Assessing the Orbital-Optimized Unitary Ansatz for Density Cumulant Theory

Abstract

The previously proposed ansatz for density cumulant theory that combines orbital-optimization and a parameterization of the 2-electron reduced density matrix cumulant in terms of unitary coupled cluster amplitudes (OUDCT) is carefully examined. Formally, we elucidate the relationship between OUDCT and orbital-optimized unitary coupled cluster theory and show the existence of near-zero denominators in the stationarity conditions for both the exact and some approximate OUDCT methods. We implement methods of the OUDCT ansatz restricted to double excitations for numerical study, up to the fifth commutator in the Baker-Campbell-Hausdorff expansion. We find that methods derived from the ansatz beyond the previously known ODC-12 method tend to be less accurate for equilibrium properties and less reliable when attempting to describe $H2$ dissociation. New developments are needed to formulate more accurate DCT variants.

17 pages, 4 figures, appendices added

References in corpus (6)

• Array Programming with NumPy
• Exact Parameterization of Fermionic Wave Functions via Unitary Coupled Cluster Theory
• The Pauli principle revisited
• A canonical transformation theory from extended normal ordering
• Relating the pure and ensemble density matrix functional
• Connected three-body terms in single-reference unitary many-body theories: Iterative and perturbative approximations

Cited by in corpus (3)

• Unitary coupled-cluster based self-consistent polarization propagator theory: a quadratic unitary coupled-cluster singles and doubles scheme
• Spin adaptation of the cumulant expansions of reduced density matrices
• Cumulants as the Variables of Density Cumulant Theory: A Path to Hermitian Triples