Ekström Ulf, Visscher Lucas, Bast Radovan, Thorvaldsen Andreas J, Ruud Kenneth
Division of Theoretical Chemistry, Amsterdam Center for Multiscale Modeling, VU University - Faculty of Sciences, De Boelelaan 1083, NL-1081 HV Amsterdam, The Netherlands, and Centre for Theoretical and Computational Chemistry, Department of Chemistry, University of Tromsø, N-9037 Tromsø, Norway.
J Chem Theory Comput. 2010 Jul 13;6(7):1971-80. doi: 10.1021/ct100117s.
We demonstrate how the functional derivatives appearing in perturbative time-dependent 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 exchange-correlation 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.
我们展示了如何使用自动微分来计算含时密度泛函微扰理论中出现的泛函导数。该方法从交换关联能量泛函的计算机实现开始，由此自动生成任意阶导数。结果表明，自动微分能提供一种准确、通用且高效的高阶交换关联泛函导数实现方式，且易于维护。当与任意阶响应求解器结合使用时，该方法使我们能够从含时密度泛函理论生成任意阶响应函数。
