Analytic gradients are important for efficient calculations of stationary points on potential energy surfaces, for interpreting spectroscopic observations, and for efficient direct dynamics simulations. For excited electronic states, as are involved in UV–Vis spectroscopy and photochemistry, analytic gradients are readily available and often affordable for calculations using a state-averaged complete active space self-consistent-field (SA-CASSCF) wave function. However, in most cases, a post-SA-CASSCF step is necessary for quantitative accuracy, and such calculations are often too expensive if carried out by perturbation theory or configuration interaction. In this work, we present the analytic gradients for multiconfiguration pair-density functional theory based on SA-CASSCF wave functions, which is a more affordable alternative. A test set of molecules has been studied with this method, and the stationary geometries and energetics are compared to values in the literature as obtained by other methods. Excited-state geometries computed with state-averaged pair-density functional theory have similar accuracy to those from complete active space perturbation theory at the second-order.

中文翻译：

---

状态平均多配置对密度泛函理论的解析梯度。

解析梯度对于有效计算势能表面上的固定点，解释光谱观察以及有效的直接动力学模拟非常重要。对于激发的电子态，如涉及紫外可见光谱和光化学的领域，使用状态平均的完整活动空间自洽场（SA-CASSCF）波函数进行计算，分析梯度很容易获得，并且通常可以承受。但是，在大多数情况下，SA-CASSCF后步骤对于定量精度是必需的，并且如果通过扰动理论或构型相互作用进行这种计算通常会过于昂贵。在这项工作中，我们提出了基于SA-CASSCF波函数的多配置对密度泛函理论的解析梯度，这是一种更经济的选择。已经用这种方法研究了分子的测试集，并将固定的几何形状和能量学与通过其他方法获得的文献中的值进行了比较。用状态平均对密度泛函理论计算出的激发态几何形状，其精度与二阶完全有源空间摄动理论的精度相似。