本项目中，我们计划采用运动方程耦合簇方法，针对重元素分子体系，发展含旋轨耦合电子激发态解析能量梯度的计算方法和计算程序。我们将在现有的闭壳层体系含旋轨耦合运动方程耦合簇程序基础上，实现激发态、电离态和电子亲和态的解析能量梯度计算。计算闭壳层体系的电离态和电子亲和态实质上是对相应开壳层体系的基态和激发态的计算。在此方法中，我们在求解参考态的耦合簇方程时引入旋轨耦合，这样能以相对较小的计算量精确地描述重元素分子的旋轨耦合效应。在程序化过程中，我们还将利用时间反演对称性和空间对称性降低计算量。此基础上，我们将针对含重元素的分子体系，优化含旋轨耦合激发态的几何构型并计算振动频率。通过计算激发态和基态之间的偶极跃迁矩阵元，模拟一些有实验数据的重元素分子吸收光谱、荧光或磷光光谱等。

In this project, we propose to implement analytical energy gradients for excited states of molecules containing heavy elements using the equation of motion coupled-cluster theory (EOM-CC) with spin-orbit coupling. Analytical energy gradients will be calculated based on a previously developed closed-shell EOM-CC program for excited, ionized as well as electron-attached states with spin-orbit coupling. Ionized or electron-attached states for a closed-shell system are equivalent to the ground and some excited states of the corresponding open-shell system. Spin-orbit coupling will be introduced when solving the coupled-cluster equations for the reference state. This approach can provide an accurate description for spin-orbit coupling effects. Both time-reversal symmetry and spatial symmetry will be exploited in the implementation to reduce computational effort. Equilibrium structures and harmonic frequencies of excited states with spin-orbit coupling for molecules containing heavy elements can thus be calculated with the available analytical energy gradient program. By calculating transition dipole moments between the ground and excited states, we will simulate electronic absorption spectra, fluorescence or phosphorescence spectra for some heavy element compounds with available experimental data.