def get_LDA_potential(vxct, kxct, s):
    """Evaluating the potential of LDA functional in a batch of spherical projection directions.

    Parameters
    ----------
    vxct: tuple of (vrho, vs), where vrho and vs are np.ndarray with shape (Ngrid)
        The exchange-corelation energy of original LDA function.
        
    kxct: tuple of (rho_rho, rho_s, s_s, rho_Nrho, Nrho_Nrho, s_Nrho, s_Ns, rho_Ns, Nrho_Ns, Ns_Ns)
        Only the second and third are used in this function
        
    s: np.ndarray
        The spin density (Ngrid)

    Returns:
    ----------
    vrho np.ndarray with the shape (Ngrid)
        The rho dependent exchange-corelation potential of a single direction of the multi-collinear approach.
        
    vs np.ndarray with the shape (Ngrid)
        The spin dependent exchange-corelation potential of a single direction of the multi-collinear approach.
    """
    vrhot, vst = vxct
    rho_st, s_st = kxct[1:3]
    
    vrho = vrhot + s*rho_st
    vs = 2*vst + s*s_st
    
    return vrho, vs