Vibrational Raman Spectra from the Self-Consistent Charge Density Functional Tight Binding Method via Classical Time-Correlation Functions

Abstract

The Self-Consistent Charge Density Functional Tight Binding (SCC-DFTB) method has been extended for the calculation of vibrational Raman spectra employing the Fourier Transform of Time-Correlation Function (FTTCF) formalism. As Witek and co-workers have already shown for a set of various organic molecules, the minimal basis SCC-DFTB approach performs surprisingly good in terms of polarizability calculations. Therefore, we were encouraged to use this electronic structure method for the purpose of Raman spectra calculations via FTTCF. The molecular polarizability was accessed via second order numeric derivatives of the SCC-DFTB energy with respect to the components of an external electric field “on-the-fly” during a molecular dynamics (MD) simulation. The finite electric field approach delivers Raman spectra that are in overall good agreement for most of 10 small organic model compounds examined in the gas phase compared to a standard Normal Mode Analysis (NMA) approach at the same (SCC-DFTB) and at a higher level of theory (BLYP aug-cc-pVTZ). With the use of reparametrized SCC-DFTB repulsive potentials, a distinct improvement of the Raman spectra from the SCC-DFTB/FTTCF protocol of conjugated hydrocarbons has been observed. Further QM/MM test calculations of l-phenylalanine in aqueous solution revealed larger deviations concerning vibrational frequencies and relative intensities for several stretching and bending modes in the benzene ring as compared to experimental results. Our SCC-DFTB/FTTCF approach was also tested against a hybrid method, in which polarizability calculations at the B3YLP 6-31G(d) level were performed on a trajectory at the SCC-DFTB level. We found that our SCC-DFTB/FTTCF protocol is not only much more efficient but in terms of the resulting Raman spectra also of similar accuracy compared to the hybrid approach. In our opinion, the more accurately calculated polarizabilities at the B3YLP 6-31G(d) level cannot compensate for the usually insufficient sampling of phase space when employing high level QM methods in a FTTCF framework.