SENIORITY-ZERO CANONICAL TRANSFORMATION THEORY

Abstract

The standard method for solving the electronic Schrodinger equation for chemical systems is to add dynamic (CI, CC, MBPT) correlation to a single reference wave function, usually Hartree-Fock. When static correlation is important, i.e., when there are multiple important electron configurations—one instead uses explicitly multireference methods like CASSCF or DMRG, and then adds corrections for dynamic correlation. Such approaches are typically very expensive, with cost growing exponentially with the orbital subspace that contains the dominant electron configurations. There are very few methods in the literature that treat both static (multireference) and dynamic correlation together, and they usually suffer from poor scalability and/or technical/numerical problems like intruder states. In this thesis, we propose a method based on the ideas of canonical transformation (CT) theory to add dynamic correlation on top of multireference wave functions. Specifically, we are interested in seniority-zero (SZ) wave functions. This type of wave function is used to describe the static part of the correlation, and due to the facility to compute its reduced density matrices, it becomes the perfect reference for a method based on CT theory. Because our static correlation model is determined simultaneously with its dynamic correlation correction, our method treats static and dynamic correlation on equal footing.Specifically, we apply a unitary transformation to a Hamiltonian of a physical system, seeking the specific transformation that makes the final Hamiltonian seniority-zero. This strategy is motivated by the realization that it is relatively easy to solve seniority-zero Schrodinger equations, a task that would be especially easy on a quantum computer. To evaluate the action of the unitary transformation we use the Baker–Campbell–Hausdorff (BCH) formula, with two different truncation schemes. In the first scheme, we truncate each commutator in the expansion to a maximum of two-body terms using the operator decomposition technique introduced in CT theory; we call this method seniority-zero LCT (SZ-LCT). In the second, we delay the truncation to every double commutator, expecting thereby to recover more information about the system’s correlation; we call this method seniority-zero QCT (SZ-QCT). We tested SZ-LCT in H4, H6, BeH2; and SZ-QCT in H4, H6. For H4, both truncation schemes yielded energy errors ∼ 1mEh. Although SZ-QCT is an improvement over linear truncation, our results indicate that when the seniority-zero reference already provides a good approximation to the true wave function, the added complexity of the transformation does not enhance accuracy. For H6 and BeH2, the SZ-LCT method produced average energy errors ∼ 10−2Eh, with the largest deviations occurring near the equilibrium bond length. In contrast, testing SZ-QCT on H6 revealed an improvement over linear truncation; while the average energy error remains of the same order, with SZ-QCT the errors are stable along the entire dissociation curve.