* B86b [#zfe74a91]
\[
F_x(s)=1+\frac{\mu s^2}{(1+\mu s^2/\kappa)^{4/5}}
\]
|CENTER:Method|CENTER:$\mu$|CENTER:$\kappa$|CENTER:Reference|h
|B86b|0.2449|0.5757|A. D. Becke, J. Chem. Phys. 85, 7184 (1986)|
|optB86b|0.1234 (=10/81)|1|J. Klimes et al., Phys. Rev. B 83, 195131 (2011)|
|B86R|0.1234 (=10/81)|0.7114|I. Hamada, Phys. Rev. B 89, 121103(R) (2014)|
* PW86 [#jb0f34cb]
\[
F_x(s)=(1+15as^2+bs^4+cs^6)^{1/15}
\]
|CENTER:Method|CENTER:$a$|CENTER:$b$|CENTER:$c$|CENTER:Reference|h
|PW86|0.0864|14|0.2|J. P. Perdew and Y. Wang, Phys. Rev. B 33, 8800(R) (1986)|
|PW86R|0.1234 (=10/81)|17.33|0.163|E. D. Murray et al., J. Chem. Theory Comput. 10, 2754 (2009)|
* B88 [#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 [#a62f0db3]
\[
F_x(s)=1+\kappa-\frac{\kappa}{1+\mu s^2/\kappa}
\]
|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)|
|optPBE|0.175519|1.04804|J. Klimes et al., J. Phys. Cond. Mat. 22, 022201 (2010)|
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