We report multiplet‐specific vibrationally resolved photoionization cross sections and photoelectron angular distributions for the 3σ_g orbital of O_2 leading to the v^+=0–3 levels of the b^4Σ^−_g and B^2Σ^−_g states of O^+_2. These studies were motivated by recent work which shows significant nonstatistical behavior in the vibrationally unresolved spectrum at low photoelectron energies arising from the sensitivity of the kσ_u shape resonance to the multiplet‐specific exchange potentials. In addition to the anticipated non‐Franck–Condon vibrational distributions arising from the kσ_u shape resonance, we also find substantial nonstatistical effects in our vibrationally resolved cross sections and particularly in our photoelectron angular distributions over a broad energy range. Extensive electronic autoionization due to Rydberg levels leading to the c^ 4Σ^−_u (2σ^(−1)_u) ion makes it difficult to assess these effects in the available experimental data

Braunstein, M.

McKoy, V.

English

Caltech Authors - Main

Downloaded 11 Dec 2006 to 131.215.225.181. Redistribution subject to AIP license or copyright, see http://jcp.aip.org/jcp/copyright.jsp
Multiplet-specific shape resonant features in vibrationally resolved 3a 9 
photoionization of 02 
M. Braunstein and V. McKoy 
A. A. Noyes Laboratory of Chemical Physics, California Institute of Technology, Pasadena, 
California 91125 
(Received 7 February 1989; accepted 21 March 1989) 
We report multiplet-specific vibrationally resolved photoionization cross sections and 
photoelectron angular distributions for the 3u8 orbital of 0 2 leading to the v+ = 0-3 levels of 
the b 4.1:8- and B 2 .1:8- states ofOt. These studies were motivated by recent work which shows 
significant nonstatistical behavior in the vibrationally unresolved spectrum at low 
photoelectron energies arising from the sensitivity of the ku u shape resonance to the multiplet-
specific exchange potentials. In addition to the anticipated non-Franck -Condon vibrational 
distributions arising from the kuu shape resonance, we also find substantial nonstatistical 
effects in our vibrationally resolved cross sections and particularly in our photoelectron 
angular distributions over a broad energy range. Extensive electronic autoionization due to 
Rydberg levels leading to the c 4.l:u- (2u; 1) ion makes it difficult to assess these effects in the 
available experimental data. 
INTRODUCTION 
Previous theoretical studies of vibrationally unresolved 
3u8 photoionization of 0 2 leading to the B 
2
.1:8- and b 
4
.1:8-
ions have shown significant nonstatistical behavior in the 
spectral region of the well known u u shape resonance. 1'2 The 
sensitivity of this shape resonance to the multiplet-specific 
exchange potentials of these molecular ions gives rise to 
shifts in the oscillator strength distributions near threshold. 
In fact, the b 4 .1:8- cross section peaks around 4 eV above 
threshold, while the oscillator strength associated with the 
uu shape resonance in the B 2 .1:8- cross section shifts closer 
to threshold, perturbing the spectral distribution of the nuu 
Rydberg states leading to the B 2.1:8- ion.
2 This shift in oscil-
lator strength associated with the uu shape resonance is also 
reflected in large differences in the multiplet-specific photo-
electron angular distributions. 2 These differences are diffi-
cult to assess in the experimental spectra due to extensive 
electronic autoionization of Rydberg states leading to the 
c 4 .l:
8
- (2uu- 1) ion.3-6 However, recent high-resolution 
measurements do show a relatively broad maximum in the 
B 2.1:8- cross section at considerably lower photoelectron en-
ergies than the shape-resonant maximum seen in the b 4l:8-
cross section. 7•8 Similar multiplet-specific behavior has also 
been observed in the Suphotoionization of NO leading to the 
A 1 n and b 3ll ions, where a difference of as much as 3 e V is 
seen in the positions of the shape resonance. 9- 11 In ( 2 + 1) 
resonance-enhanced multi photon ionization ( REMPI) of 
0 2 via the C 3ll8 ( 1T8 3su8 ) and d 
1ll( 1T8 3su8 ) states, signifi-
cant multiplet-specific effects were also seen in the vibration-
ally resolved ion cross sections and photoelectron angular 
distributions. 12•13 
In the present work we extend our previous vibrational-
ly unresolved studies of multiplet-specific 3u 8 photoioniza-
tion in 0 2 (Ref. 2) by obtaining vibrationally resolved cross 
sections and photoelectron angular distributions for 
v+ = 0-3 to further assess multiplet-specific effects. Our vi-
brationally resolved cross sections show the expected large 
non-Franck-Condon effects in the region of the uu shape 
resonance as well as significant multiplet-specific behavior 
in the cross sections. Comparison with experimental mea-
surements 7 is again made difficult by the role of electronic 
autoionization in the region of these shape resonances. The 
photoelectron angular distributions also show both non-
Franck-Condon behavior and multiplet-specific differences 
well beyond the energy range of autoionizing features in the 
measured cross sections. Measurements of these photoelec-
tron angular distributions using tunable radiation would be 
of considerable importance in understanding these multi-
plet-specific effects. 
THEORY 
Our procedure for obtaining vibrationally resolved pho-
toionization cross sections and photoelectron angular distri-
butions has been described extensively elsewhere. 2•14-17 
Briefly, we include full kinetic energy and internuclear de-
pendence in the bound-free transition moment, 
Mo-v+ = J dRXof..tif(k,R)Xv+· (1) 
Here f..tif(k,R) is the transition moment between the initial 
bound state of02 (X 3l:8- ) and final continuum state (ionic 
core+ photoelectron). In Table I we give the internuclear 
distances at which the transition moments are determined. 
For the ground state of 0 2 we used a Hartree-Fock SCF 
wave function obtained with a [ 4s3p2d] Cartesian Gaussian 
basis set. 14 For the final state we used the frozen-core ap-
proximation with Hartree-Fock photoelectron orbitals for 
the dipole-allowed 3l:; (kuu) and 3 llu (k1Tu) channels ob-
tained with the interative Schwinger variational technique 
and multiplet-specific static-exchange potentials.2 All inte-
grations associated with obtaining the transition moments 
were carried out via partial-wave expansions with the result-
ing radial integrals evaluated by Simpson's rule. The partial-
wave expansion parameters and radial grid are the same as 
those of Ref. 14. 
The vibrational wave functions X of Eq. ( 1) were ob-
150 J. Chern. Phys. 91 (1 ), 1 July 1989 0021-9606/89/130150-05$02.10 © 1989 American Institute of Physics 
Downloaded 11 Dec 2006 to 131.215.225.181. Redistribution subject to AIP license or copyright, see http://jcp.aip.org/jcp/copyright.jsp
M. Braunstein and V. McKoy: 3cr9 photoionization of 0 2 151 
TABLE I. Internuclear distances of02 at which photoionization transition 
moments were evaluated. 
Continuum symmetry 
ku. b 
• In atomic units. 
b Resonant channel. 
Internuclear distance• 
2.0,2.1,2.182,2.232,2.282 
2.332,2.382,2.482,2.6,2.8,3.0 
2.0,2.182,2.282,2.382,3.0 
tained by numerical integration. For the ground and b 4 l:g-
ion states, we used the Rydberg-Klein-Rees (RKR) poten-
tials of Krupenie. 18 A Morse potential was used for the 
B 2l:.g- ion potential with spectroscopic constants given by 
Huber and Herzberg. 19 Franck-Condon factors obtained 
with these potentials are given in Table II along with other 
calculated values20 and measured vibrational intensities at 
high energy,21•22 well away from the influence of the kuu 
shape resonance. 
RESULTS AND DISCUSSION 
In Figs. l(a) and l(b) we show our calculated multi-
plet-specific photoionization cross sections for the 
3ug -.kuu transition in 0 2 at various internuclear distances 
for the b 4 l:.g- and B 2 l:.g- ions, respectively. The most 
prominent feature here is the large maximum in the cross 
section caused by the well known kuu shape reso-
nance. 1- 8•23- 26 These resonant cross sections show the ex-
pected dependence on internuclear distance, becoming 
broader and peaking at higher energy with decreasing inter-
nuclear distance (R). This dependence leads to deviations 
from Franck-Condon behaviorY-29 For a particular R, the 
TABLE II. Franck -Condon factors for transitions from the ground state of 
0 2 (Re =2.282 a.u.) to vibrational levels of the b 4~8-(3u;'> and 
B 2~.- (3u8- 1 ) states ofOt. 
b ·~.- (Re = 2.418 a.u.) 
Ref. 20 Ref. 21 
v+ Present work (theory) (experiment)" 
0 0.408 0.411 0.452 
1 0.336 0.337 0.319 
2 0.164 0.163 0.154 
3 0.062 0.062 0.057 
B 2~8- (Re = 2.453 a.u.) 
Ref. 22 Ref. 21 
v+ Present work (experiment) (experiment) 
0 0.245 0.247 0.265 
1 0.293 0.316 0.307 
2 0.213 0.211 0.220 
3 0.125 0.130 0.135 
• Experimental quantities are obtained at the He 11 resonance line ( 40.8 eV) 
and have been normalized by taking the total relative intensitites to be 
unity. This energy is far enough away from any shape and/or autoionizing 
resonances so that Franck-Condon behavior is expected. 
25 
,------. 20 
.D 
2 
c 15 
0 
-+-' 
u 
Q) 
(f) 10 
(f) 
(f) 
0 u 5 
,------. 
.D 
15 
~ 10 
c 
0 
-+-' 
U· 
Q) 
(f) 
(f) 5 
(f) 
0 R = 2.282 
L 
u 
(a) 
a.u. 
2.000 a.u. 
25 35 45 
Photon Energy ( eV) 
(b) 
R = 2.232 
25 35 45 
Photon Energy ( eV) 
FIG. 1. (a) and (b) Photoionization cross sections (dipole length) for the 
shape resonant 3u8 - ku" channel in 0 2 at several internuclear distances for 
the b ·~.- and B 2~.- ions, respectively. 
peak of the shape resonance for each multiplet is at consider-
ably different photoelectron energies. At R. of the ground 
state (2.282 a.u.) the shape resonance is seen -4 eV above 
threshold for the b 4 l:.g- ion, while the oscillator strength 
associated with the B 2l:g- cross section is shifted toward 
threshold, 1•2 and, in fact, significantly perturbs the discrete 
spectral distribution. 2 This shift arises from the sensitivity of 
the uu shape resonance to differences in the exchange com-
ponent of the multiplet potentials and is not seen in studies 
using multiplet-averaged potentials. 23- 26 This behavior leads 
to large differences in the cross sections and photoelectron 
angular distributions for these multiplets. 
Figures 2(a) and 2(b) show our vibrationally resolved 
photoionization cross sections for the b 4 l:.; and B 2 l:.g- ion 
states, respectively. These multiplet-specific cross sections 
for the b 4 l:.g- ion agree with the static-exchange multiplet-
averaged calculations ofRaseev et a/.,26 but are consistently 
J. Chern. Phys., Vol. 91, No. 1, 1 July 1989 
Downloaded 11 Dec 2006 to 131.215.225.181. Redistribution subject to AIP license or copyright, see http://jcp.aip.org/jcp/copyright.jsp
152 M. Braunstein and V. McKoy: 3u9 photoionization of 0 2 
5 
,...--.., 
4 
...0 + 0 v 
L 
'-./ 
c 3 
0 
-+-' v + u 
Q) 
(/) 2 
Cll 
Cll 
0 
L + u v 2 
FIG. 2. (a) and (b) Vibrationally resolved photoionization cross sections 
(dipole length) for the b 41:8- and B 21:8- ions, respectively. Dipole-veloc-
ity results are nearly the same but are sometimes slightly Jess in magnitude. 
See Ref. 2 for more details. 
slightly larger. The vibrationally resolved cross sections of 
both studies peak at successively higher photon energies 
with increasing vibrational excitation. For the vibrationally 
resolved B 2I.8- cross sections, however, there are significant 
differences between the multiplet-averaged calculations of 
Raseev et a/., 26 which are expectedly similar to the b 4 l:,8-
cross sections, and the present multiplet-specific results. 
These differences reflect the strong multiplet-specific behav-
ior seen in the fixed-nuclei cross sections. Shape-resonant 
behavior appears closer to threshold in the vibrationally re-
solved B 2l:-8- cross sections than in the b 4l:.; cross sec-
tions. The B 2I.8- cross sections also show a strong minimum 
around a photoelectron energy of 5 e V. This is due to cancel-
lation between partial-wave contributions to the transition 
moment in the kuu channel and can be understood by exam-
ining the partial-wave composition of the initial bound 3u8 
and final continuum ku u orbitals. The 3u 8 orbital is -50% s 
wave and -50% d wave for the internuclear distances of 
interest here. Theses and d waves both show a radial node at 
-1.2 a.u. from the molecular center. The principle-value 
transition moments for the t'k = 1 and 4 = 3 continuum 
partial waves-made up of mostly p and f waves-go 
through zero at this energy producing a minimum in the ku u 
cross section. This is akin to the so-called Cooper mini-
mum30·31 seen in atoms, except that the anisotropic molecu-
lar potential induces partial-wave mixing. The dominant 
contribution to the total cross sections arises from the ktr u 
partial channel in this region. This cancellation also occurs 
in the b 4 l:,8- channel at a higher energy ( 15 eV photoelec-
tron kinetic energy) where the krr u cross section is larger 
thus obscuring the effect in the total cross section. Studies of 
fluorescence polarization for the b 4 I.8- ion do show the 
1r u :u u cross section ratio growing rapidly from threshold to 
-30 eV photon energy.32•33 Measurements of the fluores-
J. Chern. Phys., Vol. 91, No. 1, 1 July 1969 
Downloaded 11 Dec 2006 to 131.215.225.181. Redistribution subject to AIP license or copyright, see http://jcp.aip.org/jcp/copyright.jsp
M. Braunstein and V. McKoy: 3o-9 photoionization of 0 2 153 
cence polarization at slightly higher energy should show this 
behavior clearly as the ku u cross section goes through a min-
imum there. 
High resolution vibrationally resolved photoionization 
measurements from threshold up to -24 e V photon energy 
show differences between the vibrationally resolved multi-
plet cross sections.7 However, electronic autoionization 
from Rydberg levels leading to the c 4:Iu- ion (IP = 24.5 
eV) in the energy region of the shape resonance makes com-
parisons difficult. Experiments over a broader energy range 
and theoretical studies which include these autoionizing 
states are needed to better understand these multiplet-specif-
ic effects. 
Ion vibrational branching ratios for the b 4:Ig- and 
B 2:Ig- ions are shown in Figs. 3(a) and 3(b), respectively, 
where we use the notation n:O to denote the branching ratio, 
CT(V = o ..... v+ = n)/u(v = o ..... v+ = 0). Dramatic devia-
2.0 (a) 
1.5 
1.0 
<:t:l. 0. 5 
0.0 
-0.5 
-1.0+----.----,---~----,---~---, 
15 25 35 45 
Photon Energy ( eV) 
2.0 
(b) 
1 .5 
1.0 3 
<:t:l. 0. 5 I 
0.0 
-0.5 
-1 . 0 +------r-----r---~----,---~---, 
15 25 35 45 
Photon Energy ( eV) 
FIG. 4. (a) and (b) Vibrationally resolved photoelectron asymmetry pa-
rameters (dipole length) for the b 4 l:g- and B 2l:g- ions, respectively. The 
open circles are experimental data from Ref. 34 for the v+ = 0 level (b •:t; 
ion) and v+ = I level (B 2 l:g- ion). 
tions from Franck-Condon behavior are seen in these 
branching ratios. For the b 4:Ig- ion this behavior extends 
over a large energy range similar to that seen in 3ug pho-
toionization of N2, 17•27- 29 while the B 2:Ig- branching ratios 
show non-Franck-Condon behavior only in a limited energy 
range near threshold. These features reflect differences seen 
in the vibrationally resolved multiplet-specific cross sections 
of Figs. 2(a) and 2(b). 
Vibrationally resolved photoelectron angular distribu-
tions for these two multiplets of Ot ( 3ug- 1 ) are shown in 
Figs. 4(a) and 4(b). These photoelectron asymmetry pa-
rameters are vibrational-state dependent. This non-Franck-
Condon behavior extends over a broader energy range than 
in the vibrational branching ratios. The vibrationally re-
solved {3 's also show strong multiplet-specific effects. In par-
ticular, there is a shoulder in theB 2:Ig- {J's at around 25 eV 
photon energy, the same energy where the CTu cross section 
goes through a minimum, which is not seen in the {3 's for the 
b 4:Ig- ion. These multiplet-specific differences extend over a 
broad range, well beyond the complicating effects of auto-
ionization due to states leading to the c 4:Iu- ion. Measured 
photoelectron asymmetry parameters of Katsumata et a/. 34 
at 21.2 and40.8 eV are also shown in Figs. 4(a) and4(b). At 
low energy there is a significant difference between the mea-
sured multiplet {3 's, while at higher energy, away from the 
shape resonance, this difference is considerably less. Contin-
uum source measurements are needed to fully assess the ac-
curacy of these calculations. 
ACKNOWLEDGMENTS 
This material is based upon research supported by the 
National Science Foundation under Grant No. CHE85-
21391. The authors also acknowledge use of the resources of 
the San Diego SuperComputer Center which is supported by 
the National Science Foundation. 
1C. L. Winstead and P.W. Langhoff (to be published); see also C. L. Win-
stead, Ph.D. thesis, Indiana University, 1987. 
2M. Braunstein, V. McKoy, and M. E. Smith, J. Chern. Phys. 90, 3931 
(1989). 
3J. A. R. Samson,J. L. Gardner, and G. N. Haddad,J. Electron. Spectrosc. 
Relat. Phenom.12, 281 (1977). 
4C. E. Brion, K. H. Tan, M. J. Vander Wiel, and Ph. E. Vander Leeuw, J. 
Electron. Spectrosc. Relat. Phenom. 17, 101 (1979). 
5T. Gustafsson, Chern. Phys. Lett. 75, 505 ( 1980). 
6A. Tabche-Fouhaile, I. Nenner, P.-M. Guyon, and J. Delwiche, J. Chern. 
Phys. 75, 1129 ( 1981 ). 
7P. Morin, I. Nenner, M. Y. Adam, M. J. Hubin-Fransk.in, J. Delwiche, J. 
Lefebvre-Brion, and A. Giusti-Suzor, Chern. Phys. Lett. 92, 609 ( 1982). 
8M. Ukai, A. Kimura, S. Arai, P. Lablanquie, K. Ito, and A. Yagashita, 
Chern. Phys. Lett. 135, 51 (1987). 
9M. E. Smith, V. McKoy, and R. R. Lucchese, J. Chern. Phys. 82, 4147 
(1985). 
10M. R. Hermann, C. W. Bauschlicher Jr., W. M. Huo, S. R. Langhoff, and 
P. W. Langhoff, Chern. Phys. 109, I (1986). 
11M. R. Hermann, S. R. Langhoff, T. J. Gill, and P. W. Langhoff, Chern. 
Phys. Lett. 125, 336 ( 1986). 
12P. J. Miller and W. A. Chupka (private communication). 
13J. A. Stephens, M. Braunstein, and V. McKoy (to be published). 
14M. Braunstein and V. McKoy, J. Chern. Phys. 90, 2575 ( 1989). 
15R. R. Lucchese, K. Takatsuka, and V. McKoy, Phys. Rep. 131, 147 
( 1986). 
16R. R. Lucchese, R. Raseev, and V. McKoy, Phys. Rev. A25, 2572 ( 1982). 
17R. R. Lucchese and V. McKoy, J. Phys. B 14, L629 (1981 ). 
J. Cham. Phys., Vol. 91, No. 1, 1 July 1989 
Downloaded 11 Dec 2006 to 131.215.225.181. Redistribution subject to AIP license or copyright, see http://jcp.aip.org/jcp/copyright.jsp
154 M. Braunstein and V. McKoy: 3o-g photoionization of 0 2 
18P. H. Krupenie, J. Phys. Chern. Ref. Data 1, 423 ( 1972). 
19K. P. Huber and G. Herzberg, Molecular Spectra and Molecular Struc-
ture, Vol IV. Constants of Diatomic Molecules (Van Nostrand Reinhold, 
New York, 1979). 
20D. L. Albritton, A. L. Schmeltekopf, and R.N. Zare, Diatomic Intensity 
Factors (Wiley, New York, to be published). 
21 J. L. Gardner and J. A. R. Samson, J. Electron. Spectrosc. Relat. Phenom. 
13, 7 (1978). 
220. Edqvist, E. Lindholm, L. E. Selin, and L. Asbrink, Phys. Scr. 1, 25 
(1970). 
23P. M. Dittman, D. Dill, and J. L. Dehmer, J. Chern. Phys. 76, 5703 
(1982). 
24P. W. Langhoff, A. Gerwer, C. Asaro, and B. V. McKoy, Int. J. Quant. 
Chem.: Quant. Chern. Symp. 13,645 (1979). 
25A. Gerwer, C. Asaro, B. V. McKoy, and P. W. Langhoff, J. Chern. Phys. 
72, 713 (1980). 
26G. Raseev, H. Lefebvre-Brion, H. Le Rouzo, and A. L. Roche, J. Chern. 
Phys. 74, 6686 (1981). 
27J. L. Dehmer, D. Dill, and S. Wallace, Phys. Rev. Lett. 43, 1005 ( 1979). 
28J. B. West, A. C. Parr, B. E. Cole, D. L. Ederer, R. Stockbauer, and J. L. 
Dehmer, J. Phys. B 13, LI05 (1980). 
29See, for example, J. L. Dehmer, A. C. Parr, and S. H. Southworth, in 
Handbook on Synchrotron Radiation, edited by G. V. Marr (North-Hol-
land, Amsterdam, 1986), Vol. II. 
30U. Fano and J. W. Cooper, Rev. Mod. Phys. 40,441 (1968). 
31S. T. Manson, Phys. Rev. 31, 3968 (1985). 
32J. W. Keller, W. T. Hill III, D. L. Ederer, T. J. Gil, and P. W. Langhoff, J. 
Chern. Phys. 87, 3299 (1987). 
33M. A. O'Halloran, J. A. Guest, and R.N. Zare, SSRL Activity Report, 
May II, 1983. 
34S. Katsumata, Y. Achiba, and K. Kimura, J. Electron. Spectrosc. Relat. 
Phenom. 17, 229 ( 1979). 
J. Chern. Phys., Vol. 91, No. 1, 1 July 1989 


Multiplet-specific shape resonant features in vibrationally resolved 3σ_g photoionization of O_2

https://authors.library.caltech.edu/31730/1/BRAjcp89e.pdf

Multiplet-specific shape resonant features in vibrationally resolved 3σ_g photoionization of O_2

Abstract

Similar works

Full text

Available Versions

Caltech Authors - Main