ct9b00228_si_001.pdf (1.56 MB)
Efficient Semi-Numerical Implementation of Relativistic Exact Exchange within the Infinite-Order Two-Component Method Using a Modified Chain-of-Spheres Method
journal contribution
posted on 2019-08-23, 15:04 authored by Toni M. Maier, Yasuhiro Ikabata, Hiromi NakaiWe
present an efficient implementation of relativistic exact exchange
within the infinite-order two-component method (IOTC) by employing
a state-of-the-art seminumerical integration technique. For accurate
consideration of the picture change, inherent to two-component methods,
we propose a new scheme based on a relativistic or picture-change
transformation of the density matrix, which provides a simple and
efficient formulation of relativistically transformed quantities such
as the electron density or exact exchange and thus avoids expensive
integral transformations. We show that the new scheme does not introduce
additional numerical or theoretical errors beyond the approximations
of the IOTC method. For the efficient implementation of exact-exchange
integrals, we build upon a modified version of the chain-of-spheres
exact-exchange (COSX) method. In addition to the conventional overlap
and density matrix screening by S- and P-junctions, respectively,
we introduce a new simple screening technique in the sense of the
original COSX method by additionally considering the asymptotic decay
of the integrals over the Coulomb operator within the new F-junctions.
Together with the picture-change transformation of the density matrix,
this modified COSX method is shown to provide superior efficiency
for the calculation of relativistic exact exchange compared to a conventional
analytical direct self-consistent-field implementation of exact exchange.