18.1.7 B97: B97=B97DF + 0.1943Exact Exchange

A. D. Becke, J. Chem. Phys. 107, 8554 (1997)

B97DF is given by

$$K = \left (\epsilon(\rho_{\alpha},\rho_{\beta})-\epsilon(\rho_{\alpha... ...(A_{{0}}+A_{{1}}\eta(d,\lambda_{{ 1}})+A_{{2}}\eta^{2}(d,\lambda_{{1}})\right )$$

$$+ \sum_s \epsilon(\rho_{s},0)\left (B_{{0}}+B_{{1}}\eta(\chi_{s}^ {2},\lambda_{{2}})+B_{{2}}\eta^{2}(\chi_{s}^{2}, \lambda_{{2}})\right )$$ (36)

$$-\frac{3}{2}\left (\frac{3}{4\pi}\right ) ^{1/3}\rho_{s}^{4/3}\le... ...i_{s}^{2},\lambda_{{3}})+C_{{2}}\eta^{2}( \chi_{s}^{2},\lambda_{{3}})\right ) ,$$ (37)

where

$$d=(\chi_{\alpha}^{2}+\chi_{\beta}^{2})/2 ,$$ (38)

$$\eta(\theta,\mu)={\frac {\mu \theta}{1+\mu \theta}} ,$$ (39)

$$A = [ 0.9454, 0.7471,- 4.5961] ,$$ (40)

$$B = [ 0.1737, 2.3487,- 2.4868] ,$$ (41)

$$C = [ 0.8094, 0.5073, 0.7481] ,$$ (42)

$$\lambda = [ 0.006, 0.2, 0.004]$$ (43)

and ${\epsilon(\alpha,\beta)}$ is the correlation energy per particle of the Local Spin Density Approximation(PW92C).