Arbitrary-Order Density Functional Response Theory from Automatic Differentiation

We demonstrate how the functional derivatives appearing in perturbative timedependent density functional theory can be calculated using automatic differentiation. The approach starts from a computer implementation of the exchange-correlation energy functional, from which arbitrary-order derivatives are generated automatically. Automatic differentiation is shown to provide an accurate, general, and efficient implementation of higher-order exchangecorrelation functional derivatives that is easy to maintain. When used in combination with an arbitrary-order response solver, the methodology allows us to generate arbitrary-order response functions from time-dependent density functional theory. © 2010 American Chemical Society.