Assessing the orbital-optimized unitary Ansatz for density cumulant theory

Area of Science:

• Quantum chemistry
• Computational physics
• Theoretical chemistry

Background:

• Density cumulant theory offers a framework for electronic structure calculations.
• Combining orbital optimization with density matrix cumulant parameterization is an active research area.

Purpose of the Study:

• To rigorously examine the orbital-optimized unitary coupled cluster amplitudes (OUDCT) Ansatz.
• To investigate the relationship between OUDCT and other advanced electronic structure methods.
• To assess the numerical performance and limitations of OUDCT variants.

Main Methods:

• Formal analysis of the OUDCT Ansatz and its stationarity conditions.
• Implementation of OUDCT methods restricted to double excitations.
• Numerical studies up to the fifth commutator in the Baker-Campbell-Hausdorff expansion.

Main Results:

• Identified near-zero denominators in the stationarity conditions of OUDCT methods.
• Found that OUDCT variants beyond ODC-12 exhibit reduced accuracy for equilibrium properties.
• Observed decreased reliability in describing H2 dissociation with higher-order OUDCT methods.

Conclusions:

• The OUDCT Ansatz requires further theoretical development for improved accuracy and reliability.
• New strategies are necessary to formulate more robust density cumulant theory variants.
• Current OUDCT implementations face challenges in accurately capturing molecular behavior, particularly during dissociation.