Lda x

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Functional: Slater Exchange
Type: LDA
XC: Exchange
References:

  • U. von Barth and L. Hedin, J. Phys. C, 5, 1629 (1972).
  • O. Gunnarsson and B.I. Lundqvist, Phys. Rev. B 13, 4274 (1976); ibid 15, 6006(E) (1977). APS

The exchange energy per particle can be written in the form:

e_x(r_s, \xi) = e_x^P(r_s) + [e_x^F(r_s)-e_x^P(r_s)]f(\xi)

where P/F stand for para/ferro-magnetic states, respectively, with

e_x^P(r_s) = -3/2\pi\alpha r_s = e_x^F(r_s)/2^{1/3}

α = (4 / 9π)1 / 3

and

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

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