Automatic Differentiation of Explicitly Correlated MP2

For a long time, explicitly correlated (F12) methods have offered a solution to the slow convergence of the one-electron basis set. Although there have been numerous studies in which F12 methods have improved the accuracy of single-point energies, most of these methods have not been extended to gradients and Hessians. One such method is the highly robust explicitly-correlated second-order Moeller-Plesset perturbation theory within the 3C(FIX) Ansatz [MP2-F12/3C(FIX)]. Despite MP2-F12/3C(FIX) showing a scaling similar to MP2 and an accuracy two levels of basis set cardinality better than MP2, the method's complexity has made its derivatives elusive. Automatic differentiation (AD) offers a different way to compute derivatives than its predecessors. By utilizing the chain rule, one can compute derivatives through tracing through the computational graph of the energy evaluation. This work shows that AD can be applied to MP2-F12/3C(FIX) to make the computation of its gradient and Hessian possible.