Cluster Expansion of the Wavefunction Theory and its Applications

波函数理论的簇展开及其应用

• 批准号: 01470008
• 负责人: HIRAO Kimihiko
• 金额: $ 4.03万
• 依托单位: Nagoya University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for General Scientific Research (B)
• 财政年份: 1989
• 资助国家: 日本
• 起止时间: 1989 至 1990
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-01470008/
• 关键词: Cluster Expansion; SAC (Symmetry Adapted Cluster) Theory; SAC-CI Theory; Correlation Energy; Multi-Reference SAC Theory; Analytic Derivative Theory; Hellmann-Feynman Theorem; 電子状態理論; 電子相関問題; electron cusp条件; 電子間の座標をあらわに含む理論; SAC-CI法

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

提出了对称适应群集（SAC）理论的非关闭壳版本。我们将总相关效应分为两组，即动态（可转移）或特定（不可转移）相关效应。特定的相关效应包括近一化，内部和半内部相关性以及自旋极化。一旦包括特定的相关效应，其余效果就会像封闭壳中的效果一样。我们从RHF/CASSCF轨道开始，但重新定义了参考函数，其中包括特定于状态的相关效应。特定的相关效应以线性算子的形式表达，并且通过指数运算符处理动态相关性。目前的理论是确切的，不包括非交通性代数。标准单一参考SAC理论与其非关闭壳版本之间存在非常紧密的相似之处。我们已经讨论了基于多引用函数（MRSAC）的开放式SAC理论和SAC理论。该理论提供了低覆盖的激发态解决方案以及基态溶液。还通过与[4S2P]基集的完整CI结果进行比较，还检查了SAC-CI方法的SAC-CI方法的精度。兴奋能量一致的SAC-CI结果占完整CI结果的1.4％以内。对于分子的核坐标，第二，第三和第四个衍生物的一般公式来自Hellmann-Feynman定理。该过程等同于使用扰动变化方法得出这些较高的能量衍生物。与直接分析衍生物相比，有几个重要的优势。这些较高的能量衍生物的表达比直接分析衍生方法的表达要简单得多。静电计算仅涉及一个电子间隔。不需要积分涉及基础函数的导数。无需求解获得波函数衍生物的耦合的扰动的hartree-fock方程。一个只需要线性等价的解决方案。不涉及迭代。与这些较高的衍生物相关的直观物理图片是与第一衍生物相关的Hellmann-Feynman Force图片。较少的

项目成果

H. Wasada and K. Hirao: "Theoretical Study of the Pennta-Coordinated Trigonal Bipyramidal Compounds"

H. Wasada 和 K. Hirao：“五角配位三角双锥化合物的理论研究”

K.Hirao: "The NonーClosedーShell Symmetry Adapted Cluster (SAC) Theory.The OpenーShell SAC theory and MultiーReference SAC theory" submitted for J.Chem.Phys.

K.Hirao：“非闭壳对称自适应簇 (SAC) 理论。开壳 SAC 理论和多参考 SAC 理论”提交给 J.Chem.Phys。

K.HIRAO: "Floating Functions Satisfying the HellmannーFeynman Theorem" Submitted for J.Chem.Phys.

K.HIRAO：“满足赫尔曼-费曼定理的浮点函数”提交给 J.Chem.Phys。

H.Nakatsuji,K.Hirao,Y.Mizukami: "SACーCI and Full CI Calculations for the Singlet and Triplet Excited States of H_2O" Chem.Phys.Lett.in press.

H.Nakatsuji、K.Hirao、Y.Mizukami：“H_2O 的单线态和三线态激发态的 SAC-CI 和完整 CI 计算”Chem.Phys.Lett.in 出版社。

H.Wasada and K.Hirao: "Theoretical Study of the reaction of pentaーcoordinated trigonalibipyramidal compounds" submitted for J.Amer.Chem.Soc.

H.Wasada 和 K.Hirao：“五配位三方双锥化合物反应的理论研究”提交给 J.Amer.Chem.Soc。