Attenuated coupled cluster: a heuristic polynomial similarity transformation incorporating spin symmetry projection into traditional coupled cluster theory

Abstract

In electronic structure theory, restricted single-reference coupled cluster (CC) captures weak correlation but fails catastrophically under strong correlation. Spinprojected unrestricted Hartree-Fock (SUHF), on the other hand, misses weak correlation but captures a large portion of strong correlation. The theoretical description of many important processes, e.g. molecular dissociation, requires a method capable of accurately capturing both weak-and strong correlation simultaneously, and would likely benefit from a combined CC-SUHF approach. Based on what we have recently learned about SUHF written as particle-hole excitations out of a symmetry-adapted reference determinant, we here propose a heuristic coupled cluster doubles model to attenuate the dominant spin collective channel of the quadratic terms in the coupled cluster equations. Proof of principle results presented here are encouraging and point to several paths forward for improving the method further.

Variational method for integrability-breaking Richardson-Gaudin models

“…While such models are solvable by U (1)-breaking BCS mean-field theory in the thermodynamic limit, it is important to obtain an accurate description for mediumsize systems as well 46,108,109 . In fact, it has been shown that the Richardson-Gaudin equations are equivalent to the BCS mean-field equations for thermodynamically large systems, and as such the BCS wave function and the Bethe ansatz wave function coincide in this limit 53 .…”

Employing broken symmetry effects from unrestricted coupled cluster wave function to determine dynamic and non‐dynamic electron correlation during triple bond breaking in the N2 molecule

“…However, in the case of projected CC wave functions, there are two possibilities that differ in the way of generating the broken symmetry CCSD wave function, namely by variational approach or similarity transformation . But, the most encouraging seems to be the possibilities of the projected CCSD method.…”

Spin-projected generalized Hartree-Fock method as a polynomial of particle-hole excitations

“…17 we have explored the simple wave function ansatz |Ψ = exp(T )|PHF in a variational framework as a precursor to more computationally useful approaches which use the correlator exp(T ) to define a similarity-transformed Hamiltonian as in traditional coupled cluster theory. Our work on attenuated coupled cluster [26] follows similar ideas. Much earlier work explored writing the PHF wave function as an exponential of higher-order cluster operators (e.g.…”

“…where both contain only double excitation operators which, like the SGHF excitation operators, are parameterized in terms of the Thouless transformation taking RHF to the broken-symmetry determinant. This observation for number and S 2 spin projection forms the basis for our work on what we call attenuated coupled cluster, [26] in which we add the SUHF or PBCS polynomial to the coupled cluster exponential, thereby substantially mitigating the failures of traditional coupled cluster theory in the stongly correlated limit. Both the SUHF and the PBCS polynomials are examples of (univariate) hypergeometric functions, as indeed is the exponential of coupled cluster theory; the SGHF polynomial is a multivariate generalization.…”