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分子や固体の電子状態を解明する、密度行列汎関数理論の開発

发展密度矩阵泛函理论来阐明分子和固体的电子态

基本信息

批准号：
12042234
负责人：
安田耕二
金额：
$ 0.96万
依托单位：
Nagoya University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research on Priority Areas (A)
财政年份：
2000
资助国家：
日本
起止时间：
2000 至 2001
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-12042234/
关键词：
電子状態理論電子相関密度行列密度汎関数理論密度汎関数法

项目摘要

原子分子、固体の基底電子状態を解明できる、密度行列汎関数理論(DMFT)の開発を行った。前年度までに、波動方程式の密度行列表現を用い、エネルギー帆関数の決定方程式を得た。本年度はこの汎関数決定方程式を可能な限り手で解き、相関エネルギーを陽に与えた。再構成したハミルトニアンの主要項のみ残して得られる偏微分方程式を解くと、相関エネルギーに対す幾つかの表式を与える。この表式から、局所近似の仮定下で相関エネルギーを良く近似する局所変数を決定した。幾つかの原子分子でエネルギー値を調べると、これらは真の値を良く表す事がわかった。そこで電子ガスの相関エネルギー表式に基づき、電子密度とこの局所変数を使った、相関エネルギーの局所近似を提案した。電子ガスの相関エネルギーはビリアル定理、摂動級数解析、電子ガスの正確な運動量分布関数から計算した。一様な座標スケール則を満たすために、電子の質量を基本変数の汎関数とした。このエネルギー表式は1電子系でも正しい結果を与え、交換エネルギーの誤差は小さく、スピン分極した系へ簡単に拡張できる。原子分子に対して、我々の汎関数で変分計算を行うと、平均場近似や密度汎関数法での局所近似よりずっと良い全エネルギー、一般勾配補正汎関数と同程度のエネルギーを与えた。我々の汎関数は正確で実用的であり、更なる改良への良い出発点になる事を示している。縮約シュレーディンガー方程式は、基礎変数を選択する信頼できる方法を与える。勾配補正項を加えると現在の密度汎関数理論より大幅に精度が高まる事が期待できる。開殻系や分散力への拡張など更なる研究が期待できる。

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