Improving Aufbau Suppressed Coupled Cluster Through Perturbative Analysis (2501.10515v2)

Abstract: Guided by perturbative analysis, we improve the accuracy of Aufbau suppressed coupled cluster theory in simple single excitations, multi-configurational single excitations, and charge transfer excitations while keeping the cost of its leading-order terms precisely in line with ground state coupled cluster. Combining these accuracy improvements with a more efficient implementation based on spin-adaptation, we observe high accuracy in a large test set of single excitations, and, in particular, a mean unsigned error for charge transfer states that outperforms equation-of-motion coupled cluster theory by 0.25 eV. We discuss how these results are achieved via a systematic identification of which amplitudes to prioritize for single- and multi-configurational excited states, and how this prioritization differs in important ways from the ground state theory. In particular, our data show that a partial linearization of the theory increases accuracy by mitigating unwanted side effects of Aufbau suppression.

• The paper introduces perturbative adjustments in ASCC to accurately capture weak correlation effects in excited states.
• It employs a partial linearization scheme to mitigate side effects from suppressing the Aufbau determinant in coupled cluster theory.
• Benchmark results reveal reduced mean unsigned errors, notably enhancing charge transfer excitation accuracy compared to standard EOM-CCSD.

Overview of "Improving Aufbau Suppressed Coupled Cluster Through Perturbative Analysis"

This paper presents advancements in the field of quantum chemistry, specifically focusing on improving the accuracy of excited-state calculations within coupled cluster (CC) theory by employing perturbative analysis techniques. The paper elaborates on Aufbau suppressed coupled cluster (ASCC) theory, which aims to enhance the treatment of excited states while maintaining computational efficiency akin to ground state coupled cluster with singles and doubles (CCSD).

ASCC is constructed to address excited-state calculations by introducing a de-excitation operator in conjunction with the traditional excitation operator. This approach effectively suppresses the original referential determinant, termed the Aufbau determinant, to achieve a more accurate description of excited states. The perturbative analysis in this paper identifies the critical excitation amplitudes needed to capture weak correlation effects in excited states accurately.

Perturbative Improvements

The primary focus is the systematic analysis and improvement of ASCC using many-body perturbation theory (MBPT). The authors explore the implementation of first-order amplitudes specific to excited configurations, revealing differences in the perturbative hierarchy compared to ground state CCSD. Key findings include:

• Identification of specific higher-order excitation amplitudes that appear at lower perturbative orders in ASCC compared to ground state CCSD.
• Introduction of a partial linearization scheme aimed at mitigating undesirable side effects resulting from the Aufbau suppression strategy.
• Recognition of multiple ansatz definitions within ASCC to accommodate varied excited-state characteristics, bridged by a practical solution of averaging outcomes for cases where non-zero Aufbau determinant coefficients exist.

Numerical and Practical Implications

The paper benchmarked ASCC's performance against standard EOM-CCSD methods on a comprehensive set of excited states, particularly highlighting its accuracy in handling charge transfer excitations. ASCC demonstrated comparable efficacy in single-configurational valence excited states and significantly improved results for charge transfer excitable states, reducing mean unsigned errors by up to 0.25 eV compared to EOM-CCSD. These findings underscore its potential for tackling complex excitations where orbital relaxation effects are prominent.

Despite maintaining parity with CCSD in leading-order computational cost, ASCC shows higher accuracy in certain excited-state types due to its state-specific approach. The strategic incorporation of primary and mixed amplitudes, informed by perturbative analysis, ensures accuracy improvements without burdening computational overhead.

Future Directions

The findings in this paper indicate several future research pathways:

• Expansion to include non-iterative corrections to address the perturbative imbalance in energy calculations between excited states and ground states.
• Exploration of alternative reference wave functions to investigate the impact of initial approximations on ASCC accuracy.
• Application of local correlation methods to efficiently handle large systems, particularly in charge transfer scenarios or systems involving significant long-range interactions.
• Extension to more complex excitations, such as those involving core orbitals or exhibiting multiconfigurational characters.

In conclusion, this paper advances ASCC theory by leveraging perturbative techniques and identifies opportunities for further refinement. This work also highlights the importance of state-specific methodologies in accurately predicting excited-state properties, paving the way for broader applications in computational chemistry.