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

1# SPDX-FileCopyrightText: 2021 The eminus developers 

2# SPDX-License-Identifier: Apache-2.0 

3"""Chachiyo GGA exchange. 

4 

5Reference: Molecules 25, 3485. 

6""" 

7 

8import numpy as np 

9from scipy.linalg import norm 

10 

11from .lda_x import lda_x 

12 

13 

14def gga_x_chachiyo(n, dn_spin=None, **kwargs): 

15 """Chachiyo parametrization of the exchange functional (spin-paired). 

16 

17 Corresponds to the functional with the label GGA_X_CHACHIYO and ID 298 in Libxc. 

18 

19 Reference: Molecules 25, 3485. 

20 

21 Args: 

22 n: Real-space electronic density. 

23 

24 Keyword Args: 

25 dn_spin: Real-space gradient of densities per spin channel. 

26 **kwargs: Throwaway arguments. 

27 

28 Returns: 

29 Chachiyo exchange energy density, potential, and vsigma. 

30 """ 

31 norm_dn = norm(dn_spin[0], axis=1) 

32 ex, _, _ = lda_x(n, **kwargs) 

33 

34 x = norm_dn / n ** (4 / 3) * 2 / 9 * (np.pi / 3) ** (1 / 3) 

35 x1 = x + 1 

36 logx1 = np.log(x1) 

37 div = 3 * x + np.pi**2 

38 tmpgex = 3 * x**2 + np.pi**2 * logx1 

39 gex = tmpgex / (div * logx1) 

40 

41 term1 = 8 * ex / tmpgex * (x**2 + x * np.pi**2 / (6 * x1)) + 2 / 3 * norm_dn / n * ( 

42 1 / div + 1 / (3 * logx1 * x1) 

43 ) 

44 gvx = (1 + 1 / 3) * ex - term1 

45 

46 vsigmax = n * 3 * term1 / (8 * norm_dn**2) 

47 return ex * gex, np.array([gvx]) * gex, np.array([vsigmax]) * gex 

48 

49 

50def gga_x_chachiyo_spin(n, zeta, dn_spin=None, **kwargs): 

51 """Chachiyo parametrization of the exchange functional (spin-polarized). 

52 

53 Corresponds to the functional with the label GGA_X_CHACHIYO and ID 298 in Libxc. 

54 

55 Reference: Molecules 25, 3485. 

56 

57 Args: 

58 n: Real-space electronic density. 

59 zeta: Relative spin polarization. 

60 

61 Keyword Args: 

62 dn_spin: Real-space gradient of densities per spin channel. 

63 **kwargs: Throwaway arguments. 

64 

65 Returns: 

66 Chachiyo exchange energy density, potential, and vsigma. 

67 """ 

68 # Use the spin-scaling relationship Exc(n_up, n_down)=(Exc(2 n_up)+Exc(2 n_down))/2 

69 n_up = zeta * n + n # 2 * n_up 

70 n_dw = -zeta * n + n # 2 * n_down 

71 ex_up, vx_up, vsigma_up = gga_x_chachiyo(n_up, np.array([2 * dn_spin[0]]), **kwargs) 

72 ex_dw, vx_dw, vsigma_dw = gga_x_chachiyo(n_dw, np.array([2 * dn_spin[1]]), **kwargs) 

73 

74 vsigmax = np.array([2 * vsigma_up, np.zeros_like(vsigma_up), 2 * vsigma_dw]) 

75 return 0.5 * (ex_up * n_up + ex_dw * n_dw) / n, np.array([vx_up, vx_dw]), vsigmax