Improved self-consistent and resolution-of-identity approximated Becke'05 density functional model of nondynamic electron correlation

In a recent letter E. Proynov, Y. Shao, and J. Kong, Chem. Phys. Lett. 493, 381 (2010)], Becke's B05 model of nondynamic electron correlation in density functional theory was implemented self-consistently with computational efficiency (the "SCF-RI-B05" scheme). Important modifications of the algorithm were done in order to make the self-consistency feasible. In the present work, we give a complete account of the SCF-RI-B05 algorithm, including all the formulae for the analytical representation of the B05 functional and for its self-consistent field (SCF) potential. The average performance of the SCF-RI-B05 method reported in the above letter was somewhat less accurate, compared to the original B05 implementation, mainly because the parameters of the original B05 model were optimized with post-local-spin-density calculations. In this work, we report improved atomization energies with SCF-RI-B05, based on a SCF re-optimization of its four linear parameters. The re-optimized SCF-RI-B05 scheme is validated also on reaction barriers, and on the subtle energetics of NO dimer, an exemplary system of strong nondynamic correlation. It yields both the binding energy and the singlet-triplet splitting of the NO dimer correctly, and close to the benchmarks reported in the literature.