Franck–Condon factors in curvilinear coordinates: the photoelectron spectrum of ammonia

Abstract

An approach to the calculation of FranckCondon factors in curvilinear coordinates is outlined. The approach is based on curvilinear normal coordinates, which allows for an easy extension of Duschinsky's transformation to the case of curvilinear coordinates, and on the power series expansion of the kinetic energy operator. Its usefulness in the case of molecules undergoing large displacements of their equilibrium nuclear configurations upon excitation is then demonstrated by an application to the vibrational structure of the photoelectron spectrum of ammonia, using an anharmonic potential only for the symmetric stretching and bending coordinates of the radical cation.

Quantum Dynamics of Radiationless Electronic Transitions Including Normal Modes Displacements and Duschinsky Rotations: A Second-Order Cumulant Approach

“…[32][33][34] Second-order effects such as variations of vibrational frequencies and the directions of normal vibrations, are usually not included in most of the Hamiltonian models used in qunatum dynamics, though a number of works suggest that their effect can be quite relevant. [35][36][37][38][39][40] The coupling operator V AF is in general a function of the vibrational coordinates of the system, although it is quite common to assume its value constant, since electronic transitions take place in a restricted region of the nuclear coordinates.…”

“…47 The Duschinsky transformation has been computed using the internal coordinate representation of normal modes. 33,[48][49][50] The use of curvilinear internal coordinates is of crucial importance to avoid the appearance of fictious vibrational progressions in the computed density of states. 48,51,52 In the present case the reorganization energies of B A /B − A and H A /H − A pairs computed using Cartesian coordinates and harmonic approximation are 3396 cm −1 and 1454 cm −1 , respectively, while those obtained using internal coordinates are 925 cm −1 and 993 cm −1 , respectively.…”

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.…”

Vibronic couplings and coherent electron transfer in bridged systems

“…That is unavoidable in rectilinear Cartesian coordinates and requires the use of high order anharmonic potentials for its correction. 38,113,[115][116][117][118] The numerical solution of the time-dependent Schödinger equation has been carried out with an orthogonalised Krylov subspace method. 29,119 …”