We present the formulation and implementation of an analytical gradient algorithm for extended multiconfiguration quasidegenerate perturbation theory (XMCQDPT2) with the resolvent-fitting approximation by Granovsky. This algorithm is powerful when optimizing molecular configurations with a moderate-sized active space and many electronic states. First, we present the powerfulness and accuracy of resolvent-fitting approximations compared to canonical XMCQDPT2 theory. Then, we demonstrate the utility of the current algorithm in frequency analyses, optimizing the minimum energy conical intersection geometries of the retinal chromophore model RPSB6 and evaluating nuclear gradients when there are many electronic states. Furthermore, we parallelize the algorithm using the OpenMP/MPI hybrid approach. Additionally, we report the computational cost and parallel efficiency of the program.

中文翻译：

---

Resolvent-Fitted 二阶扩展多重配置微扰理论的解析梯度理论 (XMCQDPT2)

我们提出了一种解析梯度算法的公式和实现，用于扩展多配置准生成扰动理论 (XMCQDPT2) 和 Granovsky 的解析拟合近似。该算法在优化具有中等大小活性空间和许多电子状态的分子构型时非常强大。首先，我们展示了与规范 XMCQDPT2 理论相比的解析度拟合近似值的强大性和准确性。然后，我们展示了当前算法在频率分析中的实用性，优化了视网膜发色团模型 RPSB6 的最小能量锥形相交几何形状，并在存在许多电子状态时评估核梯度。此外，我们使用 OpenMP/MPI 混合方法并行化算法。此外，