Range Separation Method for Density Functional Theory Based on Two-Electron Infinite-Order Two-Component Hamiltonian.

Abstract

The range separation method for density functional theory (DFT) was extended to a two-component relativistic theory based on the unitary transformation of one- and two-electron operators and a density operator. In the framework of the spin-free infinite-order two-component Hamiltonian, we implemented several types of two-electron integrals of range-separated two-electron interactions arising from the unitary transformation. Numerical assessments were performed using long-range-corrected (LC)-DFT, which utilizes the range separation of an exchange functional. The present method successfully reproduced the reference values obtained by the four-component LC-DFT calculations when the whole unitary transformations of one-electron, full-range, and range-separated two-electron operators and a density operator were considered. An efficient scheme for the unitary transformation, which is termed the local unitary transformation (LUT), was also applied to the range-separated two-electron term and other operators. The LUT method reduced the computational costs of the LC-DFT calculations significantly without any loss of accuracy.