Seniority‐Zero Quadratic Canonical Transformation Theory

We propose a method to solve the Schrödinger equation for systems with static/strong electron correlation using Hamiltonian transformations. Building on our previous work on seniority‐zero canonical transformation theory, which seeks a unitary transformation that maps the Hamiltonian into the seniority‐zero space, this method presents an alternative way of evaluating the Baker–Campbell–Hausdorff (BCH) expansion based on quadratic canonical transformation theory. The extension aims to relax the small‐generator constraint by allowing approximate four‐body contributions in the expansion, thus expanding the class of excitations previously allowed in SZ‐LCT, where only approximate three‐body operators were retained. Numerical tests reveal that the seniority‐zero quadratic canonical transformation method (SZ‐QCT) delivers good accuracy, with most errors within chemical accuracy. In particular, SZ‐QCT shows sub‐milli Hartree errors in cases where larger generators are needed to recover the residual dynamic correlation. The computational scaling of SZ‐QCT is the same as that of SZ‐LCT, , where is the number of cores available for the computation.