Coverage for eminus/xc/gga_c_pbe.py: 100.00%
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« prev ^ index » next coverage.py v7.6.4, created at 2024-11-08 12:59 +0000
1# SPDX-FileCopyrightText: 2021 The eminus developers
2# SPDX-License-Identifier: Apache-2.0
3"""Perdew-Burke-Ernzerhof GGA correlation.
5Reference: Phys. Rev. Lett. 77, 3865.
6"""
8import numpy as np
9from scipy.linalg import norm
11from .lda_c_pw_mod import lda_c_pw_mod, lda_c_pw_mod_spin
14def gga_c_pbe(n, beta=0.06672455060314922, dn_spin=None, **kwargs):
15 """Perdew-Burke-Ernzerhof parametrization of the correlation functional (spin-paired).
17 Corresponds to the functional with the label GGA_C_PBE and ID 130 in Libxc.
19 Reference: Phys. Rev. Lett. 77, 3865.
21 Args:
22 n: Real-space electronic density.
24 Keyword Args:
25 beta: Functional parameter.
26 dn_spin: Real-space gradient of densities per spin channel.
27 **kwargs: Throwaway arguments.
29 Returns:
30 PBE correlation energy density, potential, and vsigma.
31 """
32 gamma = (1 - np.log(2)) / np.pi**2
34 pi34 = (3 / (4 * np.pi)) ** (1 / 3)
35 rs = pi34 * n ** (-1 / 3)
36 norm_dn = norm(dn_spin[0], axis=1)
37 ec, vc, _ = lda_c_pw_mod(n, **kwargs)
39 kf = (9 / 4 * np.pi) ** (1 / 3) / rs
40 ks = np.sqrt(4 * kf / np.pi)
41 divt = 2 * ks * n
42 t = norm_dn / divt
43 expec = np.exp(-ec / gamma)
44 A = beta / (gamma * (expec - 1))
45 t2 = t**2
46 At2 = A * t2
47 A2t4 = At2**2
48 divsum = 1 + At2 + A2t4
49 div = (1 + At2) / divsum
50 nolog = 1 + beta / gamma * t2 * div
51 gec = gamma * np.log(nolog)
53 factor = A2t4 * (2 + At2) / divsum**2
54 dgec = beta * t2 / nolog * (-7 / 3 * div - factor * (A * expec * (vc - ec) / beta - 7 / 3))
55 gvc = gec + dgec
57 vsigmac = beta / (divt * ks) * (div - factor) / nolog
58 return ec + gec, np.array([vc + gvc]), np.array([0.5 * vsigmac])
61def gga_c_pbe_spin(n, zeta, beta=0.06672455060314922, dn_spin=None, **kwargs):
62 """Perdew-Burke-Ernzerhof parametrization of the correlation functional (spin-polarized).
64 Corresponds to the functional with the label GGA_C_PBE and ID 130 in Libxc.
66 Reference: Phys. Rev. Lett. 77, 3865.
68 Args:
69 n: Real-space electronic density.
70 zeta: Relative spin polarization.
72 Keyword Args:
73 beta: Functional parameter.
74 dn_spin: Real-space gradient of densities per spin channel.
75 **kwargs: Throwaway arguments.
77 Returns:
78 PBE correlation energy density, potential, and vsigma.
79 """
80 gamma = (1 - np.log(2)) / np.pi**2
82 pi34 = (3 / (4 * np.pi)) ** (1 / 3)
83 rs = pi34 * n ** (-1 / 3)
84 norm_dn = norm(dn_spin[0] + dn_spin[1], axis=1)
85 ec, vc, _ = lda_c_pw_mod_spin(n, zeta, **kwargs)
86 vcup, vcdw = vc
88 kf = (9 / 4 * np.pi) ** (1 / 3) / rs
89 ks = np.sqrt(4 * kf / np.pi)
90 phi = ((1 + zeta) ** (2 / 3) + (1 - zeta) ** (2 / 3)) / 2
91 phi2 = phi**2
92 phi3 = phi2 * phi
93 t = norm_dn / (2 * phi * ks * n)
94 expec = np.exp(-ec / (gamma * phi3))
95 A = beta / (gamma * (expec - 1))
96 t2 = t**2
97 At2 = A * t2
98 A2t4 = At2**2
99 divsum = 1 + At2 + A2t4
100 div = (1 + At2) / divsum
101 nolog = 1 + beta / gamma * t2 * div
102 gec = gamma * phi3 * np.log(nolog)
104 # Handle divisions by zero
105 with np.errstate(divide="ignore", invalid="ignore"):
106 dfz = ((1 + zeta) ** (-1 / 3) - (1 - zeta) ** (-1 / 3)) / 3
107 dfz = np.nan_to_num(dfz, nan=0, posinf=0, neginf=0)
108 factor = A2t4 * (2 + At2) / divsum**2
109 bfpre = expec / phi3
110 bfup = bfpre * (vcup - ec)
111 bfdw = bfpre * (vcdw - ec)
112 dgecpre = beta * t2 * phi3 / nolog
113 dgecup = dgecpre * (-7 / 3 * div - factor * (A * bfup / beta - 7 / 3))
114 dgecdw = dgecpre * (-7 / 3 * div - factor * (A * bfdw / beta - 7 / 3))
115 dgeczpre = (
116 3 * gec / phi
117 - beta * t2 * phi2 / nolog * (2 * div - factor * (3 * A * expec * ec / phi3 / beta + 2))
118 ) * dfz
119 dgeczup = dgeczpre * (1 - zeta)
120 dgeczdw = -dgeczpre * (1 + zeta)
121 gvcup = gec + dgecup + dgeczup
122 gvcdw = gec + dgecdw + dgeczdw
124 vsigma = beta * phi / (2 * ks * ks * n) * (div - factor) / nolog
125 vsigmac = np.array([0.5 * vsigma, vsigma, 0.5 * vsigma])
126 return ec + gec, np.array([vcup + gvcup, vcdw + gvcdw]), vsigmac