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.

本研究将基于冻结虚自然轨道（frozen virtual natural orbital）与自然辅助函数（natural auxiliary function）方法的降本方案[J. Chem. Phys. 2018, 148, 094111]拓展至芯激发体系。针对结合了芯价分离（core–valence separation, CVS）与密度拟合（density fitting）方法的二阶代数图解构造（second-order algebraic-diagrammatic construction, ADC(2)）模型，本文验证了该近似方案的计算效率。针对涵盖碳、氮、氧K边激发，以及1s→π*与里德堡跃迁在内的200余组激发能数据与80组振子强度数据，本方案引入的误差得到了全面分析。研究结果表明，该方案可在仅付出适度误差代价的前提下，显著降低计算开销。具体而言，激发能的平均绝对误差低于0.20 eV，较CVS-ADC(2)的本征误差小一个数量级；而振子强度的平均相对误差处于0.06至0.08之间，仍处于可接受范围。由于未观测到不同激发类型间存在显著差异，进一步证实了该近似方案的鲁棒性。针对拓展型分子的计算开销优化效果被量化评估：此类体系的实际运行时间整体实现7倍加速，同时内存占用也得到大幅降低。此外，本研究还证实，该新方法可使含100个原子的体系在合理运行时间内，采用可靠基组完成CVS-ADC(2)计算。