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Coupled-cluster methods based on Brueckner orbitals are well known to resolve the problems of symmetry breaking and spin contamination that are often associated with Hartree-Fock orbitals. However, their computational cost is large enough to prevent application to large molecules. Here the authors present a simple approximation where the orbitals are optimized with the mean-field energy plus a correlation energy taken as the opposite-spin component of the second-order many-body correlation energy, scaled by an empirically chosen parameter (recommended as 1.2 for general applications). This "optimized second-order opposite-spin" (abbreviated as O2) method requires fourth-order computation on each orbital iteration. O2 is shown to yield predictions of structure and frequencies for closed-shell molecules that are very similar to scaled second-order Moller-Plesset methods. However, it yields substantial improvements for open-shell molecules, where problems with spin contamination and symmetry breaking are shown to be greatly reduced.

Orbital-optimized opposite-spin scaled second-order correlation: An economical method to improve the description of open-shell molecules