Basis set limit MP2 energies for extended molecules via a reduced-cost explicitly correlated approach

A reduced-cost explicitly correlated second-order Moller-Plesset (MP2-F12) approach is presented. Based on our recent reduced-cost explicitly correlated coupled-cluster method [J. Chem. Theory Comput., 19, 174 (2023)], the frozen natural orbital, the natural auxiliary basis, and the natural auxiliary function approximations are utilised to decrease the size of the molecular orbital basis and the auxiliary basis sets required for the density fitting and for the expansion of the explicitly correlated geminals. The necessary modifications of the above approximations for MP2-F12 are discussed. The performance of the new method is tested for atomisation and reaction energies. Our results demonstrate that speedups of 1.5-4 can be achieved in the calculation of MP2-F12 correlation energies with a moderate loss of accuracy.