Photoelectron spectroscopy of excited molecular states

597

Journal of Electron Spectroscopy and Related Phenomena, 52 (1990) 597-612 Elsevier Science PublishersB.V., Amsterdam- Printed in The Netherlands

PHOTOELECTRON

SPECTROSCOPY

OF

EXCITED

MOLECULAR

STATES

V. McKay, M. Braunstein, H. Rudolph, and J. A. Stephens: S. N. Dixitz and D. L. Lynch’ 1 Noyes Laboratory of Chemical Physics,

California Institute

of Technology, Pasadena,

CA

91125, USA ‘Lawrence a Department

Livermore National Laboratory, of Chemistry,

Livermore, CA 94550, USA

University of Nevada, Reno, NV 89557, USA

SUMMARY Resonance Enhanced Multiphoton Ionization (REMPI), coupled with high-resolution photoelectron spectroscopy, is becoming an important probe of the photoionization

dy-

namics of molecular excited states at a quantum-state specific level. In this paper we will discuss some results of our studies of ionic rotational and vibrational distributions for REMPI of several small molecules such as Hz, 02, NO, OH, and CH which illustrate some dynamically important features of these processes. 1.

INTRODUCTION Resonance enhanced multiphoton ionization (REMPI) utilizes the tunable radiation of

dye lasers to ionize a molecule by preparing an excited state via absorption of one or more photons and subsequently ionizing that state before it can decay. A remarkable feature of REMPI is that the very narrow bandwidth of laser radiation makes it possible (z) to select a specific rovibrational level in the ground electronic state of a molecule, (is) to resonantly pump this level up to a specific rovibrational level of an excited electronic state, and (iii) to subsequently ionize the prepared state via absorption of one or more photons which may be of a differnt color from that of the excitation laser. Coupled with high-resolution and angle-resolving photoelectron spectroscopy, REMPI is clearly an important probe of the photoionization

dynamics of excited molecular states at a highly quantum-state specific

level. This extreme state-selectivity gives rise to many basic and practical applications of REMPI. In this paper we will discuss some results of our studies of ionic rotational and vibrational distributions for REMPI of small molecules such as Hz, Oz, NO, OH, and CH which illustrate some dynamically important features of these processes. Some highlights of these results include (i) non-F’ranck-Condon ion vibrational distributions arising from

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0 1990 Eleevier Science PublishersB.V.

the presence of autoionizing and shape resonances in the electronic continuum and from the rapid evolution of the orbital angular momentum composition of the resonant state. Such non-Franck-Condon

ion distributions will be seen in the photoionization of molecu-

lar Rydberg states which is generally expected to occur with preservation of vibrational quantum numbers, i.e., Au = v+ - v’ = 0. This behavior can introduce serious complications both in the extraction

of state populations from REMPI

signals and in the use of

this technique for state-specific production of ions; (i:) rotational distribution of ions and their associated photoelectron

angular distributions.

These rotationally-resolved

studies

provide dynamical insight into the angular momentum composition of the photoelectron wave function which is often not evident in rotationally-unresolved 2.

FORMULATION

AND

In the (n + l)-type

spectra.

METHODOLOGY

resonance enhanced multiphoton

ionization process of interest

here a molecule in its initial state absorbs n photons of linearly polarized light of a given frequency to make a resonant transition to an intermediate state which is subsequently ionized by absorption of an additional photon of the same or different frequency. Such an intermediate

state

is

aligned, i.e., states of different MJ values have different populations

but those with the same 1 MJ

1 values have equal populations.

This is geometrically

equivalent to the molecules in state J having a preferred plane of rotation. of the dynamics of these processes, we view (n + 1) REMPI state -all MJ levels of a .7 state equally populatedaligned (intermediate) this aligned state.

state.

In our analysis

from an isotropic initial

as single-photon ionization from an

The ionization simply probes the anisotropic population of

Our studies of REMPI

of molecules are based on a theory of such

processes which we have developed recently (1). In this approach the calculation of cross sections for a REMPI process consists of determining the anisotropy created in the resonant state and then coupling this anistropic population to ionization out of it. The details of this theory are given in ref. 1. The determination sociated bound-bound

of REMPI

cross sections requires (;) excitation

energies and as-

dipole transition matrix elements arising in the perturbation

pansions which determine populations in the resonant state and (i:) bound-continuum

exor

photoelectron matrix elements which govern photoionization from the resonance state. The excitation

energies and dipole transition matrix elements between bound states required

in (I) can be obtained straightforwardly

using standard electronic structure methods. The

photoionization step, however, requires dipole matrix elements between the resonant state and a final state in which the photoelectron moves in a continuum orbital of the molecular ion potential.

The nonspherical character of molecular ion potentials leads to significant

599

coupling between the angular momentum components of the photoelectron wave function. The extent of this coupling varies with distance from the molecular ion and can be quite strong in the near-molecular

region.

This angular momentum coupling, along with the

nonlocality of the molecular ion potential (exchange), is important at the low photoelectron energies of interest in most REMPI

studies and introduces additional complexities

into the solution of the associated Schrijdinger equation beyond those arising in the related atomic problem.

The angular momentum composition of molecular photoelectron

wave functions exerts a strong influence on the dynamics of the photoionization

process.

For example, rotational distributions of molecular ions simply reflect the interplay between the angular momentum of the photoelectron and that of the molecular ion. In our studies we will take the photoelectron orbitals to be solutions of the one-electron Schrijdinger equation

(-fp

+V,_,(r,R)

-

5’> &(r,R)

= 0,

where VN _ 1 (r, R) is the potential produced by the Hartree-Fock

charge density of the

molecular ion, t” is the photoelectron kinetic energy, and dl. satisfies appropriate scattering boundary conditions. respectively.

In eq. (l), r and R designate electronic and nuclear coordinates

For these nonspherical potentials VN _ 1 (r, R), the Qlk of eq. (1) are not an-

gular momentum eigenfunctions, i.e., they are not s or p or d orbitals but some admixture of such angular momentum components.

This can be readily seen by expanding & (r, R)

in spherical harmonics about & and i

inserting this expansion in eq. (1) and noting that the resulting integrodifferential

equa-

tions for go,, ,c,,,, I are coupled. Our approach for solving eq. (1) for the molecular photoelectron

orbitals has been

discussed in detail in refs. 2 and 3. We work with the integral equation form of eq. (1)

h(r) = 4 + G(-)V&, E

where 4; (r) is a Coulomb function, G!-)

131

is the Coulomb Green’s function with incoming-

wave boundary conditions, and V is the short-range part of V, _ 1

v = v,_, + ;.

PI

To begin we expand & (r) in spherical harmonics about k

I51 substitute this expansion in eq. (3), and observe that each &,,,

satisfies the same integral

equation as &

km (r) = 4L, +

G(-)V4ktm.

I61

E

Eq. (6) is solved using an iterative procedure (2) based on Schwinger’s variational principle. The photoelectron orbitals used throughout these studies have been obtained with this procedure. Numerical details are given in ref. 2. 3.

APPLICATIONS

3.1

Ionic Vibrational

Distributions

in REMPI of Molecules and Fragments

Possible non-Franck-Condon behavior in the ionic vibrational distributions produced by REMPI is of considerable interest in any use of this technique for state-specific production of ions and for the extraction of state populations from ion signals. For example, the resonant level accessed in many REMPI schemes is often chosen to be a Rydberg state. For Rydberg levels which are well described by a single, highly-excited electron with a specific ion core, the potential energy surfaces of the ion and resonant state should be nearly identical. On the basis of the Fran&Condon

principle, photoionisation of such resonant

states can be expected to occur without any change in vibrational quantum number, i.e., Au = v+ - v’ = 0. We now look at some results of our studies of ion vibrational distributions arising from REMPI of such Rydberg states which display significant non-Franck-Condon

behavior.

The examples we have chosen along with the underlying origin of this behavior are: (i) electronic autoionization of repulsive doubly-excited states

I&(X

‘c:)

shvH,(C ‘l-II,) +

H,+(v+)+e

where we schematically indicate the presence of both direct and indirect (H;)

ionization

channels, (ii) shape (ont+electron) resonances e.g., O,(X’C;)

2

02(C ‘I&) -% O,'(aII,)

+e

(iii) rapid evolution of resonant Rydberg orbitals with internuclear distance, e.g.,

601

OH(X

“l-q ahu OH(D ‘c-

(50)) hY: OH+ (X “c-)

+ e.

In some early and very seminal studies, Pratt et al. (4) measured the vibrational branching ratios resulting from (3+1) REMPI of Ha via the C ‘II, (la, lz,,) state. Due to the Rydberg nature of the C ‘II, state, its potential energy curve is nearly identical to that of H,’ (X a C:)

and photoionization of this state can be expected to occur with preservation

of vibrational quantum numbers. This behavior clearly suggests schemes for state-specific production of vibrationally excited ions. However, their photoelectron spectra measured along the laser polarization axis (5,6) showed significant non-Franck-Condon behavior with Au # 0 peaks of increasing intensities for excitation through higher vibrational levels (vi > 2). These results are shown in fig. 1. Subsequent measurements of angle-integrated branching ratios (7~3) also displayed similar behavior. In an early attempt to understand the origin of this behavior we included the dependence of the photoionization

matrix

elements on kinetic energy and internuclear distance in calculations of these vibrational branching ratios (9). While these calculated (not shown in fig. 1) and measured branching ratios agreed well for ionization via the O-2 levels, significant differences remained for v, = 3-6. More recently, Chupka (10) and Hickman (11) have proposed that the anomalous distributions in these photoelectron spectra arise from electronic autoionization via the doubly excited dissociative lIJ(la,

lz,)

state: Autoionization of this doubly excited state

introduces an indirect contribution to the ionization process which interferes with the direct amplitude and leads to non-Fran&Condon

vibrational branching ratios. A quan-

titative treatment of this process must include contributions from both the direct and resonant channels and allow for interference between them.

The model calculations of

these vibrational state distributions by Hickman (11) only included a contribution from the resonant channel. It is certainly important and desirable to assess the adequacy of this approximation on the basis of first-principles calculations (12). We have completed calculations of the vibrational branching ratios in (3+1) REMPI of Ha via the Q(1) line of the C ‘II, state which include the effects of this ‘II, autoionizing state and properly account for interference between direct and resonant channels (12). In fig. 1 we compare our calculated branching ratios with the experimental values (5,6) for REMPI via the vi = 0 - 6 levels. These vibrational branching ratios are normalized such that their sum is unity. The overall agreement between the calculated and measured vibrational distributions is encouraging. The calculations also show that, while the autoionizing contribution is small for ionization via the vi 5 2 levels (9)) the direct and resonant contributions are comparable for vi = 3 - 6. Further details of these calculations and extensive

602

‘fJn-l--l-l0.0

1.,1 1 2 V,-2

0.6 0.7 0.6 0.6 0.4 0.2 0.2 0.1

6

1.0

‘(.4

4

2

2

1

0

7

0

7

Adi 6

6

6

6

4

6766

Od

0, 0.7 0.16 “F

% 10

4 v+

11

2

6

7

6

6 V.

a

2

1 4

3

2

0.9 0.6

Vi80

0.7 0.6 0.6 0.4 0.16 0.1 0.06 i 6

Figure

4

1. Vibrational

the C III, state.

branching ratios in (3+1) REMPI of H, via the Q(1) line of

Experimental and theoretical results are for detection along the laser

polarization axis (0 = 0”).

Central dark bars: Experimental data for u, = 0 - 4, from

Table I of ref. 5 and for u, = 5 and 6 from Fig. 4 of ref. 6; Bars to the right of central ones: Calculations with direct channel only; Bars to the left of central ones: Calculations with direct and indirect channels. All branching ratios are normalized such that the sum total equals unity.

discussion of the results can be found in ref. (12). These results (12) represent the first ab initio studies of the role of autoionizing states on ion vibrational distributions in REMPI of molecules.

Such dissociative autoionizing states can generally be expected to perturb

the ion vibrational

spectra produced in REMPI

spectral perturbations determination

of molecules e.g., 0,

and Cl,.

These

introduce serious complications in the use of this technique for the

of state populations and for the production of state-specific

ions. On the

other hand REMPI via high vibrational levels can become a major probe of doubly-excited states at large internuclear distances, where very little is known experimentally about their potential energy curves. Recent measurements of the vibrationally-resolved

(2+1) REMPI

the C ‘II,, (1~~33~0,) Rydberg state showed non-Franck-Condon

spectra of Oz via

ion distributions

These distributions were in strong contrast to the “clean” production of 0: levels expected on the basis of the Fran&Condon cause of this behavior and to quantitatively

(13,14).

in specific u+

principle. To understand the underlying

account for the observed ion distributions,

we have carried out calculations of these REMPI

spectra of Oz (13,14).

These studies

(15) establish that in photoionization of this resonantly prepared Rydberg state, a shape resonance near threshold significantly alters vibrational distributions from those based on Fran&Condon

arguments.

This shape resonance of a, symmetry

is well known from

single-photon studies of first-row diatomic molecules (16).Shape resonances are simply quasibound one-electron states formed by trapping of the photoelectron arising from centrifugal and electrostatic

forces.

behind barriers

They make the photoionization

matrix

element strongly dependent on internuclear geometry leading to a breakdown of the FranckCondon principle (16). In fig. 2 we compare our calculated ionic branching ratios (15)for REMPI C ‘II,

state of Oz via the u’ = 1 - 3 levels with the measurements of Miller

The calculations

predict pronounced non-Franck-Condon

distributions

et

of the al.

(14).

for all u’ levels.

Note that the corresponding Au#O Franck-Condon factors are negligible when plotted on the scale of this figure. For the u’ = 2 and 3 levels, the Au < 0 ratios are in satisfactory agreement with experiment, while those for Au > 0 appear to show systematic deviation. The calculated and measured spectra for u’ = 1 show substantial

disagreement.

These

discrepancies could be due to the presence of autoionizing states such as the C ‘A-, A “Cz , and B ‘C;

states arising from a lx:l~$ + lrzl$ excitation.

valence states are not dipole accessible from the C ‘IIr

Although these

state, they can couple to the

direct ionization continuum via electron correlation and hence influence the photoionization step. We have also determined the photoelectron

angular distributions for these REMPI

spectra (17). These photoelectron angular distributions show a substantial dependence on

604

0 Experiment

10

H Theory -

length

q Theory -

velocity

1

0 .+ c,

hv =

a 0.4 &

43oacV

MO3 c ii 0

0.2

ii L al

0.1

0.0

Figure

2. Calculated

tion, compared were normalized both the length

vibrational

to experiment and velocity

branching

ratios for 0,

by dividing

of dissociative

distributions states

rive from considerations

of final-state

matrix

another

mechanism

that

leads to significant

butions

but which

derives

This requirement

is that the Rydberg

orbital

results

obtained

using

are shown.

of Miller et al. (18). resonances.

dynamics.

non-FYanck-Condon

solely from a property

Results elements

in the above examples

and shape

photoionization

= 1 - 3) photoioniza-

14). The theoretical

by the Au = 0 peak.

forms of the photoionization

of the ion vibrational

autoionization

CslT,(u’

of Miller et al. (Ref.

level and agree quite well with the measurements

The behavior electronic

vibrational

with the measurements

of the resonant

should evolve rapidly

arose from

These features

de-

We have also identified ionic vibrational Rydberg

orbital

into its united

distri(19). or sep-

605 arated atom limits over a range of internuclear distance associated with low vibrational levels. Molecular Rydberg orbital6 with these characteristics typically occur in diatomic hydrides e.g., OH, CH, NH, photodissociation,

24.0

an important class of molecules in multiphoton ionization,

and photofragmentation problems.

-l

20.0

516.0 w $2.0 k z w

6.0

%22ps2P

,k O(2p’ 3P) + H(ls)

4.0

u/

0.0 1.0

i0 Figure

I

I

I

(DAI

x2n(1n3) (B&

I

4.0

I

5.0

3. Potential energy curves for the ground and first ionic state of OH, and the

excited states of the electronic configuration ‘D- (1s’~).

See, for example, E. F. van

Dishoeck and A. Dalgarno, J. Chem. Phvs., 79, (1983) 873.

We now discuss these ideas specifically in terms of electronic structure and with predictions of ion vibrational distributions for a proposed (3+1) REMPI measurement of OH via the D 2C- state. In fig. 3 we show potential energy energy curves for the X ‘II(llr’)

ground state of OH, the X 3C- (1~‘) state of OH+, and several excited states with electronic configurations a C- (l?r’n a).

The repulsive nature of the “C- (lnz4o)

known and arises from “Rydbergization”

of an antibonding 2p,, - lsu

state is well

molecular orbital

into the fluorine 3s orbital at small R (20). The 50 orbital of the aC- (1~~50) state correlates with a 3p atomic orbital at small R and a 3s at large R. The angular momentum composition of this orbital varies rapidly as the internuclear distance changes (19). Accompanying this rapid variation in angular momentum composition are changes in the nodal structure of the excited state wave function. The principal result of this behavior is that the dipole transition moment is a strong function of internuclear distance and the usual Franck-Condon

factorization becomes invalid. We can hence expect significant departures

from the Av = 0 propensity rule for producing ions in different vibrational states.

Our

calculated branching ratios for photoionization for the v’ = 0 - 3 levels of the a C- (1~~50) Rydberg state of OH, shown in fig. 4, substantiate branching ratios are at most 0.2. over the Franck-Condon enhancements 3.2

this prediction.

The Franck-Condon

For the Av = 1 branching ratios the enhancement

results are typically about 3. For the Av = 2 transitions,

the

are much larger.

Ionic Rotational Distributions While much interest has been focussed on vibrationally resolved REMPI

spectra and

the insight such spectra provide on the excited and ionized state dynamics, rotationally resolved spectra not only extend our understanding

of the underlying photoionization

dynamics but are also important for use of the technique in highly state-specific production of ions. We now discuss two examples from our studies of rotationally resolved REMPI spectra. The first example illustrates the striking and significant influence that rapid orbital evolution, shown above to lead to non-Franck-Condon

ion vibrational

distributions,

has

on the ionic rotational distributions as the level of vibrational excitation in the resonant Rydberg state increases (21). To illustrate this effect we present results for (2+ 1’) REMPI of CH via the E’ ‘C+ (3~0) state. lu22a23025a. distance.

The dominant electron configuration of this state is

The evolution of the 50 orbital is very rapid as a function of internuclear

As in the case of OH it changes from predominantly 3p character at small in-

ternuclear distances to predominantly 3s character at larger internuclear distances.

This

orbital evolution also results in a dramatic dependence of the partial wave composition of the photoelectron

transition moment on internuclear distance. An atomic photoioniza-

tion picture would predict, as a function of internuclear distance, the even partial waves (3p -+ ks,kd)

to be dominant at small R and the odd partial waves (3s --+ &pep) at larger

internuclear distances. For the C + C transition in the photoionization step of the (2 + 1’)

607

1.0 0 .r(

4

2 0.4 pj 0.3 .H c 0 0.2 E= 2 0.1 a 0.0

V+

1.0 1 0.6

t

i

mi v’=

3

0.4 0.2 0

1

2

3

4

Vi

0.0

n v

1a

3_

Figure 4. Calculated vibrational branching ratios for OH D "C- (v'= 0 - 3) photoionization. The one-photon energies for the u’ = 0 - 3 frames respectively are 3.42,3.52,3.62, and 3.73 eV. In each frame the ratios were obtained by dividing by the Av = 0 absolute intensity.

Franck-Condon

ratio (solid bar); full, length form (crossed bar); full, velocity

form (cross-hatched bar).

REMPI

process considered here

CH’II(u,,Jo)%CH

E’“C+(vi,Ji,Ni)~CH+X’C+(v+,J+

=N+)+C,

a AN + e =odd selection rule applies (22), where AN is the change in the rotational quantum number (exclusive of spin) between the intermediate and final state, and L denotes

608 an angular that

momentum

at smaller

transitions

component

internuclear

should

of the photoelectron

distances

be favored

odd AN

at larger internuclear

orbital.

transitions

This selection are favored

rule suggests

while even AN

distances.

l-l

15

16

21

21 16

3-3

17 20

?6

I

15

ti

20

0.s

21

hi_

550 Rotational Figure

5. Ionic rotational

branching

ratios for (2 + 1')REMPI

of the E’ ‘C+ (3~x7) state of CH for various vibrational vi and II+ is indicated is indicated

LIL 21

=IW’;

peak.

The photoelectron

950

via the Or1 (20.5) branch

levels of the E’ state.

(Au = 0) in the upper right corner of each frame.

over each photoelectron

(meV)

The value of

The value of N+

kinetic energy is 100 meV.

609

In fig. 5 we show calculated ionic rotational branching ratios for the 011 (20.5) branch

via the E’ 2 C+ state of CH for the vi = 0 - 3 vibrational levels of the resonant state. The branching ratios have been convoluted with a Gaussian detector function with a FWHM of 6 meV. Only the Au = 0 branches are shown. For this 011 (20.5) branch, N, = 18 and hence the AN = 0 peak corresponds to N+ = 18. The rotational branching ratios are seen to be very dependent on the vibrational level accessed in the intermediate state with a strong AN =odd (e =even) propensity rule evident in lower vibrational levels and a AN =even (! =odd) propensity rule for higher vibrational excitation.

This vibrational

dependence of the propensity rule is caused by the extended portion of the potential well sampled by the higher vibrational levels, i.e., the region where the Rydberg orbital itself has evolved from 3pu to mainly 350 type. The photoelectron kinetic energy is kept constant at 100 meV in these calculations.

This vibrational dependence of ionic rotational distributions

is expected to occur in the other diatomic hydrides in which the Rydberg orbital of the resonant intermediate state should also exhibit rapid evolution with internuclear distance. These hydrides are particularly suitable for ionic rotationally resolved experiments due to their large rotational constants. Combined with photoelectron

angular detection, rotationally resolved spectra can be

expected to provide a highly detailed dynamical picture of the photoionization For example, photoelectron

larization vector of the light by Reilly et al. (23) in rotationally resolved REMPI D2C+ (3~)

process.

angular measurements parallel and perpendicular to the povia the

state of NO made it possible to explicitly identify the surprisingly large p

wave character

of the photoelectron

wave function.

Two very significant features of such

spectra are obviously the dependence of these angular distributions on the rotational state of the ion and on the alignment of the resonant state (24). These angular distributions are a highly specific probe of the angular momentum composition of the photoelectron

wave

function by virtue of propensity rules such as AN + L =odd discussed above for a C -+ C ionizing transition. We have recently studied ionic rotational branching ratios and the associated photoelectron

angular distributions

for (1 + 1’) REMPI

via the &I (20.5), s1

+ Qll (25.5)

and PII (22.5) branches of the AaC+ (380) state of NO (24). The details of these studies are given in ref._ 24. Fig. 6 compares our calculated photoelectron

angular distributions

for the mixed PaI + Qll (25.5) branch with the very recent measurements et al.

(25).

of Allendorf

Also shown are the calculated distributions for the pure Pll(22.5)

branch.

The agreement between these calculated and measured angular distributions is very good for the mixed s1 rotationally

+ Qll (25.5) branch.

resolved photoelectron

These results illustrate the dynamical richness of

angular distributions.

On the basis of the propensity

610

AN -1

0

rnres.

~,+Q,(25.5) experimental

P,,+Q,(25.5) calculated

c3

8

8

13 8

8

P,

(22.5)

calculated

Figure

0.

0

8

Rotationally resolved (AN)

8

8

and unresolved (from ref.

0

8

25) and calculated

photoelectron angular distributions for the mixed PaI + Qrr (25.5) branch. Also shown are the calculated distributions for the pure PII (22.5) branch.

rule AN + .C=odd which holds here, the AN = ~1 spectra reflect the presence of even angular momentum components in the photoelectron orbital while the AN = ~2 spectra are associated with its odd components (L = 1,3,. . .). In contrast to the strong 4 = 1 character of the angular distributions of AN = 0 peaks, the AN = ~2 clearly show a sig-

611 nificant f-wave contribution.

Finally, differences in the calculated photoelectron angular

distributions for ionization via the P,, + Qil (25.5) and the Sa(22.5)

branches primarily

reflect changes in the alignments of the resonant states accessed in these branches.

4.

ACKNOWLEDGMENTS Work at the California Institute of Technology was supported by grants from the

National Science Foundation (CHE-8521391), Air Force Office of Scientific Research (Contract No. 87-0039), and the Office of Health and Environmental Research of the U. S. Department of Energy (DE-FG03-87ER60513)

and made use of resources of the San Diego

SuperComputer Center. Work at the Lawrence Livermore National Laboratory by SND was performed under the auspices of the U. S. Department of Energy Contract No. W7405-ENG-48. REFERENCES S. N. Dixit and V. McKay, J. Chem. Phys., 82 (1985) 3546. R. R. Lucchese, G. Raseev, and V. McKay, Phys. Rev. A, 25 (1982) 2572. R. R. Lucchese, K. Takatsuka, and V. McKay, Phys. Rept., 131 (1986) 147. S. T. Pratt, P. M. Dehmer, and J. L. Dehmer, Chem. Phys. Lett., 28 (1984) 28. S. T. Pratt, P. M. Dehmer, and J. L. Dehmer, J. Chem. Phys., 85 (1986) 3379. S. T. Pratt, M. A. O’HaIloran, P. M. Dehmer, and J. L. Dehmer, in: S. J. Smith and P. L. Knight (Eds), Multiphoton Processes, University Press, Cambridge, 1988. 7 M. A. O’Halloran, S. T. Pratt, P. M. Dehmer, and J. L. Dehmer, J. Chem. Phys., 87 (1987) 3288. 8 E. Y. Xu, T. Tsuboi, R. Kachru, and H. Helm, Phys. Rev. A, 36 (1987) 5645. 9 S. N. Dixit, D. L. Lynch, and V. McKay, Phys. Rev. A, 30 (1984) 3332. 10 W. A. Chupka, J. Chem. Phys., 87 (1987) 1488. 11 A. P. Hickman, Phys. Rev. Lett., 59 (1987) 1553. 12 S. N. Dixit, D. L. Lynch, B. V. McKay, and A. U. Hazi, Phys. Rev. A, accepted for publication (1989). 13 S. Katsumata, K. Sato, Y. Achiba, and K. Kimura, J. Electron Spectrosc. Relat. Phenom., 41 (1986) 325. 14 P. J. Miller, L. Li, W. A. Chupka, and S. D. Coison, J. Chem. Phys., 89 (1988) 3921. 15 J. A. Stephens, M. Braunstein, and V. McKay, J. Chem. Phys., 89 (1988) 3923. 16 See, for example, J. L. Dehmer, A. C. Parr, and S. H. Southworth, in: G. V. Marr (Ed), Handbook on Synchrotron Radiation, North-Holland, Amsterdam, 1986., Vol. II. 17 M. Braunstein, J. A. Stephens, and V. McKay, J. Chem. Phys., 90 (1989) 633. 18 P. J. Miller, W. A. Chupka, J. Winniczek, and M. G. White, J. Chem. Phys., 89 (1988) 4058. 19 J. A. Stephens and V. McKay, Phys. Rev. Lett., 62 (1989) 889. 1 2 3 4 5 6

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