Reduced-Cost Second-Order Algebraic-Diagrammatic Construction Method for Core Excitations

Our
reduced-cost scheme [J. Chem. Phys. 2018, 148, 094111] based on the frozen
virtual
natural orbital and natural auxiliary function approaches is extended
to core excitations. The efficiency of the approximation is presented
for the second-order algebraic-diagrammatic construction [ADC(2)]
method invoking the core–valence separation (CVS) and density
fitting approaches. The errors introduced by the present scheme are
comprehensively analyzed for more than 200 excitation energies and
80 oscillator strengths, including C, N, and O K-edge excitations,
as well as 1s → π* and Rydberg transitions.
Our results show that significant savings can be gained in computational
requirements at the expense of a moderate error. That is, the mean
absolute error for the excitation energies, being lower than 0.20
eV, is an order of magnitude smaller than the intrinsic error of CVS-ADC(2),
while the mean relative error for the oscillator strengths is between
0.06 and 0.08, which is still acceptable. As significant differences
for different types of excitations cannot be observed, the robustness
of the approximation is also demonstrated. The improvements in the
computational requirements are measured for extended molecules. In
this case, an overall 7-fold speedup is obtained in the wall-clock
times, while dramatic reductions in the memory requirements are also
achieved. In addition, it is also proved that the new approach enables
us to perform CVS-ADC(2) calculations within reasonable runtime for
systems of 100 atoms using reliable basis sets.

我们将基于冻结虚拟自然轨道（frozen virtual natural orbital）与自然辅助函数（natural auxiliary function）法的降本方案[J. Chem. Phys. 2018, 148, 094111]拓展至核激发体系。针对结合了核价分离（core–valence separation, CVS）与密度拟合（density fitting）方法的二阶代数图解构造法（second-order algebraic-diagrammatic construction, ADC(2)），本文展示了该近似方案的计算效率。我们针对超过200个激发能与80个振子强度（oscillator strengths）的体系，涵盖碳、氮、氧的K边激发（K-edge excitations）以及1s→π*和里德堡跃迁（Rydberg transitions），全面分析了本方案引入的误差。
研究结果表明，本方案可在仅付出适度误差代价的前提下，大幅降低计算资源需求：激发能的平均绝对误差（mean absolute error）低于0.20 eV，较CVS-ADC(2)的本征误差小一个数量级；振子强度的平均相对误差（mean relative error）处于0.06至0.08之间，仍处于可接受范围。未观测到不同激发类型间存在显著误差差异，验证了该近似方法的鲁棒性。我们针对大尺寸分子测试了计算资源需求的优化效果，最终获得了整体7倍的墙钟时间（wall-clock times）加速比，同时内存占用也得到了显著降低。此外，本研究证实该新方法可在合理运行时内，使用可靠基组完成包含100个原子体系的CVS-ADC(2)计算。