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Aufbau Suppressed Coupled Cluster Theory for Doubly Excited States

Qasim Javed, Harrison Tuckman, Eric Neuscamman

TL;DR

This work extends Aufbau suppressed coupled cluster (ASCC) theory to doubly excited states by initializing the zeroth-order wavefunction to capture the dominant doubly excited configurations while preserving CCSD-like scaling ($O(N^6)$). It develops a perturbative, multi-space framework with a de-excitation operator to suppress the Aufbau determinant and carefully partitions the cluster operator into non-primary, mixed, and primary parts, enabling accurate 1-CSF and multi-CSF doubly excited states at CCSD-level cost. Across 1-CSF and 2-CSF tests, ASCC achieves excitation energies within roughly $0.15$–$0.30$ eV of benchmark references, substantially outperforming EOM-based approaches and rivaling higher-level CC methods in this challenging regime. The results demonstrate strong potential for applying ASCC to multi-configurational double excitations while highlighting open questions about generalizing to larger primary spaces and more complex multi-reference cases, with promising implications for photochemistry and spectroscopy.

Abstract

We generalize the Aufbau suppressed coupled cluster formalism into the realm of doubly excited states by deriving, implementing, and testing a wave function initialization strategy that allows the zeroth order wave function to match the largest configurations of a doubly excited reference wave function while maintaining the method's overall asymptotic cost parity with ground state singles and doubles theory. Starting from state-averaged complete active space self consistent field references, this approach produces highly accurate excitation energies for states dominated by a single doubly excited determinant, as well as states in glyoxal and similar molecules where two different doubly excited determinants have large weights. Typical excitation energy errors in both types of states are on the order of 0.15 eV, with the largest observed error being 0.3 eV. These errors stand in stark contrast to equation of motion methods, where typical errors are 4 to 6 eV at the singles and doubles level and 0.4 to 0.8 eV at the full triples level. It remains an open question how best to generalize the Aufbau suppression approach into an even wider variety of multi-configurational double excitations, but these early results offer strong motivation for further investigation.

Aufbau Suppressed Coupled Cluster Theory for Doubly Excited States

TL;DR

This work extends Aufbau suppressed coupled cluster (ASCC) theory to doubly excited states by initializing the zeroth-order wavefunction to capture the dominant doubly excited configurations while preserving CCSD-like scaling (). It develops a perturbative, multi-space framework with a de-excitation operator to suppress the Aufbau determinant and carefully partitions the cluster operator into non-primary, mixed, and primary parts, enabling accurate 1-CSF and multi-CSF doubly excited states at CCSD-level cost. Across 1-CSF and 2-CSF tests, ASCC achieves excitation energies within roughly – eV of benchmark references, substantially outperforming EOM-based approaches and rivaling higher-level CC methods in this challenging regime. The results demonstrate strong potential for applying ASCC to multi-configurational double excitations while highlighting open questions about generalizing to larger primary spaces and more complex multi-reference cases, with promising implications for photochemistry and spectroscopy.

Abstract

We generalize the Aufbau suppressed coupled cluster formalism into the realm of doubly excited states by deriving, implementing, and testing a wave function initialization strategy that allows the zeroth order wave function to match the largest configurations of a doubly excited reference wave function while maintaining the method's overall asymptotic cost parity with ground state singles and doubles theory. Starting from state-averaged complete active space self consistent field references, this approach produces highly accurate excitation energies for states dominated by a single doubly excited determinant, as well as states in glyoxal and similar molecules where two different doubly excited determinants have large weights. Typical excitation energy errors in both types of states are on the order of 0.15 eV, with the largest observed error being 0.3 eV. These errors stand in stark contrast to equation of motion methods, where typical errors are 4 to 6 eV at the singles and doubles level and 0.4 to 0.8 eV at the full triples level. It remains an open question how best to generalize the Aufbau suppression approach into an even wider variety of multi-configurational double excitations, but these early results offer strong motivation for further investigation.
Paper Structure (19 sections, 20 equations, 3 figures, 2 tables)

This paper contains 19 sections, 20 equations, 3 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Theory
  3. Aufbau Suppression
  4. Doubly Excited States
  5. Truncating the Cluster Operator
  6. Perturbative Setup
  7. Zeroth Order
  8. Mixed Amplitudes with 4+ Non-Primaries
  9. All-Non-Primary Doubles
  10. Other Amplitudes
  11. Multi-Configurational Considerations
  12. Comparison to Singly Excited ASCC
  13. Results
  14. Computational Details
  15. Single-CSF Tests
  16. ...and 4 more sections

Figures (3)

  • Figure 1: The primary hole (h) and particle (p) orbitals of the CASSCF reference for the 1-CSF doubly excited states.
  • Figure 2: The primary hole (h) and particle (p) orbitals of the (3o,4e) CASSCF reference for the 2-CSF examples.
  • Figure 3: Comparison of CASPT2 and ASCC on seven 1-CSF states and one 2-CSF state, with mean unsigned errors across these eight states shown as dashed lines. We report CASPT2 results both for the the same (2o,2e) or (3o,4e) active spaces used by ASCC and for the larger active spaces employed by the QUEST benchmark's CASPT2 results.