Abbott Adam S, Abbott Boyi Z, Turney Justin M, Schaefer Henry F
Center for Computational Quantum Chemistry, University of Georgia, Athens, Georgia 30602, United States.
J Phys Chem Lett. 2021 Apr 1;12(12):3232-3239. doi: 10.1021/acs.jpclett.1c00607. Epub 2021 Mar 25.
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.
在此，我们首次提出了一种通用方法，用于获得源自量子化学方法的电子能量的任意阶核坐标导数。通过利用自动微分软件的现代进展，我们证明了可以为任何方法获得精确导数。这一创新完全绕过了与应用数值微分方法的计算稳定性相关的问题，并且无需为解析能量导数推导具有挑战性的公式。我们描述了我们方案的一个免费可用的开源软件实现，并展示了其在从哈特里 - 福克理论、二阶莫勒 - 普莱塞特微扰理论（MP2）以及具有单、双和微扰三激发的耦合簇理论[CCSD(T)]中获得能量的精确核导数方面的应用。我们的示例计算包括高达六阶导数，并涵盖了具有多达100个基函数的各种测试系统，证实了该方案在广泛应用中的可行性。由于缺乏高阶导数公式，许多获得的结果迄今无法通过精确方法得到。我们讨论了我们实现的细节以及可能的进一步发展。
