第一原理分子動力学プログラム STATE Senri Wiki

• バックアップ一覧
• 差分 を表示
• 現在との差分 を表示
• バックアップ を表示
• 交換増強因子 へ行く。
  • 1 (2015-08-20 (木) 19:15:28)
  • 2 (2015-08-20 (木) 21:36:55)
  • 3 (2015-08-21 (金) 03:46:36)
  • 4 (2015-08-21 (金) 13:26:20)
  • 5 (2015-08-21 (金) 18:50:58)
  • 6 (2015-08-26 (水) 20:32:18)
  • 7 (2015-08-27 (木) 00:33:19)
  • 8 (2017-11-30 (木) 20:22:39)

* 交換増強因子の表式とパラメータ [#l39be222]
** 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:$(\mu\kappa^4)^{1/5}$|CENTER:Reference|h
|B86b|$0.2449$|$0.5757$|$0.485$|A. D. Becke, J. Chem. Phys. 85, 7184 (1986)|
|optB86b|$0.1234$ $(=10/81)$|$1$|$0.658$|J. Klimes et al., Phys. Rev. B 83, 195131 (2011)|
|B86R|$0.1234$ $(=10/81)$|$0.7114$|$0.501$|I. Hamada, Phys. Rev. B 89, 121103(R) (2014)|

** 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:$c^{1/15}$|CENTER:Reference|h
|PW86|$0.0864$ $(=7/81)$|$14$|$0.2$|$0.898$|J. P. Perdew and Y. Wang, Phys. Rev. B 33, 8800(R) (1986)|
|PW86R|$0.1234$ $(=10/81)$|$17.33$|$0.163$|$0.886$|E. D. Murray et al., J. Chem. Theory Comput. 10, 2754 (2009)|

** B88型 [#z125b612]
\[
F_x(s)=1+\frac{\mu s^2}{1+\frac{9}{4\pi}\mu s\,{\rm sinh}^{-1}(\lambda s)}
\]
|CENTER:Method|CENTER:$\mu$|CENTER:$\lambda$|CENTER:Reference|h
|B88|$0.2743$|$2(6\pi^2)^{1/3}$|A. D. Becke, Phys. Rev. A 38, 3098 (1988)|
|optB88|$0.22$|$1.2\times(9/2)(6/\pi)^{1/3}$|J. Klimes et al., J. Phys. Cond. Mat. 22, 022201 (2010)|

** PBE型 [#a62f0db3]
\[
F_x(s)=1+\frac{\mu s^2}{1+\mu s^2/\kappa}=\left\{
\begin{array}{ll}
1+\mu s^2&s\rightarrow0\\
1+\kappa&s\rightarrow\infty
\end{array}
\right.
\]
|CENTER:Method|CENTER:$\mu$|CENTER:$\kappa$|CENTER:Reference|h
||$0.235$|$0.967$|A. D. Becke, J. Chem. Phys. 84, 4524 (1986)|
|PBE|$0.21951$|$0.804$|J. P. Perdew et al., Phys. Rev. Lett. 77, 3865 (1996)|
|revPBE|$0.21951$|$1.245$|Y. Zhang and W. Yang, Phys. Rev. Lett. 80, 890 (1998)|
|PBEsol|$0.1235$ $(=10/81)$||J. P. Perdew et al., Phys. Rev. Lett. 100, 136406 (2008)|
|optPBE|$0.175519$|$1.04804$|J. Klimes et al., J. Phys. Cond. Mat. 22, 022201 (2010)|

** 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:Reference|h
|RPBE|$0.21951$|$0.804$|B. Hammer et al. 59, 7413 (1999)|