第一原理分子動力学プログラム STATE Senri Wiki
開始行:
* 交換増強因子の表式とパラメータ [#l39be222]
交換エネルギー汎関数
\[
E_{x}[n]=\int{\rm d}\bm{r}\,n\varepsilon_{x}^{\rm LDA}(n)...
\varepsilon_{x}^{\rm LDA}(n)=-\frac{3}{4\pi}k_F,\quad k_F...
\]
における$F_x(s)$を交換増強因子と呼ぶ。
** B86b型 [#zfe74a91]
\[
F_x(s)=1+\frac{\mu s^2}{(1+\mu s^2/\kappa)^{4/5}}=\left\{
\begin{array}{ll}
1+\mu s^2&s\rightarrow0\\
(\mu\kappa^4)^{1/5}s^{2/5}&s\rightarrow\infty
\end{array}
\right.
\]
|CENTER:Method|CENTER:$\mu$|CENTER:$\kappa$|CENTER:$(\mu\...
|B86b|0.2449|0.5757|0.485|[[A. D. Becke, JCP 85, 7184 (19...
|optB86b|0.1234|1|0.658|[[J. Klimes et al., PRB 83, 19513...
|B86R|0.1234|0.7114|0.501|[[I. Hamada, PRB 89, 121103(R) ...
ただし$\mu_{\rm GEA}=10/81\simeq0.1234$である。
** PW86型 [#jb0f34cb]
\[
F_x(s)=(1+15as^2+bs^4+cs^6)^{1/15}=\left\{
\begin{array}{ll}
1+a s^2&s\rightarrow0\\
c^{1/15}s^{2/5}&s\rightarrow\infty
\end{array}
\right.
\]
|CENTER:Method|CENTER:$a$|CENTER:$b$|CENTER:$c$|CENTER:$c...
|PW86|0.0864|14|0.2|0.898|[[J. P. Perdew and Y. Wang, PRB...
|PW86R|0.1234|17.33|0.163|0.886|[[E. D. Murray et al., JC...
ただし$7/81\simeq0.0864, \mu_{\rm GEA}=10/81\simeq0.1234$...
** B88型 [#z125b612]
\[
F_x(s)=1+\frac{\mu s^2}{1+\frac{9}{4\pi}\mu s\,{\rm sinh}...
\]
|CENTER:Method|CENTER:$\mu$|CENTER:$\lambda$|CENTER:Refer...
|B88|$0.2743$|$2(6\pi^2)^{1/3}$|[[A. D. Becke, Phys. Rev....
|optB88|$0.22$|$1.2\times(9/2)(6/\pi)^{1/3}$|J. Klimes et...
** PW91型 [#udd45bd2]
** PBE型 [#a62f0db3]
\[
F_x(s)=1+\kappa-\frac{\kappa}{1+\mu s^2/\kappa}=1+\frac{\...
\begin{array}{ll}
1+\mu s^2&s\rightarrow0\\
1+\kappa&s\rightarrow\infty
\end{array}
\right.
\]
|CENTER:Method|CENTER:$\mu$|CENTER:$\kappa$|CENTER:Refere...
||0.235|0.967|A. D. Becke, J. Chem. Phys. 84, 4524 (1986)|
|PBE|0.21951|0.804|J. P. Perdew et al., Phys. Rev. Lett. ...
|revPBE|0.21951|1.245|Y. Zhang and W. Yang, Phys. Rev. Le...
|PBEsol|0.1235||J. P. Perdew et al., Phys. Rev. Lett. 100...
|optPBE|0.175519|1.04804|J. Klimes et al., J. Phys. Cond....
ただし$\mu_{\rm GEA}=10/81\simeq0.1235$である。
** RPBE型 [#v8c3ded0]
\[
F_x(s)=1+\kappa(1-e^{-\mu s^2/\kappa})=\left\{
\begin{array}{ll}
1+\mu s^2&s\rightarrow0\\
1+\kappa&s\rightarrow\infty
\end{array}
\right.
\]
|CENTER:Method|CENTER:$\mu$|CENTER:$\kappa$|CENTER:Refere...
|RPBE|0.21951|0.804|B. Hammer et al. Phys. Rev. B 59, 741...
** C09型 [#o170764e]
\[
F_x(s)=1+\mu s^2 e^{-\alpha s^2}+\kappa(1-e^{-\alpha s^2/...
\begin{array}{ll}
1+(\mu+\kappa\alpha/2) s^2&s\rightarrow0\\
1+\kappa&s\rightarrow\infty
\end{array}
\right.
\]
|CENTER:Method|CENTER:$\mu$|CENTER:$\kappa$|CENTER:$\alph...
|C09|0.0617|1.245|0.0483|V. R. Cooper Phys. Rev. B 81, 16...
終了行:
* 交換増強因子の表式とパラメータ [#l39be222]
交換エネルギー汎関数
\[
E_{x}[n]=\int{\rm d}\bm{r}\,n\varepsilon_{x}^{\rm LDA}(n)...
\varepsilon_{x}^{\rm LDA}(n)=-\frac{3}{4\pi}k_F,\quad k_F...
\]
における$F_x(s)$を交換増強因子と呼ぶ。
** B86b型 [#zfe74a91]
\[
F_x(s)=1+\frac{\mu s^2}{(1+\mu s^2/\kappa)^{4/5}}=\left\{
\begin{array}{ll}
1+\mu s^2&s\rightarrow0\\
(\mu\kappa^4)^{1/5}s^{2/5}&s\rightarrow\infty
\end{array}
\right.
\]
|CENTER:Method|CENTER:$\mu$|CENTER:$\kappa$|CENTER:$(\mu\...
|B86b|0.2449|0.5757|0.485|[[A. D. Becke, JCP 85, 7184 (19...
|optB86b|0.1234|1|0.658|[[J. Klimes et al., PRB 83, 19513...
|B86R|0.1234|0.7114|0.501|[[I. Hamada, PRB 89, 121103(R) ...
ただし$\mu_{\rm GEA}=10/81\simeq0.1234$である。
** PW86型 [#jb0f34cb]
\[
F_x(s)=(1+15as^2+bs^4+cs^6)^{1/15}=\left\{
\begin{array}{ll}
1+a s^2&s\rightarrow0\\
c^{1/15}s^{2/5}&s\rightarrow\infty
\end{array}
\right.
\]
|CENTER:Method|CENTER:$a$|CENTER:$b$|CENTER:$c$|CENTER:$c...
|PW86|0.0864|14|0.2|0.898|[[J. P. Perdew and Y. Wang, PRB...
|PW86R|0.1234|17.33|0.163|0.886|[[E. D. Murray et al., JC...
ただし$7/81\simeq0.0864, \mu_{\rm GEA}=10/81\simeq0.1234$...
** B88型 [#z125b612]
\[
F_x(s)=1+\frac{\mu s^2}{1+\frac{9}{4\pi}\mu s\,{\rm sinh}...
\]
|CENTER:Method|CENTER:$\mu$|CENTER:$\lambda$|CENTER:Refer...
|B88|$0.2743$|$2(6\pi^2)^{1/3}$|[[A. D. Becke, Phys. Rev....
|optB88|$0.22$|$1.2\times(9/2)(6/\pi)^{1/3}$|J. Klimes et...
** PW91型 [#udd45bd2]
** PBE型 [#a62f0db3]
\[
F_x(s)=1+\kappa-\frac{\kappa}{1+\mu s^2/\kappa}=1+\frac{\...
\begin{array}{ll}
1+\mu s^2&s\rightarrow0\\
1+\kappa&s\rightarrow\infty
\end{array}
\right.
\]
|CENTER:Method|CENTER:$\mu$|CENTER:$\kappa$|CENTER:Refere...
||0.235|0.967|A. D. Becke, J. Chem. Phys. 84, 4524 (1986)|
|PBE|0.21951|0.804|J. P. Perdew et al., Phys. Rev. Lett. ...
|revPBE|0.21951|1.245|Y. Zhang and W. Yang, Phys. Rev. Le...
|PBEsol|0.1235||J. P. Perdew et al., Phys. Rev. Lett. 100...
|optPBE|0.175519|1.04804|J. Klimes et al., J. Phys. Cond....
ただし$\mu_{\rm GEA}=10/81\simeq0.1235$である。
** RPBE型 [#v8c3ded0]
\[
F_x(s)=1+\kappa(1-e^{-\mu s^2/\kappa})=\left\{
\begin{array}{ll}
1+\mu s^2&s\rightarrow0\\
1+\kappa&s\rightarrow\infty
\end{array}
\right.
\]
|CENTER:Method|CENTER:$\mu$|CENTER:$\kappa$|CENTER:Refere...
|RPBE|0.21951|0.804|B. Hammer et al. Phys. Rev. B 59, 741...
** C09型 [#o170764e]
\[
F_x(s)=1+\mu s^2 e^{-\alpha s^2}+\kappa(1-e^{-\alpha s^2/...
\begin{array}{ll}
1+(\mu+\kappa\alpha/2) s^2&s\rightarrow0\\
1+\kappa&s\rightarrow\infty
\end{array}
\right.
\]
|CENTER:Method|CENTER:$\mu$|CENTER:$\kappa$|CENTER:$\alph...
|C09|0.0617|1.245|0.0483|V. R. Cooper Phys. Rev. B 81, 16...
ページ名: