Source code for eminus.xc.lda_c_chachiyo

# SPDX-FileCopyrightText: 2021 The eminus developers
# SPDX-License-Identifier: Apache-2.0
"""Chachiyo LDA correlation.

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

import numpy as np


[docs] def lda_c_chachiyo(n, **kwargs): """Chachiyo parametrization of the correlation functional (spin-paired). Corresponds to the functional with the label LDA_C_CHACHIYO and ID 287 in Libxc. Reference: J. Chem. Phys. 145, 021101. Args: n: Real-space electronic density. Keyword Args: **kwargs: Throwaway arguments. Returns: Chachiyo correlation energy density and potential. """ a = -0.01554535 # (np.log(2) - 1) / (2 * np.pi**2) b = 20.4562557 rs = (3 / (4 * np.pi * n)) ** (1 / 3) rs2 = rs**2 ecinner = 1 + b / rs + b / rs2 ec = a * np.log(ecinner) vc = ec + a * b * (2 + rs) / (3 * (b + b * rs + rs2)) return ec, np.array([vc]), None
[docs] def chachiyo_scaling(zeta): """Weighting factor between the paramagnetic and the ferromagnetic case. Reference: J. Chem. Phys. 145, 021101. Args: zeta: Relative spin polarization. Returns: Weighting factor and its derivative. """ fzeta = ((1 + zeta) ** (4 / 3) + (1 - zeta) ** (4 / 3) - 2) / (2 * (2 ** (1 / 3) - 1)) dfdzeta = (2 * (1 - zeta) ** (1 / 3) - 2 * (1 + zeta) ** (1 / 3)) / (3 - 3 * 2 ** (1 / 3)) return fzeta, dfdzeta
[docs] def lda_c_chachiyo_spin(n, zeta, weight_function=chachiyo_scaling, **kwargs): """Chachiyo parametrization of the correlation functional (spin-polarized). Corresponds to the functional with the label LDA_C_CHACHIYO and ID 287 in Libxc. Reference: J. Chem. Phys. 145, 021101. Args: n: Real-space electronic density. zeta: Relative spin polarization. Keyword Args: weight_function: Functional function. **kwargs: Throwaway arguments. Returns: Chachiyo correlation energy density and potential. """ a0 = -0.01554535 # (np.log(2) - 1) / (2 * np.pi**2) a1 = -0.007772675 # (np.log(2) - 1) / (4 * np.pi**2) b0 = 20.4562557 b1 = 27.4203609 rs = (3 / (4 * np.pi * n)) ** (1 / 3) rs2 = rs**2 fzeta, dfdzeta = weight_function(zeta) ec0inner = 1 + b0 / rs + b0 / rs2 ec1inner = 1 + b1 / rs + b1 / rs2 ec0 = a0 * np.log(ec0inner) ec1 = a1 * np.log(ec1inner) ec = ec0 + (ec1 - ec0) * fzeta factor = -1 / rs2 - 2 / rs**3 dec0drs = a0 / ec0inner * b0 * factor dec1drs = a1 / ec1inner * b1 * factor decdrs = dec0drs + (dec1drs - dec0drs) * fzeta prefactor = ec - rs / 3 * decdrs decdf = (ec1 - ec0) * dfdzeta vc_up = prefactor + decdf * (1 - zeta) vc_dw = prefactor - decdf * (1 + zeta) return ec, np.array([vc_up, vc_dw]), None