Acceleration of Relativistic Electron Dynamics by Means of X2C Transformation: Application to the Calculation of Nonlinear Optical Properties

• Published in: Journal of chemical theory and computation 2016-12, Vol.12 (12), p.5823-5833
• Main Authors: Konecny, Lukas, Kadek, Marius, Komorovsky, Stanislav, Malkina, Olga L, Ruud, Kenneth, Repisky, Michal
• Format: Article
• Language: English
• Subjects: Acceleration; Evolution; Mathematical analysis; Mathematical models; Nonlinear dynamics; Nonlinearity; Optical properties; Time dependence
• ISSN: 1549-9618; 1549-9626
• DOI: 10.1021/acs.jctc.6b00740

The Liouville–von Neumann equation based on the four-component matrix Dirac–Kohn–Sham Hamiltonian is transformed to a quasirelativistic exact two-component (X2C) form and then used to solve the time evolution of the electronic states only. By this means, a significant acceleration by a factor of 7 or more has been achieved. The transformation of the original four-component equation of motion is formulated entirely in matrix algebra, following closely the X2C decoupling procedure of Ilias and Saue [ J. Chem. Phys. 2007, 126, 064102 ] proposed earlier for a static (time-independent) case. In a dynamic (time-dependent) regime, however, an adiabatic approximation must in addition be introduced in order to preserve the block-diagonal form of the time-dependent Dirac–Fock operator during the time evolution. The resulting X2C Liouville–von Neumann electron dynamics (X2C-LvNED) is easy to implement as it does not require an explicit form of the picture-change transformed operators responsible for the (higher-order) relativistic corrections and/or interactions with external fields. To illustrate the accuracy and performance of the method, numerical results and computational timings for nonlinear optical properties are presented. All of the time domain X2C-LvNED results show excellent agreement with the reference four-component calculations as well as with the results obtained from frequency domain response theory.