A Fourier transform method for generation of anharmonic vibrational molecular spectra

Ivan Ivani ^1*, Vladimír Baumruk¹ and Petr Bouř ²

¹ Faculty of Mathematics and Physics, Institute of Physics, Ke Karlovu 5, 12116, Prague, Czech Republic

² Institute of Organic Chemistry and Biochemistry, Academy of Sciences, 166 10 Prague, Czech Republic

ivan.ivani@centrum.cz

Keywords: vibrational spectra, anharmonic corrections, Hamiltonian diagonalization, Raman spectra, ROA

Abstract

Accurate computations of vibrational energies and vibrational spectra of molecules require inclusion of the anharmonic forces [1]. In standard computational protocols, a large vibrational Hamiltonian matrix is diagonalized, and spectral intensities are calculated for individual transitions separately.

We propose an alternate direct generation of the spectral curves based on a temporal propagation of a trial vibrational wavefunction followed by a Fourier transformation [2]. For example, the absorption intensity is calculated as

, (1)

where

(2)

is Fourier transform of a time-dependent electric dipole moment. The lack of the lengthy and computer-memory demanding diagonalization makes the method suitable for larger molecules. It is especially convenient for sparse Hamiltonians that are commonly obtained within the harmonic oscillator basis set, and the algorithm is amendable to parallelization. On a model water dimer basic convergence properties are discussed. The method is then applied to vibrational Raman intensities of the fenchone compound, were it provides spectral shapes comparable with those obtained by the classical approaches.

References

1. Daněček, P.; Bouř, P. J. Comp. Chem. 2007, 28, 1617-1624

2. Kubelka, J.; Bouř, P. J. Chem. Theory Comput. 2009, 5, 200-207