title: Acceleration of Relativistic Electron Dynamics by Means of X2C Transformation: Application to the Calculation of Nonlinear Optical Properties.
abstract: 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.
authors: Department of Inorganic Chemistry, Faculty of Natural Sciences, Comenius University , 811 02 Bratislava, Slovak Republic.
authors: Lukas
authors: L
authors: Konecny
authors: The Centre for Theoretical and Computational Chemistry, Department of Chemistry, UiT The Arctic University of Norway , 9019 Tromsø, Norway.
authors: Marius
authors: M
authors: Kadek
authors: The Centre for Theoretical and Computational Chemistry, Department of Chemistry, UiT The Arctic University of Norway , 9019 Tromsø, Norway.
authors: Stanislav
authors: S
authors: Komorovsky
authors: Department of Inorganic Chemistry, Faculty of Natural Sciences, Comenius University , 811 02 Bratislava, Slovak Republic.|Institute of Inorganic Chemistry, Slovak Academy of Sciences , Bratislava 814 38, Slovak Republic.
authors: Olga L
authors: OL
authors: Malkina
authors: The Centre for Theoretical and Computational Chemistry, Department of Chemistry, UiT The Arctic University of Norway , 9019 Tromsø, Norway.
authors: Kenneth
authors: K
authors: Ruud
authors: The Centre for Theoretical and Computational Chemistry, Department of Chemistry, UiT The Arctic University of Norway , 9019 Tromsø, Norway.
authors: Michal
authors: M
authors: Repisky