Photoelectron angular distributions for states of any mixed character: An experiment-friendly model for atomic, molecular, and cluster anions

Abstract

We present a model for laboratory-frame photoelectron angular distributions in direct photodetachment from (in principle) any molecular orbital using linearly polarized light. A transparent mathematical approach is used to generalize the Cooper-Zare central-potential model to anionic states of any mixed character. In the limit of atomic-anion photodetachment, the model reproduces the Cooper-Zare formula. In the case of an initial orbital described as a superposition of s and p-type functions, the model yields the previously obtained s-p mixing formula. The formalism is further advanced using the Hanstorp approximation, whereas the relative scaling of the partial-wave cross-sections is assumed to follow the Wigner threshold law. The resulting model describes the energy dependence of photoelectron anisotropy for any atomic, molecular, or cluster anions, usually without requiring a direct calculation of the transition dipole matrix elements. As a benchmark case, we apply the p-d variant of the model to the experimental results for NO(-) photodetachment and show that the observed anisotropy trend is described well using physically meaningful values of the model parameters. Overall, the presented formalism delivers insight into the photodetachment process and affords a new quantitative strategy for analyzing the photoelectron angular distributions and characterizing mixed-character molecular orbitals using photoelectron imaging spectroscopy of negative ions.

Solvated Electrons in Clusters: Magic Numbers for the Photoelectron Anisotropy

“…However, to the best of our knowledge no magic numbers related to the photoelectron anisotropy for solvated electrons in clusters have been reported so far, even though many clusters with high symmetry have been predicted by calculations (see references in 5,[7][8][9][10][11][12]. This might be a consequence of the fact that the photoelectron anisotropy has not received broad attention, likely because measurements of the photoelectron angular distribution (PAD) of clusters are rather sparse 5,[13][14][15][16][17][18][19][20][21][22][23] _ENREF_13_ENREF_7_ENREF_7_ENREF_7_ENREF_7_ENREF_7 and because it is difficult to calculate the anisotropy. 15,17,[24][25][26][27][28] For metallic clusters, by contrast, magic numbers related to the anisotropy have been reported, typically for clusters of high symmetry.…”

“…This might be a consequence of the fact that the photoelectron anisotropy has not received broad attention, likely because measurements of the photoelectron angular distribution (PAD) of clusters are rather sparse 5,[13][14][15][16][17][18][19][20][21][22][23] _ENREF_13_ENREF_7_ENREF_7_ENREF_7_ENREF_7_ENREF_7 and because it is difficult to calculate the anisotropy. 15,17,[24][25][26][27][28] For metallic clusters, by contrast, magic numbers related to the anisotropy have been reported, typically for clusters of high symmetry. 14,29 In contrast to metallic clusters, molecular clusters are held together by a fine balance of weak intermolecular forces with different distance-and orientation-dependencies (electrostatic, induction, dispersion, hydrogen bonds).…”

High-resolution photoelectron spectroscopy of the pyridinide isomers

“…The photoelectron angular distributions have been modeled using a three-component implementation of the generalized mixing model proposed by Sanov,42 revealing chemically intuitive isomeric trends in the highest-occupied molecular orbitals of the pyridinide anions. Whereas the p-pyridinide PAD is found to be well-described by a HOMO consisting only of s and p components, the o-pyridinide PAD suggests substantially more d-character in the detached orbital.…”

“…(S5) gives a single-parameter expression for β(ε) that can be fit to experimental data to extract the fractional p-character of the detached orbital, giving a direct link between the experimental PAD and the orbital hybridization of the anion. 29,32 The formulation of the mixed-sp model has since been expanded to a generalized mixing model, 42 described in Sec. S3c of the supplementary material.…”

“…While the majority of features in all three spectra are well-described by harmonic Franck-Condon (FC) simulations, anharmonic mixing between vibrational levels of the p-pyridyl radical is proposed as the cause of ∼10 cm −1 experimental peak splittings observed for several detachment transitions from the corresponding anion isomer. To describe the photoelectron angular distributions for all three anions in a unified framework, the mixed-sp model has been expanded to include a d-component following the generalized mixing model developed by Sanov,42 and the results of this treatment highlight isomeric trends in orbital hybridization for deprotonated pyridine. Finally, the experimental and theoretical results presented here are used to consider the origin of the relative isomeric stabilities for both charge states, and estimates of the CH BDEs of pyridine are obtained using a combined experimental-theoretical approach.…”