# SPDX-FileCopyrightText: 2021 The eminus developers# SPDX-License-Identifier: Apache-2.0"""Chachiyo LDA correlation.Reference: J. Chem. Phys. 145, 021101."""importnumpyasnp
[docs]deflda_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=20.4562557rs=(3/(4*np.pi*n))**(1/3)rs2=rs**2ecinner=1+b/rs+b/rs2ec=a*np.log(ecinner)vc=ec+a*b*(2+rs)/(3*(b+b*rs+rs2))returnec,np.array([vc]),None
[docs]defchachiyo_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))returnfzeta,dfdzeta
[docs]deflda_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=20.4562557b1=27.4203609rs=(3/(4*np.pi*n))**(1/3)rs2=rs**2fzeta,dfdzeta=weight_function(zeta)ec0inner=1+b0/rs+b0/rs2ec1inner=1+b1/rs+b1/rs2ec0=a0*np.log(ec0inner)ec1=a1*np.log(ec1inner)ec=ec0+(ec1-ec0)*fzetafactor=-1/rs2-2/rs**3dec0drs=a0/ec0inner*b0*factordec1drs=a1/ec1inner*b1*factordecdrs=dec0drs+(dec1drs-dec0drs)*fzetaprefactor=ec-rs/3*decdrsdecdf=(ec1-ec0)*dfdzetavc_up=prefactor+decdf*(1-zeta)vc_dw=prefactor-decdf*(1+zeta)returnec,np.array([vc_up,vc_dw]),None