Addressing first derivative discontinuities in orbital-optimized opposite-spin scaled second-order perturbation theory with regularization
Orbital-optimized opposite-spin scaled second-order perturbation theory (O 2 ) generates a single-reference wave function composed of approximate Brueckner orbitals with fourth-order computational scaling. While O 2 provides significantly improved treatment of radicals by reducing spin contamination, it has been shown to suffer from first derivative discontinuities for bond stretching near the unrestriction point. That qualitative failure is resolved in this work by the implementation of regularized O 2 , which includes a regularization parameter in the denominator of its second-order term. The value of the regularization parameter is semi-empirically chosen to qualitatively describe bond stretching energetics of hydrogen, ethane and ethene, while also considering the effect of the regularization parameter on thermochemical errors for the well-known Gaussian-2 (G2) test set. The generality of the empirical scaling and semi-empirical regularization parameter is studied by application to the 3dMLBE20, DBH24, RSE43 and W4-11 test sets. We demonstrate that accuracy of O 2 is roughly maintained and sometimes even improved by regularization, with root mean squares of regularised O 2 between factors of 1.6 and 0.8 from corresponding root mean squares of O 2 .