Cluster Expansion of the Wavefunction Theory and its Applications

给出了对称适应团簇(SAC)理论的非闭壳形式。我们将总体相关效应分为动态(可转移)相关效应和特定(不可转移)相关效应。具体的关联效应包括近简并效应、内部关联和半内部关联以及自旋极化。一旦包括了特定的关联效应，剩下的效应就像闭合壳中的效应一样。我们从RHF/CASSCF轨道开始，但重新定义了参考函数，它包括特定于状态的关联效应。具体的关联效应用线性算符的形式表示，而动态关联则用指数算符来处理。目前的理论是精确的，不包括非对易代数。标准的单参考SAC理论和它的非封闭壳版本之间有非常接近的相似之处。我们讨论了开壳层(激发态…SAC理论和基于多参考函数的SAC理论(MRSAC)。该理论提供了低激发态解和基态解，并与[4s2p]基组的完整计算结果进行了比较，验证了SAC-CI方法对H2O单重态和三重态的计算精度。由Hellmann-Feynman定理导出了激发能相对于分子核坐标的二阶、三阶和四阶导数的一般公式。这个过程相当于用微扰变分方法推导出这些高能导数。与直接解析导数法相比，它有几个显著的优点。这些高能导数的表达式比直接解析导数法简单得多。静电计算只涉及一个电子积分。基函数的导数不需要积分。不需要求解耦合的摄动Hartree-Fock方程，即可得到波函数的导数。人们只需要线性方程的解。不涉及任何迭代。有一些直观的物理图像与这些更高的导数相关，如与一阶导数相关的Hellmann-Feynman力图。较少

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