Size-consistent wavefunction for non-dynamical correlation energy: Valence active space variational Brueckner coupled-cluster doubles model

A. I. Krylov, C. D. Sherrill, E. F. C. Byrd, and M. Head-Gordon
J. Chem. Phys. 109, 10669 – 10678 (1998)

The non-dynamical correlation energy may be defined as the difference between full configuration interaction within the space of all valence orbitals and a single determinant of molecular orbitals (Hartree-Fock theory). In order to describe bond breaking, diradicals, and other electronic structure problems where Hartree-Fock theory fails, a reliable description of non-dynamical correlation is essential as a starting point. Unfortunately, the exact calculation of non-dynamical correlation energy, as defined above, involves computational complexity that grows exponentially with molecular size and is thus unfeasible beyond systems of just two or three heavy atoms. We introduce a new hierarchy of feasible approximations to the non-dynamical correlation energy based on coupled-cluster theory with variationally optimized orbitals. The simplest member of this hierarchy involves connected double excitations within the variationally optimized valence active space and may be denoted as VOO-CCD, or VOD. VOO-CCD is size-consistent, has computational complexity proportional to the sixth power of molecule size, and is expected to accurately approximate the non-dynamical correlation energy in such cases as single bond dissociation, diradicals, and anti-ferromagnetic coupling. We report details of our implementation of VOO-CCD and illustrate that it does indeed accurately recover the non-dynamical correlation energy for challenging multi-reference problems such as the torsion of ethylene and chemical bond breaking.

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