An efficient implementation of two-component relativistic exact-decoupling methods for large molecules

TL;DR

This paper introduces an efficient algorithm for large-scale two-component relativistic calculations that incorporate spin-orbit coupling, utilizing local approximations and symmetry to significantly speed up computations for large molecules.

Contribution

The paper presents a new, optimized implementation of relativistic exact-decoupling methods that reduces computational cost for large molecules by combining local schemes and symmetry considerations.

Findings

Successfully applied to silver clusters with up to 309 atoms

Achieved significant speed-up in relativistic density functional calculations

Demonstrated accurate extrapolation of cohesive energy to bulk materials

Abstract

We present an efficient algorithm for one- and two-component relativistic exact-decoupling calculations. Spin-orbit coupling is thus taken into account for the evaluation of relativistically transformed (one-electron) Hamiltonian. As the relativistic decoupling transformation has to be evaluated with primitive functions, the construction of the relativistic one-electron Hamiltonian becomes the bottleneck of the whole calculation for large molecules. For the established exact-decoupling protocols, a minimal matrix operation count is established and discussed in detail. Furthermore, we apply our recently developed local DLU scheme [J. Chem. Phys. 136 (2012) 244108] to accelerate this step. With our new implementation two-component relativistic density functional calculations can be performed invoking the resolution-of-identity density-fitting approximation and (Abelian as well as non-Abelian) point group symmetry to accelerate both the exact-decoupling and the two-electron part. The capability of our implementation is illustrated at the example of silver clusters with up to 309 atoms, for which the cohesive energy is calculated and extrapolated to the bulk.