Efficient Structure Optimization with Second-Order Many-Body Perturbation Theory: The RIJCOSX-MP2 Method.

Efficient energy calculations and structure optimizations employing second-order Møller-Plesset perturbation theory (MP2) are presented. The application of the RIJCOSX approximation, which involves different approximations for the formation of the Coulomb- and exchange-type matrices, to MP2 theory is demonstrated. The RIJCOSX approximation incorporates the 'resolution of the identity' approximation in terms of a Split-RI-J variant for the evaluation of the Coulomb matrices and a seminumeric exchange treatment via the 'chain-of-spheres' algorithm for the formation of the exchange-type matrices. Beside the derivation of the working equations, the RIJCOSX-MP2 method is benchmarked against the original MP2 and the already highly efficient RI-MP2 method. Energies as well as gradients are computed employing various basis sets and are compared to the conventional MP2 results concerning accuracy and total wall clock times. Speedups of typically a factor of 5-7 in comparison to MP2 can be obeserved for the largest basis set employed in our study. Total energies are reproduced with an average error of ≤0.8 kcal/mol and minimum energy geometries differ by ∼0.1 pm in bond lengths and typically ∼0.2 degrees in bond angles. The RIJCOSX-MP2 gradient parallelizes with a speedup of 8.2 on 10 processors. The algorithms are implemented into the ORCA electronic structure package.