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

Abstract

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.

Theoretical and experimental determination of the absorption and emission spectra of a prototypical indolenine-based squaraine dye

“…1,2 Fast growing research fields such as organic LED technology 3 and dye-sensitized solar cells (DSSC), 4 would strongly benefit from the application of robust and easy-to-use methodologies for the simulation of spectral lineshapes of organic dyes. The research in this field is quickly growing [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21] (see also Borrelli et al 22 for a recent review) but standardize procedures have not yet been established, and specific computational strategies must be carefully designed and require validation and testing on several class of molecules. [23][24][25][26] In this paper we apply state of the art tools of computational spectroscopy to simulate the absorption and emission lineshapes of squaraine dyes in solution.…”

Boson sampling for molecular vibronic spectra

“…First, we introduce the boson sampling problem and the Duschinsky relation in terms of unitary operators, then we compare the two physical problems and suggest how to obtain molecular vibronic spectra with a boson sampling device. We also provide examples concerning the photoelectron spectra of formic acid and thymine [23]. Finally, we conclude with an outlook for the use of boson sampling devices in chemistry and molecular physics.…”

“…In this work, we present a connection between boson sampling and the calculation of molecular vibronic (vibrational and electronic) spectra related to molecular processes such as absorption, emission, photoelectron and resonance Raman (see Table I) [19][20][21][22][23][24] . The proposed simulation scheme provides a second, chemically-relevant reason to realize boson sampling machines.…”

“…Refs. [22][23][24]). We show that the quantum simulation, and hence the calculation of FC factors lying at the heart of linear spectroscopy, can be efficiently performed on a boson sampling machine simply by modifying the input state.…”

Vibronic couplings and coherent electron transfer in bridged systems

“…In the field of molecular spectroscopy this approach has been exploited by Santoro et al and formalised by Janckowiack et al. 30,31 Since in our methodology the coupling between two vibronic states is directly proportional to the corresponding FC integrals, it is expected that the effect of states with a significant number of excited vibrations on the overall dynamics. will only be marginal.…”