1(* 2 Copyright (C) 2017 M.A.L. Marques 3 4 This Source Code Form is subject to the terms of the Mozilla Public 5 License, v. 2.0. If a copy of the MPL was not distributed with this 6 file, You can obtain one at http://mozilla.org/MPL/2.0/. 7*) 8 9(* type: mgga_exc *) 10 11(* Equations are from the Appendix of Kurth1999_889 *) 12 13$include "gga_c_gapc.mpl" 14 15gap_par0[10] = 0.06483*((9*Pi)/4)^(2/3): (* this is approximately equal to 0.23878 *) 16 17(* Eq. (A4) *) 18kcis_G := (rs, xt) -> xt^2*n_total(rs)^(2/3)/8: 19 20(* Eq. (A9) *) 21kcis_t := (rs, xt) -> 2^(2/3)*xt/(8*sqrt(rs)): 22 23kcis_beta := 0.066725: 24 25(* Eq. (A7) *) 26kcis_gga0 := (rs, xt) -> f_pw(rs, 0)/(1 + kcis_beta*log(1 + kcis_t(rs, xt)^2/m_abs(f_pw(rs, 0)))): 27 28(* Eq. (A8) *) 29kcis_gga1 := (rs, xt) -> f_pw(rs, 1)/(1 + kcis_beta*log(1 + 2^(-1/3)*kcis_t(rs, xt)^2/m_abs(f_pw(rs, 1)))): 30 31(* Eq. (A5) *) 32(* The polarized parameters are the same as the unpolarized ones *) 33(* except that c_1, c_2, c_3 are multiplied by 0.7. 1.5, and 2.59 respectively *) 34kcis_eps_0 := (rs, xt) -> 35 + (kcis_gga0(rs, xt) + gap_c1(rs, 0, gap_par0)*kcis_G(rs, xt)) 36 / (1 + gap_c2(rs, 0, gap_par0)*kcis_G(rs, xt) + gap_c3(rs, 0, gap_par0)*kcis_G(rs, xt)^2): 37 38(* Eq. (A6) *) 39kcis_eps_1 := (rs, xt) -> 40 + (kcis_gga1(rs, xt) + 0.7*gap_c1(rs, 0, gap_par0)*kcis_G(rs, xt)) 41 / (1 + 1.5*gap_c2(rs, 0, gap_par0)*kcis_G(rs, xt) + 2.59*gap_c3(rs, 0, gap_par0)*kcis_G(rs, xt)^2): 42 43(* Eq. (A2) *) 44gap_f := (rs, z, xt) -> 45 + kcis_eps_0(rs, xt) 46 + f_zeta(z)*(kcis_eps_1(rs, xt) - kcis_eps_0(rs, xt)): 47 48(* Eq. (A1) *) 49if evalb(Polarization = "ferr") then 50 kcis_f := (rs, z, xt, xs0, xs1, ts0, ts1) -> 51 + gap_f(rs, z, xt) 52 - xs0^2/(8*ts0) * gap_f(rs, 1, xs0): 53else 54 kcis_f := (rs, z, xt, xs0, xs1, ts0, ts1) -> 55 + gap_f(rs, z, xt) 56 - xs0^2/(8*ts0) * (1 + z)/2 * gap_f(rs*(2/(1+z))^(1/3), 1, xs0) 57 - xs1^2/(8*ts1) * (1 - z)/2 * gap_f(rs*(2/(1-z))^(1/3), -1, xs1): 58end if: 59 60f := (rs, z, xt, xs0, xs1, us0, us1, ts0, ts1) -> 61 kcis_f(rs, z, xt, xs0, xs1, ts0, ts1): 62