Cluster Expansion of the Wavefunction Theory and its Applications
Project/Area Number 
01470008

Research Category 
GrantinAid for General Scientific Research (B)

Allocation Type  Singleyear Grants 
Research Field 
物理化学一般

Research Institution  Nagoya University 
Principal Investigator 
HIRAO Kimihiko Nagoya University, Department of Chemistry, College of General Education, Professor, 教養部 教授 (70093169)

CoInvestigator(Kenkyūbuntansha) 
NAKATSUJI Hiroshi Kyouto University, Faculty of Engineering, Professor, 工学部, 教授 (90026211)

Project Period (FY) 
1989 – 1990

Project Status 
Completed (Fiscal Year 1990)

Budget Amount *help 
¥6,300,000 (Direct Cost: ¥6,300,000)
Fiscal Year 1990: ¥2,400,000 (Direct Cost: ¥2,400,000)
Fiscal Year 1989: ¥3,900,000 (Direct Cost: ¥3,900,000)

Keywords  Cluster Expansion / SAC (Symmetry Adapted Cluster) Theory / SACCI Theory / Correlation Energy / MultiReference SAC Theory / Analytic Derivative Theory / HellmannFeynman 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 / SACCI法 
Research Abstract 
The nonclosedshell version of the SymmetryAdaptedCluster (SAC) theory is presented. We classified the total correlation effects into two groups, the dynamical (transferable) or specific (nontransferable) correlation effects. The specific correlation effects consist of neardegeneracies, the internal and semiinternal correlation and the spin polarization. Once specific correlation effects are included, the remaining effects are just like those in closedshells. We started with the RHF/CASSCF orbitals but redefined the reference function which includes the statespecific 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 noncommutative algebra. There is a very close parallel between the standard single reference SAC theory and its nonclosedshell version. We have discussed the openshell (excited state
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) SAC theory and the SAC theory based on a MultiReference Function (MRSAC). The theory provides lowlying excited state solutions as well as the ground state solution. The accuracy of the SACCI 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 SACCI 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 HellmannFeynman 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 oneelectron intergrals. No integrals are necessary involving derivatives of the basis functions. There is no need of solving the coupled perturbed HartreeFock 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 HellmannFeynman force picture associated with the first derivatives. Less

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Research Products
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