* 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|$0.0864$|$14$|$0.2$|$0.898$|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] \[ F_x(s)=1+\kappa(1-e^{-\mu s^2/\kappa}) \] |CENTER:Method|CENTER:$\mu$|CENTER:$\kappa$|CENTER:Reference|h |RPBE|$0.21951$|$0.804$|B. Hammer et al. 59, 7413 (1999)|