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Unitary Coupled-Cluster based Self-Consistent Electron Propagator Theory for Electron-Detached and Electron-Attached States: A Quadratic Unitary Coupled-Cluster Singles and Doubles Method and Benchmark Calculations

Yu Zhang, Junzi Liu

TL;DR

This work develops a Hermitian, unitary-CC-based self-consistent electron propagator framework (UCC-EPT) and implements two practical IP/EA schemes: IP/EA-UCC3 (perturbative) and IP/EA-qUCCSD (quadratic commutator truncation). By deriving and solving the corresponding 2×2 eigenvalue problems within a self-consistently defined excitation manifold, the authors benchmark these methods against IP/EA-EOM-CCSD, IP/ADC(3-4), and FCI references. The IP-qUCCSD method delivers the highest accuracy among Hermitian IP methods for 1h-dominated states (MAD ≈ 0.19 eV, SD ≈ 0.13 eV) and even surpasses IP-ADC(4) without triple contributions, while EA results show parity with lower-order methods for 1p-dominated energies and EA-ADC(4) performing best for open-shell cases. Overall, UCC-EPT offers a promising non-perturbative, Hermitian route to accurate IP and EA predictions, with planned extensions to higher-order commutator schemes to further improve performance and robustness.

Abstract

A unitary coupled-cluster (UCC)-based self-consistent electron propagator theory (EPT) is proposed for the description of electron-detached and electron-attached states. Two practical schemes, termed IP/EA-UCC3 and IP/EA-qUCCSD, are developed and implemented within the UCC singles and doubles (UCCSD) framework using the perturbative and commutator-based truncation strategy for the similarity-transformed Hamiltonian $\bar{H}$. The numerical performance of these UCC-based EPT methods is extensively evaluated against full configuration interaction (FCI) reference data and compared with established approaches, including IP/EA-ADC(3), IP/EA-ADC(4) and IP/EA-EOM-CCSD. Benchmark calculations demonstrate that IP-qUCCSD achieves the highest overall accuracy among Hermitian ionized-state methods for one-hole (1h)-dominated IPs of closed-shell systems, with a mean absolute deviation (MAD) of 0.19 eV and standard deviation (SD) of 0.13 eV. Remarkably, despite the absence of triple-excitation contributions, IP-qUCCSD outperforms the higher-order ADC(4) method. For one-particle (1p)-dominated EA calculations, all tested methods exhibit comparable accuracy.

Unitary Coupled-Cluster based Self-Consistent Electron Propagator Theory for Electron-Detached and Electron-Attached States: A Quadratic Unitary Coupled-Cluster Singles and Doubles Method and Benchmark Calculations

TL;DR

This work develops a Hermitian, unitary-CC-based self-consistent electron propagator framework (UCC-EPT) and implements two practical IP/EA schemes: IP/EA-UCC3 (perturbative) and IP/EA-qUCCSD (quadratic commutator truncation). By deriving and solving the corresponding 2×2 eigenvalue problems within a self-consistently defined excitation manifold, the authors benchmark these methods against IP/EA-EOM-CCSD, IP/ADC(3-4), and FCI references. The IP-qUCCSD method delivers the highest accuracy among Hermitian IP methods for 1h-dominated states (MAD ≈ 0.19 eV, SD ≈ 0.13 eV) and even surpasses IP-ADC(4) without triple contributions, while EA results show parity with lower-order methods for 1p-dominated energies and EA-ADC(4) performing best for open-shell cases. Overall, UCC-EPT offers a promising non-perturbative, Hermitian route to accurate IP and EA predictions, with planned extensions to higher-order commutator schemes to further improve performance and robustness.

Abstract

A unitary coupled-cluster (UCC)-based self-consistent electron propagator theory (EPT) is proposed for the description of electron-detached and electron-attached states. Two practical schemes, termed IP/EA-UCC3 and IP/EA-qUCCSD, are developed and implemented within the UCC singles and doubles (UCCSD) framework using the perturbative and commutator-based truncation strategy for the similarity-transformed Hamiltonian . The numerical performance of these UCC-based EPT methods is extensively evaluated against full configuration interaction (FCI) reference data and compared with established approaches, including IP/EA-ADC(3), IP/EA-ADC(4) and IP/EA-EOM-CCSD. Benchmark calculations demonstrate that IP-qUCCSD achieves the highest overall accuracy among Hermitian ionized-state methods for one-hole (1h)-dominated IPs of closed-shell systems, with a mean absolute deviation (MAD) of 0.19 eV and standard deviation (SD) of 0.13 eV. Remarkably, despite the absence of triple-excitation contributions, IP-qUCCSD outperforms the higher-order ADC(4) method. For one-particle (1p)-dominated EA calculations, all tested methods exhibit comparable accuracy.

Paper Structure

This paper contains 11 sections, 37 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Theory
  3. Electron propagator theory
  4. UCC-based self-consistent electron propagator theory
  5. The working equations for the IP(EA)-qUCCSD scheme
  6. Relation between working equations of UCC-EPT and UCC-PPT
  7. Computational details
  8. Results and discussion
  9. Benchmark calculations of ionization potentials (IPs)
  10. Benchmark calculations of electron affinities (EAs)
  11. Conclusion and outlook

Figures (3)

  • Figure 1: Block structure and constituent terms of the similarity-transformed Hamiltonian ($\bar{H}$) and amplitude equations in practical UCC-based electron propagator implementations. In the UCC3 scheme, the superscripts on $\bar{H}$ denote the perturbation order to which both $\bar{H}$ and the amplitude equations are expanded in each block. In the qUCCSD scheme, the superscripts instead indicate commutator rank, as defined in eq \ref{['hbar_total']} -\ref{['hbar3']}.
  • Figure 2: Violin plot of 25 1h-dominated ionization potentails obtained for systems with closed-shell reference.
  • Figure 3: Violin plot of 35 1p-dominated electron affinities obtained for systems with closed-shell reference.