Time development of many-electron wave functions based on the time-dependent variational principle toward separation of collective coordinates
| Project/Area Number |
17550003
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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, Associate Professor, 工学部, 助教授 (50152129)
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| Project Period (FY) |
2005 – 2006
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| Project Status |
Completed (Fiscal Year 2006)
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| Budget Amount *help |
¥2,000,000 (Direct Cost: ¥2,000,000)
Fiscal Year 2006: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 2005: ¥1,200,000 (Direct Cost: ¥1,200,000)
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| Keywords | time-dependent variational principle / TDVP / constraints / consistency conditions / sensitivity analysis / geodesic deviation |
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| Research Abstract |
Time-dependent variational principle (TDVP) is formulated in many-electron wave functions for electron-transfer processes in molecules. The stationary action principle in the TDVP leads to the pseudo classical-mechanics of variational parameters. All the rich apparatus developed for the study of classical mechanics can be applied to the TDVP. The sensitivity analysis for the TDVP is also investigated. The sensitivity analysis is a technique to assess how the solutions in nonlinear systems depend on external parameters. The obtained sensitivity equations can be considered as an extension of the Jacobi equation to the geodesic deviation which is caused by external parameters. For example, in the Born-Oppenheimer approximation for molecules, the sensitivity analysis enables us to calculate the dynamical variation of electronic states due to nuclear coordinates. From the viewpoint of the pseudo classical-mechanics of the TDVP, the sensitivity analysis assesses the deviation between nearby
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trajectories, i.e., the geodesic deviation caused by external parameters. Moreover, if we consider constraints in the TDVP, the structure of the pseudo classical-mechanics enables us to utilize Dirac's constrained classical-mechanics. The constraints in the TDVP are classified into the first-and second-classes according to Dirac's terminology. The Lagrange multipliers for the constraints are determined by the consistency conditions. The sensitivity analysis inherits the constraints in the TDVP. The consistency conditions for the constraints are, however, satisfied automatically in the sensitivity analysis. We need to impose the constraints only on initial values of the sensitivity functions. Two illustrative examples of the sensitivity analysis are investigated. One is a simple analysis for wave functions which are linearly expanded in adiabatic bases. The other example is the geodesic deviation in the neighborhood of stationary states for general wave functions and the dynamical and the statical stabilities are related with each other. Less
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Report
(3 results)
Research Products
(1 results)
