Shea Jacqueline A R, Gwin Elise, Neuscamman Eric
Department of Chemistry, University of California, Berkeley, California 94720, United States.
Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States.
J Chem Theory Comput. 2020 Mar 10;16(3):1526-1540. doi: 10.1021/acs.jctc.9b01105. Epub 2020 Feb 22.
We present a generalization of the variational principle that is compatible with any Hamiltonian eigenstate that can be specified uniquely by a list of properties. This variational principle appears to be compatible with a wide range of electronic structure methods, including mean field theory, density functional theory, multireference theory, and quantum Monte Carlo. Like the standard variational principle, this generalized variational principle amounts to the optimization of a nonlinear function that, in the limit of an arbitrarily flexible wave function, has the desired Hamiltonian eigenstate as its global minimum. Unlike the standard variational principle, it can target excited states and select individual states in cases of degeneracy or near-degeneracy. As an initial demonstration of how this approach can be useful in practice, we employ it to improve the optimization efficiency of excited state mean field theory by an order of magnitude. With this improved optimization, we are able to demonstrate that the accuracy of the corresponding second-order perturbation theory rivals that of singles-and-doubles equation-of-motion coupled cluster in a substantially broader set of molecules than could be explored by our previous optimization methodology.
我们提出了一种变分原理的推广形式，它与任何能由一组性质唯一确定的哈密顿本征态兼容。这种变分原理似乎与广泛的电子结构方法兼容，包括平均场理论、密度泛函理论、多参考理论和量子蒙特卡罗方法。与标准变分原理一样，这种广义变分原理相当于对一个非线性函数进行优化，在波函数具有任意灵活性的极限情况下，该函数以所需的哈密顿本征态作为其全局最小值。与标准变分原理不同的是，它可以针对激发态，并且在简并或近简并情况下能选择单个状态。作为这种方法在实际中如何有用的初步证明，我们用它将激发态平均场理论的优化效率提高了一个数量级。通过这种改进的优化，我们能够证明，在比我们之前的优化方法所能探索的分子集合大得多的一组分子中，相应的二阶微扰理论的精度可与单双激发运动方程耦合簇方法相媲美。
