复势能面：基于投影CAP技术的梯度
Complex potential energy surfaces: gradients with projected CAP technique
AI总结：
本文提出基于投影CAP的通用梯度方法，将束缚态电子结构的梯度与非绝热耦合推广到共振态，并在SA-CASSCF和MR-CIS中验证精度，给出多个瞬态阴离子的平衡几何结构。
摘要：
复吸收势（CAP）技术是表征电子共振的常用非厄米量子力学方法之一。CAP与各种电子结构方法相结合，在量化分子体系中电子共振的能量和宽度方面已显示出良好的结果。虽然基于CAP的方法可用于绘制共振态的复势能面，但对这些势能面的高效探索，例如几何优化或动力学模拟，需要核梯度信息。目前，基于CAP的方法中唯一可用的核梯度是针对Hartree-Fock和含单双激发的运动方程耦合簇方法（J. Chem. Phys. 146, 031101 (2017)）。在此，我们提供一种通用方法，该方法依赖于投影CAP公式，并将为束缚态电子结构方法开发的梯度和非绝热耦合公式扩展到共振态。该方法不限于特定的电子结构方法，只要束缚态的梯度和非绝热耦合信息可用，就普遍适用于任何电子结构方法。在此，我们重点关注态平均完全活性空间自洽场（SA-CASSCF）和含单激发的多参考组态相互作用（MR-CIS）作为我们选择的方法。我们确定了所开发梯度的准确性，并报告了几种代表性瞬态阴离子物种（$\mathrm{N_2^-}$、$\mathrm{H_2CO^-}$、$\mathrm{H_2CO_2^-}$ 和 $\mathrm{C_2H_4^-}$）的平衡几何结构。
英文摘要：
The complex absorbing potential (CAP) technique is one of the commonly used Non-Hermitian quantum mechanics approaches for characterizing electronic resonances. CAP combined with various electronic structure methods has shown promising results in quantifying the energies and widths of electronic resonances in molecular systems. While CAP-based methods can be used to map complex potential energy surfaces for resonance states, efficient exploration of these surfaces, e.g. geometry optimization or dynamical simulations, require information on the nuclear gradient. Currently, the only nuclear gradients available for CAP-based methods are for Hartree-Fock and Equation-of-Motion Coupled-Cluster method with single and double excitations (J. Chem. Phys. 146, 031101 (2017)). Here we provide a general approach that relies on projected CAP formulation and extends gradients and non-adiabatic couplings formulations developed for bound-state electronic structure methods to resonances. The approach is not limited to a specific electron structure method and is generally applicable to any electronic structure methods, provided the information on the gradients and non-adiabatic couplings is available for bound states. Here, we focus on the State-Averaged Complete Active Space Self-Consistent Field (SA-CASSCF) and Multi-Reference Configurational Interaction with Single excitation (MR-CIS) as our methods of choice. We establish the accuracy of the developed gradients and report equilibrium geometries for several representative temporary anion species ($\mathrm{N_2^-}$, $\mathrm{H_2CO^-}$, $\mathrm{H_2CO_2^-}$ and $\mathrm{C_2H_4^-}$).
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