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(*
Copyright (C) 2017 M.A.L. Marques
This Source Code Form is subject to the terms of the Mozilla Public
License, v. 2.0. If a copy of the MPL was not distributed with this
file, You can obtain one at http://mozilla.org/MPL/2.0/.
*)
(* These numbers are taken from the original reference, but divided by
two to convert from Rydbergs to Hartrees *)
A_vwn := [ 0.0310907, 0.01554535, -1/(6*Pi^2)]:
b_vwn := [ 3.72744, 7.06042, 1.13107 ]:
c_vwn := [12.9352, 18.0578, 13.0045 ]:
x0_vwn := [-0.10498, -0.32500, -0.0047584]:
A_rpa := [ 0.0310907, 0.01554535, -1/(6*Pi^2)]:
b_rpa := [13.0720, 20.1231, 1.06835 ]:
c_rpa := [42.7198, 101.578, 11.4813 ]:
x0_rpa := [-0.409286, -0.743294, -0.228344 ]:
Q_vwn := (b, c) -> sqrt(4*c - b^2):
f1_vwn := (b, c) -> 2*b/Q_vwn(b, c):
f2_vwn := (b, c, x0) -> b*x0/(x0^2 + b*x0 + c):
f3_vwn := (b, c, x0) -> 2*(2*x0 + b)/Q_vwn(b, c):
fpp_vwn := 4/(9*(2^(1/3) - 1)):
fx_vwn := (b, c, rs) -> rs + b*sqrt(rs) + c:
f_aux := (A, b, c, x0, rs) -> A*(
+ log(rs/fx_vwn(b, c, rs))
+ (f1_vwn(b, c) - f2_vwn(b, c, x0)*f3_vwn(b, c, x0))*arctan(Q_vwn(b, c)/(2*sqrt(rs) + b))
- f2_vwn(b, c, x0)*log((sqrt(rs) - x0)^2/fx_vwn(b, c, rs))
):
DMC := (rs, z) ->
+ f_aux(A_vwn[2], b_vwn[2], c_vwn[2], x0_vwn[2], rs)
- f_aux(A_vwn[1], b_vwn[1], c_vwn[1], x0_vwn[1], rs):
DRPA := (rs, z) ->
+ f_aux(A_rpa[2], b_rpa[2], c_rpa[2], x0_rpa[2], rs)
- f_aux(A_rpa[1], b_rpa[1], c_rpa[1], x0_rpa[1], rs):
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