In this work, rigorous prescreening conditions for the calculation of Franck-Condon factors (FCFs) are derived and implemented. These factors play an important role in numerous applications including the prediction and simulation of vibronic spectra, electron transfer rates, and nonradiative transition probabilities. For larger systems it is crucial to calculate only relevant FCFs, as the computational burden becomes otherwise prohibitive due to the sheer number of Franck-Condon integrals. By exploiting rigorous prescreening criteria one can significantly reduce the computational effort and systematically refine results to the desired target accuracy. In this work, such criteria are derived via the use of sum rules obtained through a coherent state generating function for the FCFs in the harmonic oscillator approximation, following the prescription of Doktorov et al. These sum rules allow efficient and rigorous prescreening prior to the calculation of entire batches of Franck-Condon integrals, reducing the subsequent computational burden. To illustrate the benefit of employing such conditions, they are applied in this work to calculate FC profiles for vibronic spectra of formic acid, thymine, anthracene, and a polycyclic aromatic hydrocarbon derivative containing about 450 vibrational degrees of freedom. Since the prescreening step gives stringent upper and lower bounds for the loss of FC intensity in these spectra arising from the neglected FCFs, the present approach renders most previous a priori selection schemes obsolete and has the potential to complement or even replace other approximate treatments.

Vibronic transitions in large molecular systems: Rigorous prescreening conditions for Franck-Condon factors

Time‐Independent Approaches to Simulate Electronic Spectra Lineshapes: From Small Molecules to Macrosystems

A general scheme to predict anharmonic vibrational frequencies and vibrationally-averaged structures and rotational constants of molecules is presented with applications to some key species in hydrocarbon combustion (some also of importance in atmospheric and/or interstellar chemistry): HCO+, HCO, HNO, HOO, HOO–, , and CH3. A combination of coupled-cluster singles and doubles (CCSD), CCSD with a second-order perturbation correction in the space of triples [CCSD(2) T ] and in the space of triples and quadruples [CCSD(2) TQ ], and a correlation-consistent basis set series has been employed to achieve the complete-correlation, complete-basis-set limits of the potential energy surfaces (PESs) of these species near equilibrium geometries. A new, compact representation of PESs that combines two existing representations, namely, a fourth-order Taylor expansion and numerical values on a rectilinear grid, has been proposed and shown to yield accurate frequencies, when combined with vibrational general-order config...

Anharmonic vibrational frequencies and vibrationally-averaged structures of key species in hydrocarbon combustion: HCO+, HCO, HNO, HOO, HOO–, CH3 +, and CH3

A general formula of two-dimensional Franck-Condon integral and the photoelectron spectroscopy of sulfur dioxide

The uranyl-SO(2) adduct, UO(2)(CH(3)SO(2))(SO(2))(-), was prepared and characterized by mass spectrometric studies as well as by density functional theory. Collision induced dissociation of UO(2)(CH(3)SO(2))(2)(-) in an ion trap resulted in the formation of UO(2)(CH(3)SO(2))(SO(2))(-), which spontaneously reacted with O(2) to give UO(2)(CH(3)SO(2))(O(2))(-), with SO(2) released. The UO(2)(CH(3)SO(2))(SO(2))(-) complex is computed to have a triplet ground state at the B3LYP level, and the SO(2) ligand is coordinated to uranium through two oxygen atoms, similar to the coordination mode of SO(2) in its complexes with hard metals. On the basis of the calculated geometric parameters and vibrational frequencies of the SO(2) ligand, the UO(2)(CH(3)SO(2))(SO(2))(-) complex can be considered as a U(V)O(2)(+) cation coordinated by SO(2)(-) and CH(3)SO(2)(-) anions. The UO(2)(CH(3)SO(2))(O(2))(-) complex is computed to have a peroxo ligand, suggesting that U(V) in UO(2)(CH(3)SO(2))(SO(2))(-) is oxidized to the U(VI) state upon O(2) substitution for SO(2).

Jun Liang

Papers

Franck-Condon simulation of photoelectron spectroscopy of HOO− and DOO−: including Duschinsky effects

Franck–Condon simulation of the photoelectron spectrum of SO2- including Duschinsky effects