## 1 Introduction: Thermodynamics of Hydrogen Evolution Reaction  
The mechanisms of electrochemical hydrogen evolution and oxidation reactions (HER and HOR) are becoming a topic of interest again as hydrogen is expected to become the environmentally friendly fuel of the future. In the recent literature [1; 2; 3; 4; 5; 6; 7; 8; 9], the interpretations of the mechanism of these processes taking place on the surface of various platinum group electrodes are based on the concept of adsorbed hydrogen atoms \(\rm H_{ad}\) as the intermediate. In [1], it was suggested that in the range of low potential values, adsorbed \(\rm H_{ad}\) atoms are formed through a dissociative adsorption of \(\rm H_{2}\) rather than the discharge of \(\rm H^{+}\) ions. It is defined by thermodynamics [10] that under the standard conditions, the processes of HER and HOR are described by the equation:  
\[2\rm H^{+}+2e^{-}\rightleftarrows\rm H_{2}, \tag{1}\]  
with the value of standard potential \(E_{\rm 2H^{+}/H_{2}}^{0}=0\) V vs. the standard hydrogen electrode (SHE). However, it is also well known that the Volmer reaction:  
\[\rm H^{+}+e^{-}\rightleftarrows\rm H, \tag{2}\]  
thermodynamically cannot proceed at \(E=0\) V (SHE), because the standard potential of Equation (2) is \(E_{\rm H^{+}/H}^{0}=-2.106\) V [10]. As the hydrogen evolution reaction on the Pt surface actually takes place at \(E=0\) V (SHE), it is assumed that the binding energy of H atoms in the \(\rm H_{2}\) molecule is compensated by the energy of adsorption of H atoms leading to the formation of \(\rm H_{ad}\) on the electrode surface as intermediates of Reaction (1). The energy of interaction between Pt electrode and \(\rm H_{ad}\), \(\rm\Delta\)\(H_{chem}\), is considered to be about 260 kJ mol\({}^{-1}\)[8], i.e., slightly higher than \(\frac{1}{2}D_{\rm H_{2}}\approx 226.8\) kJ mol\({}^{-1}\)[11]; \(D\) is the bond energy in \(\rm H_{2}\). In accordance with the commonly accepted concept [1; 7] formulated about 50 years ago [12; 13; 14], when the first H atom is adsorbed on the electrode surface in the form of \(\rm H_{ad}\), fully compensating half of the binding energy in the \(\rm H_{2}\) molecule, the electrochemical discharge of the second \(\rm H^{+}\) ion and formation of \(\rm H_{2}\) at the equilibrium potential of 0 V (SHE) proceed without any hindrance. In other words, irreversible formation of the \(\rm H_{2}\) molecule according to the summary Equation (1) is possible with the formation of the first adsorbed \(\rm H_{ad}\) atom, i.e.,  
\[\rm H^{+}+e^{-}\to H_{ad}, \tag{3}\]  
followed by recombination according to the Heyrovsky or Tafel paths as follows:  
\[\rm H_{ad}+H^{+}+e^{-}\to H_{2}, \tag{4}\]  
\[\rm 2H_{ad}\to H_{2}. \tag{5}\]  
If the \(\rm H_{ad}\) treated in various HER models exists, thermodynamics requires acknowledging that in the case of Pt, for instance, the energy of interaction between \(\rm H_{ad}\) and the electrode surface should be equivalent to the energy of chemical bond, which can amount up to 260 kJ mol\({}^{-1}\)[8]. The latter value, however, is obviously incomparable with those corresponding to the energy of adsorption. Moreover, it is well established [10] that the hydrogen atom does not form any stable hydride-type compounds with many metals, including the Pt group ones. It can also be noted that current peaks observed in cyclic voltammograms (CVs) of the Pt electrode at \(E>E_{\rm 2H^{+}/H_{2}}^{0}\) cannot be ascribed to the formation of the monolayer of \(\rm H_{ad}\) atoms weakly and strongly bonded to the electrode surface, because, from the thermodynamic point of view, in the \(E\) range above 0 V (SHE), only oxidation of the \(\rm H_{2}\) molecule can take place rather than the underpotential discharge of \(\rm H^{+}\) to \(\rm H_{ad}\).