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

Abstract

In this brief review, an overview about recent efforts to simulate the spectroscopic signatures of chiral molecules is given with focus on real time propagation approaches to solve the time-dependent Schrödinger equation. In particular the simulation of electric circular dichroism spectra and vibrational Raman optical activity is discussed. In comparison to linear absorption spectra, where only the response of the electric dipole moment is necessary, the response of the magnetic dipole moment and electric quadrupole moment is more intricate. Issues such as gauge origin dependence, basis set dependence, non-local potentials and the dipole approximation are addressed.

Analyzing Excitation-Energy Transfer Based on the Time-Dependent Density Functional Theory in Real Time

“…Time-dependent (TD) density functional theory (DFT) using propagation of the Kohn–Sham orbitals in real time is ideally suited for studying large-scale problems of electronic structure and dynamics and is used in different technical realizations. − As a theory, it is attractive because with the exchange–correlation (xc) approximation properly chosen, it is a first-principles approach, it allows one to follow electron dynamics with temporal and atomistic resolution, and it allows one to study all kinds of excitations within and beyond the linear-response regime. On the technical level, it is very attractive because the computational effort for the propagation scales favorably with the particle number and the calculations parallelize excellently.…”

The position operator problem in periodic calculations with an emphasis on theoretical spectroscopy

“…For this reason, a complex electron density matrix must be employed to obtain non-vanishing expectation values. This can be achieved, for example, by TD-DFT 42,97 or imaginary perturbations. 98 Additionally, the equality〈 a | ṙ | b 〉 = − i ( E b − E a ) 〈 a | r | b 〉for two eigenstates | a 〉 and | b 〉 with corresponding energy eigenvalues E a and E b is only fulfilled for exact wavefunctions, and otherwise the position operator and velocity operator do not yield identical results.…”

Chiral Spectroscopy of Bulk Systems with Propagated Localized Orbitals

“…8,25−27 Moving into the time domain, an approach to vibrational dynamics based on the short time approximation method has been successfully applied to real-time TDDFT by Mattiat and Luber. 8,9,27,28 It naturally includes off-, pre-, and on-resonance effects in a single simulation framework, reducing the computational time needed for a full picture. An extension of the method to bulk systems has been successful for absorption and Raman spectra.…”