18.1.14 HCTH93:

F. A. Hamprecht, A. J. Cohen, D. J. Tozer and N. C. Handy, J. Chem. Phys. 109, 6264 (1998)

The original HCTH functional with parameters optimized on a set of 93 training systems.

$$K = \left (\epsilon(\rho_{\alpha},\rho_{\beta})-\epsilon(\rho_{\alpha... ...1}})+A_{{3}}\eta^{3} (d,\lambda_{{1}})+A_{{4}}\eta^{4}(d,\lambda_{{1}})\right )$$

$$+ \sum_s \epsilon(\rho_{s},0)\left (B_{{0}}+B_{{1}}\eta(\chi_{s}^ {... ...chi_{s}^{ 2},\lambda_{{2}})+B_{{4}}\eta^{4}(\chi_{s}^{2},\lambda_{{2}})\right )$$

$$-\frac{3}{2}\left (\frac{3}{4\pi}\right )^{1/3}\rho_{s}^{4/3} \le... ...hi_{s}^{2},\lambda_{{3}})+C_{{4}} \eta^4(\chi_{s}^{2},\lambda_{{3}}) \right ) ,$$ (65)

where

$$d=(\chi_{\alpha}^{2}+\chi_{\beta}^{2})/{2} ,$$ (66)

$$\eta(\theta,\mu)={\frac {\mu \theta}{1+\mu \theta}} ,$$ (67)

$$A = [ 0.72997, 3.35287,- 11.543, 8.08564,- 4.47857] ,$$ (68)

$$B = [ 0.222601,- 0.0338622,- 0.012517,- 0.802496, 1.55396] ,$$ (69)

$$C = [ 1.0932,- 0.744056, 5.5992,- 6.78549, 4.49357] ,$$ (70)

$$\lambda = [ 0.006, 0.2, 0.004]$$ (71)

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