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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Harris functional ： ウィキペディア英語版 Harris functional In density functional theory (DFT), the Harris energy functional is a non-self-consistent approximation to the Kohn-Sham density functional theory. It gives the energy of a combined system as a function of the electronic densities of the isolated parts. The energy of the Harris functional varies much less than the energy of the Kohn-Sham functional as the density moves away from the converged density. Assuming that we have an approximate electron density $\backslash rho(\backslash vec\; r)$, which is different from the exact electron density $\backslash rho\_0(\backslash vec\; r)$. We construct exchange-correlation potential $v\_(\backslash vec\; r)$ and the Hartree potential $v\_(\backslash vec\; r)$ based on the approximate electron density $\backslash rho(\backslash vec\; r)$. Kohn-Sham equations are then solved with the XC and Hartree potentials and eigenvalues are then obtained. The sum of eigenvalues is often called the band energy: $E\_=\backslash sum\_i\; \backslash epsilon\_i,$ where $i$ loops over all occupied Kohn-Sham orbitals. Harris energy functional is defined as $E\_\; =\; \backslash sum\_i\; \backslash epsilon\_i\; -\; \backslash int\; dr^3\; v\_(\backslash vec\; r)\; \backslash rho(\backslash vec\; r)\; -\; \backslash frac\; \backslash int\; dr^3\; v\_(\backslash vec\; r)\; \backslash rho(\backslash vec\; r)\; +\; E\_()$ It was discovered by Harris that the difference between the Harris energy $E\_$ and the exact total energy is to the second order of the error of the approximate electron density, i.e., $O((\backslash rho-\backslash rho\_0)^2)$. Therefore, for many systems the accuracy of Harris energy functional may be sufficient. The Harris functional was originally developed for such calculations rather than self-consistent convergence, although it can be applied in a self-consistent manner in which the density is changed. Many density-functional tight-binding methods, such as (DFTB+ ), (Fireball ), and (Hotbit ), are built based on the Harris energy functional. In these methods, one often does not perform self-consistent Kohn-Sham DFT calculations and the total energy is estimated using the Harris energy functional. These codes are often much faster than conventional Kohn-Sham DFT codes that solve Kohn-Sham DFT in a self-consistent manner. While the Kohn-Sham DFT energy is Variational method (never lower than the ground state energy), the Harris DFT energy was originally believed to be anti-variational (never higher than the ground state energy). This was however conclusively demonstrated to be incorrect. == References == 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Harris functional」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.