Assessing the Orbital-Optimized Unitary Ansatz for Density Cumulant Theory

TL;DR

This paper critically evaluates the orbital-optimized unitary ansatz in density cumulant theory, revealing limitations in accuracy and reliability, and highlighting the need for improved formulations.

Contribution

It clarifies the relationship between OUDCT and orbital-optimized unitary coupled cluster theory and assesses the accuracy of various OUDCT methods.

Findings

Methods beyond ODC-12 are less accurate for equilibrium properties.

OUDCT methods face issues with near-zero denominators in stationarity conditions.

Current variants are less reliable for H2 dissociation.

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.