Using N2 2σu-1 photoionization as an example, we present the first measurements and calculations of photoion vibrational distributions for an extended energy range ( 5≤Ek≤230 eV). The results show a striking breakdown of the Franck-Condon approximation over a 100 eV range. We show that this coupling between vibrational and electronic motion arises from a dependence of Cooper minima on molecular bond length. Based on this mechanism, the effect is expected to be common for molecular systems

McKoy, V.

Poliakoff, E. D.

Rao, R. M.

Wang, Kwanghsi

Caltech Authors - Main

VOLUME 76, NUMBER 15 P HY S I CA L REV I EW LE T T ER S 8 APRIL 1996
2666Global Franck-Condon Breakdown Resulting from Cooper Minima
R.M. Rao1 and E. D. Poliakoff1,2
1Department of Physics and Astronomy, Louisiana State University, Baton Rouge, Louisiana 70803
2Department of Chemistry, Louisiana State University, Baton Rouge, Louisiana 70803
Kwanghsi Wang and V. McKoy
Arthur Amos Noyes Laboratory of Chemical Physics, California Institute of Technology, Pasadena, California 91125
(Received 1 December 1995)
Using N2 2s21u photoionization as an example, we present the first measurements and calculations
of photoion vibrational distributions for an extended energy range (5 # Ek # 230 eV). The results
show a striking breakdown of the Franck-Condon approximation over a 100 eV range. We show that
this coupling between vibrational and electronic motion arises from a dependence of Cooper minima on
molecular bond length. Based on this mechanism, the effect is expected to be common for molecular
systems.
PACS numbers: 33.80.Eh, 31.15.–p, 33.50.DqThe energy dependence of vibrationally resolved par-
tial cross sections is central in the interpretation of
molecular photoionization and detachment data. A clear
picture of vibrational aspects of photoionization is a
prerequisite for interpreting intensities quantitatively [1],
and consequently for extracting accurate ionic potential
surfaces. As examples, note that vibrationally resolved
photoelectron spectra are essential ingredients for probing
the chemical transition state [2] and extracting the struc-
ture of atomic and molecular clusters [3]. In interpre-
tations of photoionization and photodetachment spectra,
it is usually assumed that the vibrational intensities are
governed by the Franck-Condon (FC) approximation, and
hence that the ratio of cross sections for alternative vi-
brational levels is constant with photon energy. In this
Letter, we report the first observation of coupling between
electronic and vibrational motion which is global in ex-
tent, extending over a range of more than 100 eV. With
N2 2s21u photoionization as an example, we show that
the source of this Franck-Condon breakdown is a strong
dependence of Cooper minima on internuclear separation
over a broad energy range. Moreover, because of the
underlying dynamics of the breakdown, this behavior is
expected to be the rule rather than the exception in molec-
ular photoionization. Viewed in a larger context, these
results provide fundamental insights into the correlation
between nuclear and electronic degrees of freedom.
Cooper minima [4,5] are ubiquitous for atomic and
molecular systems. They originate from a change in sign
of the dipole matrix element as a function of photon en-
ergy, so that the matrix element goes through zero. For
molecular systems, the effects of Cooper minima on pho-
toelectron angular distributions are well documented [5].
However, the influence of cooper minima on molecular
vibration over a wide spectral range has never been ex-
plored [6,7], and that is the topic of the current study.
We show—both experimentally and theoretically—that0031-9007y96y76(15)y2666(4)$10.00the N2 2s21u Cooper minima are strongly R dependent,
and that an important manifestation of this R dependence
is a coupling between electronic and nuclear motion. This
study demonstrates that Cooper minima can result in devi-
ations from Franck-Condon behavior over a broader range
than any previously studied mechanism (by more than an
order of magnitude). In so doing, this study highlights the
molecular character of the photoelectron dynamics, even
for scattering energies well in excess of those normally
deemed relevant (i.e., energies on the order of a chemical
bond, or approximately 4 eV).
Our experiment accesses vibrationally resolved pho-
toionization data over a wide spectral range by exploiting
dispersed fluorescence from excited photoions [8]. Gas-
phase nitrogen molecules are ionized by monochroma-
tized synchrotron radiation, and the fluorescence from the
excited photoions is collected, dispersed, and detected:
N2sX1S1g , y0 ­ 0d 1 hnexc ! N2 1sB2S1u , y1d 1 e2
#
N21sX2S1g , y00d
1 hny1y00 . (1)
The strategy is that the fluorescence intensity originating
from a particular vibrational level is proportional to the
partial photoionization cross section for that level [9]. An
important feature of this method is that the fluorescence
bandwidth is uncoupled from the excitation bandwidth,
thereby enabling us to obtain highly resolved data on
the photoions while simultaneously exploiting the broad
tunability of synchrotron radiation [10]. Synchrotron
radiation from the Louisiana State University Center for
Advanced Microstructures and Devices (CAMD) facility
is monochromatized sDhnexc ø 0.5 eVd by a 6-m plane
grating monochromator [11] and used to ionize the target
molecules. The N2 gas is introduced into the interaction
region via a free-jet supersonic expansion. Data are© 1996 The American Physical Society
VOLUME 76, NUMBER 15 P HY S I CA L REV I EW LE T T ER S 8 APRIL 1996obtained over a range of stagnation pressures to test for
secondary processes. The results are free of artifacts
and are reproducible at pressures below 1024 Torr. A
complete discussion of the experiment will be given
elsewhere [12].
The computational procedure used here has been dis-
cussed in detail previously [13]. To obtain the photoelec-
tron orbitals, we use an iterative procedure based on the
Schwinger variational principle to solve the Lippmann-
Schwinger equation [13]. Calculations are performed at
the Hartree-Fock frozen-core level, which is sufficient to
characterize the key dynamical aspects. The ground state
wave function of N2 is obtained at the self-consistent-field
level [12]. A single-center expansion around the center
of mass shows the 2su orbital to have 90.65% p, 6.66%
f, and 1.52% h character at the equilibrium internuclear
distance of Re ­ 2.0743 a.u. This orbital composition
changes slowly from 96.86% p and 2.62% f character
at an internuclear distance of 1.25 a.u. to 81.25% p and
11.30% f character at R ­ 3.5 a.u. Note that the cal-
culations assume the validity of the Born-Oppenheimer
approximation [12,13], i.e., the electronic wave func-
tion depends parametrically on bond distance. Thus, the
observation of nonconstant vibrational branching ratios
reflects this parametric, rather than dynamic, electronic-
nuclear coupling.
Figure 1 shows the portion of the fluorescence spec-
trum for N21sB2S1u , y1 ! X2S1g , y00d which includes
transitions originating from the y1 ­ 0, 1, and 2 lev-
els. Vibrational branching ratios are extracted from the
intensity ratios, as described elsewhere [9]. Spectra are
obtained for photon energies from 25 # hnexc # 250 eV,
and the derived vibrational branching ratios are plotted
as a function of excitation photon energy in Fig. 2.
(The I.P. for 2s21u is 18.76 eV [14].) The deviations
from Franck-Condon behavior are significant in the
y1 ­ 1yy1 ­ 0 ratio. The FC breakdown is even more
evident in the much weaker y1 ­ 2 channel. This behav-
FIG. 1. Fluorescence spectrum from N2 1 showing B2S1u ,
y1 ! X2S1g , y00 transitions. y1 2 y00 ­ 21 for transitions
shown [14].ior is expected as deviations from Franck-Condon behavior
are usually enhanced for weaker channels [9]. While the
absolute partial cross sections do not deviate substantially
from Franck-Condon predictions, the branching ratios
(which emphasize their relative magnitude) highlight
the deviations clearly. The agreement between theory
and experiment is quite good for the y1 ­ 1yy1 ­ 0
results, while there is only qualitative agreement for the
y1 ­ 2yy1 ­ 0 results. It is not surprising that the
agreement is not as good for the y1 ­ 2yy1 ­ 0 curves,
because the cross section is so weak that effects not
included at the independent particle level can influence the
ratios [15]. For comparison, the top frame of Fig. 2 shows
the y1 ­ 1yy1 ­ 0 curve for 3s21g yN2 photoionization
on the same energy scale as the present 2s21u results.
The top frame exhibits the well-known 3sg ! ksu shape
resonance [16,17], which is usually considered to be very
broad, but its width is dwarfed by the features in the
2s21u curves. We emphasize two empirical aspects of
the results, namely, the energy at which the excursion
FIG. 2. Top frame: shape resonance induced FC breakdown
(expt: Ref. [16], theory: Ref. [17]). Middle frame: y1 ­
1yy1 ­ 0 ratio curve for N2 2s21u photoionization showing
Cooper minimum-induced FC breakdown. Bottom frame:
y1 ­ 2yy1 ­ 0 ratio curve for N2 2s21u photoionization. The
deviation from FC behavior is even more pronounced. All three
frames have the same energy axis. Diamonds are experimental
data and the solid lines are theoretical.2667
VOLUME 76, NUMBER 15 P HY S I CA L REV I EW LE T T ER S 8 APRIL 1996occurs, and its range. First, the dominant deviations
begin at hnexc ø 100 eV and peaks at 160 eV, indicating
that molecular aspects of the process (i.e., vibrational
coupling) become pronounced at more than 80 eV above
the electron ejection threshold. It is usually implicit
that molecular effects in such spectra are limited in
extent in the continuum. The current results clearly belie
this assumption. The second characteristic of the FC
breakdown, the width of the feature, is important for
interpretations of photoelectron spectra. When one tests
for the validity of the FC approximation, it is generally
assumed to be sufficient to check at photon energies
separated by a few eV, and to conclude that the FC
approximation is valid if the relative vibrational intensities
do not change substantially. The results shown in Fig. 2
demonstrate that changes in relative intensities can occur
so gradually that normal tests for vibrational coupling
are not sufficient. Experiments cannot be performed for
all systems over such extended ranges, underscoring the
importance of employing theory as a tool for interpreting
experimental results.
To interpret the observed Franck-Condon breakdown,
we note that there is a clue provided by a recent rotationally
resolved study of N2 2s21u photoionization [8,10], where
we observed that the rotational branching ratios exhibit
inflection points at hnexc ø 120 eV. Theoretical work
showed that the energy dependence of these rotational
branching ratios resulted from Cooper minima in the l ­ 2
and l ­ 4 partial waves of the 2su ! ksg channel. We
therefore turn our attention to the dipole strengths for these
components, which are shown in Fig. 3 for different values
of R. Cooper minima are clearly visible for both these
components. Moreover, the minima show a pronounced
shift to lower photon energies with increasing internuclear
separation. The peaks in the bottom two frames of Fig. 2
can be traced directly to the Cooper minima shifts in Fig. 3.
While we have explained the basis for the Franck-
Condon breakdown phenomenologically—as illustrated
by Figs. 2 and 3—it is still necessary to explain why
the Cooper minima are shifting in the first place. There
are two likely mechanisms which can contribute to the
Cooper minima shifts, and both may play a role here.
First, there is a gradual change of the angular momentum
composition of the target molecular orbital with bond
length. As a result, the Cooper minima are sampled to
differing extents by alternative vibrational levels, and this
can result in an R dependence in the cross section curve [7].
Second, coupling of the angular momentum components
of the molecular photoelectron orbital changes as the bond
length changes. The first and second explanations can be
characterized as initial and final state effects, respectively.
Both effects may contribute to the observed behavior, and
will be discussed in detail elsewhere [12].
Finally, it is helpful to describe other mechanisms
for Franck-Condon breakdown in order to place the
current study in context. Previous examples result from2668FIG. 3. Dipole strengths for the N2 2su ! ksg l ­ 2 and
l ­ 4 partial waves. Note the R dependence.
resonant excitation, either autoionization [18] or shape
resonance [16,17,19]. In these cases, the eigenphase sum
goes through p, and the cross section goes through
an extremum. For the N2 2s21u channel, the cross
section exhibits an inflection [12] rather than a local
maximum or minimum. More importantly, the effect
observed here is nonresonant, i.e., the eigenphase sum
does not go through p in the vicinity of the Cooper
minimum [20]. We believe that this is unique, i.e., that
a nonresonant mechanism is observed to cause coupling
between electronic and vibrational degrees of freedom
over a broad range.
The possibility of non-FC behavior due to a Cooper
minimum has been recognized before [6,7]. In partic-
ular, Franck-Condon breakdown has been predicted for
the pathological case of photoionization of hydrides in
Rydberg target states [8]. The Franck-Condon breakdown
predicted for hydrides is quite different from the effects
observed in the current work. First, Rydberg states of
hydrides are unusual in that an avoided crossing results
in strong changes in the molecular orbital composition
with internuclear separation. Stephens and co-workers
[6] noted that this R dependence could yield strong
non-Franck-Condon effects in a resonance-enhanced mul-
tiphoton ionization and photoemission spectroscopy ex-
periment. However, the non-Franck-Condon effects are
limited to a narrow class of systems, and are also pre-
dicted to be limited in their spectral scope.
VOLUME 76, NUMBER 15 P HY S I CA L REV I EW LE T T ER S 8 APRIL 1996In summary, we have observed Cooper minima induced
Franck-Condon breakdown in vibrational branching ratios
for N2 2s21u photoionization over an extremely broad
range sDEexc ø 100 eVd. This behavior is attributed to
the R dependence of the Cooper minima. Such effects are
unexpected, and have the following implications. First,
it is the broadest deviation from Franck-Condon behavior
ever observed. Second, it is the first nonresonant mech-
anism which exhibits Franck-Condon breakdown. Third,
it is expected to be phototypical for both simple and com-
plex molecular systems. Fourth, very molecular aspects
of photoionization are seen to be prevalent in a regime
usually assumed to be dominated by atomiclike behav-
ior. Fifth, it is a simple process which can be exploited
for studying the correlation of electronic and nuclear mo-
tion. Indeed, the unifying theme provided by this and
several previous studies [8–10,15] is that photoioniza-
tion opens many avenues for probing correlations between
electronic and nuclear degrees of freedom. The present
work demonstrates that the dynamics of Cooper minima
provide a means of investigating electronic and vibra-
tional correlations which are both accessible and useful.
We thank the CAMD staff for assistance. E. D. P.
acknowledges support from the NSF (CHE-9315857) and
the Louisiana LEQSF program. Work at Caltech was
supported by the Air Force Office of Scientific Research,
the Office of Health and Environmental Research of the
U.S. Department of Energy, and the JPL/Caltech CRAY
Y-MP2E/232 Supercomputer.
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Global Franck-Condon breakdown resulting from Cooper minima

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Global Franck-Condon breakdown resulting from Cooper minima

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