Department of Chemistry, Washington State University, Pullman, Washington 99164, USA.
J Chem Phys. 2009 Nov 21;131(19):194105. doi: 10.1063/1.3265857.
Accurate extrapolation to the complete basis set (CBS) limit of valence correlation energies calculated with explicitly correlated MP2-F12 and CCSD(T)-F12b methods have been investigated using a Schwenke-style approach for molecules containing both first and second row atoms. Extrapolation coefficients that are optimal for molecular systems containing first row elements differ from those optimized for second row analogs, hence values optimized for a combined set of first and second row systems are also presented. The new coefficients are shown to produce excellent results in both Schwenke-style and equivalent power-law-based two-point CBS extrapolations, with the MP2-F12/cc-pV(D,T)Z-F12 extrapolations producing an average error of just 0.17 mE(h) with a maximum error of 0.49 for a collection of 23 small molecules. The use of larger basis sets, i.e., cc-pV(T,Q)Z-F12 and aug-cc-pV(Q,5)Z, in extrapolations of the MP2-F12 correlation energy leads to average errors that are smaller than the degree of confidence in the reference data (approximately 0.1 mE(h)). The latter were obtained through use of very large basis sets in MP2-F12 calculations on small molecules containing both first and second row elements. CBS limits obtained from optimized coefficients for conventional MP2 are only comparable to the accuracy of the MP2-F12/cc-pV(D,T)Z-F12 extrapolation when the aug-cc-pV(5+d)Z and aug-cc-pV(6+d)Z basis sets are used. The CCSD(T)-F12b correlation energy is extrapolated as two distinct parts: CCSD-F12b and (T). While the CCSD-F12b extrapolations with smaller basis sets are statistically less accurate than those of the MP2-F12 correlation energies, this is presumably due to the slower basis set convergence of the CCSD-F12b method compared to MP2-F12. The use of larger basis sets in the CCSD-F12b extrapolations produces correlation energies with accuracies exceeding the confidence in the reference data (also obtained in large basis set F12 calculations). It is demonstrated that the use of the 3C(D) Ansatz is preferred for MP2-F12 CBS extrapolations. Optimal values of the geminal Slater exponent are presented for the diagonal, fixed amplitude Ansatz in MP2-F12 calculations, and these are also recommended for CCSD-F12b calculations.
已使用施文克（Schwenke）风格方法研究了用显式相关 MP2-F12 和 CCSD(T)-F12b 方法计算的价相关能量，对完全基组（CBS）极限的精确外推。对于包含第一和第二行原子的分子，用于优化分子系统的外推系数不同于用于优化第二行类似物的外推系数，因此还提出了针对第一和第二行系统组合的优化系数。新系数在施文克风格和等效幂律两点 CBS 外推中均产生了出色的结果，MP2-F12/cc-pV(D,T)Z-F12 外推的平均误差仅为 0.17 mE(h)，最大误差为 0.49，适用于 23 个小分子的集合。在 MP2-F12 相关能量的外推中使用更大的基组，即 cc-pV(T,Q)Z-F12 和 aug-cc-pV(Q,5)Z，会导致平均误差小于参考数据的置信度（约为 0.1 mE(h)）。后者是通过在包含第一和第二行元素的小分子上使用 MP2-F12 计算非常大的基组获得的。对于常规 MP2 获得的 CBS 极限，仅当使用 aug-cc-pV(5+d)Z 和 aug-cc-pV(6+d)Z 基组时，才与 MP2-F12/cc-pV(D,T)Z-F12 外推的精度相当。CCSD(T)-F12b 相关能量被外推为两个不同的部分：CCSD-F12b 和 (T)。虽然使用较小基组的 CCSD-F12b 外推在统计学上不如 MP2-F12 相关能量准确，但这可能是由于 CCSD-F12b 方法与 MP2-F12 相比，基组收敛速度较慢。在 CCSD-F12b 外推中使用更大的基组会产生精度超过参考数据置信度的相关能量（也在大型 F12 计算中获得）。结果表明，对于 MP2-F12 CBS 外推，使用 3C(D) 假设更为可取。对于 MP2-F12 计算中的对角固定幅度假设，给出了 geminal Slater 指数的最佳值，并建议在 CCSD-F12b 计算中使用这些值。
