Seniority-zero Linear Canonical Transformation Theory

Abstract: We propose a method to solve the electronic Schr\"odinger 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, since such Hamiltonians are computationally more tractable while still capturing strong correlation within electron pairs. The unitary rotation is evaluated using the Baker--Campbell--Hausdorff (BCH) expansion, truncated to two-body operators via the operator-decomposition strategy of canonical transformation (CT) theory, which rewrites higher-rank terms approximately in terms of one- and two-body operators. The method was tested on three molecular systems: H$6$ in the STO-6G basis, BeH$_2$ along the standard C${2v}$ insertion pathway, and BH in the 6-31G basis. In all cases, the Seniority-zero Linear Canonical Transformation (SZ-LCT) method delivers highly accurate results, with most errors on the order of $10^{-4}$ Hartree. Additionally, SZ-LCT has a cost of $O(N^7/n_c)$, where $n_c$ is the number of CPU cores, making it comparable to single-reference methods when the number of available cores is at least equal to the number of orbitals.