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

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• 作者：Lukas Konecny ; Marius Kadek ; Stanislav Komorovsky ; Olga L. Malkina ; Kenneth Ruud ; Michal Repisky
• 刊名：Journal of Chemical Theory and Computation
• 出版年：2016
• 出版时间：December 13, 2016
• 年：2016
• 卷：12
• 期：12
• 页码：5823-5833
• 全文大小：484K
• ISSN：1549-9626

文摘

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.