Automatic Differentiation for Explicitly Correlated MP2

Automatic differentiation (AD) offers a route to achieve arbitrary-order derivatives of challenging wave function methods without the use of analytic gradients or response theory. Currently, AD has been predominantly used in methods where first- and/or second-order derivatives are available, but it has not been applied to methods lacking available derivatives. The most robust approximation of explicitly correlated MP2, MP2-F12/3C(FIX)+CABS, is one such method. By comparing the results of MP2-F12 computed with AD versus finite-differences, it is shown that (a) optimized geometries match to about 10^-3 Å for bond lengths and a 10^-6 degree for angles, and (b) dipole moments match to about 10^-6 D. Hessians were observed to have poorer agreement with numerical results (10^-5), which is attributed to deficiencies in AD implementations currently. However, it is notable that vibrational frequencies match within 10^-2 cm^-1. The use of AD also allowed the prediction of MP2-F12/3C(FIX)+CABS IR intensities for the first time.