Global Franck-Condon Breakdown Resulting from Cooper Minima

Abstract

Using N 2 2s 21 u photoionization as an example, we present the first measurements and calculations of photoion vibrational distributions for an extended energy range (5 # E k # 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, 33.50.Dq The energy dependence of vibrationally resolved partial 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 structure of atomic and molecular clusters [3]. In interpretations 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 vibrational 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 extent, extending over a range of more than 100 eV. With N 2 2s 21 u 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 molecular 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 energy, so that the matrix element goes through zero. For molecular systems, the effects of Cooper minima on photoelectron angular distributions are well documented [5]. However, the influence of cooper minima on molecular vibration over a wide spectral range has never been explored [6,7], and that is the topic of the current study. We show-both experimentally and theoretically-that the N 2 2s 21 uCooper 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 deviations 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 ener...

Vibrational branching ratios in photoionization of CO and N2

“…The bottom frames show the v ϩ ϭ1/v ϩ ϭ0 vibrational branching ratio data for CO and the top frames show the results for N 2 . 6 The calculated results are in excellent agreement with experiment for both molecules. There are obvious qualitative differences between N 2 and CO.…”

“…The high energy behavior results from the strong dependence of the Cooper minima on bond length. 5,6 The low energy region is featureless because there is no shape resonance corresponding to the one observed in CO. This stems from symmetry, i.e., the lϭ3 partial wave is forbidden in the case of N 2 because the final electronic wave function is of gerade symmetry and therefore contains only even partial waves.…”

“…The fluorescence spectra compared well with those obtained previously over a more limited range. 23 The theoretical methods employed in these studies have been discussed previously 5,6 and only a brief discussion is given here. The photoelectron orbitals are obtained using a procedure based on the Schwinger variational principle.…”

“…5 As a result, these Cooper minima led to a wide-ranging Franck-Condon breakdown, i.e., the vibrational branching ratios for the N 2 ϩ (B 2 ⌺ u ϩ ) state depended on energy, even 200 eV above the ionization threshold. 6 However, there has not been a comparable vibrationally resolved investigation into CO. One expects that the energy dependence of the vibrational branching ratios for CO ϩ (B 2 ⌺ ϩ ) would differ significantly from those of N 2 , as the Cooper minima responsible for the higher energy excursions in N 2 are absent in CO. The current investigation addresses this issue by determining CO ϩ (B 2 ⌺ ϩ )v ϩ ϭ1/v ϩ ϭ0 vibrational branching ratios over a wide energy range for comparison with those of N 2 ϩ (B 2 ⌺ u ϩ ).…”

Molecular photoionization as a probe of vibrational–rotational–electronic correlations

“…[1][2][3][4][5][6][7][8][9][10][11][12][13] Vibrationally resolved spectra probe correlations between photoelectron motion and molecular geometry, 1-4 while rotationally resolved data elucidate the coupling of angular momenta between the continuum electron and the ion core. [5][6][7][8][9][10]12,13 Our group has recently performed both types of measurements over an extremely broad range, [11][12][13] emphasizing that molecular aspects of the photoejection process extend far ͑i.e., Ͼ200 eV͒ into the ionization continuum. These vibrationally resolved studies of N 2 2 u Ϫ1 photoionization showed that Cooper minima can lead to non-Franck-Condon behavior over a broad energy range.…”