Novel stochastic methods in electronic structure theory and their application

Abstract

This cumulative thesis is based on four publications that describe newly developed methods within full CI quantum Monte-Carlo (FCIQMC) and their application to challenging systems of biochemical interest. FCIQMC is a well parallelised, stochastic electronic structure method that enables the correlation of many electrons by taking advantage of the sparsity of the wave function expressed in a finite basis. The new methods are about: a.) an improved excitation generator, that benefits the performance of FCIQMC, in particular for localised orbital bases, b.) fine-grained control over the structure of the wave function by developing a stochastic version of the generalized active space (GAS) method, including its mean-field optimised variant GASSCF, and c.) targeting states of desired spin in a basis of Slater determinants (SDs). The improved excitation generator is an extension of the precomputed heat bath (PCHB) strategy with more effective sampling of double excitations and a novel approach for non-uniform sampling of single excitations. The non-uniform sampling of single excitations relies on spatially decaying integrals and matrix elements. An overall efficiency gain by a factor of two to four, as measured by variance reduction per wall-clock time, is shown. In the GAS method the active space is partitioned into multiple disjoint subspaces. A full configuration interaction (CI) expansion is generated for each subspace, while the interspace excitations are restricted using chemically motivated constraints on the occupation numbers per subspace. Within FCIQMC these constraints are efficiently encoded in precomputed probability distributions which removes nearly all runtime overheads of GAS. Stochastic GAS reduced density matrices (RDMs) are stochastically sampled, allowing orbital relaxations via stochastic GASSCF, and direct evaluation of properties that can be extracted from density matrices, such as the spin expectation value. Restricted active space (RAS) or other truncated wave function schemes are special cases of the GAS strategy, thus they are promptly available by an appropriate choice of the GAS subspaces and corresponding constraints. The efficient implementation of the stochastic GAS method, using hybrid parallelisation, allowed e.g. uncontracted stochastic MRCISD calculations on the quintet - triplet spin gap in a Fe-porphyrin model complex, with up to 96 electrons and 159 orbitals and a large CAS(32, 34) active space reference wave function, greatly improving previous estimates. The spin-purification method allows targeting states of desired spin in SDs. This is achieved by using a modified Hamiltonian H' = H + J S², with a suitable J > 0 that artificially enforces anti-ferromagnetic order. While a basis of configuration state functions (CSFs) can target spin states by construction, there are conceptual and practical advantages of using a SD basis while ensuring the correct spin. It can be directly coupled with other rich theory and codes that are (not yet) available in a CSF basis; an incomplete list includes: transcorrelated Hamiltonians, tailored coupled cluster, or stochastic perturbation theory. In addition, while convergence with respect to walker number is usually faster for CSFs, the SD basis is numerically cheaper and allows more walkers for the same computational effort. A particular notable application of the new method is a trinuclear [Mn3O4] metal complex, serving as a biomimetic for the active centre of the oxygen evolving complex (OEC), with a non-monotonic spin ladder whose particular electronic features could be reproduced within a CAS(55, 38) model active space.