Direct determination of optimal pair-natural orbitals in a real-space representation: The second-order Moller-Plesset energy.

An efficient representation of molecular correlated wave functions is proposed, which features regularization of the Coulomb electron-electron singularities via the F12-style explicit correlation and a pair-natural orbital factorization of the correlation components of the wave function expressed in the real space. The pair-natural orbitals are expressed in an adaptive multiresolution basis and computed directly by iterative variational optimization. The approach is demonstrated by computing the second-order Moller-Plesset energies of small- and medium-sized molecules. The resulting MRA-PNO-MP2-F12 method allows for the first time to compute correlated wave functions in a real-space representation for systems with dozens of atoms (as demonstrated here by computations on alkanes as large as CH), with precision exceeding what is achievable with the conventional explicitly correlated MP2 approaches based on the atomic orbital representations.