Förster Arno, van Lenthe Erik, Spadetto Edoardo, Visscher Lucas
Theoretical Chemistry, Vrije Universiteit, De Boelelaan 1083, 1081 HV Amsterdam, The Netherlands.
Software for Chemistry and Materials NV, 1081 HV Amsterdam, The Netherlands.
J Chem Theory Comput. 2023 Sep 12;19(17):5958-5976. doi: 10.1021/acs.jctc.3c00512. Epub 2023 Aug 18.
We report an all-electron, atomic orbital (AO)-based, two-component (2C) implementation of the approximation (GWA) for closed-shell molecules. Our algorithm is based on the space-time formulation of the GWA and uses analytical continuation (AC) of the self-energy, and pair-atomic density fitting (PADF) to switch between AO and auxiliary basis. By calculating the dynamical contribution to the self-energy at a quasi-one-component level, our 2C- algorithm is only about a factor of 2-3 slower than in the scalar relativistic case. Additionally, we present a 2C implementation of the simplest vertex correction to the self-energy, the statically screened 32 correction. Comparison of first ionization potentials (IPs) of a set of 67 molecules with heavy elements (a subset of the SOC81 set) calculated with our implementation against results from the WEST code reveals mean absolute deviations (MAD) of around 70 meV for @PBE and @PBE0. We check the accuracy of our AC treatment by comparison to full-frequency calculations, which shows that in the absence of multisolution cases, the errors due to AC are only minor. This implies that the main sources of the observed deviations between both implementations are the different single-particle bases and the pseudopotential approximation in the WEST code. Finally, we assess the performance of some (partially self-consistent) variants of the GWA for the calculation of first IPs by comparison to vertical experimental reference values. @PBE0 (25% exact exchange) and @BHLYP (50% exact exchange) perform best with mean absolute deviations (MAD) of about 200 meV. Explicit treatment of spin-orbit effects at the 2C level is crucial for systematic agreement with experiment. On the other hand, eigenvalue-only self-consistent (ev) and quasi-particle self-consistent (qs) significantly overestimate the IPs. Perturbative 32 corrections increase the IPs and therefore improve the agreement with experiment in cases where alone underestimates the IPs. With a MAD of only 140 meV, 2C-@PBE0 + 32 is in best agreement with the experimental reference values.
我们报告了一种基于全电子、原子轨道（AO）的闭壳层分子近似（GWA）的双分量（2C）实现方法。我们的算法基于GWA的时空公式，使用自能的解析延拓（AC）以及对原子密度拟合（PADF）在AO基和辅助基之间进行切换。通过在准单分量水平上计算自能的动态贡献，我们的2C - 算法仅比标量相对论情形慢约2至3倍。此外，我们给出了对自能最简单的顶点修正——静态屏蔽32修正的2C实现。将我们实现方法计算的一组67个含重元素分子（SOC81集合的一个子集）的第一电离势（IP）与WEST代码的结果进行比较，对于@PBE和@PBE0，平均绝对偏差（MAD）约为70 meV。我们通过与全频计算结果比较来检验AC处理的准确性，结果表明在不存在多解情况时，AC引起的误差很小。这意味着两种实现方法之间观察到的偏差的主要来源是不同的单粒子基以及WEST代码中的赝势近似。最后，我们通过与垂直实验参考值比较来评估GWA的一些（部分自洽）变体在计算第一IP时的性能。@PBE0（25%精确交换）和@BHLYP（50%精确交换）表现最佳，平均绝对偏差（MAD）约为200 meV。在2C水平上明确处理自旋轨道效应对于与实验系统地一致至关重要。另一方面，仅本征值自洽（ev）和准粒子自洽（qs）显著高估了IPs。微扰32修正增加了IPs，因此在单独计算低估IPs的情况下改善了与实验的一致性。2C - @PBE0 + 32的MAD仅为140 meV，与实验参考值的一致性最佳。
