Efficient low-scaling computation of NMR shieldings at the second-order Møller-Plesset perturbation theory level with Cholesky-decomposed densities and an attenuated Coulomb metric.

A method for the computation of nuclear magnetic resonance (NMR) shieldings with second-order Møller-Plesset perturbation theory (MP2) is presented which allows to efficiently compute the entire set of shieldings for a given molecular structure. The equations are derived using Laplace-transformed atomic orbital second-order Møller-Plesset perturbation theory as a starting point. The Z-vector approach is employed for minimizing the number of coupled-perturbed self-consistent-field equations that need to be solved.

Linear and sublinear scaling computation of the electronic g-tensor at the density functional theory level.

We present an efficient and low-scaling implementation of a density functional theory based method for the computation of electronic g-tensors. It allows for an accurate description of spin-orbit coupling effects by employing the spin-orbit mean-field operator. Gauge-origin independence is ensured by the use of gauge-including atomic orbitals.

Gauge-origin dependence in electronic g-tensor calculations.

We present a benchmark study on the gauge-origin dependence of the electronic g-tensor using data from unrestricted density functional theory calculations with the spin-orbit mean field ansatz. Our data suggest in accordance with previous studies that g-tensor calculations employing a common gauge-origin are sufficiently accurate for small molecules; however, for extended molecules, the introduced errors can become relevant and significantly exceed the basis set error. Using calculations with the spin-orbit mean field ansatz and gauge-including atomic orbitals as a reference, we furthermore show that the accuracy and reliability of common gauge-origin approaches in larger molecules depends strongly on the locality of the spin density distribution.

Selected-Nuclei Method for the Computation of Hyperfine Coupling Constants within Second-Order Møller-Plesset Perturbation Theory.

We introduce a new ansatz to compute hyperfine coupling constants of selected nuclei at the level of second-order Møller-Plesset perturbation (MP2) and double-hybrid density functional theory with reduced computational effort, opening the route to the analyis of hyperfine coupling constants of large molecular structures. Our approach is based on a reformulation of the canonical MP2 term in atomic orbitals, thus exploiting the locality of electron correlation. We show that a perturbation-including integral screening reduces the scaling behavior of the number of significant two-electron integrals to sublinear.

Low-scaling first-order properties within second-order Møller-Plesset perturbation theory using Cholesky decomposed density matrices.

An efficient implementation of energy gradients and of hyperfine coupling constants in second-order Møller-Plesset perturbation theory (MP2) is presented based on our fully atomic orbital (AO)-based approach. For the latter, an unrestricted AO-based MP2 formulation is introduced. A reduction in the dependency of the computational efficiency on the size of the basis set is achieved by a Cholesky decomposition and the prefactor is reduced by the resolution-of-the-identity approximation.