Arbitrary-Order Derivatives of Quantum Chemical Methods via Automatic Differentiation

Herein, we present for the first time a general methodology for obtaining arbitrary-order nuclear coordinate derivatives of electronic energies derived from quantum chemistry methods. By leveraging modern advances in automatic differentiation software, we demonstrate that exact derivatives can be obtained for any method. This innovation completely bypasses the issues associated with the computational stability of applying numerical differentiation methods and dispenses the need to derive challenging formulae for analytic energy derivatives. We describe a freely available and open-source software implementation of our scheme and demonstrate its use in obtaining exact nuclear derivatives of energies from Hartree–Fock theory, second-order Møller–Plesset perturbation theory (MP2), and coupled cluster theory with single, double, and perturbative triple excitations [CCSD­(T)]. Our sample computations include up to sextic derivatives and span a variety of test systems with up to 100 basis functions, confirming the viability of this scheme for a wide range of applications. Many of the results obtained have hitherto been unobtainable by exact means due to a lack of higher-order derivative formulae. The details of our implementation and possible further developments are discussed.