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Open-source implementation of the anti-Hermitian contracted Schrödinger equation for electronic ground and excited states

Daniel Gibney, Anthony W Schlimgen, Jan-Niklas Boyn

Abstract

Efficient simulation of strongly correlated electrons has become a routine tool in molecular electronic structure theory due to recent advances in approximate configuration interaction (CI) techniques. Nonetheless, the quantitative and predictive description of molecular electronic states remains a significant challenge due to the difficulty of computing all-electron correlation beyond CI. Here, we describe a new open-source implementation of the anti-Hermitian contracted Schrödinger equation (ACSE) for use in accurate simulation of all-electron correlation in molecules. In contrast to standard approaches via multireference perturbation theory, the scaling of the ACSE does not depend on the complexity of the strongly correlated reference wavefunction. Furthermore, the ACSE employs the exact electronic Hamiltonian, rather than an approximate perturbative Hamiltonian. Our benchmark results demonstrate good accuracy for main group and transition metal systems, in weakly and strongly correlated regimes, with various basis sets, and for ground and excited states. The results suggest that the ACSE has potential as a scalable and robust technique for simulating all-electron correlation in molecular ground and excited states.

Open-source implementation of the anti-Hermitian contracted Schrödinger equation for electronic ground and excited states

Abstract

Efficient simulation of strongly correlated electrons has become a routine tool in molecular electronic structure theory due to recent advances in approximate configuration interaction (CI) techniques. Nonetheless, the quantitative and predictive description of molecular electronic states remains a significant challenge due to the difficulty of computing all-electron correlation beyond CI. Here, we describe a new open-source implementation of the anti-Hermitian contracted Schrödinger equation (ACSE) for use in accurate simulation of all-electron correlation in molecules. In contrast to standard approaches via multireference perturbation theory, the scaling of the ACSE does not depend on the complexity of the strongly correlated reference wavefunction. Furthermore, the ACSE employs the exact electronic Hamiltonian, rather than an approximate perturbative Hamiltonian. Our benchmark results demonstrate good accuracy for main group and transition metal systems, in weakly and strongly correlated regimes, with various basis sets, and for ground and excited states. The results suggest that the ACSE has potential as a scalable and robust technique for simulating all-electron correlation in molecular ground and excited states.

Paper Structure

This paper contains 13 sections, 33 equations, 4 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Theory
  3. Methods
  4. Results and discussion
  5. Conclusions
  6. Data Availability
  7. Spin block normalizations
  8. Obtaining the residual expression in terms of the 2- and 3-RDMs
  9. Cumulant decomposition of the 3-RDM
  10. 3-RDM reconstructions
  11. Valdemoro
  12. Nakatsuji-Yasuda
  13. Ethylene Geometry

Figures (4)

  • Figure 1: Diagram of the ACSE workflow.
  • Figure 2: Ethylene (C$_2$H$_4$) dihedral barrier height a) absolute energies (H) and b) the relative energies (kcal/mol) using extrapolated DMRG-FCI ($M=1100,1300,1500$), NEVPT2, and ACSE in a cc-pVDZ basis. The top inset shows the log of the absolute error, and the bottom inset shows the relative error.
  • Figure 3: Energy convergence (in Hartree) and log$_{10}$ residual norm convergence vs $\lambda=\epsilon n$ for the 0 and 90° dihedral angles of ethylene.
  • Figure 4: The dissociation of the two lowest energy singlets and triplets of N$_2$ in a cc-pVDZ basis set, computed with NEVPT2 and ACSE with a [6,6] CASSCF reference, and DMRG-FCI ($M=1200$). The insets show the log of the absolute error with respect to DMRG-FCI