| Project/Area Number |
13640496
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Physical chemistry
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| Research Institution | MURORAN INSTITUTE OF TECHNOLOGY |
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Principal Investigator |
OHTA Katsuhisa Muroran Institute of Technology, Applied Chemistry, Associate Professor, 工学部, 助教授 (50152129)
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| Project Period (FY) |
2001 – 2002
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| Project Status |
Completed (Fiscal Year 2002)
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| Budget Amount *help |
¥2,200,000 (Direct Cost: ¥2,200,000)
Fiscal Year 2002: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 2001: ¥1,500,000 (Direct Cost: ¥1,500,000)
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| Keywords | time-dependent variational principle / TDVP / inequality constraints / Weierstrass-Erdmann's corner condition / UHF wavefunction / radical orbital / Koopmans' theorem / variational duality |
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| Research Abstract |
Time-dependent variational principle (TDVP) under inequality constraints with general physical quantity expectation values has been investigated to apply for the time-development of many-electron wavefunctions in the electron- and spin-transfer processes in molecules. The Hilbert subspace in which the inequality constraints are satisfied is defined as phase-I. The subspace in which the equality constraints are active is defined as phase-II. The total action for the TDVP is defined with the direct sum of actions in subspaces. Weierstrass-Erdmann's corner condition is also considered.
The spin-unrestricted Hartree-Fock (UHF) wavefunctions are often adopted as initial states of spin- and electron-transfer processes. The unpaired orbitals in the UHF wavefunctions take an important role in the transfer processes. We have investigated a handy way to find radical orbitals buried in UHF wavefunctions and the variational meaning of Koopmans' theorem. For doublet radicals, the highest occupied molecular orbital (HOMO) of α-orbitals usually corresponds to the radical orbital which is occupied by an unpaired electron. Occasionally, however, the α-HOMO fails to identify the radical orbital while the lowest unoccupied MO (LUMO) of β-orbitals indicates the radical orbital correctly. In this work, we have examined the applicability of the handy way to identify the radical orbital with the α -HOMO or the β -LUMO of UHF wavefunctions. Koopmans' theorem not only provides a numerical method to calculate approximate ionization potential energies but also has another variational meaning. We have shown that an extension of the variational meaning of the theorem to many-electron ionization processes leads naturally to the SCF equation for hole orbitals.
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