aD (1971), Bennewitz, eU ^ (1971), and Mariella, et. al. (1973).

However, the true elegance of the molecular beam kinetics approach is its ability to

deploy a variety of specific selectors for particular quantum levels. ]

I

!

)

III.B.l. Electric Deflection 3

i

The deflection of an alkali halide or other polar molecule with dipole moment in \

a X! electronic state in a inhomogeneous electric field, is discussed in detail in other
chapters of this volume. Since the rotational angular momentum is perpendicular to the
polar axis, the first order projection of the dipole moment onto the direction of (? time
averages to zero. However, a second order effective dipole component survives, i.e.

J(J + 1)-3m5

= (P«<?/E ) (J ^ 0) (12)

^ (2J-1) (2J + 3)

ll

ri

ll

- 35 -

in terms of the rotational energy quantum number (3), and projection quantum

number (‘Vlj). all of which should be primed if the technique is being used to analyze
scattered products rather than select reactants. Mosech, e^ aL (1975) have discussed
various molecular beam analyzer techniques based on the behavior given in Eq. (12). It is
well known that states for which 3 (3 + 1) - 3 M. <0 will undergo sinusoidal trajectories
about the field axis in an electrostatic quadrupole field so that molecules in a particular
state which enter with the proper velocity on the axis of the field will be refocussed onto
the axis after a characteristic distance. Stolte, e^ aU (1975) were able to exploit this
refocussing to achieve a sufficiently intense CsF beam to determine that rotational

energy is less effective than translational energy in promoting the endoergic K + CsF — ►
KF + Cs reaction. In addition, Bromberg, et.al. (1975) have described the production of a
beam of CsF in a specific rotational, vibrational, and translational state by the molecular
beam electric resonance method described in the following subsection; with some
technical improvements, the intensity should be adequate for reactive scattering studies.

In contrast to the alkali halides, polar symmetric top molecules suffer a first order
Stark effect interaction. This arises because the projection of the rotational angular
momentum vector onto the body-fixed polar symmetry axis may assume only the integer
values of Kfi where |K| S3. The resultant first order time averaged projection of the
dipole moment onto the direction of S is given by

= KMy3(3+l). (13)

In a classical picture of precessing angular momentum vectors, this implies that the
molecular symmetry axis precesses about the direction of S. Thus, electric deflection
may be used to align the symmetric top molecular symmetry axis at an average inclination

- 36 -

r

angle of cos ^ (KMj/J (J + 1) with respect to the incoming direction of a second reactant
beam so as to experimentally study the "steric effect" in a reactive or non-reactive
collision, i.e. the dependence of the collision probability on this inclination angle.

Brooks, eU ah (1969) and Beuhler and Bernstein (1969) give details of this molecular
beam scattering technique. Jones and Brooks (1970) point out that the same technique
may be applied to asymmetric tops in favorable cases. A hexapole field provides the
optimal refocussing geometry in the case of the first order interaction given by Eq. (13).
Since this geometry orientates the molecules with respect to the local radially-directed
field direction, a transition to a weaker two pole field is necessary in order to
adiabatically rotate the molecules into the LAB alignment. A simple reversal of polarity
on this terminal field serves to reverse the alignment direction in the UtB. Distribution
over K, M, and J rotational quantum numbers as well as beam speed distributions all
contribute to broaden the distribution in inclination angles and to increase the
deconvolution problem in the quantitative analysis of the collisional steric effect. Results
on different chemical systems are cited in Section IV. However, Figure 8 is included here
as an illustration of the variety of chemical behavior which is observed. It is ironic that
oblate tops (e.g. CHClj) are eeisier to align experimentally because thermal population
favors higher K states, but the interesting chemical behaviors have been observed with the
prolate tops.

in.B.2. Other State Selectors in Use

The broad spectral range currently available with lasers makes possible potential
laser excitation of specific rotational, vibrational, and electronic states of a reactant. No
reactive scattering studies have been reported as yet which employed laser excitation to

- 37 -

some higher reactant electronic state. Some reactive scattering studies have employed
reactants in metastable electronic states prepared by other methods. These studies have
analyzed the subsequent product chemiluminescence, however, and are beyond the scope
of this present chapter.

Two reactive scattering studies have successfully employed laser promoted
vibrational excitation of a hydrogen halide reactant. Odiorne, et.al. (1971) employed a
multi-line HCl laser to study the effect of HCl vibrational excitation on the magnitude of
the K + HCl reaction cross reaction. Pruett and Zare (1976) employed a single line HF
laser in order to assess the effect of HF vibrational excitation on the energy partitioning
in the Ba HF reaction. These studies directly measure the difference induced in the
scattered spectrum upon reactant laser excitation so that their quantitative interpretation
is dependent upon the fraction of the reagent gas which is excited. Pruett and Zare (1976)
discuss the extent to which the uncertainity in this fraction complicates the subsequent
data analysis. It's effect is not too severe because of the very large effect of HF
vibrational excitation on the Ba + HF reaction dynamics.

In addition to laser excitation, alkali halide beams with very high average vibrational
excitation have been prepared by a chemical activation technique. The alkali halide beam
source in these "triple beam" studies consists of crossed beams of the alkali atom and
halogen molecule because these reactions are known to produce a relative sharp
distribution over highly excited vibrational levels. Moulton and Herschback (1966) first
used this technique to observe the production of electronically excited potassium atoms in
the reaction of Na with highly excited KBr. Fisk and co-workers subsequently used it to
study energy transfer from highly excited KBr to a variety of collision partners; this work
is discussed in Section IV.

- 38 -

III.B.3.

Elastic Scattering from Reactive Systems

I

Even for potentially reactive partners, the majority of the collision are elastic.
Experimentally, it is observed that the elastic differential cross sections are similar for
reactive versus non-reactive collision partners at narrow scattering angles which
correspond to relatively large collision impact parameters, b. At wider scattering angles
corresponding to smaller impact parameters, however, the elastic scattering from
reactive partners is observed to b^ attenuated relative to that observed from non-reactive
partners. The probability of reaction as a function of impact parameter can be obtained
from these elastic scattering measurements as

p (b,E) = 1 - (14)

2 2

where 3 cr/9 w is the elastic differential cross section transformed into the CV1

system measured at a particular collision energy, E. A "reference" cross section,

(9 cr/ 8 w )^, obtained by fitting the 9 cr/8 u, narrow angle measurements, describes the

wide angle scattering which would be expected in the absence of attenuation by reaction

and determines the b — ► 6 correspondence. The data symbols and solid curves shown

2 2 2 2

in Fig. 9 indicate the contrasting behaviors of 9 o-/9 w and (9 cr/8 which were
determined for the K + CCl^ reaction in Harris and Wilson (1971).

Details of this technique are discussed and reviewed elsewhere [e.g., Fluendy and
Lawley (1973); Greene, et.al. (1966); Greene and Ross (1968); Ross and Greene (1970);
Toennies (1974)] and only a few comments are offered here. The simple treatment of the
elastic scattering given in Eq. (14) has been upgraded by the development of an optical
model [reviewed in Kinsey (1972)] wherein a complex potential is responsible for a

- 39 -

complex phase shift; the imaginary part of the phase shift accounts for the attenuation
(i.e., non-unitarity) of the elastic scattering. This more formal treatment serves to
define the region of validity of Eq. (U) and provides a better treatment in other cases. It
also shows promise as a convenient vehicle for correlating or extrapolating reactivity
measurements for a particular chemical reaction or family of reactions [Roberts and
lasonidou Nelson (1974), Roberts (1976)].

The quantitative interpretation of these measurements (e.g., Fig. 9) are somewhat

2 2

hampered by difficulty in assigning the proper (9 (r/3 ui)^ and b ■* — ► 6 correspondence;
the resulting uncertainty in p (b, E) varies widely with the chemical system. Another
problem is that both inelastic and reactive collisions can attenuate the elastic scattering,
and the inelastic scattering can dominate in the case of an appreciable reaction threshold
energy [e.g., Odiorne and Brooks (1976) and Truhlar (1971)]. In cases where both
measurements exist, however, the assignment of the attenuated elastic scattering to
chemical reaction appears to be a good approximation because the total reaction cross
sections calculated from the inferred p (b, E) agree within experimental errors with
estimates from direct measurements of the scattered product flux. Moreover, these
measurements remain the only ones which provide information on the probability of
reaction versus impact parameter in the collision. An alternate expression of p (b, E) in
terms of probability of reaction versus distance of closest approach in the elastic
trajectory is sometimes useful because it weakens or eliminates the dependence on E
[ e.g., Harris and Wilson (1971)].

L

- 40 -

m.c.

Dependence upon Product Quantum States

The use of an SDVS to measure the product recoil velocity spectra and thus the

distribution in recoil energy was discussed in Section III A. The ability of magnetic

2

deflection to distinguish between "Z, and other electronic states of diatomic molecules
was noted in Section II. This same Section noted the phenomenal resolution afforded by
LIF in favorable cases, i.e. the ability to measure the distribution over product vibrational
(vO and rotational (J') quantum numbers. Other beam measurements of product internal
excitation have employed electric deflection. Except for the observation of a pseudo-first
order Stark interaction for the CSNO 2 product from Cs + CH 2 NO 2 reported in Maltz and
Herschbach (1967), these studies have all exploited the second order Stark interaction of a
product alkali halide.

For a random distribution in product Mj' states, Eqs. (2) and (12) indicate that the
extent of deflection of a product alkali halide molecule varies inversely as the product
rotational energy, E^', time the LAB recoil kinetic energy. Herm and Herschbach (1965)
and Maltz and Herschbach (1967) employed deflection in a two pole field to determine E^'
for a number of reactions of alkali atoms with molecules containing halogens, although the
results reported for E^' have been revised in Maltz (1969). Grice, eL aL (1970), Mosch, eL
al. (1974), and Mosch, et.al. (1975) exploited the intensity enhancement provided by a
quadrupole refocussing field as well as an SDVS to eliminate the distribution in LAB
product kinetic energy to determine E^' for the Rb + HBr and Br 2 reactions. The use of
the SDVS should make it possible to determine the distribution over E^' by either
technique from the observed dependence of the deflection on the applied field strength.
In practice, however, results thus far have been analyzed by assuming some functional

form for the E^,’ distribution (e.g., thermal) and determining the average product

rotational energy. Mosch, et.al. (1974) point out that a thermal E^' distribution will
usually be approximately correct in the absence of beam velocity selection, owing to the
thermal reactant distributions. It should also be noted that Hill and Gallagher (1975) have
described a new deflection concept using an inhomogeneous resonant deflecting field
which might prove useful as a product state analyzer.

Perhaps the most elegant manifestation of the electric deflection technique is the
molecular beam electric resonance spectrometer described in other chapters of this book.
Here, a quadrupole field focusses a particular rotational quantum state into a region of
homogeneous field strength where RF or microwave radiation may induce a transition to
some other quantum state; upon leaving this homogeneous field, a second deflecting field
is used to test whether a transition has taken place. The molecular dipole moment and
rotation constant depends weakly on the vibrational quantum number, v, so that resonant
transitions for different v levels occur at easily resolvable transition frequencies. An
electric resonance spectrometer has been used to analyze the product alkali fluoride
vibrational distribution for the reactions of Cs + SF^ [Freund, eu ah (1971)], Cs + SF^^
and SF^ [Sennewitz, et.al. (1971)], and Li SF^ [Mariella, e^ ah (1973)]. Mariella, et.
al. (1974) also used it to study the vibrational relaxation of a thermal LIF beam by a
variety of molecules.

Mosch, eh ah (1975) discuss the merits of the electric resonance method as a
product state aneilyzer. Its most critical limitation is its restriction to very low 3' values
(3'<5) because of the sensitivity loss which would be occasioned by the larger path lengths
needed to refocus the higher J' levels. Since the most probable 3' value from an alkali
atom plus halide molecule reaction is typically ~ 50-1 00 [e.g., Maltz and Herschbach
(1967)], the conclusion that the measured distribution over v' is characteristic of the

- 42 -

reaction is critically dependent on an assumed independence of the v' and 3' distributions.
Indeed, the 3' values which are studied are so unrepresentative of a typical product that
this question would cause serious concern even if the same vibrational distribution were
measured for different 3' values. In this regard, it is fortunate that the technique has thus
far been applied to chemical systems where this assumed independence of the 3' and v'
distributions seems most plausible, i.e. a highly exothermic reaction of an atom with a
large polyatomic molecule possessing thermally distributed internal excitation which
appears to proceed via statistical equipartitioning of energy in a long-lived collision
complex.

Angular momentum conservation in a reactive collision requires that the orbital and
rotational angijlar momenta of reactants and products be related by

T + T = T = 7+L'. (15)

Here, F is the total rotational angular momentum of the collision intermediate, and
electron or nuclear angular momenta have been ignored. Since L must be othogonal to g,
F and thus 3' will not be isotropically distributed in space in general. Conceptually, the
distribution in F can be calculated or, at least, estimated so that a measurement of the
joint distribution over 3' and determines the angular momenta coupling in the
reaction. Equation (12) indicates that the second order Stark effect is dependent on
as well as 3' so that information on both parameters can be obtained from the direction
and extent of deflection of a product alkali halide beam as the spatial direction of the
inhomogeneous deflecting field is varied. A two pole deflecting field is the better choice
for these studies because the field direction in a refocussing field is randomly distributed
in the plane perpendicular to the beam axis.

- 43 -

The first successful observation of an anisotropic distribution in alkali halide

product molecules was reported by Maltz, eu ^(1972) who used this two pole deflection

technique. Their apparatus inadvertently included a field-free region between buffer and

deflecting fields so that they had to correct for a sudden, non-adiabatic reprojection of

quantization axis. Hsu, et. al. (1975) describe an improved apparatus which eliminates this

reprojection correction and an improved data analysis procedure which indicate that the

2 4

measurements yield < cos X> and < cos X>, the first two moments of the distribution
over cos X where X is the angle between 3' and g. Results on different chemical
systems are cited in Section IV. It should also be noted that polarization studies with LIF
can provide information on the distribution. Although no reports of its application to
reactive scattering have appeared as yet, Sinha, et. al. (1973) have provided an analysis of
the technique and used it to measure the alignment of dimers in a supersonic nozzle beam
expansion [see also Visser, et. al. (1977)].

IV. Results for Different Chemical Systems

Results obtained with the various beam techniques on inelastic and reactive
scattering of alkali halides and on reactive scattering of metal atoms are listed in tables
and are discussed in this section. Abbreviations used in these tables to identify the
various types of beam measurements are defined in Table I. A study which combined a
couple of techniques is indicated by two or more abbreviations; for example, LECT-LIF
would describe the Pruett and Zare (1976) study of the Ba + HF (v) — ► BaF (v') + H
reaction. An entry of P (y) under results indicates a determination of the dependence of
the scattering cross section upon parameter y, where y might denote E, E^, E^, b, ©, E',
E^' E^', etc. or some combination. For example, the Pruett and Zare (1976) study is

denoted P(Ey; E^'). A y = K/3 entry denotes a determination of the reaction steric effect,
whereas y = M^'/ J' denotes a determination of the polarization of product rotational
angular momentum. Product recoil angular and velocity measurements are denoted 1 (®)
and 1 (®,v), respectively, rather than the entries for the corresponding CM recoil
functions. This is meant to emphasize the widely varying qualities of different LAB ^
CM transformation procedures. The reader may judge the quality of this procedure in any
particular study in terms of the discussion given in second III. A. An entry of <r(E)
indicates a determination of the energy dependence of relative values of the total
reaction cross section in addition to recoil function measurements.

- 45 -

IV.A. Scattering of Alkali Halide Molecules

IV. A. 1. Vibrational Inelasticity

Crossed molecular beam studies of vibrationally inelastic collisions of alkali halide
molecules are listed in Table 11. Related studies of elastic and rotationally inelastic [e.g.,
Toennies (1965)] collisions and of high energy collisional dissociation into ion pairs [e.g.,
Tully, et. al. (1971), Parks et. al. (1973a and b) and Piper, et. al. (1972)] are discussed
elsewhere and aren't included here. The studies listed in table II span a wide range in
Eint/E, the ratio of alkali halide internal excitation to relative collision energy.

Fisk and co-workers crossed beams of K and Br 2 to produce a beam of KBr with a

well characterized, resonably narrow vibrational energy distribution peaked at 180

3 2

kJ/mole. They proceeded to measure 9 or/9 ui9w differential cross sections for transfer
of this very large initial vibrational excitation into recoil energy with which the collision
partners separate for a wide variety of non-reactive collision partners, and reported
different mechanistic behavior for different classes of collisions partners. Crim, et. al.
(1973) reported total cross sections of the order of 2oR^ for transfer of large amounts of
vibrational energy into translation in collision with Ne and Ar atoms and with nonpolar (Nj
and CO 2 ) or weakly polar (CO) small molecules. They suggested that energy transfer
proceeds mainly through impulsive interactions and that long range attractive forces are
relatively unimportant in these systems. Quantitative differences in observed energies
transferred led them to suggest that some energy also appeared as vibrational excitation
in CO and 00,^, but not in N,^. However, a more recent surprisal analysis of these

measurements reported in Crim and Fisk (1976) suggests some V-V transfer even in the

case of KBr^ + N 2 . In contrast, Donohue, et. al. (1973) reported that attractive forces

appear important in the relaxation of KBr^ by small polar molecules. Inelastic collisions

proceeded through a short lived energy randomizing collision complex with total cross

o2

sections as large as 300 A . However, they saw no evidence that the energy equilibrated
with internal vibrational modes in these small molecules. Crim, et. al. (1976) subsequently
reported that several internal modes in CH 2 NO 2 did participate in energy randomization
in the complex formed in the KBr^ + CH 2 NO 2 collission. Nitromethane was specifically
chosen as a collision partner to demonstrate this effect because it is highly polar and also
has several low frequency skeletal vibrations. KBr recoil velocity spectra recorded with
KBr^ + (CH 2 ) 20 , C 2 HgOH, and C^Hg showed features suggestive of both the impulsive
and the collision complex energy transfer models.

At the opposite extreme of the E.^^/E ratio range, Loesch and Herschbach (1972)
crossed a ~1000°K thermal Csl beam with an Ar beam obtained from a seeded nozzle to
obtain collision energies from 34 to 106 kJ/mole. Their measured recoil velocity spectra
indicated total cross sections of ~20^^ for transfer of >90% of this collision energy into
Csl internal excitation (both rotational and vibrational excitations are probably
important). They point out that completely impulsive collision could transfer a maximum

- 47 -

of only 40% of the collision energy for the masses of these collision partners. This
indicates a qualitively different energy transfer mechanism which they've referred to as
"ballistic". They suggest that it might be due to a resonant or quasibound CslAr complex.
King, et. al.(1973) report a similar ballistic effect in Ar + CsF collisions and argue that
their interpretation is not an artifact of their data analysis because the tendency of the
CM — ► LAB transformation Jacobiam to strongly weigh low recoil events in the LAB
frame of reference is offset by a density of states dependence on E*.

Armstrong, et. al. (1975) and Green, et. al. (1977) measured recoil spectra in two
prpendicular planes containing the cesuim halide beam for ratios of order unity.

They employed a velocity selected thermal cesium halide beam and reported that Lxith
excitation and deexcitation occurred with cross sections apparoching that for wide angle
( ^40°) elastic scattering. They did not observe individual peaks in the recoil velocity
spectra corresponding to different vibrational transitions which indicated that both
rotational and vibrational transitions were involved. Greene, et. al. (1977) suggest that a
long-lived collision complex between alkali halides and rare gases may randomize the

energy over degrees of freedom at low E + Ej^^. They further suggest that a statistical
energy partitioning might account for all of the results listed in Table II on collisions of
rare gases with alkali halides.

IV.A.2. Reactive Scattering of Alkali Halides

Practically no information on the gas phase reaction kinetics of alkali halide
molecules existed prior to the advent of crossed molecular beam studies. Beam studies of
three reaction families involving alkali halide reactants which are reviewed in Table III all
produced surprising results. Although chemists had grown accustomed to discussing
reactions in terms of a transition state collision complex, early molecular beam studies of

- 48 -

I

[

t

!

I

i

I

I

t

i

interaction mechanism, i.e. the lifetime of the collision intermediate, t^, was less than its
rotational period, The distinction between a direct ( < t^) and long-lived complex

( > Tj,) reaction mechanism is readily established from beam measurements because
the product angular distribution must be symmetric about 0 = 90° for the case of »
Tj,. It would be a rare accident for a direct interaction mechanism to produce such a
symmetric angular distribution. Thus, it was a refreshing contrast to these early reactive
scattering results when Miller, et. al. (1967) reported a long-lived complex mechanism in
the reactions of alkali atoms with alkali halide molecules. Reactions between K1 and CsCl
[Miller, et. al. (1972)] provided one of the rare examples of fast bimolecular reaction
between two compounds in saturated valance configurations. Reactions of alkali [King
and Herschbach (1973)] and alkaline earth [Freedman, et. al. (1976)] halides with halogen
and hydrogen halide molecules subsequently provided an even more surprising example of
this behavior. All of these reaction dynamic features have been interpreted in terms of
the unique electronic structure of the alkali halides, i.e. they are well approximated as
polarizable ion spheres which exhibit long-range Coulombic, inductive, and dispersive
forces as well as shorter-range repulsive forces.

IV.A.2.a. Alkali Halides plus Alkali Atoms

Table III indicates that a variety of molecular beam techniques have been deployed
in the study of the exchange reactions of alkali halides with alkali atoms. The large dipole
moments of the alkali halide molecules make them especially well suited to electric
deflection techniques. More significantly, however, this family of reactions has been and
will continue to be important in testing predictions of statistical theories of reaction

- 49 -

proceeding via a long-lived complex. The recent extension to include studies of alkaline
earth metals [Oagdigian and Zare (1974) and Smith and Zare (1976)] is noteworthy
because the ability to deploy the LIF technique will provide better resolution of the
reaction energy partitioning.

Miller, et. al. (1967) first reported that Cs and K + RbCl and their reverse reactions |

proceeded via formation of a long-lived complex. They observed large cross sections for
formation of the complexes which they attributed to the strong long-range dipole-induced I

J

dipole forces present in these systems. The RRKM treatment of unimolecular
decomposition indicates that the formation of a long-lived collision complex is ordinarily
dependent upon a substantial binding energy of the complex relative to either reactants or
products. Miller, et. al. (1967) plausibly attributed the formation of a long-lived complex
in these reactions to the fact that the reactions are close to thermoneutral and that the
known bonding in the diatomics alkali ions, M2^, suggests substantial binding energy in the
intermediate because the complex formation can be viewed as M' + M^X — ► (M'M)*X .

This picture was reinforced by reports that Cs + TlCl and Til [Fisk, et. al. (1967)] as well
as Li + MX [Kwei, et. al. (1971); Lees and Kwei (1973)] failed to exhibit this symmetric

, angular distribution; a weaker complex binding energy is expected in these cases.

The K, Cs + RbCl and other early beam studies of long-lived collision complexes
[Ham, et. al. (1967); Ham and Kinsey (1970)] prompted the development of statistical
theories of reaction dynamics. These may take the form of a phase space theory (PST)
wherein decomposition of the complex into any particular set of quantum states is judged
equably probable within the constraints of conservation of energy and angular momentum.

Alternatively, a transition state theory (TST) may envision a statistical distribution over

degrees of freedom in an activated complex.

I

I

II

- 50 -

For example. Miller, et. al. (1967) analyzed their product angular distribution in
terms of a TST patterned after the compound nucleus treatment of nuclear fission.
Recently, Case and Herschbach (1976) have pointed out that a variety of directional
properties (e.g. product angular distribution, product rotational polarization ) of long-
lived complex reactions can be calculated from PST in terms of A= L/ (L + J) and A' = LV
(L' + J'). These authors also reviewed previous TST and PST treatments of these
properties. In the limit that both A and A' go to unity, for example, the product
differential cross section approaches the sharply peaked (sin e ) ^ whereas ein isotropic
distribution is obtained if either A or A' goes to zero. The rigorous PST formulation of
the energy partitioning was given by Pechukas, et. al. (1966), but this can be complicated
to apply. Pechuhas, et. al. (1966) give formulas for tne 3-atom complex, and Dagdigian,
et. al. (1974) treat the 4-atom complex. For this reason, an approximate TST formulation
of Safron, et. al. (1972) has commonly been employed in analyzing beam measurements
because it provides simple expressions for the energy partitioning. Care must be taken in
applying it, however, because it was derived only for the case of A« A' ~ 1 [Safron, et.
al. (1972); Marcus (1975)] . Moreover, it (and many other existing TST's) cannot be
confidently applied to the breakup of a tight activated complex because of the neglect of
possible product channel interactions [Herschbach (1973), Marcus (1973), Marcus (1975)].
Even within these limits, Holmlid and Rynefors (1977) have recently emphasized that some
approximations employed in the Safron, et. al. (1972) derivation seriously restrict the
permissible applications of this TST formulation.

In addition to the possibility that such statistical theories describe experimental
measurements in the case of a long-lived complex mechanism, it was long recognized that
they also served to define a reaction dynamic baseline, i.e. measured deviations from PST

1

must be due to dynamical effects. This qualitative argument was made quantitative by
Bernstein and Levine (1972) who used information theory and introduced the surprisal
function, i.e. the negative of the natural logarithm of the ratio of the measured
distribution function to that predicted by PST. This has proven very valuable because a
surprisal analysis may reduce an overwhelming quantity of reaction dynamic data to a few
parameters.

With reference to the alkali atom plus alkali halide exchange reactions, the most
recent measurements [Aniansson, et. al. (1974), Stolte, et. al. (1976)]confirm the initial
suggestions of Miller, et. al. (1967) that reaction proceeds via a long-lived collision
complex. Product recoil angular and energy distributions are consistent with
equipartitioning of reaction energy in a long-lived complex; experimental resolution is
probably incapable of distinguishing between approximate TST formulations and rigorous
PST. However, the measured branching ratio for decomposition of the complex into
products or back into reactants clearly disagrees with statistical predictions. It has been
suggested that this non-statistical branching ratio may be due to the centrifugal force
produced by the relatively high angular momentum in the complex. This tends to promote
a linear M'MX complex and inhibits the bending required to interchange alkali atoms.

IV.A.2.b. Alkali Halide plus Alkali Halide

Exchange reactions between two alkali halide molecules are especially difficult to
study because of the high probability for fragmentation upon ionization. Nevertheless,
Miller, et. al. (1972) managed to study the Cs Cl + K1 — ►Csl + KCl reaction by exploiting
the kinematics of comparable masses of reactants but a large mass difference in the
products which restricted the scattering of the heavy Csl product to a limited range of
LAB recoil velocity space. They reported a large cross section for a reaction which

- 52 -

proceeded via a long-lived complex with symmetric angular distribution and product
recoil energy distribution consistent with TST. As in the case of M + M'X, however, the
branching ratio for reactive versus non-reactive decomposition of the complex was
considerably less than that expected from TST.

These observations are generally consistent with the electronic structure of the
reagents. The very strong long-range dipole-dipole forces can account for the large total
reaction cross section. The formation of a long-lived complex is consistent with the
known large binding energies of alkali halide dimers. The stable isomer of these dimers is
known to be a cyclic, planar rhomboid. Miller, et. al. (1972) attribute the discrepancy
between measured and TST branching ratio to a less stable, linear-chain isomer which
might be favored for high complex angular momentum states and predominantly decom-
pose back into reactants. Concerted four-center reactions ordinarily exhibit very large
activation energies. The rapid reaction reported here at only modest energies
H7kJ/mole collison energy, k3/mole total reactant energy) can be attributed to the
special ionic nature of the bonding, i.e. the reaction proceeds by

cs^cr + k't — ► cs'r + K*cr d)

so that there is no reason to expect any significant energy barrier to formation or decay

IV.A.2.C. Alkali Halide plus Halogen Molecule

King and Herschbach (1973) reported large cross sections for the exhange of halogen j

atoms in thermal energy reactions of Csl with CI 2 and CsBr with ICl. The product recoil
angular and energy distributions from Csl + CI 2 were again consistent with TST. For CsBr
+ ICl, only CsCl + IBr products were observed. Here, the product angular distribution was
asymmetric about 0= 90°, and the recoil energy distribution was inconsistent with TST.

Observation of fast reactions in these systems is much more surprising than in the
case of two alkali halides where the behavior was readily understood in terms of the
ionically bound complex. King and Herschbach (1973) attribute the fast reaction observed
in these systems to an ion-pair intermediate as well. This can arise because the trihalide
negative ions are known stable species which follow the rule that the least electronegative
halogen atom is always the centred atom. Thus, the Csl + CI 2 reaction is pictured as
proceeding bv

. /ci\‘

Cs"^ r + Cl„ — *> Cs'^ I I I — * Cs'^cf + ICl. (2)

\ci/

They argue that insertion of the l” anion into the CI 2 bond promotes a long-lived complex ;

mechanism. The CsBr + ICl reaction, on the other hand, involves an end-on attack of Br

on ICl, ^

I

Cs"^ Br“ + ICl — *> Cs"^ (Br- I-C1)‘ — ► Cs'^ Cf + IBr, (3)

which apparently promotes a direct mechanism and accounts for the absence of the Csl +

BrCl product channel.

- 54 -

Further support for this picture was provided by Freedman, et. al. ( 1976 ) who studied

F

t

<

the thermal energy reactions of alkaline earth dihalides with CI2 and HCl. The bonding in
the heavier alkaline earth halides is also largely ionic. In order to draw the analogy to the
alkali halide systems, B£.l2 may be pictured as (Bal)* 1 . Freedman, et. al. ( 1976 ) reported

3

halogen exchange product recoil angular and energy distributions in Bal2 + CI2 consistent
with TST, in direct analogy to 4 ie Csl + CI2 results. They were unable to establish
whether the product was BalCl + ICl or BaCl2 + ^2 because of the absence of a BaX2^
parent ion in the EB mass spectrum. In contrast, a direct reaction mechanism was
observed for Bal2 + HCl — ► BalCl + HI. This is directly analagous to CsBr ICl because
the IHCl anion is known to be bound with the H-atom in the center. Two additional
obsevations also supported this ion-pair intermediate model of these reactions. Reaction
was observed between BaF2 and BCl y where a (BaF^) (BFCl^) ion-pair intermediate is
quite plausible, whereas no reaction was observed for Bal2 + CH^CHCl2. C2H2Cl2» or
C2H3CI. Furthermore, reactivity with CI2 followed the sequence Bal2 > Srl2 '^S*2
which correlates nicely with the decreasing ionic character of the alkaline earth dihalide
bonding.

IV.B. Reactive Scattering of Alkali Atoms

Magee originally suggested the electron-transfer or "harpoon" model to account

for the large cross sections for reactions of alkali atoms with halogen molecules. This

model recognizes that the potential energy surface correlating asymptotically to neutral

M + X2 reactants intersects a surface correlating to W* + X2 at an approximate reactant
2

separation of r^ = e /A where A is the difference between the ionization potential of
the alkali atom and the electron affinity of the halogen molecules. This simple model

- 55 -

and its refinement to include such features as the nature of the mixing of these two

zeroth order electronic states in the vicinity of r and the inclusion of the vibrational

c

degree of freedom in X2 is discussed in detail in another chapter of this volume.

This electron transfer model provides a convenient language for discussing the
range of dynamical behaviors observed with different reagents. As often happens, the
language of the model is applicable to a broaden range of reactions than is suggested by
its original derivation. All of the reactions discussed in this section involve the cleavage
of a "covalent" bond in the RX halide reagent to form an "ionic" metal halide bond so that
charge density must flow from the metal atom during the reaction, i.e.

M + RX — ► M""... RX’ — ► VI ""X’ + R. (4)

For halogen molecules and other good electron acceptors, it is reasonable to discuss a
well-developed ion-pair intermediate. For other reagents, such as CH^l, with a small or
negative electron affinity, the M^... RX’ symbol in reaction (4) simply indicates the
inception of polar bonding as the reactants begin to interact. In either case, the metal
atom electron density begins to flow into the lowest unfilled molecular orbital(s) (LUMO)
on R-X so that the nature of this LUMO is very important in determining features of the
reaction dynamics, e.g. the recoil energy of the products. Thus, it is expected and
observed that the reaction dynamics vary widely for differing R-X reagents but show
weaker sensitivity to the identity of the metal atom. For this reason, tne discussion that
follows is grouped into families of different R-X reagents. Furthermore, the review is
not restricted to alkali atom reactions because it is the similarities rather than the
differences which are most striking in comparing reactions of an alkali atom and a non-
alkali metal atom with a particular halogen-containing reagent.

- 56 -

IV. B.l. Metal Atom plus Halogen Molecule

Molecular beam studies of the reactions of metal atoms with halogen molecules and
related reagents are listed in Table IV. Related studies of bimolecular chemiluminescence
[ e.g., Mims and Brophy (1977)] and chemi-ionization [e.g., Diebold, et. al. (1977)] with
the alkaline earth metals are not included. All of the listed studies indicate the following
general features of the reactions: (1) large total reaction cross sections (> 100 R^); (2)
severe attenuation of the wide-angle elastic scattering with no rainbow angle feature
present [e.g. Greene, et. al. (1969)]; (3) a direct reaction mechanism producing an
asymmetric product angular distribution peaked in the forward direction [e.g., Gillen,
et. al. (1971)]; and (4) a preference for low recoil energy events channelling most of the
reaction exoergicity into alkali halide vibrational excitation [e.g., Gillen, et. al. (1971) for
the product recoil energy distribution and Grice, et. al. (1970) which indicates only
moderate alkali halide rotational excitation]. Properties (l)-(3) are all qualitatively
consistent with the large r^ crossing radius and reactive collision impact parameters
predicted by the electron transfer model. Since the halogen molecular negative ions are
bound and have a large vertical electron affinity, the harpoon model is also qualitatively
consistent with property (4) because the electron transfer transition can reach a bound
region of the X2' ion which subsequently dissociates in the force field produced by the
approaching M*. Sholeen, et. al. (1976) and Lin, et. al. (1973) discuss weak trends in the
product angular distribution with changing halogen molecule or metal atom. For a given
halogen molecule, the product metal monohalide angular distribution narrows with
increasing metal atom mass in both the alkali and alkaline earth familities. This could be
a true mass effect or it could be due to the decrease in metal atom ionization potentials
in these sequences. This is a relatively weak effect, however, and only primitive product

- 57 -

angular distribution measurements are available for most chemical combinations so that it
would be misleading to quantitatively compare features of the alkali and alkaline earth
reactions in detail. Lin, et. al (1973) do observe that the product angular distributions
from Ba + CI 2 and Br 2 resemble more closely those of Cs, where the mass factors are
comparable, than those of Li, where the metal atom ionization potentials are similar.
Another weak trend in both metal atom families is observed w.th CI 2 producing a more
sharply peaked product angular distribution than Br 2 . However, the most striking aspect
of the comparison of features of the different chemical systems listed in Table IV is their
qualitative similarity. In unpublished work from the author's own laboratory, this
similarity has been extended to include the reaction of Sn atoms with CI 2 [Parr (1977)].

Precise determinations of the product recoil velocity spectra, d a/a w w, are
important for these reactions as quantitative tests of refined theories built around the
electron transfer model. In view of this, the limited number of such measurements for
this family of reactions *s surprising. Some of the earliest product recoil velocity mea-
surements were obtained for the K + Br 2 reaction [Grosser and Bernstein (1965); Birely
and Herschbach (1966); Warnock, et. al. (1967)]. Since experimental and LAB — ► CM
transformation techniques were still evolving during this period, these studies only
determined a range of possible K + Br 2 CM recoil functions. This was followed by the
careful study of the K + I 2 reaction by Gillen, et. al. (1971) as a function of collision

energy. They reported the reaction dynamics to be relatively insensitive to collision

3 2

energy, and Fig. 5 shows their composite 9 a/3 oj 3 w derived by combining results at
! different energies. This illustrates the direct, asymmetric product angular distribution

' favoring forward scattering with only modest recoil energy. It further illustrates that

i there is typically appreciable breadth to the product recoil angular and energy

i

I

I

- 58 -

I

distributions from these reactions. Sholeen, et. al. (1976) subsequently reported
aw determinations for Li + CI 2 and Br 2 at lower resolution than that of Gillen, et. al.
(1971) because they employed crossed thermal beams. They reported a significant
coupling of the recoil angular and energy distributions from Li + Cl^ with higher product
recoil energies favored at lower scattering angles. However, they failed to resolve similar
coupling in K + Br 2 , and the higher resolution data of Gillen, et. al. (1971) show only very
weak coupling in K + I 2 . Sholeen, et. al. (1976) review the somewhat unsatisfactory status
of existing trajectory calculations for these reactions based on potential surfaces
suggested by the electron transfer model and point out that the published data and other
unpublished measurements [referenced in Siska (1973) and Grice (1975)] represent a stiff
test of our ultimate ability to understand the alkali atom plus halogen molecule reaction
dynamics is terms of the electronic structure rearrangement embodied in the electron
transfer model. In particular, it is important to understand the recoil angle-energy
coupling because the contrasting behaviors of related chemical systems suggest that this
reaction feature might be especially sensitive to some subtle topological feature of the
potential energy hypersurface.

In general, the reactions with the interhalogens are less well characterized. Moulton
and Herschbach (1966) obtained indirect evidence that both product channels arc formed
in the K + ICl reaction. Mims, et. al. (1973) observed both product channels in reactions of
alkaline earths with ICl, and reported that MI is formed with broader product angular
distributions and higher recoil energies than is MCI. Kinematic blurring of the LAB — ►
CM transformation of their measured primitive product angular distributions precluded a

more quantiative comparison of these CM recoil functions, however.

I

- 59 -

'I

The NO 2 molecule is included in Table IV because reaction cross sections
comparable to those of the halogen molecules are predicted by the electron transfer
model by virtue of the high electron affinity of NO 2 . In contrast to the direct alkali atom
plus halogen molecule reaction mechanism, however, a long-lived collision complex
mechanism for the Li + NO 2 reaction is suggested by the much larger exoergicity for the
association reaction to give LiNO^ than for the exchange reaction to give LiO + NO. This
5 long-lived complex behavior is well-established in collisions of alkali atoms with other,

nonreactive oxides [Ham, et. al. (1967), Ham and Kinsey (1970)]. The history of crossed
beams studies of reactions of alkali atoms with NO 2 is somewhat unusual. Herm and
Herschbach (1970) found the differential surface ionization technique to be impractical
with NO 2 because of filament surface "poisoning". Product magnetic deflection- surface
ionization analysis of the Cs + NO 2 scattering failed to indicate formation of a
"diamagnetic" species, whereas product electric deflection revealed a polar cesium-
containing molecule. This led them to suggest that the ground electronic state of the
alkali monoxides shifted from the n symmetry known for LiO to E in the case of CsO, a
suggestion which was confirmed by a matrix-isolation EPR study of Lindsay, et. al.
(1974). Parrish and Herm (1971) subsequently successfully studied the Li NO 2 reaction
by product magnetic deflection, and Sholeen and Herm (1976a) reported the product recoil
velocity spectra shown in Fig. 6 . Contrary to prior expectations of symmetry, the
measured LiO (^n) + NO product angular distribution is shaply peaked forward in analogy
to the halogen molecule reactions. Sholeen and Herm (1976a) suggest that this indicates
reactions through the excited as well as ground electronic states of the LiN 02
intermediate.

- 60 -

1V.B.2.

Metal Atom plus Organic Halide

The alkali atom plus methyl iodide reaction was one of the first to be studied by the
crossed molecular beam technique. Indeed, these early studies [Herschbach, et. al.
(1961); Hersc’ibach (1962)] comprised the first experimental information on a CM product
angular distribution. The qualitative features of the product angular distribution were
correctly inferred in these very early studies, but the recoil energy distribution proved
more troublesome. The initial estimate [Herschbach, et. al. (1961); Herschbach (1962)]
that most of the reaction exoergicity appears as product internal excitation was in error
because of a neglect of the insidious effect of the LAB — ► CM Jacobian [Entemann and
Herschbach (1967)] . As Fig. 7 illustrates, the experimental determination of the

M + CHgl — ► MI + CHj (5)

recoil energy distributions has continued to be troublesome because of the awkward
kinematics. The most careful study is that of Rulis and Bernstein (1972) for the K + CH^I
reaction who determined the KI recoil velocity spectra with a velocity selected K beam.

Bernstein and Rulis (1973) reviewed the experimental status of M + CHjI studies.
The variety of beam techniques applied to these reactions which are listed in Table V is
impressive. In addition to simple angular distribution measurements, these include
product recoil velocity spectra [Sholeen and Herm (1976b); Rulis and Bernstein (1972)] ,
the dependence of the LAB angular distribution on collision energy [Rotzoll, et. al.
(1975); Gonzalez-Urena and Bernstein (1974)] , optical potential analysis of the
attenuation of wide-angle elastic scattering [e.g., Harris and Wilson (1971)], product

I

i

t

- 61 -

B

g

magnetic deflection analysis [Sholeen and Herm (1976b)] , CH^l spatial orientation in a
refocussing electric field to measure the steric effect [e.g. Brooks and Jones (1966);
Beuhler, et. al. (1969); Marcelin and Brooks (1973)] , integration over the in-plane and
out-of-plane LAB product angular distribution to measure the energy dependence of the
total reaction cross section [Gersch and Bernstein (1972); Litrak, et. al. (1974); Pace, et.-
al. (1977)] , product electric deflection analysis of the rotational energy [Maltz and
Herschbach (1967)] and polarization [Maltz, et. al. (1972); Hsu and Herschbach (1973)] as

I

well as polarization-scattering angle correlation [Hsu, et. al. (1974)], and LIF
determination of the product metal halide vibrational state distribution for the Ba atom
reaction [Dagdigian, et. al. (1976)] . The collective reaction features of M CH^l have
come to be described as a "rebound" mechanism wherein reaction is favored for relatively
small impact parameter collisions with the iodine end of the H^C-l bond which scatters
the MI product predominately backward (e.g.. Fig. 4) with a recoil velocity corresponding
to a substantial fraction of the total reaction exoergicity (e.g.. Figs. 4 and 7). All of these
features are qualitatively consistent with the electron transfer model and the electronic
structure of CHjl whose LUMO is a strongly antibonding cr-orbital localized along the C-I
bond. The zero or negative electron affincity of CH^I is consistent with the smaller
reactive impact parameters and total reaction cross section relative to the reactions with
halogen molecules (the M + CHjI total cross section is approximately gas kinetic) which
favors backward scattering. The strongly antibonding nature of the LUMO imparts
considerable C-I repulsion upon the electron transfer and accounts for the efficient
conversion of reaction exoergicity into recoil energy which is observed.

The energy partitioning in these M I-CH 2 -R reactions is especially well-suited to
pertrubation treatments on the impulsive limit because of the repulsive energy release

1

i

;

1

]

i

■■ i

\

i

ja

-62-

character of these reactions [Parrish and Herm (1970); Harris and Herschbach (1971)]. In

the two-body limit that this repulsive energy is impulsively released along the I-CH 2 bond,

the Ml CM recoil momentum would be independent of the identity of M or R in this family

of reactions for a constant repulsive energy produced by the electron transfer. Figure 10

illustrates the similarity in measured alkali halide recoil momentum distributions for a

series of M + I-CH 2 -R reactions. Herschbach (1973) has discussed the Gaussian shapes of

these distributions and the weak trend with changing alkyl iodide in terms of the known '

alkyl iodide photodissociation spectrum [see also Poliak and Levine (1977)]. The model

calculations of Parrish and Herm (1970) suggest that the degree of internal excitation of

the alkyl radical product is especially sensitive to the reaction potential surface, i.e. the

degree to which the actual energy partitioning deviates from the simple impulsive limit.

Unfortunately, very little is known about this feature of the reaction energy partitioning.

Bernstein and Rulis (1973) do cite indirect evidence which indicates little CH^ excitation

in the K + CH^I reaction. Dagidian, et. al. (1976) determined an average Bal vibrational

excitation of only 1S% of the Ba + CH^l reaction exoergicity by LIF. This suggests that

the CHj product possesses more internal excitation than the Bal product based upon the

recoil energy estimates from the primitive LAB Bal angular distribution measurements of

Lin, et. al. (1973b) which are shown in Fig. 4. Since this is a surprising result of utmost

importance to our understanding of the M + CH^I systems, it should be confirmed by )

product recoil velocity spectra measurements on Ba + CH^l. Assuming that it is true, it

need not imply a corresponding high CH^ excitation in the alkali atom plus CH^l

reactions. The low resolution Bal LAB angular distributions reported by Lin, et. al.

(1973b) are certainly similar to those observed in the alkali reactions, and unpublished
product recoil velocity spectra reported in Parr (1977) for Sn + CH^l indicate similar

1

product recoil spectra for alkali and tin atoms plus CH^l. Nevertheless, Dagidgian et. al.
(1976) suggest that high CH^ internal excitation from Ba + CH^l might be due to an
intersection of the Bal + CH^ and Bal^ + CH^ potential surfaces in the exit channel. This
second electron transfer interaction is plausible for Ba (or other alkaline earth atoms) by
virture of the low ionization potential of MI, whereas it is unlikely in the alkali or tin
atom systems.

The organic halides provided a particularly fruitful system for the establishment of
chemical trends in total reaction rate constant measurements in the early M. Polanyi
diffusion flame studies, and they have proven equally interesting in molecular beam
studies in exhibiting a broad spectrum of reaction dynamic behaviors. Entemann and Kwei
(1971), Entemann (1971), Goldbaum and Martin (1975), Wilson and Herschbach (196S), and
Lin, et. al. (1973b) provide particularly interesting low resolution chemical studies of this
type. In addition to CH^I, the behavior of a few other reagents have proven especially
interesting and are discussed below.

Di and tri-iodomethane show a strikingly different behavior from CH^I. Only low
resolution Ml LAB product angular distributions are available for alkali atoms plus CH 2 I 2
and CHIj [Entemann (1971); Lin, et. al. (1974b)]. These indicate that CH 2 I 2 behaves
more like I 2 than CH^I in that forward scattering is favored, although the peaking is less
sharp with CH 2 I 2 than with I 2 . Lin, et. al. (1974b) report that CHl^ produces more sharply
peaked forward product scattering than does CH 2 I 2 . They also point out that trends in the
alkali atom plus various organic halide reaction dynamics correlate nicely with the
corresponding known trends for dissociative electron attachment in these organic halides.
These dissociative electron attachment studies indicate that the electron affinity
increases and the repulsive energy along the carbon-halogen bond upon electron

I

- 64 -

r

attachment decreases as the number of halogens on the carbon increases. For a fixed
number of halogens, an iodide is a better electron acceptor than a bromide which is better
than a chloride. Lin, et. al. (1973b) reported LAB angular distributions of MI^ from
I crossed beams of Ba, Sr, or Ca and CH 2 I 2 obtained with an electron bombardment ionizer-

^ quadrupole mass filter unit. They suggested that most of the MI^ signal observed arose-

from ionization of MI 2 rather than MI product because: (1) MI 2 as well as MI gives MI^
almost exclusively upon ionization; and (2) the MI^ angular distribution was only slightly
■ ' broader than the calculated centroid angular distribution which suggested that the

I detected product was much heavier than the undetected product. This indicated that MI 2

+ CH 2 is an important product channel of the alkaline earth CH 2 I 2 reaction, although not
necessarily the dominant channel since kinematic factors could render their measurements
more sensitive to MI 2 than MI. Dagidigian, et. al. (1976) subsequently reported the LIF
spectrum of product Bal from Ba + CH 2 l 2 - Although they saw no LIF from Bal 2 product,
their results in conjunction with Lin, et. al. (1973b) suggest that Bal 2 and Bal are formed
in comparable yields in the Ba + CH 2 I 2 reaction since LIF may be insensitive to Bal 2 -

The K -t- CFjI reaction provided a surprising result with the report [Brooks (1969);
Brooks (1973); Marcelin and Brooks (1973b), see Fig. 8] of an unusual steric effect. A
strong steric effect in K [Brooks and Jones (1966); Marcelin and Brooks (1973 a and b)]

I and Rb [Beuhler, et. al. (1966); Beuhler, et. al. (1968); Beuhler, et. al. (1969)] -t- CH,I had

I

been established by spatial orientation of CHjI in an electric refocussing field. For CH^I,
results agreed with intinctive expectations that reaction was strongly favored for
approach of the metal atom on the iodine side of the H^C-I molecule. In contrast, FjC-I
reacts to product KI for either orientation. Approach from the -I end scatters KI
I backward, whereas approach from the FjC- end scatters KI forward. Rulis, et. al. (1974)

-65-

L

subsequently reported KI recoil velocity spectra which failed to show any appreciable
coupling of the recoil angle and energy. This suggests that only one LUMO is important in
the CFjI case. The difference between the FjC-1 and HjC-I cases suggests a greater
delocalization of the LUMO in F^C-I so that the electron transfer probability is less
orientation dependent. Smith, et. al. (1977) have also recently reported the LIF spectrum'
of Bal from Ba + CF^l which indicates a biomodj vibrational distribution with the Bal
high vibrational component scattered more predominatly forward. Since Rulis, et. al.
(1974) report no angle-recoil energy coupling in K + CF^I, this report suggest that the
alkaline earth reaction dynamics are more complex than are the alkali; indirect evidence
of Lin, et. al. (1973b) that BalF as well as Bal is formed in the Ba + CF^I reaction further
supports this possibility. Again, the possibility of a second electron transfer in the
alkaline earth atom reaction could account for this difference.

The alkali atom plus CCl^ reaction provides a classic example of a sideways peaked
product angular distribution. The high symmetry of CCl^ suggests that this conical
distribution could be a "rainbow" phenomenon associated with averaging the reactive
trajectories over CCl^ orientations. The only published product recoil velocity data are
those of Sholeen and Herm (1976b) on Li + CCl^. Figure 7 illustrates the similar product
recoil energy distributions from Li + CH^I and CCl^, which suggests comparable repulsive
J energy releases. Figure 7 indicates an average Li + CCl^ recoil energy which represents

j 31% of the energy available to the products of the Li + CCl^ reaction. Schmidt, et. al.

(1976) recently reported the LIF spectrum of BaCl from Ba + CCl^. They concluded that
vibration (75%) and rotation (4%) of BaCl accounted for 79% of the reaction energy.

i

\

1 ’

Ik

- 66 -

After subtracting are estimated CCl^ internal excitation, 6% of the reaction energy was
left for BaCl + CCl^ recoil. Here again, these comparisons suggest different reaction
mechanisms for alkali and alkaline earth atoms.

Sholeen and Herm (1976b) point out that the energy partitioning in the Li + CH^NO^

— ► LiNO, + CHj reaction shown in Fig. 7 is surprising. In contrast to CH^I or CCl^, the

♦

CHjN 02 LUMO is a it (bj) orbital weakly antibonding along the N-O bonds in the nitro

group which cannot account for any substantial repulsive energy release along the C-N
2

bond. However, the CHjN02 anion state produced by an electron transfer into this

LUMO dissociates adiabatically into CH^ plus the excited B^ state of NO 2 ”. The next

highest orbital in CH^N02 is probably a o- (aj) which is strongly antibonding along the C-

2 -

N bond. An electron transfer into this orbital would produce a Aj CH^N02 state

correlating asymptotically with CH^ plus the ground state of NO 2 . The observed LiN02

+ CHj product recoil energy indicates the participation of this Li^-CH 2 N 02 charge

2

transfer state, possibly due to an internal conversion from the B^ anion state produced
initially. Here again, Herm, et. al. (1973) have emphasized the contrasting dynamics of
alkali and alkaline earth atom reactions with nitromethane. It is less surprising here,
however, because the much stronger monoxide bond in the alkaline earth family favors the
metal monoxide product channel which is energetically inaccessible in the alkali atom
reactions.

IV. B. 3. Metal Atom plus Inorganic Polyhalide

Molecular beam studies of the reactive scattering of alkali atoms from various
inorganic polyhalides are listed in Table VI. The history of these studies is interesting and
was recently reviewed in Behrens, et. al. (1976b). With the exceptions of SCl 2 » PCl^, and

- 67 -

PBPg, the reactions listed in Table VI appear to proceed via formation of long-lived or
osculating complexes. This is particularly well established for the Cs + SFg — ► CsF +
SFg reaction. Here PRVS show the forward-backward product angular distribution
symmetry expected of a long-lived complex, and the product recoil energy distribution is
consistent with an TST equipartitioning of reaction energy over degrees of freedom
within the complex [Riley and Herschbach (1973)]. Product electric resonance spectra
indicates a Boltzman distribution in CsF vibration levels. Both the magnitude of this CsF
vibrational temperature and its variation with SFg beam temperature also indicate a
reaction energy equipartitioning within the complex [Bennewitz, et. al. (1971) and Freund,
et. al. (1971)] . Similar experiments on Li + SFg — ►LiF + SFg also indicate a Boltzman
distribution over LIF vibrational levels [Mariella, et. al. (1973)]. Here, however, both
the magnitude of the LIF vibrational temperature and its insensitivity to the SFg beam
temperature are inconsistent with an equipartitioning of reaction energy. This is
surprising and still not well understood since the LiF PRVS from the same reaction is
consistent with a long-lived complex, TST energy-equipartitioning reaction mechanism
[Behrens, et. al. (1976b)] .

Alkali atom reactions with SnCl^ are interesting in that both alkali chloride (MCI)
and alkali chlorostannite (MCl.SnCl 2 ) products apparently form. The evidence for this is
strong but indirect since the surface ionization detection technique cannot distinguish
between these two possible products. The possibility of both products channels was first
suggested by Whitehead, et. al. (1972b). Product recoil velocity spectra measurements on
K, Rb, and Cs + SnCl^ by Riley and Herschbach (1973) and subsequently on Li + SnCl^ by
Behrens, et. al. (1976b) provided much stronger kinematic evidence for both product
channels because the measured bimodal product recoil velocity spectra were well fit by a

- 68 -

long-lived, TST energy equipartitioning complex which could decompose into either
product channel. Behrens, et. al. (1976b) obtained some evidence that the LiCl.
SnCl 2 + Cl product angular distribution is less sharply peaked than is that of the LiCl +
SnClj product channel, although this is not established with high confidence due to severe
kinematic blurring of the LAB — ► CM transformation for the case of the LiCl. SnCl 2
product. They point out, however, that these contrasting angular distributions would
correlate nicely with different plausible angular momenta couplings within the complex
leading to decomposition into the alternate product channels.

1V.B.4. Metal Atom plus Hydrogen Halide

The status of product recoil angular and energy distribution measurements on K (the
best studied metal) plus H-, D-, and T-Br has been review by Kinsey (1972), and Table VII
lists the metal atom + HX studies. Grosser, et. al. (1965), Riley, et. al. (1967), and
Gillen, et. al. (1969) studied the K + HBr and DBr reactions using velocity selection of the
K-beam and velocity analysis of the KBr product. They subjected hundreds of individual
LAB data points to a careful numerical LAB — ►CM inversion analysis to extract the CM
distributions. Owing to the extemely unfavorable kinematics, a broad range of CM
functions were computable with the data. Nevertheless, their results indicate that the K
+ HBr reaction favors backward scattering whereas the K + DBr reaction yields a
practically isotropic angular distribution with a slight preference for forward scattering
despite the fact that the HBr total reaction cross reaction is 40% larger than that of DBr.
Martin and Kinsey (1967) developed a method for detecting atomic tritium (but not TBr)
by adsorbing it on a molybdenum trioxide surface, and used this technique to measure the
LAB angular distribution of T from K (and Cs) + TBr. Although neither velocity selection

- 69 -

j

I

nor analysis was employed, the very favorable kinematics in this study clearly indicated
that their measured LAB T product angular distribution implied that the K + TBr
reaction favors backward scattering of the KBr. It is still not clear why these product
angular distribution do not follow a simple trend in the HBr, DBr, TBr isotopic sequence.
This may be due to some unusual quantum effect associated with the large zero point-
energies or limited number of product channel partial waves in these reactions.

Perhaps the most interesting recent studies on the alkali atom reactions are the
series of papers by Odiorne and Brooks (1969), Odiorne, et. al. (1971), and Pruett, et. al.
(1974 and 1975). These indicate that the K + HCl total reaction cross section is increased
by increasing the reactant relative translational or vibrational energy, but that vibrational
energy is more effective. Pruett, et. al. (1975) have emphasized the importance of
expressing results in terms of an average state-of-state transition rate. They report that
the K -*■ HCl reaction rate constant increases monotonically as the collision energy
increases from 8.8 to 50.5 kJ/mole, but that the ratio of this rate constant to the density
of possible product states shows a simple exponential decay with the square root of the
energy in excess of thermodynamic threshold.

Much more detailed information is potentially available on the alkaline earth atom
reactions because of the ability to deploy the LIF technique. Cruse, et. al. (1973), for
example, have reported LIF determination of the BaX vibrational level distributions in
reactions of Ba with HF, HCl, HBr, and HI. Because of the relatively small exoergicities
of these reactions, however, the implications of the results are somewhat obscurred by the
small uncertainties in the barium monohalide bond dissociation energies. For example, the
most recent D° (BaX) determination [Hildebrand (1977)] indicates that the Ba + HCl
reaction is only marginally exoergic and the Ba + HBr reaction is actually endoergic.

1

Thus, the interpretation of the results of Cruse, et. al. (1973) is critically dependent on
the energy distribution of species which react which is poorly characterized in the absence
of experimental control of reactant energy. This is especially critical for the Ba + HF
reaction because Cruse, et. al. (1973) report that a surprisely low 12% of the reaction
energy appears in the BaF vibration on the average. However, this is based upon a D°
(BaF) from chemiluminescent spectra which is 23.9 kJ/mole higher than the best high-
temperature gaseous equiliLrium value [Hildebrand (1968)]. Cole and Preuss (1977) have
recently emphasized the need for careful temperature dependence studies in
chemiluminescent bond energy determinations, and have reported an activation energy of
~17kJ/mole for the Sr + F 2 chemiluminescent reaction. Pruett and Zare (1976) have also
reported a particularly striking study of the Ba + HF (v = 1) reaction wherein an HF laser
was employed for reactant excitation and LIF determined the distribution over BaF
product vibrational states. They report than an average of 57% of the HF vibrational
energy appears as BaF vibrational energy.

IV.C. Alkali Dimers plus Various Halides

Studies of reactions of the alkali dimers with halogen-containing compounds are
listed in Table VIII. In contrast to the variety of beam techniques which have been applied
to the study of alkali atom reactions, the alkali dimer studies have been confined to LAB
product angular distribution measurements. However, the kinematic situation is better
than in many of the simple primitive LAB product angular distribution measurements in
the alkali atom reaction families because the alkali dimers are produced by condensation
in a nozzle expansion so that the beam has a sharp speed distribution. Thus, these studies
have provided semi-quantitative CM recoil functions, particularly for the product angular

lii

-71-

distributions, and have certainly characterized the qualitative reaction mechanisms. Most
of these studies are due to R. Grice and his co-workers, and the results have been
reviewed in Grice (1975).

The reactions of Kg with the halogen molecules proceed with total cross sections
comparable to those of K + Xg to scatter KX predominately forward (relative to the
direction of the original Kg velocity). This immediately indicates that formation of an
alkali halide, alkali atom, and halogen atom (Reaction (6)) must dominate over formation
of two alkali halides (Reaction (7)),

KX + K +X

(6)

KX + KX,

(7)

because momentum conservation would dictate symmetry about 6= 90° for reaction (7)
irrespective of the reaction dynamics. Indeed, Whitehead, et. al. (1972a and 1973) have
shown that the approximate K product LAB angular distribution from Reaction (6) can be
obtained by comparing the sum of Kg plus K scattering with a Kg beam with the elastic
scattering of a supersonic K-beam, although this technique is only practical in the case of
large total reaction cross sections. For Kg + Brg, IBr, and BrCN, Whitehead, et. al.
(1972a and 1973) report that both the K and KX product angular distributions are peaked
forward with comparable product flux intensities, but that the K-product differential
cross section falls off more rapidly at wider angles. This indicates that Reaction (6) is the
dominant product channel with reaction at large impact parameters producing small
deflection angles, but that Reaction (7) probably occurs as well for smaller impact
nnrnmptpr cftl!ision.s. The large reaction cross section and other similarities to the alkali
atom plus halogen molecule reactions for this reaction of a singlet spin Kg molecule is no

more surprising than was the analogous behavior for the alkaline earth atoms. Here again,
the electron transfer model accounts nicely for the observations by virtue of the low K 2
ionization potential. Thus, the reaction mechanism may be viewed as

Kg + XY — + XY’ — KgX + Y — ♦K + KX + Y. (8)

Lin, et. al. (1974a) actually report that the K-product flux in the forward direction from
Kg + I 2 exceeds that of KI which suggests that, for this reaction, the Kg* dissociates as
fast or faster than the Ig resulting in a stripping type mechanism for the K product.

For all of the reactions listed in Table VIII, the potassium halide product peaks in the
forward direction defined by the orginal Kg velocity. This is sometimes accompanied by a
secondary peak in the backward direction indicative of an osculating complex. The
reactions with the polyhalides typically convert both potassium atoms into potassium
halide products. This may account for the entries in Table ''Ml of reactions with BHr^ and
SiCl^; the cross sections for reactions of alkali atoms with these reagents are too small
to permit beam studies. This unanimity of mechanistic behavior contrasts sharply with
the broad spectrum of dynamical behaviors observed in the alkali atom reactions with this
spectrum of reagents. Grice and his co-workers have pointed out the importance of a
second electron transfer in all of these systems. The ionization potential of KgX can be
comparable to or less than that of Kg so that an electron transfer from KgX to the
departing radical can give rise to an attractive interaction in the product channel which is
not present in the alkali atom reactions. The observation of chemiluminescence [Struve,
et. al. (1975)] and, more significantly, chemi-ionization [Lin and Grice (1973), Lin, et. al.
(1974c)] in some of these systems is a direct manifestation of this second electron jump.

- 73 -

Nevertheless, this second electron transfer doesn't seem to fully account for the
difference between the K 2 and K reaction behaviors. In particular, the forward scattered
K1 component from the K 2 + CH^l reaction requires additional explanation. As noted
earlier, the barium monohalides have ionization potentials comparable to or lower than
that of a barium atom so that this second electron transfer should be operative in barium
atom reactions as well. Indeed, it was noted previously that differences in the details of
energy partitioning between some alkali and alkaline earth atoin reactions suggested that
this second electron transfer gave rise to product channel attractions in the alkaline earth
systems. Again, a more direct manifestation of this effect was noted in the chemi-
ionization reactions of Ca, Sr, and Ba with the halogen molecules [Oiebold, et. al.
(1977)]. Nevertheless, Fig. 4 illustrates tnat the 8al product angular distribution from Ba
CH^l is similar to that of alkali atom reactions and favors backward scattering.

Thus, it is at least plausible that the "double rebound" mechanism depicted
schematically in Fig. 11 could account for the unusual K 2 + CH^l product angular
distribution. This is drawn for collinear approach; other geometries would serve to
broaden the distribution. Reaction is initiated by approach of K 2 on the I- end of CH^l in
accordance with the steric effect established for the alkali reactions. The initial electron
transfer ejects the methyl radical and the iodine atom (more properly I anion after the
electron transfer) is propelled toward the K 2 . However, a second rebound reaction of 1
with K 2 causes the KI to recoil in the direction of the original K 2 . Since the

reaction is only ^6.2 k3/mole exoergic, this simple double rebound picture might be overly
simplistic. The true explanation might require some combination of the second electron
transfer and double rebound mechanism. Nevertheless, it seems likely that this double
rebound mechanism is an important component of the + CH^l reaction dynamics be-
cause it accounts for the contrasting K2 and Ba behaviors and is nicely consistent with
the results of Struve, et. al. (1975) who report a preference for reversal in halogen atom
direction in the reactions of halogen atoms with K^.

- 75 -

V. Closing Remarks

I

!

i

I

f

5

i

ii

Related beam studies of reactions of non-alkali metal atoms with various oxides and
of other reactions of alkali dimers are listed in Tables IX and X. It seemed inappropriate
to discuss these studies because they are somewhat outside the subject matter implied by
the title of this volume.

It seems appropriate in closing to note some especially important studies which are
needed to complete our understanding of gas-phase, thermal-energy metal atom
chemistry. The various beam techniques, especially PRVS measurements, should be
applied to some of the reactions of alkaline earth atoms with halogen- containing
compounds in order to compliment the completely resolved VIX vibrational distributions
which can be and are being provided by LIF studies. U also seems important to extend
these studies to other metal atoms (and semi-metals such as boron atoms) in order to
assess the sensitivity or insensitivity of the reaction dynamics to the electronic structure
of the metal atoms. The recent LIF studies seem to suggest significant differences
between the reaction dynamics of alkali and alkaline earth atoms. In this regard, it is the

author's opinion that the alkalies will prove to be representative of a typical metal atom
and that the alkaline earths are unusual because of the ease of the "second electron
transfer".

-77-

rnaCauI.'*! i'AOE BJLAfOC-NOT FTIKSD

I

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Table 1. Abbreviations of Different Experimental Techniques

Abbreviation

ANGD

OPANGD

CEANGD

PRVS

CEPRVS

LECT

CHMACT

RMAGDF

REDORT

red:s

ELASOP

PMAGDF

Technique

product angular distribution without velocity selection
of either beam or scattered species

product angular distribution out of reactant beams
plane

product angular distribution with collision energy defined
via SDV5 or nozzle beam

product recoil velocity spectra

product recoil velocity spectra for well-defined collision
energy

laser excitation of some reactant internal state
chemical activation of high product internal excitation

magnetic deflection of a reactant beam (e.g., to prepare
a beam of alkali dimers)

orientation of a symmetric top reactant by electric
deflection

selection of a particular reactant rotational quantum
number by electric deflection

optical potential analysis of attenuation of wide angle
elastic scatteing

magnetic deflection of a scattered beam (e.g., to confirm
differential surface ionization)

- 95 -

PRSCKDL-'O page ELANK-ITOT

electric deflection of a scattered beam in a two-pole
field

electric deflection of a scattered beam in a quadrupole
refocussing field

electric resonance analysis of product vibrational distribution

laser induced fluorescence anailysis of product vibrational
(and possibly rotational) states.

LIF

I

Table II. VibrationaJly Inelastic Collisions of Alkali Halides.

Collision Partners

Technique

Result

Reference

LiF + Ar, Xe, N^, NO, CO, HF, HCl

CO 2 , H 2 O, NH 3 , ND 3 , CHFCI 2 , SF^

PERA

p(e;)

Mariella, et. al. (1974)

KBr + Ne, Ar, N 2 , CO, CO 2

CHMACT-PRVS

I(®,v)

Crim, et. al. (1973)

KBr + H 2 O, NH 3 , CH 3 OH

CHMACT-PRVS

I(®,v)

Donohue, et. al. (1973)

KBr + CH 3 OH

CHMACT-PRVS

I(®,v)

Donohue, et. al. (1972)

KBr + CH 3 NO 2 , C 2 H 3 OH, (CH 3 ) 20 , C 3 H^

CHMACT-PRVS

I(®,v)

Crim, et. al. (1974)

CsF + Ar

CEPRVS

l(®,v)

King, et. al. (1973)

CsCl, Csl + Ar, Xe

CEPRVS

I(®,v;E)

Armstrong, et. al.
(1975)^

Csl + Ar

CEPRVS

I(®,v;E)

Loesch and Herschbach

(1972)

Csl + Ar, Xe

CEPRVS

I(®,v;E)

Greene, et. al. (1977)

^Armstrong, et. al. (1975) didn't actually study the CsCl + Xe combination. However, this
subtle distinction is not made here or in entries in other tables in order to save space.

- 97 -

Table III. Reactive Scattering of Alkali Halides.

Reactants

Technique

Results Reference

Alkali Halide + Alkali Atom

LiCl + Ba

ANGD-LIF

P(E^';@) Dagdigian and Zare (1974)

KF, KBr + Li

ANGD

K®)

Kwei, et. al. (1971)

KF, KCl, KBr, KI, CsF, CsCl

CsBr, Csl + Li

ANGD

K®)

Lees and Kwei (1973)

KCl + Rb, RbCl + K

ANGD

K®)

Miller, et. al. (1967)

KCl + Ba

ANGD-LIF

P(E^';®)

Smith and Zare (1976)

RbF, CsF + K

CEANGD

<r(E)

Stolte, et. al. (1974)

RbF, CsF K

CEANGD

o-(E)

Stolte, et. al. (1976)

RbCl + K

ANGD

K®)

Aniansson, et. al. (1974)^

RbCl + Cs, CsCl + Rb

ANGD.PRVS

I{®,v)

Miller, et. al. (1967)

CsF + K

RED3S-CEANGD P(E^)

Stolte, et. al. (1975)

TlCl, TII + Cs

ANGD

K®)

Fisk, et. al. (1967)

- 98 -

Alkali Halide + Alkali Halide

KI + CsCl

PRVS

I(®,v)

Miller, et. al. (1967)

KI + CsCl

PRVS

I(®,v)

Miller, et. al. (1972)

Alkali Halide + Halogen

Molecules

CsBr + ICl

ANGD

K®)

King and Herchbach (1973)

Csl + CI 2

PRVS

I(®,v)

King and Herschbach (1973)

Srl^, Bal^ + CI 2 , Bal 2 + HCl

PRVS

I(®,v)

Freedman, et. al. (1976)

^Aniansson, et. al. (1974) report the absolute total reaction cross sections.

-99-

Table IV. Metal Atoms plus Halogen Molecules.

Reactants

Technique Result

Reference

Alkali Atoms

Li + CI 2 , Br2 ICl

ANGD-PMAGDF

I(®)

Parrish and Herm (1968)

Li + CI 2 , Br2, ICl

ANGD-PMAGDF

I(®)

Parrish and Herm (1969)

Li + CI 2 , Br2

PRVS-PMAGDF

I(®,v)

Sholeen, et. al. (1976)

Li + NO 2

ANGD-PMAGDF

1(®)

Parrish and Herm (1971)

Li + NO 2

PRVS-PMAGDF

(l®,v)

Sholeen and Herm (1976a)

Na + Br 2 . ICl

ANGD

I(®)

Birely, et. al. (1969)

Na, Cs + NO 2

PMAGDF & PEDTP

Herm and Herschbach (1970)®

K, Rb, Cs + CI 2

ANGD

K®)

Grice and Empedocles (1968)

K + CI 2 . Br2. 12 . ICl

ELASOP

<JtE)

Greene, et. al. (1969)

K, Cs + Br 2 . 12 . ICl, IBr

ANGD

I(®)

Wilson, et. al. (1964)

K + Br2, ICl

PMAGDF

Herm,et. al. (1964)^

K + Br2

PEDTP

P(E/)

Herm and Herschbach (1965)

K + Br2

CEPRVS

I(®,v;E)

Grosser and Bernstein (1965)

K.Cs + Br 2, 12

CEANGD-ELASOP I(®;E)

Minturn, et. al. (1966)

K.Br^

PRVS

I(®,v)

Bipely and Hepschbach (1966)

K.Br^

CEPRVS

Warnock, et. al. (1967)^

K, Rb, Cs + Br 2, 12

ANGD

K®)

Bipely, et. al. (1967)

K, Cs + Br 2

PEDTP

p(e;)

Maltz and Hepschbach (1967)

K + Br 2 . BrCN

CEANGD

I(®)

Whitehead, et. al. (1972b)

K, Cs + BP 2

PEDTP

P(MjVJ') Hsu and Hepschbach (1973)

K.Br2

CEANGD

I(®;E)

van der Meulen, et. al. (1975)

KM 2

CEPRVS

I(®,v;E) Gillen, et. al. (1971)

K + I 2 . IBr

CEANGD

K®)

Lin, eU al. (1974b)

K + ICl

ANGD

Moulton and Hepschbach (1966)

K,Rb. Cs + ICl, IBP

ANGD

K®)

Kwei and Hepschbach (1969)

K, Rb, Cs + BpCN, ICN, NOCl

ANGD

K®)

Grice, et. al. (1968)

Rb + BP 2

PEDRF

p(e;)

Grice, et. al. (1970)

Rb + BP 2

PEDRF

P(E/)

Mosch, et. al. (1975)

Rb + IBr

CEANGD

I(®,E)

Minturn, et. al. (1966)

Cs + BP 2

CEANGD

I(®,E)

Datz and Minturn (1964)

Cs + Br 2

PMAGDF

Gordon, et. al. (1968)^

Cs-^Br^ PEDTP P(M^VJ’) MaJtz, et. al. (1972)

Alkaline Earth Atoms

Mg, Ca, Sr, Ba + Cl 2 > Br.,

ANGD

U®)

Lin, et. al. (1973a)

Mg, Ca, Sr, Ba + ICl

ANGD

K®)

Mims, et. al. (1973)^

Ca, Sr, Ba + BrCN

LIF

p(e;)

Pasternack and Dagdigian (1976)^

Ca, Sr + NO 2

ANGD

K®)

Herm, et. al. (1973)

Ba + CI 2 , NO 2

ANGD

K®)

Haberman, et. al. (1972)

Ba + BrCN

ANGD

K®)

Mims, et. al. (1973)^

^Reported a ^2 CsO ground state.

^Confirmed differential surface ionization results
(2

LAB — ► CM transformation of K + Br 2 data.
^Partial resolution of K1 versus KCl product channels

Q

Data on both product channels

i

- 102 -

• MICROCOPY RESOLUTION TEST CHARI

NAIIONAI BURUU Of SIANDARO^ A

Table V. Metal Atoms plus Organic Halides

Reactants

Technique

Results

Reference

Alkali Atoms

Li + CH 3 I, CCI 4 , CH 3 NO 2

ANGD-PMAGDF

I(®)

Parrish and Herm (1971)

Li + CH 3 I. CCI 4 , CH 3 NO 2

PRVS-PMAGDF

I(®,v)

Sholeen and Herm (1976b)

Na, K, Cs + CH 3 I. CHCI 3 , CCl^

PMAGDF

Gordon, et. al. (1968)®

Na + CH 3 I

ANGD

I(®)

Birely, et. al. (1969)

Na. K, Cs + CH,NO,. C„H=ONO„.
CgHjjONCr ^ ^ ^ ^

ANGD,

PMAGDF.PEDTP

I(®)

Herm and Herschbach (1970)

K + CH 3 I

ANGD

K®)

Herschbach, et. al. (1961)

K, Rb, Cs + CH 3 I

ANGD

I(®)

Herschbach (1962)

K + CH 3 I

PMAGDF

Herm, et. al. (1964)®

K + CH 3 I

REDORT

P(K/J;®)

Brooks and Jones (1966)

K + CH 3 I, CCI 4

ELASOP

P(b,E)

Airey, et. al. (1967b)

K + CH 3 I, CgHgl, C 3 H 7 I. (CH 3 ) 2 CHI

OPANGD

I(®,®)

Kwei, et. al. (1970)

C^Hgl, (CH 3)2 CHCH 2 I, (CH 3 )(C
(CH 3)3 CI. CgHj^I, C 7 H 15 I

2 H 3 )CH 1 .

K, Rb, Cs + CH 3 I, CCI 4

ELASOP

P(b,E)

Harris and Wilson (1971)

u

\

- 103 -

K + CH 3 I

CE-OPANGD

ff(E)

Gersch and Bernstein (1971)

K + CH 3 I, CCl^

CEANGD

K®)

Whitehead, et. al. (1972b)

K + CH 3 I

CE-OPANGD

o-(E)

Gersch and Bernstein (1972)

K > CH 3 I

CEPRVS

l{®,v;E)

Rulis and Bernstein (1972)

K 4. CH 3 I

CEPRVS

l(®,v;E)

Bernstein and Rulis (1973)

K + CH 3 I, CHCJ 3

REDORT

P(K/3;®) Marcelin and Brooks (1973a)

K 4- CH 3 I, CF 3 I, CHCI 3

REDORT

P(K/3;®) Marcelin and Brooks (1973b)

K 4- CH 3 I

CEANGD

1(®;E)

Rotzoll, et. al. (1975)

K, Rb + (CH 3 l)^

ANGD

Gonzalez-Urena and Bernstein

(1975)

K, Cs 4 - CH-CHI, CH,CHCH,I,

CgHjI, CH 2 CHCH 2 Efr

ANGD

K®)

Entemann and Kwei (1971)

K 4- CF 3 I

REDORT

P(K/3;®) Brooks (1969)

K 4- CF 3 I

REDORT

P(K/3;®) Brooks (1973)

K 4- CF 3 I

CEPRVS

l(®,v)

Rulis, et. al. (1974)

K 4- CH 3 COI, CH 3 Br, CH 3 COBr,

ANGD

K®)

Goldbaum and Martin (1975)

CH 3 COCI, CH 3 CN, CH 3 NC,

CH 2 CHCH 2 CN,CH 2 CHCH 2 NC,

CH 3 COCN

K, Cs 4 . CH 2 I 2 . CH 2 Br 2 , CH 3 CHBr 2 ,

ANGD

K®)

Entemann (1971)

(CH3)2CBr2, CH2CI2

- 104 -

K + CH 2 l 2 ,CHl 3 , CBr^

CEANGD

K®)

Lin, et. al. (1974b)

K + CHjBr, CBr^

ELASOP

P(b,E)

Green, et. al. (1966)

K + (CH 3 ) 3 CBr, C 2 (CN)^

ELASOP

P(b,E)

Green, et. al. (1969)

K, Rb, Cs + CBr^, CHCI 3 , CCl^

ANGD

K®)

Wilson and Herschbach (1968)

K + CCl^

ELASOP

P(b,E)

Sloane, et. al. (1972)

Rb + CH 3 I

REDORT

P(K/J;®)

Beuhler, et. al. (1966)

Rb + CH 3 I

REDORT

P(K/J;®)

Beuhler, et. al. (1968)

Rb + CH 3 I

REDORT

P(K,J;®)

Beuhler, et. al. (1969)

Rb * CH 3 I

CE-OPANGD

o-(E)

Litvak, et. al. (1974)

Rb + CH 3 I

CE-ANGD

1(®;E)

Gonzalez Urena and

Bernstein (1974)

Rb, Cs CH 3 I, C 2 H 3 I, C 3 H 2 I,

(CH3)2 CHI,C^HgI,

OPANGD

K®,*)

Kinsey, et. al. (1976)

Rb + CH 3 I

CE-OPANGD

o-(E)

Pace, et. al. (1977)

Cs + CH 3 I, CCl^, CH 3 NO 2

PEDTP

P(E^')

Maltz, and Herschbach

(1967)

Cs CH 3 I, CCl^

PEDTP

P(M 3 '/ 0 ’)

Maltz, et. al. (1972)

Cs -K CH 3 I, CF 3 I, CCl^

PEDTP

P(V^V3’)

Hsu and Herschbach

(1973)

Cs + CH 3 I

PEDTP

PIM'^/O';®)

Hsu, et. al. (1974)

- 105 -

Cs + CCl^ CE Bull and Moon (1954)*^

Alkaline Earth Atoms

Ca, Sr, Ba + CH^l, CF^l, CH2I2, CCl^

ANGD

K®)

Lin, et. al. (1973b)

Ca, Sr, Ba + CCI3NO2, (CH3)2CHN02

ANGD

K®)

Herm, et. al. (1973)

Ba + CH3I, CH2I2

LIF

p(e;)

Dagdigian, et. al. (1976)

Ba + CF3I

ANGD-LIF

P(E^';®)

Smith, et. al. (1977)

Ba + CH^Br, CH2Br2, CHBr^, CBr^

LIF

p(e;)

Rommel and Schultz (1977)

Ba + CCl^

LIF

p(e;)

Schmidt, et. al. (1976)

^Confirmed differential surface ionization results.
*^First observation of a reactive scattering signal.

t

- 106 -

Table VI. Metal Atoms plus Inorganic Polyhaiides

Reactants

Technique

Results

Reference

Alkali Atoms

Li + PCl^, SnClj^

ANGD-PMAGDF

K®)

Parrish and Herm (1968)

Li + PClj, SnCl^

ANGD-PMAGDF

K®)

Parrish and Herm (1969)

Li + PCI 3 , SnCl^, SF^

PRVS-PMAGDF

I(®,v)

Behrens, et. al. (1976b)

Li ^ SF^

ANGD-PMAGDF

I(®)

Parrish and Herm (1971)

Li + SF^

PERA

p(e;)

Mariella, et. al. (1973)^

K, Rb, Cs + SCI 2

ANGD

1 (®)

Grice, et. al. (1968)

K + SCI 2

ANGD

1 (®)

Goldbaum and Martin (1975

K + ZnCl 2 * Znl 2 , Cdl 2 >

PRVS

I(®,v)

Bullitt, et. al. (1974)

HgBr 2 , Hgl 2

K + HgCl 2 , HgBr 2 ,Hgl 2

CEANGD

K®)

Hardin, et. al. (1973b)

K + PCI 3 , SnCl^

CEANGD

U®)

Whitehead, et. al. (1972b)

K + SiCl^, SnCl^, SFg

ELASOP

P(b,E)

Airey, et. al. (1967b)

K, Rb, Cs + SnClj^

ELASOP

Harris and Wilson (1971)

K + SnCl^, SFg

ELASOP

P(b,E)

Sloane, et. al. (1972)^

- 107 -

K, Rb, Cs + SnCl^, SF^

PRVS

K®,v)

Riley and Herschbach (1973)

K, Cs + SeFg, TeF^, MoF^, WF^, UF^

ANGD

K®)

Annis and Datz (1977)

Rb, Cs + PClj, PBr^, SnCl^

ANGD

K®)

Wilson and Herschbach (1968)

Cs SnCl^

PMAGDF

Gordon, et. al. (1968)*^

Cs + SF^, SFg

PERA

P(E ')

V

Bennewitz, et. al. (1971)^

Cs + SF^, SFg

PEDTP

P(M'j/J')

Hsu and Herschbach (1973)

Cs + SF^

PERA

p(e;)

Freund, et. al. (1971)^

Alkaline Earth Atoms

Sr, Ba + PCI3, SF^ ANGD I(®) Herm, et. al. (1973)

^Varied the beam temperature to gain information on the importance of reactant internal
energy.

*^Conf irmed differential surface ionization results.

- 108 -

Table VII. Metal atoms plus Hydrogen Halides.

Reactants

Technique

Results

Reference

Alkali Atoms

K + HCl.Hl

ELASOP

P(b,E)

Ackerman, et. al. (1964)

i

K + HCl

ANGD

o’(E)

Odiorne and Brooks (1969)

1.

1

i-'

ji

K + HCl

LECT-ANGD

P(E^)

Odiorne, et. al. (1971)

i;

K + HCl

CEANGD

(r(E)

Pruett, et. al. (1974)

Pruett, et. al. (1975)

1

K + HBr

ANGD

Taylor and Datz (1955)

i

1'

i;

K + HBr

CEANGD

Greene, et. al. (1960)

Herschbach (1960)

K + HBr

CEANGD-ELASOP

P(b,E)

Beck, et. al. (1962)

1'

K + HBr

CEPRVS

I(®,v;E)

Grosser, et. al. (1965)

K + HBr.DBr

ELASOP

P(b,E)

Airey, et. al. (1967a)

1.

K + HBr, DBr

CEPRVS

I(®,v)

Riley, et. al. (1967)

, 1
' i

i

K, Cs + TBr

ANGD

K®)

Martin and Kinsey (1967)®

,i

K, Cs + HBr

PEDTP

P(E|.')

Maltz and Herschbach (1967)

J

K + HBr, DBr

CEPRVS

I(®,v)

Gillen, et. al. (1969)

j

- 109 -

K, Cs HBr, HI

PEDTP

P(MjV3')

Maltz, et. al. (1972)

K, Cs + HBr, HI

PEDTP

P(Mj'/J') Hsu and Herschbach (1973)

K, Cs + HBr, HI

PEDTP

Hus, et. al. (1975)

Rb + HBr

PEDRF

P(E/)

Mosch, et. al. (1974)

Cs + HBr

PEDTP

P(E^')

Herm and Herschbach (1965)

Cs + HBr

ELASOP

P(b,E)

Greene, et. al. (1969)

Alkaline Earth Atoms

Ca, Sr, Ba + HI

ANGD

<r(E)

Mims, et. al. (1972)

Ba + HF, HCl, HBr, HI

LIF

P(E ')

V

Cruse, et. al. (1973)

Ba + HF

LECT-LIF

P(E ;E

V V

') Pruett and Zare (1976)

^Angular distribution of the T product from M + TBr

-no-

Table VIII. Alkali Dimers plus various Halides.^

Reactants

Technique

Results

Reference

Halogen Atoms

K 2 + Cl.Br

RMAGDF-ANGD

K®)

Struve, et. al. (1975)*^

Halogen Molecules

RMAGDF-ANGD

K®)

Struve, et. al. (1975)*^

+ Br 2 , ICl, IBr, BrCN

RMAGD-ANGD

K®)

Foreman, et. al. (1972b)

K 2 + Br 2 , BrCN

RMAGDF-ANGD

K®)

Whitehead, et. al. (1972a)'

K 2 + Br 2 , IBr, BrCN

RMAGDF-ANGD

K®)

Whitehead, et. al. (1973)^

^2 * h

RMAGDF-ANGD

K®)

Lin, et. al. (1974a)^

Organic Halides

K 2 + CHjI, C2H^I, C^H^l,
C2H^Br

RMAGDF-ANGD

K®)

Foreman, et. al. (1973b)

K 2 + CH2Br2, CCl^

RMAGDF-ANGD

I(®)

Foreman, et. al. (1973a)

K 2 + CBr^, CH2l2,CHIj

RMAGDF-ANGD

I(®)

Lin, et. al. (1974a)

-Ill-

+ HgCl2, HgBr2, Hgl2

K 2 + BBr 3 , PCI 3 , PBr 3 , SiCl^,
SnCL,

K2 + SnCl^

Inorganic Halides

RMAGDF-ANGD I(®) Hardin, et. al. (1973a)

RMAGDF-ANGD I(@) Foreman, et. al. (1973a)

RMAGDF-ANGD I(®) Whithead, et. al. (1973)

All of these experiments employ a nozzle expansion to enhance dimer formation. This also
produces improved collision energy definition relative to two crossed thermal beams.

'^Chemiluminescence also studied.

'Approximate K product angular distribution reported.

- 112 -

L

Table IX. Non-alkali Metals plus various Oxides.

Reactants

Technique

Results

Reference

Sr + O 2

CEANGD

o-(E) Batalli-Cosmovici and

Michel (1972)

Ba + O 2

ANGD

I(®) Batalli-Cosmovici and

Michel (1971)

Ba + O 2

LIF

P(Ey', E^') Schultz, et. al. (1972)

Ba + O 2 , CO 2

LIF

P(Ey',E^') Dagdigian, et. al. (1974)

Ba + SO 2

LIF

P(Ey',E^') Smith and Zare (1975)

Ba + SO 2

CEANGD

I(®) Behrens, et. al. (1976a)

A1 + 02» 0 ^

LIF

P(E^',E^') Zare (1974)

A1 O 2

LIF

P(E^,'E^') Dagdigian, et. al. (1975)

Eu + O 2

CEANGD

o-(E) Dirscherl and Michel (1976)

Yb + O 2

CEANGD

irlE) Cosmovici, et. al. (1977)

- 113 -

Table X. Miscellaneous Alkali Dimer Reactions.

Reactants

Techniques

Results

Reference

Hydrogen Atom Reactant

K 2 , Rb2, CS 2 + H, D

ANGD

K®)

Lee, et. al. (1971)

Alkali Atom Reactant

K-, Rb-, Cs- + Na

RD 2 + N

ANGD

K®)

Whitehead and Grice (1973)

Rb 2 + Na

PRVS

I(®,v)

Mascord, et. al. (1976)

Fig. 1. Schematic diagram of a product magnetic deflection slotted disk velocity
analysis apparatus (viewed from above) used to study reactions of Li atoms with
halogen-containing compounds. Items not identified in text include: Li (U) and
halide (N) sources, collimating slits (T, M, L, and F), shields (W, P, K, D, and X),
and a light cell (G) and photodiode (I) to monitor the rotational frequency of the
SDVA (3). [Taken from Sholeen and Herm (1976a)] .

- 115 -

A+B — C + D

Fig. 2. LAB ■* — ► CM coordinate systems velocity vector transformation diagram for the
collision of A and B to give C and D. The in-plane scattering angles of particle C
are denoted ® and 6 in the LAB and CM coordinate systems, respectively; C
denotes the centroid vector; "v’q, "7“^, and denote the particle LAB
velocities; and'Wj^ denote the corresponding CM velocities.

- 116 -

I

Fig, 3. LAB angular distributions measured by surface ionization with a sensitized
filament (K + KBr) and desensitized filament (K) for the scattering of K from
HBr. The product KBr angular distribution shown was obtained as the difference
of these two curves. Note that the LAB scattering angle is denoted 0 in this
figure. [Taken from Taylor and Datz (1955)].

-117-

[

Froclion of ^xoorgicity, AOq
0.2 0.5 0.8

Fig. 4. The upper panel shows three sets (i.e., dash, solid, and dot-dash curves) of
collision-energy-independent product recoil angle and energy CM distributions
which fit (solid curve) the measured LAB Bal product angular distribution data
points from the Ba + CH^I reaction. Also shown in the lower panel are a
calculated centroid distribution (dash curve) and nominal velocity vector
transformation diagram which depicts circles of constant Bal recoil velocity for
some possible product recoil energies. [Taken from Lin, e^ al. (1973b)].

- 118 -

3 2

Fig. 5. CM polar contour map of 9 <r/a udw (assumed energy independent) for

scattering for KI from crossed beams of K and I-. Heavy lines show contours of
3 2 ^

constant 9 <r/d w9w arbitrarily normalized to a peak value of 10. CM
scattering angle, 0 , is measured from the original K direction. Symmetry about
6 = 0° is forced in the data analysis, i.e. the bottom half of the map is redundant.
A cut along any 0 = constant line gives the distribution in KI recoil speed
(denoted w' in this figure). The corresponding distribution in E' would require use
of the proper Oacobian. [taken from Gillen, et. al. (1971)] ,

- 119 -

Fig. 6. Contours show plots of constant LiO (X n) product flux in the LAB coordinate
system from the LI + NO 2 reaction (LAB scattering angle measured from the
original Li direction). The black triangle denotes on arbitrary intensity of 100,
and 90, 80, 70, 60, 50, 40, 30, 20, 10, and 5 contours are shown. Fifty percent of
the centroid vectors lie within the cross hatched area. This centroid distribution
was calculated from the broad "quasi-thermal" beam speed distributions for an
energy independent reaction cross section. [Taken from Sholeen and Herm

[

9

0 50 100 150 200

PRODUCT RECOIL ENERGY (liJ/mol»)

Fig. 7. Different curves show P(E') functions [from Eq. (9)] obtained by fitting different
3 2

3 <r/8 w3w expansion functions via Eq. (5) to LiX product LAB recoil velocity
spectra measurements for the Li + CHjN02, CCl^, and CH^l reactions. [Taken
from Sholeen and Herm (1976b)].

- 121 -

Fig. 8. LAB angular distributions (normalized to unit peak heights) of reactively

scattered K1 or KCl for reactions of K with orientated (a) CH^l, (b) t-Bul, (c)

CHClj, and (d) CF^I. Darkened and open data points refer to orientation wherein
the transferred halogen pointed toward or away from the incoming K,
respectively. In all cases, intermediate behavior was observed with unorientated
molecules. [Taken from Marcelin and Brooks (1973b)] .

- 122 -

eE = 1 48 kcal/mole

E = 2 45 kcal/mole

E = 3 20 kcal/mole

f \

Tm = 3.0
Tm =4,0

(t>) -- 4.0

I rm = 5.0

Tm = 3,0

— r^=4.o
• - = 5.0

* 40° 60° 80° 100° 0° 20° 40° 60° 80° 100° 0° 20° 40° 60° 80° 100“

C.M. SCATTERING ANGLE, 0

The open circles show measured non-reactive scattering of K for CClj^
transformed into the CM system. The curves in (a) show optical model fits for
p(b,E) = 0 (solid) and its optimal values (dashed). Optical model fits in (b) show
the insensitivity of the data to the potential range parameter, r^. [Taken from
Harris and Wilson (1971)].

Fig. 10. Alkali iodide CM product recoil momentum distributions normalized to the same
peak heights. Successive curves are displaced upward. [Taken from Herschbach
(1973)].

- 124 -

Fig. 11. Schematic depiction of a possible "double rebound" mechanism to account lor
for'vard K1 scattering in the K, - CH,1 reaction.

THE IVAN A. GETTING LABORATORIES

The Laboratory Operations of The At'rospace Corporation is conducting
experimental and theoretical investigations necessary for the evaluation and
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and radiation effects on materials, lubrication and surface phenomena, photo-
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Materials Sciences Laboratory ; Development of new materials; metal
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