A combined ab initio and Franck–Condon simulation study of the photodetachment spectrum of the anion

An Efficient Analytic Approach for Calculation of Multi-Dimensional Franck–Condon Factors and Associated Photoelectron Spectra

“…Considerable efforts in the past decade have been extended toward achieving accurate predictions of photoelectron spectra and associated mechanistic aspects of molecular electronic transition processes and electron transfer reactions. − Of central interest are models based on quantum mechanical (QM) and density functional theory (DFT) schemes, − which can enable high level of predicted accuracy with a minimum of computational cost. At the core of these capabilities is the determination of highly accurate Franck–Condon Factors (FCFs).…”

“…An inherent challenge for quantitative prediction of Franck–Condon integrals, particularly for systems of high dimension, is the computational time and associated resources (e.g., memory, disk storage) required. ,, Early efforts as such were limited to 1-D methods, and determination of two-, , three- and four-dimensional FCF overlap integrals for small molecules, limiting focus to mostly diatomic molecules. ,,− In the past decade, efforts have been extended to simplify the computational expense for both analytic and recursion approaches. , Despite this, there are still challenges in terms of computational resource requirements and algorithmic redundancies, which have limited the scope of high-accuracy first-principles methodologies for large systems involving many vibrational modes with large numbers of transitions.…”

Generalized Analytic Approach for Determination of Multidimensional Franck–Condon Factors: Simulated Photoelectron Spectra of Polynuclear Aromatic Hydrocarbons

“…Many methods for determination of FCF values to predict the vibronic spectra of molecules find their roots in the 1-D analytic formalisms of Hutchinson . Several recent and extensive works have provided valuable perspectives of various theoretical approaches for determination of FCF integrals. − ,,− In terms of mathematical formulations, efforts stem either from original works involving recursion relations , or analytic formulations. , While analytical methods enable accurate numerical results for FCF integral formalism, the possible transitions must be known in advance and the formula involved are complicated for greater than about four excited normal modes . One advantage of the recursion relation approach is that overlap integrals between any of the vibrational states can be obtained once the ground state integrals are determined.…”

“…A persistent challenge for quantitative prediction of Franck–Condon integrals, particularly for systems of high dimension, has been the computational time and associated resources (e.g., memory, disk storage) required for determination of the FCFs. ,, This is why early efforts were limited to 1-D methods, , and determination of 2-, , 3-, and 4-dimensional FC overlap integrals, and only for small molecules, primarily diatomics. ,,− Only in the past decade have efforts been extended toward the simplification of the computational methodology for more efficient and less costly analytic and recursion approaches, including our recent demonstration involving systems up to 30-D. , What remains is greater accessibility to much larger dimension systems (>50-D), which we have tackled in this work.…”

“…The accurate prediction of full-feature photoelectron spectra from first-principles presents a major challenge for electronic structure theory. Franck–Condon integrals (FCI) are a necessary component governing the intensities of photoelectron bands, − optical absorption and emission bands, , and fluorescence spectral bands . Moreover, the Franck–Condon Factor (FCF) is necessary for estimation of rates of electron transfer in radiative as well as nonradiative decay processes. − Displacement and distortion effects during the excitation process, and coupling of vibrational modes, complicate theoretical treatments. − Most efforts assume the expression for FCIs to the harmonic oscillator approximation; − however, effects of anharmonicity can be very important. − Additionally, the Duschinsky Rotation Effect in polyatomic systems also need to be considered. − ,− ,− ,− …”