2006 Fiscal Year Final Research Report Summary
Theory of Electron-Pair Density Functions and Its Quantum Chemical Applications
| Project/Area Number |
17550002
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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 |
KOGA Toshikatsu Muroran Institute of Technology, Department of Applied Chemistry, Professor, 工学部, 教授 (90113688)
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| Project Period (FY) |
2005 – 2006
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| Keywords | Electron-Pair Densities / Radial Splitting / Momentum Splittin / Electron Repulsion / Atoms |
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| Research Abstract |
The motions of electron-pairs in atoms and molecules are described by the electron-pair intracule (relative motion) and extracule (center-of-mass motion) density functions. For atomic systems, these electron-pair densities are characterized by their spherical averages. The electron-pair densities are important probability density functions to understand the electron-electron interactions in atoms and molecules, but up to now we have neither sufficient knowledge about their theoretical structures nor practical applications to quantum chemical problems.
The purpose of this research project has been to clarify the theoretical structure of the electron-pair density functions and to apply new results to various chemical and physical problems. The results of this research project during the two years are summarized as follows:
1. From the viewpoint of electron-pair densities, we showed that the average electron momentum consists of two components, low momentum and high momentum.
2. The sum and difference of the inner and outer radii were shown to constitute the upper and lower bounds, respectively, of the electron-pair relative and center-of-mass radii.
3. We found that the electron momentum density consists of low momentum density and high momentum density.
4. We clarified the mathematical structure of electron-pair densities and derived a general expression for the dependence of the electron repulsion energy on the interelectronic angle.
5. Based on the simultaneous consideration of two electrons, we showed that the electron radial density is rigorously separated into inner and outer densities.
6. We showed that the subshell average momentum can be separated into low and high momenta, and their values are related to the exponents of double-zeta basis functions.
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Research Products
(12 results)
