Coverage for eminus/xc/lda_c_chachiyo.py: 100.00%

1# SPDX-FileCopyrightText: 2021 The eminus developers 

2# SPDX-License-Identifier: Apache-2.0 

3"""Chachiyo LDA correlation. 

4 

5Reference: J. Chem. Phys. 145, 021101. 

6""" 

7 

8import numpy as np 

9 

10 

11def lda_c_chachiyo(n, **kwargs): 

12 """Chachiyo parametrization of the correlation functional (spin-paired). 

13 

14 Corresponds to the functional with the label LDA_C_CHACHIYO and ID 287 in Libxc. 

15 

16 Reference: J. Chem. Phys. 145, 021101. 

17 

18 Args: 

19 n: Real-space electronic density. 

20 

21 Keyword Args: 

22 **kwargs: Throwaway arguments. 

23 

24 Returns: 

25 Chachiyo correlation energy density and potential. 

26 """ 

27 a = -0.01554535 # (np.log(2) - 1) / (2 * np.pi**2) 

28 b = 20.4562557 

29 

30 rs = (3 / (4 * np.pi * n)) ** (1 / 3) 

31 rs2 = rs**2 

32 ecinner = 1 + b / rs + b / rs2 

33 

34 ec = a * np.log(ecinner) 

35 

36 vc = ec + a * b * (2 + rs) / (3 * (b + b * rs + rs2)) 

37 return ec, np.array([vc]), None 

38 

39 

40def chachiyo_scaling(zeta): 

41 """Weighting factor between the paramagnetic and the ferromagnetic case. 

42 

43 Reference: J. Chem. Phys. 145, 021101. 

44 

45 Args: 

46 zeta: Relative spin polarization. 

47 

48 Returns: 

49 Weighting factor and its derivative. 

50 """ 

51 fzeta = ((1 + zeta) ** (4 / 3) + (1 - zeta) ** (4 / 3) - 2) / (2 * (2 ** (1 / 3) - 1)) 

52 

53 dfdzeta = (2 * (1 - zeta) ** (1 / 3) - 2 * (1 + zeta) ** (1 / 3)) / (3 - 3 * 2 ** (1 / 3)) 

54 return fzeta, dfdzeta 

55 

56 

57def lda_c_chachiyo_spin(n, zeta, weight_function=chachiyo_scaling, **kwargs): 

58 """Chachiyo parametrization of the correlation functional (spin-polarized). 

59 

60 Corresponds to the functional with the label LDA_C_CHACHIYO and ID 287 in Libxc. 

61 

62 Reference: J. Chem. Phys. 145, 021101. 

63 

64 Args: 

65 n: Real-space electronic density. 

66 zeta: Relative spin polarization. 

67 

68 Keyword Args: 

69 weight_function: Functional function. 

70 **kwargs: Throwaway arguments. 

71 

72 Returns: 

73 Chachiyo correlation energy density and potential. 

74 """ 

75 a0 = -0.01554535 # (np.log(2) - 1) / (2 * np.pi**2) 

76 a1 = -0.007772675 # (np.log(2) - 1) / (4 * np.pi**2) 

77 b0 = 20.4562557 

78 b1 = 27.4203609 

79 

80 rs = (3 / (4 * np.pi * n)) ** (1 / 3) 

81 rs2 = rs**2 

82 

83 fzeta, dfdzeta = weight_function(zeta) 

84 

85 ec0inner = 1 + b0 / rs + b0 / rs2 

86 ec1inner = 1 + b1 / rs + b1 / rs2 

87 ec0 = a0 * np.log(ec0inner) 

88 ec1 = a1 * np.log(ec1inner) 

89 

90 ec = ec0 + (ec1 - ec0) * fzeta 

91 

92 factor = -1 / rs2 - 2 / rs**3 

93 dec0drs = a0 / ec0inner * b0 * factor 

94 dec1drs = a1 / ec1inner * b1 * factor 

95 decdrs = dec0drs + (dec1drs - dec0drs) * fzeta 

96 prefactor = ec - rs / 3 * decdrs 

97 decdf = (ec1 - ec0) * dfdzeta 

98 

99 vc_up = prefactor + decdf * (1 - zeta) 

100 vc_dw = prefactor - decdf * (1 + zeta) 

101 return ec, np.array([vc_up, vc_dw]), None