def vibrational_internal_energy(self, temperature, volume):
        """
        Vibrational internal energy, U_vib(V, T).
        Eq(4) in doi.org/10.1016/j.comphy.2003.12.001

        Args:
            temperature (float): temperature in K
            volume (float): in Ang^3

        Returns:
            float: vibrational internal energy in eV
        """
        y = self.debye_temperature(volume) / temperature
        return self.kb * self.natoms * temperature * (9./8. * y +
                                                      3*self.debye_integral(y))