Seniority-zero linear canonical transformation theory

Abstract

We propose a method to solve the electronic Schrödinger equation for strongly correlated systems by applying a unitary transformation to reduce the complexity of the physical Hamiltonian. In particular, we seek a transformation that maps the Hamiltonian into the seniority-zero space: seniority-zero wavefunctions are computationally simpler, but still capture strong correlation within electron pairs. The unitary rotation is evaluated using the Baker–Campbell–Hausdorff expansion, truncated to two-body operators through the operator decomposition strategy of canonical transformation (CT) theory, which rewrites higher-rank terms approximately in terms of one- and two-body operators. Unlike conventional approaches to CT theory, the generator is chosen to minimize the size of non-seniority-zero elements of the transformed Hamiltonian. Numerical tests reveal that this Seniority-zero Linear Canonical Transformation (SZ-LCT) method delivers highly accurate results, usually with sub-milliHartree error. The effective computational scaling of SZ-LCT is O(N8/nc), where nc is the number of cores available for the computation.