Shiozaki Toru, Valeev Edward F, Hirata So
Quantum Theory Project and the Center for Macromolecular Science and Engineering, Department of Chemistry, University of Florida, Gainesville, Florida 32611-8435, USA.
J Chem Phys. 2009 Jul 28;131(4):044118. doi: 10.1063/1.3193463.
Coupled-cluster singles and doubles (CCSD) or coupled-cluster singles, doubles, and triples (CCSDT) with noniterative, perturbation corrections for higher-order excitations have been extended to include the basis functions that explicitly depend on interelectronic distances (r(12)) in the wave function expansions with the aim of dramatically accelerating the basis-set convergence of correlation energies. The extension has been based on the so-called R12 (or F12) scheme and applied to a second-order triples correction to CCSD [CCSD(2)(T)-R12], a second-order triples and quadruples correction to CCSD [CCSD(2)(TQ)-R12], a third-order triples correction to CCSD [CCSD(3)(T)-R12], and a second-order quadruples correction to CCSDT [CCSDT(2)(Q)-R12]. A simplified R12 treatment suggested by Fliegl et al. [J. Chem. Phys. 122, 084107 (2005)] has been combined with some of these methods, introducing CCSD(2)(T)(R12) and CCSD(2)(TQ)(R12). The CCSD(T)-R12 method has also been developed as an approximation to CCSD(2)(T)-R12. These methods have been applied to dissociation of hydrogen fluoride and double dissociation of water. For the molecules at their equilibrium geometries, molecular properties predicted by these methods converge extremely rapidly toward the complete-correlation, complete-basis-set limits with respect to the cluster excitation rank, perturbation order, and basis-set size. Although the R12 scheme employed in this work does not improve the basis-set convergence of connected triples or quadruples corrections, the basis-set truncation errors in these contributions have roughly the same magnitude as small residual basis-set truncation errors in the connected singles and doubles contributions even in the dissociation of hydrogen fluoride. In the double dissociation of water, the basis-set truncation errors in the connected triples contribution can be a few times as great as those in the connected singles and doubles contributions.
耦合簇单双激发（CCSD）或耦合簇单双三激发（CCSDT），并对高阶激发进行非迭代微扰校正，已得到扩展，以在波函数展开中纳入明确依赖电子间距离（r(12)）的基函数，目的是显著加速相关能的基组收敛。这种扩展基于所谓的R12（或F12）方案，并应用于CCSD的二阶三激发校正[CCSD(2)(T)-R12]、CCSD的二阶三激发和四激发校正[CCSD(2)(TQ)-R12]、CCSD的三阶三激发校正[CCSD(3)(T)-R12]以及CCSDT的二阶四激发校正[CCSDT(2)(Q)-R12]。Fliegl等人[《化学物理杂志》122, 084107 (2005)]提出的简化R12处理方法已与其中一些方法相结合，引入了CCSD(2)(T)(R12)和CCSD(2)(TQ)(R12)。CCSD(T)-R12方法也已被开发为CCSD(2)(T)-R12的近似方法。这些方法已应用于氟化氢的解离和水的双解离。对于处于平衡几何构型的分子，这些方法预测的分子性质在簇激发等级、微扰阶数和基组大小方面极其迅速地收敛到完全相关、完全基组极限。尽管本工作中采用的R12方案并未改善连接三激发或四激发校正的基组收敛，但即使在氟化氢的解离中，这些贡献中的基组截断误差与连接单双激发贡献中的小残余基组截断误差大致具有相同的量级。在水的双解离中，连接三激发贡献中的基组截断误差可能是连接单双激发贡献中的基组截断误差的几倍。
