Department of Chemistry, Washington State University, Pullman, Washington 99164-4630, USA.
J Chem Phys. 2011 Jul 28;135(4):044102. doi: 10.1063/1.3613639.
The leading cause of error in standard coupled cluster theory calculations of thermodynamic properties such as atomization energies and heats of formation originates with the truncation of the one-particle basis set expansion. Unfortunately, the use of finite basis sets is currently a computational necessity. Even with basis sets of quadruple zeta quality, errors can easily exceed 8 kcal/mol in small molecules, rendering the results of little practical use. Attempts to address this serious problem have led to a wide variety of proposals for simple complete basis set extrapolation formulas that exploit the regularity in the correlation consistent sequence of basis sets. This study explores the effectiveness of six formulas for reproducing the complete basis set limit. The W4 approach was also examined, although in lesser detail. Reference atomization energies were obtained from standard coupled-cluster singles, doubles, and perturbative triples (CCSD(T)) calculations involving basis sets of 6ζ or better quality for a collection of 141 molecules. In addition, a subset of 51 atomization energies was treated with explicitly correlated CCSD(T)-F12b calculations and very large basis sets. Of the formulas considered, all proved reliable at reducing the one-particle expansion error. Even the least effective formulas cut the error in the raw values by more than half, a feat requiring a much larger basis set without the aid of extrapolation. The most effective formulas cut the mean absolute deviation by a further factor of two. Careful examination of the complete body of statistics failed to reveal a single choice that out performed the others for all basis set combinations and all classes of molecules.
在标准耦合簇理论计算热力学性质（如原子化能和生成热）的误差中，主要原因是单粒子基组展开的截断。不幸的是，目前使用有限基组是计算的必要条件。即使使用四元基组，在小分子中也很容易出现超过 8 kcal/mol 的误差，使得结果几乎没有实际用途。为了解决这个严重的问题，人们提出了各种各样的简单完全基组外推公式的建议，这些公式利用了基组的相关一致序列的规律性。本研究探讨了六种公式在再现完全基组极限方面的有效性。尽管研究W4 方法的细节较少，但也对其进行了研究。参考原子化能是通过标准耦合簇单、双和微扰三（CCSD(T)）计算获得的，这些计算涉及质量为 6ζ 或更好的基组，涵盖了 141 个分子。此外，还对 51 个原子化能进行了用显式相关 CCSD(T)-F12b 计算和非常大的基组处理。在所考虑的公式中，所有公式都证明在减少单粒子展开误差方面是可靠的。即使是效果最差的公式，也能将原始值的误差减少一半以上，而无需外推就能实现这一目标需要更大的基组。最有效的公式进一步将平均绝对偏差降低了两倍。仔细检查完整的统计数据并没有发现一个单一的选择，在所有基组组合和所有分子类别中都优于其他选择。
