The electronic mean field configuration interaction method: III – the p-orthogonality constraint

Abstract

The concept of p-orthogonality between electronic states, which generalizes common orthogonality and strong orthogonality, provides a natural hierarchy for group function methods such as the electronic mean field configuration interaction method. In this letter, this theoretical concept is applied in numerical calculations for the first time. The accuracy of the geminal mean field configuration interaction wave functions of simple molecular systems is studied as the orthogonality constraint between the geminals relaxes from 1-orthogonality (that is strong orthogonality) to 2-orthogonality, to no orthogonality constraint at all.

2D-Block Geminals: a non 1-orthogonal and non 0-seniority model with reduced computational complexity

“…The energy of this wave function has been calculated to be −3.295805 hartree, that is about 1 millihartree below that of the APSG ansatz in the same basis, which is −3.294840 hartree (see Table 1 of Ref. 5 ). This establishes a proof of concept that the EPI2O model can be more accurate than the APSG one.…”

“…However, even in the spin-adapted case, optimizing such ansatz is extremely costly from a computational standpoint 6 and has rarely been attempted 5,7 . All popular geminal ansätze can be seen as APG with additional constraints.…”

“…Here, we investigate permutationally invariant 2orthogonality constraints already mentionned in conclusion of Ref. 5 .…”

“…In the past, we have introduced generalized orthogonality constraints between geminals to reduce the computational effort, without sacrificing the indistinguishability of the electrons nor assuming a given seniority 4,5 . In other words, the electron pairs corresponding to the geminals were not fully distinguishable, so that geminal products had still to be antisymmetrized according to the Pauli principle to form bona fide electronic wave functions, and each geminal combined linearly electronic configurations of mixed seniorities.…”

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) 12 ; doubly‐occupied configuration interaction (DOCI) 13–16 ; full CI 17 ; selected CI wavefunctions with a user‐specified set of Slater determinants; antisymmetrized products of geminals (APG) 18–28 ; antisymmetrized products of geminals with disjoint orbital sets (APsetG) 29 ; antisymmetrized product of interacting geminals (APIG) 29–57 ; antisymmetric product of 1‐reference‐orbital interacting geminals (AP1roG; equivalent to pair‐coupled‐cluster doubles) 58 ; 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) 59 ; neural network wavefunctions; coupled‐cluster (CC) with arbitrary excitations (including, but not limited to, CCSD, CCSDT, and CC with seniority‐specific excitations), 1,60–65 geminal coupled‐cluster wavefunctions, 37–39,41,58 generalized CC, and seniority‐increasing CC. We also support these wavefunctions with nonorthogonal orbitals, and linear combinations of any of the aforementioned wavefunctions. The Hamiltonian module contains Hamiltonians commonly used in electronic structure theory.…”