Time Domain Simulation of (Resonance) Raman Spectra of Liquids in the Short Time Approximation

Abstract

Real-time time-dependent density functional theory (RT-TDDFT) and ab initio molecular dynamics (AIMD) are combined to calculate non-resonant and resonant Raman scattering cross sections of periodic systems, allowing for an explicit quantum mechanical description of condensed phase systems and environmental effects. It is shown that this approach to Raman spectroscopy corresponds to a short time approximation of Heller's time-dependent formalism for the description of Raman scattering. Two ways to calculate the frequency-dependent polarizability in a periodic system are presented: (1) via the modern theory of polarization (Berry phase) and (2) via the velocity representation. Both approaches are found to be equivalent for a system of liquid (S)-methyloxirane with the computational settings used. Resulting non-resonance and resonance Raman spectra from the dynamic AIMD/RT-TDDFT approach are compared to the spectra of one gas phase molecule in the harmonic approximation highlighting finite temperature and solvation effects. Using RT-TDDFT to calculate the full frequency-dependent Placzek-type polarizability within one set of simulations covers the non-resonance, near-resonance, and on-resonance regimes on equal footing, thus allowing the calculation of full Raman excitation profiles.

Analytic calculation and analysis of atomic polar tensors for molecules and materials using the Gaussian and plane waves approach

“…where P λ is the APT of nucleus λ, S i is the mass-weighted transformation matrix from Cartesian to normal mode coordinates which can be retrieved from the dynamical matrix Ω. In the double harmonic approximation, the IR intensities can be evaluated by determining the derivatives numerically via a finite differences formula 26 or by carrying out the differentiation analytically using DFPT which we had used previously for other types of spectroscopy [29][30][31][32][33][34][35] . The APTs can be represented as 3 × 3 matrices for each nucleus and are defined in terms of an electronic contribution E λ αβ and a nuclear contribution…”

Recent Progress in the Simulation of Chiral Systems with Real Time Propagation Methods

“…Possible directions for further development include the consideration of environmental effects which is an important aspect for more realistic simulations in many cases. Apart from PCM [113] a description within periodic boundary conditions may be useful for a sophisticated modelling of condensed phase systems, as was recently done for Raman spectroscopy by combining RT‐TDDFT with ab initio molecular dynamics [32,33] …”

“…Apart from PCM [113] a description within periodic boundary conditions may be useful for a sophisticated modelling of condensed phase systems, as was recently done for Raman spectroscopy by combining RT-TDDFT with ab initio molecular dynamics. [32,33]…”

“…RT‐TDDFT has been applied to various spectroscopic approaches such as UV‐VIS absorption spectra, [10–14] pump‐probe [15] experiments, excited state absorption, [16] X‐ray absorption, [17–20] the simulation of charge transfer, [21–25] plasmons, [26,27] and exciton dynamics [5,28] and (resonance) Raman spectroscopy [29–34] . The study of chiral systems using RT‐TDDFT has also attracted more attention recently.…”

Local approaches for electric dipole moments in periodic systems and their application to real-time time-dependent density functional theory

“…15a) and Wannier (Eq. 15b) methods was conducted with the internal "RTana" analysis tools using a damping factor of 0.1E −1 h for all systems, [59][60][61][62] supplemented with Scipy 63 and the Matplotlib plotting library for visualisation. 64 Finding an optimal set of parameters for DFT embedding calculations often involves some trial and error, especially when extrapolating the initial approximate electron density as in RT-TDDFT, and small errors can add up over the course of the simulation.…”