Spin-Unrestricted Second-Order Møller–Plesset (MP2) Forces for the Condensed Phase: From Molecular Radicals to F‑Centers in Solids

To obtain consistent geometries for the computation of properties, nuclear gradients are essential. Here, we report a fully periodic Γ-point, massively parallel implementation of spin-unrestricted second-order Møller–Plesset (MP2) forces. It is based on the resolution-of-identity and Gaussian and plane waves approach to calculate electron repulsion integrals and is made available in the CP2K program. The algorithm is optimized for modern supercomputer architectures and is capable of employing both CPUs and GPUs. The asymptotic computational scaling is O(N 5), which is observed for the systems containing more than 100 second-row atoms with triple-ζ quality basis sets. For smaller systems, the energy and forces can be evaluated within minutes; for bigger systems within hours, provided that thousands of processor units are available. Spin-unrestricted MP2 calculations are, computationally, ∼3 times more demanding than spin-restricted ones, but exhibit a better parallel performance. As a bonus, the gradient implementation allows for computing spin-density distributions not available in energy calculations. The method has been successfully used for computing the crystal structure of the TEMPO radical and to obtain the spin density distribution of an F-center in lithium fluoride at a consistent geometry. We expect this computationally efficient tool to be useful for the chemistry, materials science, and solid-state physics communities.