calculate electronic contributions in pressure for the Tsuchiya equation

    :param v: unit-cell volume in A^3
    :param temp: temperature in K
    :param v0: unit-cell volume in A^3 at 1 bar
    :param a: parameter for the Tsuchiya equation
    :param b: parameter for the Tsuchiya equation
    :param c: parameter for the Tsuchiya equation
    :param d: parameter for the Tsuchiya equation
    :param n: number of atoms in a formula unit
    :param z: number of formula unit in a unit cell
    :param t_ref: reference temperature, 300 K
    :param three_r: 3 times gas constant
    :return: electronic contribution in GPa
    :note: n, z, three_r are not used but in there for consistency
        with other electronic contribution equations

def tsuchiya_pel(v, temp, v0, a, b, c, d, n, z, three_r=3. * constants.R,
                 t_ref=300.):
    """
    calculate electronic contributions in pressure for the Tsuchiya equation

    :param v: unit-cell volume in A^3
    :param temp: temperature in K
    :param v0: unit-cell volume in A^3 at 1 bar
    :param a: parameter for the Tsuchiya equation
    :param b: parameter for the Tsuchiya equation
    :param c: parameter for the Tsuchiya equation
    :param d: parameter for the Tsuchiya equation
    :param n: number of atoms in a formula unit
    :param z: number of formula unit in a unit cell
    :param t_ref: reference temperature, 300 K
    :param three_r: 3 times gas constant
    :return: electronic contribution in GPa
    :note: n, z, three_r are not used but in there for consistency
        with other electronic contribution equations
    """
    def f(temp):
        return a + b * temp + c * np.power(temp, 2.) + d * np.power(temp, 3.)
    return f(temp) - f(t_ref)