Coverage for eminus/xc/lda_c_pw.py: 100.00%
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« prev ^ index » next coverage.py v7.6.4, created at 2024-11-01 11:47 +0000
1# SPDX-FileCopyrightText: 2021 The eminus developers
2# SPDX-License-Identifier: Apache-2.0
3"""Perdew-Wang LDA correlation.
5Reference: Phys. Rev. B 45, 13244.
6"""
8import numpy as np
11def lda_c_pw(n, A=0.031091, a1=0.2137, b1=7.5957, b2=3.5876, b3=1.6382, b4=0.49294, **kwargs):
12 """Perdew-Wang parametrization of the correlation functional (spin-paired).
14 Corresponds to the functional with the label LDA_C_PW and ID 12 in Libxc.
16 Reference: Phys. Rev. B 45, 13244.
18 Args:
19 n: Real-space electronic density.
21 Keyword Args:
22 A: Functional parameter.
23 a1: Functional parameter.
24 b1: Functional parameter.
25 b2: Functional parameter.
26 b3: Functional parameter.
27 b4: Functional parameter.
28 **kwargs: Throwaway arguments.
30 Returns:
31 PW correlation energy density and potential.
32 """
33 rs = (3 / (4 * np.pi * n)) ** (1 / 3)
34 rs12 = np.sqrt(rs)
35 rs32 = rs * rs12
36 rs2 = rs**2
38 om = 2 * A * (b1 * rs12 + b2 * rs + b3 * rs32 + b4 * rs2)
39 olog = np.log(1 + 1 / om)
40 ec = -2 * A * (1 + a1 * rs) * olog
42 dom = 2 * A * (0.5 * b1 * rs12 + b2 * rs + 1.5 * b3 * rs32 + 2 * b4 * rs2)
43 vc = -2 * A * (1 + 2 / 3 * a1 * rs) * olog - 2 / 3 * A * (1 + a1 * rs) * dom / (om * (om + 1))
44 return ec, np.array([vc]), None
47def lda_c_pw_spin(n, zeta, A=(0.031091, 0.015545, 0.016887), fzeta0=1.709921, **kwargs):
48 """Perdew-Wang parametrization of the correlation functional (spin-polarized).
50 Corresponds to the functional with the label LDA_C_PW and ID 12 in Libxc.
52 Reference: Phys. Rev. B 45, 13244.
54 Args:
55 n: Real-space electronic density.
56 zeta: Relative spin polarization.
58 Keyword Args:
59 A: Functional parameters.
60 fzeta0: Functional parameter.
61 **kwargs: Throwaway arguments.
63 Returns:
64 PW correlation energy density and potential.
65 """
66 a1 = (0.2137, 0.20548, 0.11125)
67 b1 = (7.5957, 14.1189, 10.357)
68 b2 = (3.5876, 6.1977, 3.6231)
69 b3 = (1.6382, 3.3662, 0.88026)
70 b4 = (0.49294, 0.62517, 0.49671)
72 ec0, vc0, _ = lda_c_pw(n, A[0], a1[0], b1[0], b2[0], b3[0], b4[0]) # Unpolarized
73 ec1, vc1, _ = lda_c_pw(n, A[1], a1[1], b1[1], b2[1], b3[1], b4[1]) # Polarized
74 ac, dac, _ = lda_c_pw(n, A[2], a1[2], b1[2], b2[2], b3[2], b4[2]) # Spin stiffness
75 ac = -ac # The PW spin interpolation is parametrized with -ac instead of ac
77 fzeta = ((1 + zeta) ** (4 / 3) + (1 - zeta) ** (4 / 3) - 2) / (2 ** (4 / 3) - 2)
78 zeta3 = zeta**3
79 zeta4 = zeta3 * zeta
81 ec = ec0 + ac * fzeta * (1 - zeta4) / fzeta0 + (ec1 - ec0) * fzeta * zeta4
83 dac = -dac # Also change the sign for the derivative
84 dfzeta = ((1 + zeta) ** (1 / 3) - (1 - zeta) ** (1 / 3)) * 4 / (3 * (2 ** (4 / 3) - 2))
85 factor1 = vc0 + dac * fzeta * (1 - zeta4) / fzeta0 + (vc1 - vc0) * fzeta * zeta4
86 factor2 = ac / fzeta0 * (dfzeta * (1 - zeta4) - 4 * fzeta * zeta3) + (ec1 - ec0) * (
87 dfzeta * zeta4 + 4 * fzeta * zeta3
88 )
90 vc0p = factor1 + factor2 * (1 - zeta)
91 vcdw = factor1 - factor2 * (1 + zeta)
92 return ec, np.array([vc0p, vcdw]), None