Generalised Nonorthogonal Matrix Elements: Unifying Wick's Theorem and the Slater-Condon Rules

Abstract

Matrix elements between nonorthogonal Slater determinants represent an essential component of many emerging electronic structure methods. However, evaluating nonorthogonal matrix elements is conceptually and computationally harder then their orthogonal counterparts. While several different approaches have been developed, these are predominantly derived from the first-quantised generalised Slater-Condon rules and usually require biorthogonal occupied orbitals to be computed for each matrix element. For coupling terms between nonorthogonal excited configurations, a second-quantised approach such as the nonorthogonal Wick's theorem is more desirable, but this fails when the two reference determinants have a zero many-body overlap. In this contribution, we derive an entirely generalised extension to the nonorthogonal Wick's theorem that is applicable to all pairs of determinants with nonorthogonal orbitals. Our approach creates a universal methodology for evaluating any nonorthogonal matrix element and allows Wick's theorem and the generalised Slater-Condon rules to be unified for the first time. Furthermore, we present a simple well-defined protocol for deriving arbitrary coupling terms between nonorthogonal excited configurations. In the case of overlap and one-body operators, this protocol recovers efficient formulae with reduced scaling, promising significant computational acceleration for methods that rely on such terms.

17 pages, 0 figures

References in corpus (3)

• Reaching Full Correlation through Nonorthogonal Configuration Interaction: A Second-Order Perturbative Approach
• Construction of linearly independent non-orthogonal AGP states
• Efficient computation of matrix elements of generic Slater determinants

Cited by in corpus (10)

• Excited states, symmetry breaking, and unphysical solutions in state-specific CASSCF theory
• Multiscale physics of atomic nuclei from first principles
• Robust formulation of Wick's theorem for computing matrix elements between Hartree-Fock-Bogoliubov wavefunctions
• Generalized nonorthogonal matrix elements for arbitrary excitations
• Interpolating many-body wave functions for accelerated molecular dynamics on the near-exact electronic surface
• Calculation of molecular g-tensors by sampling spin orientations of generalised Hartree-Fock states
• Numerically Stable Resonating Hartree-Fock
• Natural Excitation Framework for Defining the External Space: Uncontracted and Internally Contracted Multireference Nonorthogonal Wavefunction Theories
• Precise Quantum Chemistry calculations with few Slater Determinants
• Slater-Condon Rules and Spin-Orbit Couplings: 2-(2-(2,5-Dimethoxybenzylidene)hydrazineyl)-4-(trifluoromethyl)thiazole a test case