| Project/Area Number |
01470008
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| Research Category |
Grant-in-Aid for General Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
物理化学一般
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| Research Institution | Nagoya University |
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Principal Investigator |
HIRAO Kimihiko Nagoya University, Department of Chemistry, College of General Education, Professor, 教養部 教授 (70093169)
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| Co-Investigator(Kenkyū-buntansha) |
NAKATSUJI Hiroshi Kyouto University, Faculty of Engineering, Professor, 工学部, 教授 (90026211)
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| Project Period (FY) |
1989 – 1990
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| Project Status |
Completed (Fiscal Year 1990)
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| 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)
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| Keywords | 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 |
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| Research Abstract |
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
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