Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, United States.
J Chem Theory Comput. 2020 Aug 11;16(8):5067-5082. doi: 10.1021/acs.jctc.0c00502. Epub 2020 Jul 28.
Orbital optimization is crucial when using a non-Aufbau Slater determinant that involves promotion of an electron from a (nominally) occupied molecular orbital to an unoccupied one, or else ionization from a molecular orbital that lies below the highest occupied frontier molecular orbital. However, orbital relaxation of a non-Aufbau determinant risks "variational collapse" back to the Aufbau solution of the self-consistent field (SCF) equations. Algorithms such as the maximum overlap method (MOM) that are designed to avoid this collapse are not guaranteed to work, and more robust alternatives increase the cost per SCF iteration. Here, we introduce an alternative procedure called state-targeted energy projection (STEP) that is based on level shifting and is identical in cost to a normal SCF procedure, yet converges in numerous cases where MOM suffers variational collapse. Benchmark calculations on small-molecule reference data suggest that ΔSCF calculations based on STEP are an accurate way to compute both ionization and excitation energies, including core-level ionization and excited states with significant double-excitation character. For the molecule 2,4,6-trifluoroborazine, ΔSCF calculations based on STEP afford excellent agreement with experiment for both vertical and adiabatic ionization energies, the latter requiring geometry optimization of a non-Aufbau valence hole. Semiquantitative agreement with experiment is obtained for the absorption spectrum of chlorophyll . Finally, the importance of asymptotic exchange and correlation is illustrated by application to Rydberg states using spin-scaled Møller-Plesset perturbation theory with a non-Aufbau reference determinant. Together, these results suggest that STEP offers a reliable and affordable alternative to the MOM procedure for determining non-Aufbau solutions of the SCF equations.
轨道优化在使用非 Aufbau Slater 行列式时至关重要，这种行列式涉及将电子从（名义上）占据的分子轨道提升到未占据的轨道，或者从低于最高占据前线分子轨道的分子轨道中进行电离。然而，非 Aufbau 行列式的轨道弛豫可能会导致“变分崩溃”回到自洽场（SCF）方程的 Aufbau 解。为避免这种崩溃而设计的算法，如最大重叠方法（MOM），并不保证有效，而更稳健的替代方法会增加每个 SCF 迭代的成本。在这里，我们引入了一种称为状态目标能量投影（STEP）的替代方法，该方法基于能级移动，与正常 SCF 过程的成本相同，但在 MOM 遭受变分崩溃的许多情况下都能收敛。对小分子参考数据的基准计算表明，基于 STEP 的 ΔSCF 计算是一种计算电离能和激发能的准确方法，包括具有显著双激发特征的芯级电离和激发态。对于三氟硼嗪分子 2,4,6-trifluoroborazine，基于 STEP 的 ΔSCF 计算在垂直和绝热电离能方面与实验结果非常吻合，后者需要对非 Aufbau 价孔进行几何优化。对于叶绿素的吸收光谱，也得到了半定量的实验吻合。最后，通过应用自旋缩放的 Møller-Plesset 微扰理论和非 Aufbau 参考行列式来处理 Rydberg 态，说明了渐近交换相关的重要性。总之，这些结果表明，STEP 为确定 SCF 方程的非 Aufbau 解提供了一种可靠且经济实惠的替代 MOM 方法。
