Strategies for extending geminal-based wavefunctions: Open shells and beyond

Abstract

We discuss some strategies for extending recent geminal-based methods to open-shells by replacing the geminal-creation operators with more general composite boson creation operators, and even creation operators that mix fermionic and bosonic components. We also discuss the utility of symmetry-breaking and restoration, but using a projective (not a variational) approach. Both strategies-either together or separately-give a pathway for extending geminals-based methods to open shells, while retaining the computational efficiency and conceptual simplicity of existing geminal product wavefunctions.

Density Matrices of Seniority-Zero Geminal Wavefunctions

“…In this particular representation the pairs are all localised up-down spin partners. More general pairing schemes could be engineered, 45 though for clarity we will keep the representation (1). The vacuum |θ is destroyed by each S − i and is an eigenvector of each S z i…”

“…The best known computational approach is due to Ryser, 69 which still does not scale polynomially. Like (45),…”

Fanpy: A Python Library for Prototyping Multideterminant Methods in Ab Initio Quantum Chemistry

“…The overlap can be provided as a standalone function or defined within a class structure, templated from an abstract base class. The following wavefunctions have already been implemented: configuration interaction (CI) with single and double excitations (CISD) [8]; doubly-occupied configuration interaction (DOCI) [9][10][11][12]; full CI [13]; selected CI wavefunctions with a userspecified set of Slater determinants; antisymmetrized products of geminals (APG) [14][15][16][17][18][19][20][21][22][23][24]; an-tisymmetrized products of geminals with disjoint orbital sets (APsetG) [25]; antisymmetrized product of interacting geminals (APIG) ; antisymmetric product of 1-reference-orbital interacting geminals (AP1roG; equivalent to pair-coupled-cluster doubles) [54]; antisymmetric product of rank-two interacting geminals (APr2G) [2]; determinant ratio wavefunctions [1]; antisymmetrized products of tetrets (4-electron wavefunctions) [1]; matrix product states (MPS) [55]; neural network wavefunctions; coupled-cluster (CC) with arbitrary excitations (including, but not limited to, CCSD, CCSDT, and CC with seniority-specific excitations) [1,[56][57][58][59][60][61], geminal coupled-cluster wavefunctions [33-35, 37, 54], generalized CC, and seniority-increasing CC. We also support these wavefunctions with nonorthogonal orbitals, and linear combinations of any of the aforementioned wavefunctions.…”

“…• The objective module is responsible for combining the wavefunction and the Hamiltonian to form an equation or a system of equations that represents the Schrödinger equation. In Fanpy, the objective function can be the variational optimization of the expectation value of the energy [75][76][77][78][79], the projected Schrödinger equation [25,37,50], or a local energy expression to be sampled (as in variational quantum Monte Carlo) [80][81][82][83][84][85].…”

Variational determination of the two-electron reduced density matrix within the doubly occupied configuration interaction scheme: An extension to the study of open-shell systems

“…Consequently, strategies aimed at achieving suitable descriptions of open-shell N-electron systems by means of variational determinations of the 2-RDM elements or by geminal-based approaches have been reported by several authors. [19][20][21][22] Although this task has been undertaken by means of different procedures, one of the most successful approaches proposes the addition of some hydrogen atoms, which are situated at infinite distances from chemical species of interest, e.g., an openshell molecule or radical (neutral or ionic), constituting a kind of aggregate in the singlet state. In a subsequent step, the 2-RDM elements of the whole system are variationally evaluated satisfying certain imposed N-representability conditions.…”