Seniority-Zero Canonical Transformation Theory: Reducing Truncation Error with Late Truncation

TL;DR

The paper tackles the challenge of combining static and dynamic correlation by transforming the electronic Hamiltonian into a seniority-zero form, enabling accurate treatment with a DOCI-like reference. It develops LT-SZCT, which uses a unitary transform $e^{\hat{A}}$ and the BCH expansion, computing the first three commutators exactly for a seniority-zero reference and approximating higher terms via operator decomposition to retain only one- and two-body operators plus RDMs. The approach yields near-quantitative accuracy across test cases (H$_8$, BH, and N$_2$) with mean absolute errors around $10^{-4}$ E$_h$, while achieving favorable scaling through seniority-zero reductions and parallelization. This method offers a practical route to incorporate dynamic correlation into strongly correlated, multireference contexts with potential extensions to more sophisticated SZ ansätze and automatic generator-norm control.

Abstract

We show how to add the effects of residual electron correlation to a reference seniority-zero wavefunction by making a unitary transformation of the true electronic Hamiltonian into seniority-zero form. The transformation is treated via the Baker Campbell Hausdorff (BCH) expansion and the seniority-zero structure of the reference is exploited to evaluate the first three commutators exactly; the remaining contributions are handled with a recursive commutator approximation, as is typical in canonical transformation methods. By choosing a seniority-zero reference and using parallel computation, this method is practical for small- to medium-sized systems. Numerical tests show high accuracy, with errors $\sim 10^{-4}$ Hartree.

Figures (6)

• Figure 1: Dissociation curve for the linear H8 chain in the STO-6G basis set as a function of nearest-neighbor distance. The full configuration interaction (FCI) reference is compared to the doubly-occupied configuration interaction (DOCI) seniority-zero wavefunction, with and without orbital optimization (OPT). The late-truncation seniority-zero canonical transformation approach presented in the paper is labeled LT-SZCT.
• Figure 2: The energy difference between the LT-SZCT and FCI, in $mE_h$, for the dissociation of the linear H8 chain in the STO-6G basis set. The lack of variational character indicates that there are (small) errors associated with the approximation of the BCH expansion.
• Figure 3: BH dissociation energy curve in the 6-31G basis set.
• Figure 4: Energy deviations relative to FCI for SZ-LCT and LT-SZCT, in $mE_h$, for dissociating BH dissociation in the 6-31G basis set.
• Figure 5: N2 dissociation energy curve in STO-6G basis set.