Frozen-Core Analytical Gradients within the Adiabatic Connection Random-Phase Approximation from an Extended Lagrangian

The implementation of the frozen-core option in combination with the analytic gradient of the random-phase approximation (RPA) is reported based on a density functional theory reference determinant using resolution-of-the-identity techniques and an extended Lagrangian. The frozen-core option reduces the dimensionality of the matrices required for the RPA analytic gradient, thereby yielding a reduction in computational cost. A frozen core also reduces the size of the numerical frequency grid required for accurate treatment of the correlation contributions using Curtis–Clenshaw quadratures, leading to an additional speedup. Optimized geometries for closed-shell, main-group, and transition metal compounds, as well as open-shell transition metal complexes, show that the frozen-core method on average elongates bonds by at most a few picometers and changes bond angles by a few degrees. Vibrational frequencies and dipole moments also show modest shifts from the all-electron results, reinforcing the broad usefulness of the frozen-core method. Timings for linear alkanes, a novel extended metal atom chain and a palladacyclic complex show a speedup of 35–55% using a reduced grid size and the frozen-core option. Overall, our results demonstrate the utility of combining the frozen-core option with RPA to obtain accurate molecular properties, thereby further extending the range of application of the RPA method.本工作报道了结合随机相位近似（Random-Phase Approximation, RPA）解析梯度的冻结芯选项的实现方案，该方案基于采用分辨率恒等（Resolution-of-the-Identity, RI）技术与扩展拉格朗日量的密度泛函理论参考行列式。冻结芯选项可降低RPA解析梯度所需矩阵的维度，进而降低计算开销。冻结芯同时还可缩减采用柯蒂斯-克莱肖求积法（Curtis–Clenshaw Quadratures）精确处理电子关联贡献所需的数值频率网格规模，带来额外的计算加速。针对闭壳层主族化合物、过渡金属化合物以及开壳层过渡金属配合物的优化几何构型测试表明，冻结芯方法平均仅会使化学键伸长至多数皮米，键角变化量仅为数度。振动频率与偶极矩的计算结果相较于全电子方法也仅出现小幅偏移，进一步佐证了冻结芯方法的广泛适用性。针对直链烷烃、新型延伸金属原子链以及钯环配合物的计时测试表明，采用缩减网格规模与冻结芯选项可实现35%~55%的计算加速比。综上，本研究结果证实了将冻结芯选项与RPA相结合以获取精确分子性质的实用性，从而进一步拓展了RPA方法的应用边界。