Valeev Edward F, Daniel Crawford T
Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, USA.
J Chem Phys. 2008 Jun 28;128(24):244113. doi: 10.1063/1.2939577.
To approach the complete basis set limit of the "gold-standard" coupled-cluster singles and doubles plus perturbative triples [CCSD(T)] method, we extend the recently proposed perturbative explicitly correlated coupled-cluster singles and doubles method, CCSD(2)(R12) [E. F. Valeev, Phys. Chem. Chem. Phys. 8, 106 (2008)], to account for the effect of connected three-electron correlations. The natural choice of the zeroth-order Hamiltonian produces a perturbation expansion with rigorously separable second-order energy corrections due to the explicitly correlated geminals and conventional triple and higher excitations. The resulting CCSD(T)(R12) energy is defined as a sum of the standard CCSD(T) energy and an amplitude-dependent geminal correction. The method is technically very simple: Its implementation requires no modification of the standard CCSD(T) program and the formal cost of the geminal correction is small. We investigate the performance of the open-shell version of the CCSD(T)(R12) method as a possible replacement of the standard complete-basis-set CCSD(T) energies in the high accuracy extrapolated ab initio thermochemistry model of Stanton et al. [J. Chem. Phys. 121, 11599 (2004)]. Correlation contributions to the heat of formation computed with the new method in an aug-cc-pCVXZ basis set have mean absolute basis set errors of 2.8 and 1.0 kJmol when X is T and Q, respectively. The corresponding errors of the standard CCSD(T) method are 9.1, 4.0, and 2.1 kJmol when X=T, Q, and 5. Simple two-point basis set extrapolations of standard CCSD(T) energies perform better than the explicitly correlated method for absolute correlation energies and atomization energies, but no such advantage found when computing heats of formation. A simple Schwenke-type two-point extrapolation of the CCSD(T)(R12)aug-cc-pCVXZ energies with X=T,Q yields the most accurate heats of formation found in this work, in error on average by 0.5 kJmol and at most by 1.7 kJmol.
为了逼近“金标准”耦合簇单双激发加微扰三激发[CCSD(T)]方法的完全基组极限，我们扩展了最近提出的微扰显式相关耦合簇单双激发方法CCSD(2)(R12)[E.F.瓦列耶夫，《物理化学化学物理》8，106(2008)]，以考虑连通三电子相关的影响。零阶哈密顿量的自然选择产生了一个微扰展开，由于显式相关的双电子对以及传统的三激发和更高激发，其二阶能量修正严格可分离。由此得到的CCSD(T)(R12)能量定义为标准CCSD(T)能量与一个依赖于振幅的双电子对修正之和。该方法在技术上非常简单：其实现不需要修改标准CCSD(T)程序，并且双电子对修正的形式成本很小。我们研究了CCSD(T)(R12)方法的开壳层版本作为斯坦顿等人[《化学物理杂志》121，11599(2004)]高精度外推从头算热化学模型中标准完全基组CCSD(T)能量的可能替代方法的性能。在aug-cc-pCVXZ基组中用新方法计算的生成热的相关贡献，当X为T和Q时，平均绝对基组误差分别为2.8和1.0kJ/mol。当X = T、Q和5时，标准CCSD(T)方法的相应误差分别为9.1、4.0和2.1kJ/mol。对于绝对相关能和原子化能，标准CCSD(T)能量的简单两点基组外推比显式相关方法表现更好，但在计算生成热时没有发现这样的优势。用X = T、Q的CCSD(T)(R12)/aug-cc-pCVXZ能量进行简单的施温克型两点外推，得到了本工作中最精确的生成热，平均误差为0.5kJ/mol，最大误差为1.7kJ/mol。
