A Fourier transform method for generation of anharmonic vibrational molecular spectra

Ivan Ivani^{ 1*},
Vladimír Baumruk^{1} 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