Lda c pw

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Functional: Perdew & Wang
Type: LDA
XC: Correlation
References:

  • J.P. Perdew and Y. Wang, Phys. Rev. B 45, 13244 (1992) APS
  • Ortiz and Ballone, Phys. Rev. B 50, 1391 (1994) APS
  • Ortiz and Ballone, Phys. Rev. B 56, 9970(E) (1997) APS

For finite spin-polarization ζ, Perdew and Wang parametrized the correlation energy per unit particle in the following way:

e_c(r_s,\zeta) = e_c(r_s,0) + \alpha_c(r_s)\frac{f(\zeta)}{f''(0)}(1-\zeta^4) + [e_c(r_s,1) - e_c(r_s,0)]f(\zeta)\zeta^4

The function f(ζ) is

f(\zeta) = \frac{[1+\zeta]^{4/3} + [1-\zeta]^{4/3} - 2}{2^{4/3} - 2},

while its second derivative f''(0) = 1.709921

The three functions, ec(rs,0) (the paramagnetic energy of the e-gas), ec(rs,1) (the ferromagnetic energy of the e-gas), and − αc(rs) (note the minus sign) are all parametrized by the function

g = -2 A(1+\alpha_1r_s)\log\left\{1+\frac{1}{2A(\beta_1r_s^{1/2}+\beta_2r_s+\beta_3r_s^{3/2}+\beta_4r_s^2)}\right\}

There are two parametrizations using this form, the original from Perdew and Wang, and a later version by Ortiz and Ballone. The coefficients are the following

  Perdew & Wang Ortiz & Ballone
ec(rs,0) ec(rs,1) − α(rs)   ec(rs,0) ec(rs,1) − α(rs)
A 0.031091 0.015545 0.016887   0.031091 0.015545 0.016887
α1 0.21370 0.20548 0.11125   0.026481 0.022465 0.11125
β1 7.5957 14.1189 10.357   7.5957 14.1189 10.357
β2 3.5876 6.1977 3.6231   3.5876 6.1977 3.6231
β3 1.6382 3.3662 0.88026   -0.46647 -0.56043 0.88026
β4 0.49294 0.62517 0.49671   0.13354 0.11313 0.49671
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