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This paper introduces Seniority-Zero Quadratic Canonical Transformation Theory (SZ-QCT), an extension of Seniority-Zero Linear Canonical Transformation Theory (SZ-LCT) for solving the Schr枚dinger equation in strongly correlated systems. SZ-QCT relaxes the small-generator constraint of SZ-LCT by incorporating approximate four-body contributions in the Baker-Campbell-Hausdorff expansion. Numerical results demonstrate that SZ-QCT achieves chemical accuracy, particularly in cases requiring larger generators, while maintaining the same $\mathcal{O}(N^8/n_c)$ computational scaling as SZ-LCT.
Unlock chemical accuracy for strongly correlated systems without sacrificing computational cost: SZ-QCT extends canonical transformation theory to include four-body interactions, achieving sub-millihartree errors with $\mathcal{O}(N^8/n_c)$ scaling.
We propose a method to solve the Schr枚dinger 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-millihartree 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, $\mathcal{O}(N^8/n_c)$, where $n_c$ is the number of cores available for the computation
