Cluster Expansion of the Wavefunction Theory and its Applications

非封闭壳层版本的对称适应集团（SAC）理论。我们将总的相关效应分为两组，动态（可转移）或特定（不可转移）的相关效应。具体的关联效应包括近简并、内关联和半内关联以及自旋极化。一旦包含了特定的相关效应，其余的效应就像闭壳层中的效应一样。我们从RHF/CASSCF轨道开始，但重新定义了参考函数，其中包括特定状态的相关效应。特定的相关效应以线性算子的形式表示，动态相关性通过指数算子来处理。本文的理论是精确的，不包括非交换代数。在标准的单参考SAC理论和它的非闭合壳层版本之间有非常接近的平行。我们讨论了开壳层（激发态 ...更多信息 SAC理论和基于多参考函数的SAC理论（MRSAC）。该理论不仅给出了基态解，而且给出了激发态解，并通过与[4s 2 p]基组下的全CI计算结果的比较，验证了SAC-CI方法对H_2O单重态和三重态计算的准确性。SAC-CI的激发能计算结果与全CI结果的符合率在1.4%以内，并由Hellmann-Feynman定理导出了激发能对原子核坐标的二阶、三阶和四阶导数的一般公式。这一过程等价于用微扰变分法导出这些高能导数。与直接解析导数法相比，有几个显著的优点。这些高能导数的表达式比直接解析导数方法简单得多。静电计算只涉及单电子积分。不需要涉及基函数导数的积分。不需要求解耦合摄动Hartree-Fock方程，就可以得到波函数的导数。我们只需要解线性方程组。不涉及迭代。有一些直观的物理图像与这些高阶导数相关联，如与一阶导数相关联的赫尔曼-费曼力图像。少

The non-closed-shell version of the Symmetry-Adapted-Cluster (SAC) theory is presented. We classified the total correlation effects into two groups, the dynamical (transferable) or specific (non-transferable) correlation effects. The specific correlation effects consist of near-degeneracies, the internal and semi-internal correlation and the spin polarization. Once specific correlation effects are included, the remaining effects are just like those in closed-shells. We started with the RHF/CASSCF orbitals but re-defined the reference function which includes the state-specific correlation effects. Specific correlation effects are expressed in the form of the linear operator and the dynamical correlation is treated by means of the exponential operator. The present theory is exact and does not include the non-commutative algebra. There is a very close parallel between the standard single reference SAC theory and its non-closed-shell version. We have discussed the open-shell (excited state … More ) SAC theory and the SAC theory based on a Multi-Reference Function (MRSAC). The theory provides low-lying excited state solutions as well as the ground state solution.The accuracy of the SAC-CI method is also examined for the singlet and triplet states of H_2O by comparing with the full CI results for the [4s2p] basis set. The SAC-CI results for the excitation energy agree to within 1.4% of the full CI results.General formulae for the second, third and fourth derivatives of the energy with respect to the nuclear coordinates of a molecule are derived from the Hellmann-Feynman theorem. The procedure is equivalent to deriving these higher energy derivatives by using the perturbation variation method. There are several significant advantages over the direct analytic derivative method. The expressions of these higher energy derivatives are much simpler than those of the direct analytic derivative method. The electrostatic calculation involves only one-electron intergrals. No integrals are necessary involving derivatives of the basis functions. There is no need of solving the coupled perturbed Hartree-Fock equations the obtain to wavefunction derivatives. One only needs solutions of linear equations. There is no iteration involved. There are intuitive physical pictures associated with these higher derivatives as the Hellmann-Feynman force picture associated with the first derivatives. Less