  In the framework of the Eliashberg formalism the free energy difference
between the superconducting and normal state for the molecular metallic
hydrogen was calculated. The pressure values $p_{1}=347$ GPa and $p_{2}=428$
GPa were taken into consideration. It has been shown, that together with the
increase of the pressure, grows the value of the specific heat jump at the
critical temperature and the value of the thermodynamic critical field near
zero Kelvin: $[\Delta C(T_{C})]_{p2}/[\Delta C(T_{C})]_{p1}\simeq 2.33$ and
$[H_{C}(0)]_{p2}/[H_{C}(0)]_{p1}\simeq 1.74$. Next, it has been stated, that
the ratio $\Delta C(T_{C})/C^{N}(T_{C})$ also increases from 1.91 to 2.39;
whereas $T_{C}C^{N}(T_{C})/H^{2}_{C}(0)$ decreases from 0.152 to 0.140. The
last results prove that the considered parameters significantly diverge from
the prediction based on the BCS model.
