Automatic Differentiation\nfor Explicitly Correlated\nMP2

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