We demonstrate that a Cooper minimum, close to threshold, in photoionization via an excited molecular Rydberg state can have a dramatic influence on the ionic rotational branching ratios. It is also shown that this behavior can be exploited to produce ions selectively in a specific rotational level. To illustrate this effect we present the results of ab initio calculations for (2+1′) resonance enhanced multiphoton ionization via the O_(11) (23.5) branch of the H ^2Σ^+(3d,4s) state of NO, where a Cooper minimum is found in l=3 of the kσ and kπ continua at photoelectron kinetic energies of 2.6 eV and 2.9 eV, respectively

McKoy, V.

Rudolph, H.

English

Caltech Authors - Main

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Letters to the Editor 
and (b) are Raman-UVDR difference spectra, representing 
the difference between spectra such as those in trace (c) with 
and without Raman pumping. They show decisively that the 
2~ 36 band is indeed there, but too weak to be detected spec-
troscopically under the conditions of thermal equilibrium 
which prevail in trace (c). 
Both Figs. 1 (a) and (b) were recorded with the Raman-
excitation frequency tuned to the Q( 19) peak at 1972.0 
cm- 1 in the v2 Raman bandofC2H2,7 so that the population 
of the X, v2 = 1, J = 19 rovibrational level has been dis-
placed far from thermal equilibrium. Trace (a) was obtained 
with a minimal pump-probe delay, such that the collision 
number (z = 0.08) 8 is too small to enable appreciable colli-
sion-induced "scrambling" of the nascent J = 19 population 
prepared by coherent Raman excitation. Trace (b), for 
which z = 0.65, indicates the effect of rotational energy 
transfer arising from C2H 2 self-collisions. 
There is much useful spectroscopic information in "col-
lision-free" Raman-UVDR spectra such as that in Fig. 1 (a). 
Term energies of the relevant rovibronic states are known 
from earlier spectroscopic studies,5•7 despite the fact that 
2~ 36 band has not itself previously been reported. The rota-
tional structure for a selected J, as in Fig. 1 (a), is complicat-
ed by "axis-switching" transitions,9 leading to a set of sub-
bands which are labelled Kg,K6,K~, ... according to values 
of internal angular momentum. The Raman-UVDR method 
enables us elegantly to show how the intensity of the axis-
switching transitions varies in relation to that of the "main" 
(K6) transitions; our results for a number of Raman-select-
ed J states are consistent with previous theoretical and spec-
troscopic studies. 9 ' 10 
The collision-induced effects represented by Fig. 1 (b) 
are potentially of great interest in the context of chemical 
physics. Several effects are already evident. The rotational 
energy transfer is spread over a wide range of ll.J, as we 
expect from studies of other nondipolar molecules which 
lack strongly anisotropic terms in the long-range intermole-
cular potential. 11 Only even values of ll.J are observed, which 
is consistent with the difficulty of interconverting the ortho 
and para nuclear spin modifications of C2H2. Raman-
UVDR kinetic studies of collision-induced rotational relaxa-
tion are underway. A preliminary Stern-Volmer analysis of 
the depletion rate for some of the strong J = 19 features indi-
cates that this is comparable in magnitude to corresponding 
rates observed 12 high in the vibrational manifold of C2H2, 
using infrared overtone excitation. This comparison sug-
gests that rotational relaxation may be more dominant than 
intramolecular vibrational redistribution in the mechanism 
of the latter experiment. 10 The signal-to-noise ratio of Ra-
man-UVDRspectrasuchasFigs. 1(a) and (b) augurs well 
for our ability to collect high-quality kinetic data to elucidate 
state-to-state rovibrational energy transfer processes involv-
ing C2H 2• 
This research was supported by the Australian Re-
search Council. 
"'Present address: Ginzton Laboratory, Stanford University, Stanford Cal-
ifornia 94305-2184. 
h> Present address: Surveillance Research Laboratory, Defence Science & 
Technology Organisation, P. 0. Box 1650, Salisbury S. A. 5108, Australia 
c> Author to whom correspondence should be addressed. 
'A. B. Duval, D. A. King, R. Haines, N. R. Isenor, and B. J. Orr, J. Opt. 
Soc. Am. B 2, 1570 (1985). 
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( 1983);A. B. Duval, D. A. King, R. Haines, N. R. Isenor, and B.J. Orr,J. 
Raman Spectrosc. 17, 177 ( 1986). 
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Innes, J. Chern. Phys. 22, 863 ( 1954). 
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Spectrosc. 95, I 01 ( 1982). 
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Chern. Phys. 83,453 (1985). 
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and A. Weber, Ind. J. Pure Appl. Phys. 16, 358 ( 1978). 
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(1988). 
Cooper minima and rotationally resolved resonance enhanced multiphoton 
ionization spectroscopy 
H. Rudolph and V. McKoy 
Arthur Amos Noyes Laboratory of Chemical Physics."' California Institute of Technology, Pasadena, 
California 91125 
(Received 18 September 1989; accepted 13 October 1989) 
Resonance enhanced multiphoton ionization 
(REMPI) combined with rotationally resolved photoelec-
tron spectroscopy (PES) is a sensitive probe of excited mo-
lecular states and their photoionization dynamics. 1- 5 We 
have previously shown how orbital evolution in an interme-
diate state can lead to a strong dependence of ion rotational 
distributions on vibrational excitation. 6 We have also recent-
ly predicted that this orbital evolution, in combination with 
a Cooper minimum, gives rise to significant non-Franck-
Condon behavior in vibrationally resolved REMPI ofOH. 7 
Cooper minima have been extensively studied in atoms and 
in molecular ground states. s-w Their influence has also been 
J. Chem. Phys. 91 (12), 15 December 1989 0021-9606/89/247995-03$02.10 @ 1989 American Institute of Physics 7995 
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7996 Letters to the Editor 
recently seen in photoabsorption spectra of excited molecu-
lar states in optical-optical double resonance studies near 
the ionization threshold ofN0. 11 Cooper minima, however, 
have not been identified experimentally in photoionization 
via excited molecular states. 12 The influence of a Cooper 
minimum on the total cross section is less pronounced in 
molecular than in atomic photoionization due to the partial 
wave composition of molecular orbitals, and hence Cooper 
minima are more readily identified in photoelectron angular 
distributions for molecular ground state photoionization. 10 
Since Cooper minima most .often occur in a single partial 
wave(/) of the electronic continuum its significance is most 
evident if only a few partial waves contribute to the cross 
section. To be readily detectable the Cooper minimum 
should occur for the same I in all photoionization continua 
(i.e., ku, k1r, ... ) at approximately the same kinetic energy 
and, particularly for REMPI, close to threshold so as to be 
accessible with current techniques. 
In this Communication we illustrate the dramatic influ-
ence of a Cooper minimum, close to threshold, on the ionic 
rotational branching ratios and how this behavior can be 
exploited to produce ions selectively in a specific rotational 
level. As a specific example of this effect we present the re-
sults of ab initio calculations for (2 + 1') REMPI of NO via 
the H 2~.+(3d,4s) state. We have chosen the 0 11 (23.5) 
branch, i.e., J" = 23.5, J' = 21.5, and N' = 21, but the 
effects described below are equally prominent for other 
rotational branches and J values. For a~-~ transition as in 
the photoionization step of the above excitation, a aN + I 
= odd selection rule applies, 13 where aN is the change of the 
rotational quantum number (excluding spin) between the 
intermediate and final state, and I denotes a partial-wave 
component of the photoelectron orbital. The 9u Rydberg 
orbital of the H 2~ + (3d,4s) state has mixed sand d charac-
ter and, hence, the above propensity rule predicts a aN 
= even rotational distribution, since in an atomic picture 
odd partial waves should be dominant in the photoelectron 
orbital (i.e. 4s-kp and 3d-kp,kj). 
The electronic wave function for the H 2~ + ( 3d,4s) 
state of NO, with the electronic configuration 
1~2~3~4~5~17T49u, is obtained using the improved vir-
tual orbital method 14 with an extensive Gaussian basis. 15 
Single-center expansion of the 9u ( 3du,4su) orbital around 
the center-of-mass at an internuclear separation of 2.0069 
a.u. 16 gives the following partial wave composition: 38.2% s, 
0.8% p, and 61.7% d, consistent with earlier calcula-
tions. 11 • 17 The photoelectron orbitals needed in these studies 
are obtained using the iterative Schwinger method and the 
frozen-core-approximation. 18 Coupling of the molecular ro-
tation and the partial waves of the continuum orbital is treat-
ed explicitly. 19 Both the intermediate and final states are 
treated in Hund's case (b) coupling scheme. Further details 
of the calculations will be reported elsewhere. 
The partial wave composition of the matrix element for 
photoionization of the 9u orbital of the H 2~+ (3d,4s) state 
is dominated by the p andfwaves in both the ku and the k1r 
channel, as expected on the basis of an atomic model. The/ 
wave (/ = 3) component of the photoelectron matrix ele-
ment is dominant close to threshold and shows a zero at a 
photoelectron energy of about 2.6 eV in the kuchannel and 
at around 2. 9 e V in the k1r channel (not shown). These Coo-
per minima are present in the I= 10 + 1 partial wave (where 
10 is a partial wave of the resonant orbital) as seen in Cooper 
minima for atomic ground states. 8'9 Note, however, that a 
truly atomic 3d orbital does not have a radial node and could 
not therefore exhibit a Cooper minimum, further demon-
strating the molecular nature of the Cooper minimum ob-
served here. 
Figure 1 shows calculated ionic rotational branching ra-
tios for the 0 11 (23.5) branch via the H 2~+ state of NO at 
various photoelectron kinetic energies. These branching ra-
tios have been convoluted with a Lorentzian detector func-
tion with a full width at half maximum of 4 meV. Since 
N' = 21, the aN= 0 peak corresponds to N + = 21. The 
aN= even propensity rule is very evident with neglible odd 
aN peaks throughout the energy range. However, the rota-
tional branching ratios are strongly dependent on the kinetic 
energy. Even aN peaks have contributions only from the 
odd-/ partial waves of the photoelectron orbital, due to the 
aN + I = odd selection rule, and the energy dependence of 
the aN = even peaks therefore reflects the change in the 
magnitude and/or interference in these partial waves of the 
continuum ( p,f, .. ). The behavior ofthef-wave component of 
the photoelectron matrix element close to the Cooper mini-
mum hence creates a destructive interference with the p-
wave contribution, reducing the aN= ± 2 signal from ap-
proximately 70% of the aN= 0 signal close to threshold to 
0 
eV 
1.00 eV 
2.00 eV 
2.39 eV 
6.00 eV 
FIG. 1. Ionic rotational branching ratios for (2 + 1') REMPI via the 
0 11 (23.5) branch of the H2 I+ (3d,4s) state of NO for various photoelec-
tron energies. The value of l:J.N=N + - N; is indicated above each rota-
tional signal. The kinetic energy for the l:J.N = 0 peak is shown in each 
frame. Total length of the abscissa is 120 meV. 
J. Chem. Phys., Vol. 91, No. 12, 15 December 1989 
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Letters to the Editor 
less than 2% at the (2 + 1) one-color energy level. 16 At the 
( 2 + 1 ) one-color energy the total ion signal will be more 
than 95% "l:l.N = 0 ions," and it is therefore possible to use 
the presence of the Cooper minimum to generate ions in a 
specific rotational level. The total cross section is also 
strongly energy dependent. The magnitude of the l:l.N = 0 
signal at 2.39 eV is approximately 15% of its value at thresh-
old. The photoelectron angular distributions also change 
dramatically around the Cooper minimum (not shown). 
These distributions are, however, also sensitive to intermedi-
ate state alignment as previously shown.4•15 The rotationally 
unresolved photoelectron angular distributions are less ener-
gy dependent due to the strong p-wave contribution to the 
l:l.N = 0 signal. 
This behavior of rotational ion distributions around a 
Cooper minimum should be quite general. For the case re-
ported here it can be used for production of ions in very 
specific rotational levels. These dramatic changes in rota-
tional branching ratios should also be useful in identifying 
Cooper minima in ionization via high-lying Rydberg states. 
The authors acknowledge support from the National 
Science Foundation (Grant No. CHE-8521391), Air Force 
Office of Scientific Research (Contract No. 87-0039), and 
the Office of Health and Environmental Research of the US. 
Department of Energy (Grant No. DE-FG03-87ER60513). 
We also made use of resources of the San Diego SuperCom-
puter Center, which is supported by the National Science 
Foundation. H.R. gratefully acknowledges support from the 
NATO Science Fellowship Program (Denmark). 
"' Contribution no. 8028 
'S. T. Pratt, P. M. Dehmer, and J. L. Dehmer, Chern. Phys. Lett. 105, 28 
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Phys. (in press). 
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Observation of direct and collision-induced double resonance 
of a molecular ion 
C. J. Pursell, D. P. Weliky,a> W. C. Ho, K. Takagi,b> and T. Oka 
Department of Chemistry and Department of Astronomy and Astrophysics, The University of Chicago, 
Chicago, Illinois 6063 7 
(Received 31 August 1989; accepted 9 October 1989) 
Double resonance is a powerful technique for increasing 
sensitivity, 1 for assigning complex spectra,2 for observing 
very weakly allowed transitions, 3 and for studying rotational 
energy transfer.4 We report here our recent application of 
this technique to the HN 2+ molecular ion. We have observed 
not only the direct three-level double resonance signals both 
in the ground and the excited states, but also collision-in-
duced four-level double resonance signals indicating the ex-
istence of some selection rules even for the Langevin poten-
tial dominated ion-neutral interaction. 
We used a hollow cathode ( 1" diameter and 1 m long) 
as the double resonance cell. The hollow cathode discharge 
was chosen for our ion double resonance because (a) it pro-
vides abundant ( - 1 X 1011 em- 3 ) ions5 at relatively low 
pressures (20-200 mTorr) needed for infrared and micro-
wave saturation, and (b) the metal wall of the cathode serves 
as a waveguide for the microwave radiation. A color center 
laser with 2-20 m Watts of power provided the infrared sig-
nal radiation, and a millimeter wave klystron with -400 
m Watts of power provided the microwave pump radiation. 
The frequency of the microwave radiation was swept and the 
double resonance signal was detected through the variation 
of infrared power. 
The observed J = 1 -0 rotational transitions in the 
ground and the v1 state are shown in Fig. 1. Observation of 
the signal in the v1 state indicates that the infrared radiation 
was at least partially saturating the infrared transition used 
in the experiment. In order to resolve the nitrogen nuclear 
quadrupole hyperfine structure, the pressure and microwave 
power were reduced to avoid broadening. When they were 
increased at the expense of resolution, a signal to noise ratio 
of-400 was observed. With this arrangement, we could also 
observe collision-induced four-level double resonance sig-
nals which are typically 10-100 times weaker than the direct 
double resonance signal. 
The energy level system used in the experiment is shown 
in Fig. 2. In the three-level experiment, the variation of the 
molecular population in the J = 1 level due to the micro-
J. Chern. Phys. 91 (12),15 December 1989 0021-9606/89/247997-03$02.10 © 1989 American Institute of Physics 7997 


Cooper minima and rotationally resolved resonance enhanced multiphoton ionization spectroscopy

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Cooper minima and rotationally resolved resonance enhanced multiphoton ionization spectroscopy

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