Analytic First Derivatives of Aufbau Suppressed Coupled Cluster Theory and their Perturbative Accuracy

TL;DR

This work derives analytic first derivatives for Aufbau suppressed coupled cluster (ASCC) in the single-CSF limit to access excited-state one-body properties via the 1-RDM. It introduces a Lagrangian-based framework with a perturbative analysis that guides which amplitudes to include, and proposes natural orbital refinement to reduce reference dependence. The results show that ASCC can match linear-response CC methods for dipole moments when perturbative completeness is maintained, and that natural orbital refinement can reduce starting-point dependence for certain ASCC variants, though challenges remain for symmetry and charge-transfer states. Overall, the study demonstrates the potential of ASCC derivatives for excited-state properties, outlines limitations related to symmetry violations and perturbative truncations, and points to future work on 2-RDMs, orbital relaxation, and improved partial linearization strategies to broaden applicability and accuracy.

Abstract

We derived and implemented analytic first derivatives for Aufbau suppressed coupled cluster theory to calculate the one-body reduced density matrix, from which excited state natural orbitals and one-body properties, like atomic populations and dipole moments, are obtained. We utilized the natural orbitals to refine the ASCC solution for simple valence and Rydberg systems, exploring the process of repeatedly solving the ASCC equations in successive natural orbital bases to achieve independence from the starting molecular orbitals. For dipole moments in small molecules where high-level comparison data is available, we find that the accuracy of ASCC essentially matches that of linear response and equation-of-motion coupled cluster as long as care is taken to preserve the response's perturbative completeness.

Figures (6)

• Figure 1: The CCSD and (PL)ASCC 1-RDMs with orders of perturbative correctness indicated. For CCSD, the all occupied and all virtual blocks are highlighted in purple and the occupied-virtual blocks are highlighted in orange. For ASCC, the all primary blocks are highlighted in green, the mixed blocks in blue, and the all non-primary blocks in red. The $^*$ indicates that the block is one order lower with PLASCC (e.g. ($\mathbf{3^*}$) becomes ($\mathbf{2}$) for PLASCC).
• Figure 2: Schematic of the natural orbital refinement procedure. See \ref{['NOR']} for details.
• Figure 3: The mean unsigned excitation errors of 14 valence and Rydberg states from 5 molecules when starting from CIS, TD-DFT, EOM-CCSD, or ESMF starting points for a) ASCC$^{(M,1)}$ and b) PLASCC$^{(M,1)}$ after 0, 1, or 2 natural orbital refinements.
• Figure 4: The spread in the excitation energies when starting from CIS, TD-DFT, ESMF, or EOM-CCSD starting points for a) ASCC$^{(M,1)}$ and b) PLASCC$^{(M,1)}$ after 0, 1, or 2 natural orbital refinements. The spread is measured as the difference between the maximum and minimum excitation energy predictions.
• Figure 5: A schematic of the water flyby test system is shown above the EOM-CCSD and ASCC Löwdin population changes of the CCO and NH$_2$ moieties upon excitation to the $^1A'$ CT state.