title: Laplace-transformed atomic orbital-based Møller-Plesset perturbation theory for relativistic two-component Hamiltonians.
abstract: We present a formulation of Laplace-transformed atomic orbital-based second-order Møller-Plesset perturbation theory (MP2) energies for two-component Hamiltonians in the Kramers-restricted formalism. This low-order scaling technique can be used to enable correlated relativistic calculations for large molecular systems. We show that the working equations to compute the relativistic MP2 energy differ by merely a change of algebra (quaternion instead of real) from their non-relativistic counterparts. With a proof-of-principle implementation we study the effect of the nuclear charge on the magnitude of half-transformed integrals and show that for light elements spin-free and spin-orbit MP2 energies are almost identical. Furthermore, we investigate the effect of separation of charge distributions on the Coulomb and exchange energy contributions, which show the same long-range decay with the inter-electronic/atomic distance as for non-relativistic MP2. A linearly scaling implementation is possible if the proper distance behavior is introduced to the quaternion Schwarz-type estimates as for non-relativistic MP2.
authors.affiliation: Section of Theoretical Chemistry, VU University Amsterdam, De Boelelaan 1083, 1081 HV Amsterdam, The Netherlands.
authors.forename: Benjamin
authors.initials: B
authors.lastname: Helmich-Paris
authors.affiliation: CTCC, Department of Chemistry, UIT The Arctic University of Norway, N-9037 Tromø, Norway.
authors.forename: Michal
authors.initials: M
authors.lastname: Repisky
authors.affiliation: Section of Theoretical Chemistry, VU University Amsterdam, De Boelelaan 1083, 1081 HV Amsterdam, The Netherlands.
authors.forename: Lucas
authors.initials: L
authors.lastname: Visscher