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.

中文翻译：

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广义变分原理及其在激发态平均场理论中的应用。

我们提出了与任何哈密顿本征态兼容的变分原理的概括，该哈密顿本征态可以通过属性列表唯一地指定。这种变分原理似乎与多种电子结构方法兼容，包括均场理论，密度泛函理论，多参考理论和量子蒙特卡洛理论。像标准变分原理一样，该广义变分原理相当于对非线性函数的优化，该非线性函数在任意灵活的波动函数的范围内以所需的哈密顿本征态为其全局最小值。与标准变分原理不同，它可以针对简并或简并的情况以激发态为目标并选择单个状态。作为这种方法在实践中如何有用的初步证明，我们将其用于将激发态平均场理论的优化效率提高一个数量级。通过这种改进的优化，我们能够证明相应的二阶微扰理论的精确度与我们先前研究的分子范围相比大得多的分子组中的单双运动方程耦合簇的精度相当。优化方法。