Scalable Electron Correlation Methods. 6. Local Spin-Restricted Open-Shell Second-Order Møller–Plesset Perturbation Theory Using Pair Natural Orbitals: PNO-RMP2

Abstract

We present a (near) linear scaling implementation of high-spin open-shell Møller–Plesset perturbation theory using pair natural orbitals (PNO-RMP2). The theory is based on a new variant of open-shell MP2 which is fully spin-adapted and uses a single set of spin-free amplitudes, as in closed-shell MP2. This method, denoted SROMP2, is invariant to unitary orbital transformations within the closed, open, and virtual orbital subspaces. Accordingly, only a single set of PNOs per spatial orbital pair is needed, and the efficiency is similar to closed-shell calculations. The PNOs are obtained using a semicanonical approximation with large domains of projected atomic orbitals (PAOs). Linear scaling is achieved provided that the open-shell orbitals are local, and distant pairs are treated by multipole approximations. The method is efficiently parallelized. The convergence of ionization and reaction energies as a function of the PAO and PNO domain sizes is demonstrated and found to be very similar as for closed-shell calculations. The suitability of the PNOs for explicitly correlated PNO-RCCSD-F12 calculations is also tested. So far, this method is only simulated using a conventional program with appropriate projections to the PAO and PNO subspaces. It is demonstrated for radical stabilization energies as well as ionization potentials that the errors caused by the local domain approximations with our default thresholds are negligible.

The Molpro quantum chemistry package

“…This problem is much alleviated in the explicitly correlated variants, since the explicitly correlated terms not only reduce basis set incompleteness errors, but also strongly reduce the domain errors. [44][45][46][47] Since 2012, a new generation of local coupled cluster methods has been developed, [48][49][50][51][52][53][54][55][56][57][58] which are based on domains of pair natural orbitals (PNOs). These methods, which are much more accurate and efficient than PAO methods, are described in section II D 3.…”

“…56. A new revision of the methods that supports both closed-shell and open-shell molecules, namely PNO-RMP2-F12, 57 PNO-RCCSD(T)-F12, and PNO-UCCSD(T)-F12 58 is featured in Molpro 2020 (the prefix "L" in the names of the methods is omitted for simplicity). Explicitly correlated distinguishable cluster methods (see Sec.…”

“…We describe improvements of coupled cluster methods (distinguishable cluster [33][34][35][36][37] and quasi-variational coupled-cluster [38][39][40][41][42][43] ), as well as recent developments of accurate electron correlation treatments for large molecules. This includes highly accurate explicitly correlated local coupled cluster methods based on pair natural orbitals [PNO-LCCSD(T)-F12] [44][45][46][47][48][49][50][51][52][53][54][55][56][57][58] and embedding methods. 59 In the multiref-erence area, a new multiconfiguration (complete active space) self-consistent field (MC-SCF/CASSCF) program has been developed, 60,61 which allows efficient optimizations of wavefunctions for large systems, such as transition metal clusters.…”

Linear-Scaling Open-Shell MP2 Approach: Algorithm, Benchmarks, and Large-Scale Applications

“…The DLPNO family of methods employs the multireference second-order Ansatz of the n -electron valence state perturbation theory (NEVPT2) 99 for the PNO generation, 63 while the PNO methods of Werner and Ma utilize a spin-adapted MP2 formulation (PNO-RMP2). 65 Both approaches share the benefit of spin-free amplitudes useful to obtain a spin-restricted set of PNOs at the price of a somewhat more complicated second-order treatment.…”

A case study of density functional theory and domain-based local pair natural orbital coupled cluster for vibrational effects on EPR hyperfine coupling constants: vibrational perturbation theory versus ab initio molecular dynamics

“…When it comes to the underlying electronic structure method, the advent of local correlation approximations has alleviated the most prominent bottleneck of post-HF correlation methods, namely the high computational scaling with system size [24][25][26][27][28][29][30][31]. As a consequence, modern approximations for coupled cluster methods are now applicable in cases where a few years ago only DFT was available [32].…”