Shiozaki Toru, Kamiya Muneaki, Hirata So, Valeev Edward F
Department of Chemistry, Quantum Theory Project and The Center for Macromolecular Science and Engineering, University of Florida, Gainesville, Florida 32611-8435, USA.
J Chem Phys. 2009 Feb 7;130(5):054101. doi: 10.1063/1.3068302.
Efficient computer codes for the explicitly correlated coupled-cluster (CC-R12 or F12) methods with up to triple (CCSDT-R12) and quadruple excitations (CCSDTQ-R12), which take account of the spin, Abelian point-group, and index-permutation symmetries and are based on complete diagrammatic equations, have been implemented with the aid of the computerized symbolic algebra SMITH. Together with the explicitly correlated coupled-cluster singles and doubles (CCSD-R12) method reported earlier [T. Shiozaki et al., J. Chem. Phys. 129, 071101 (2008)], they form a hierarchy of systematic approximations (CCSD-R12<CCSDT-R12<CCSDTQ-R12) that converge very rapidly toward the exact solutions of the polyatomic Schrodinger equations with respect to both the highest excitation rank and basis-set size. Using the Slater-type function exp(-gamma r(12)) as a correlation function, a CC-R12 method can provide the aug-cc-pV5Z-quality results of the conventional CC method of the same excitation rank using only the aug-cc-pVTZ basis set. Combining these CC-R12 methods with the grid-based, numerical Hartree-Fock equation solver [T. Shiozaki and S. Hirata, Phys. Rev. A 76, 040503(R) (2007)], the solutions (eigenvalues) of the Schrodinger equations of neon, boron hydride, hydrogen fluoride, and water at their equilibrium geometries have been obtained as -128.9377+/-0.0004, -25.2892+/-0.0002, -100.459+/-0.001, and -76.437+/-0.003 E(h), respectively, without resorting to complete-basis-set extrapolations. These absolute total energies or the corresponding correlation energies agree within the quoted uncertainty with the accurate, nonrelativistic, Born-Oppenheimer values derived experimentally and/or computationally.
针对显式相关耦合簇（CC - R12或F12）方法，已借助计算机化符号代数SMITH实现了高效的计算机代码，这些方法涵盖高达三重激发（CCSDT - R12）和四重激发（CCSDTQ - R12），考虑了自旋、阿贝尔点群和指标置换对称性，且基于完整的图解方程。与之前报道的显式相关耦合簇单双激发（CCSD - R12）方法 [T. Shiozaki等人，《化学物理杂志》129, 071101 (2008)] 一起，它们构成了一个系统近似层次结构（CCSD - R12 < CCSDT - R12 < CCSDTQ - R12），该层次结构在最高激发阶数和基组大小方面都非常迅速地收敛到多原子薛定谔方程的精确解。使用斯莱特型函数exp(-γr(12))作为相关函数，CC - R12方法仅使用aug - cc - pVTZ基组就能提供相同激发阶数的传统CC方法的aug - cc - pV5Z质量的结果。将这些CC - R12方法与基于网格的数值哈特里 - 福克方程求解器 [T. Shiozaki和S. Hirata，《物理评论A》76, 040503(R) (2007)] 相结合，已获得氖、硼氢化物、氟化氢和水在其平衡几何构型下薛定谔方程的解（本征值），分别为 - 128.9377±0.0004、 - 25.2892±0.0002、 - 100.459±0.001和 - 76.437±0.003 E(h)，无需借助完整基组外推。这些绝对总能量或相应的相关能量在引用的不确定度范围内与通过实验和/或计算得出的准确、非相对论、玻恩 - 奥本海默值一致。
