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On the difference between variational and unitary coupled cluster theories.

Gaurav Harsha1, Toru Shiozaki2, Gustavo E Scuseria1

  • 1Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA.

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This study definitively shows variational and unitary coupled cluster theories produce different energies, particularly under strong correlation. A generalized variant outperforms traditional methods.

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Area of Science:

  • Quantum chemistry
  • Theoretical physics

Background:

  • Coupled cluster theory is a cornerstone of quantum chemistry for accurate electronic structure calculations.
  • Previous studies presented conflicting numerical evidence regarding the equivalence of variational and unitary coupled cluster energy functionals.

Purpose of the Study:

  • To conclusively determine if variational and unitary coupled cluster theories yield identical energy functionals.
  • To investigate the impact of correlation strength on the differences between these theoretical formulations.
  • To explore a generalized coupled cluster variant for improved accuracy.

Main Methods:

  • Utilized the exactly solvable Lipkin Hamiltonian to avoid ambiguities in parameter space.
  • Performed calculations in a symmetry-adapted basis, focusing on strong correlation regimes.
  • Truncated the theory to include double excitations for analysis.
  • Introduced and tested a generalized non-unitary, non-hermitian coupled cluster variant.

Main Results:

  • Presented conclusive numerical evidence that variational and unitary coupled cluster theories yield distinct energy functionals.
  • Demonstrated that energy differences are significant under strong correlation but small in weakly correlated systems.
  • Showed that a generalized variant incorporating excitation, de-excitation, and mixed operators performs superiorly.

Conclusions:

  • The variational and unitary forms of coupled cluster theory are fundamentally different and do not yield the same energy.
  • The choice of theoretical formulation and correlation regime significantly impacts the calculated energies.
  • A generalized coupled cluster approach offers a promising avenue for more accurate electronic structure calculations.