## 3 Results and Discussion
### Isotopic Effect in SERS  
Comparison of spectra collected in the solutions of normal and heavy water (Figure 4a vs. Figure 4b and Figure 5a vs. Figure 5b) did not reveal a clear isotopic effect in vibrational spectra of ions or molecules. In the case of bands attributed to Cu(I) and Cu(II) oxides, such a result was logical as their origin was not dependent on the solvent. This was also the case for weak ionic adsorption of (H\({}_{2}\))\({}^{+}\)\({}_{\text{ad}}\), (D\({}_{2}\))\({}^{+}\)\({}_{\text{ad}}\), (H\({}_{3}\)O\({}^{+}\))\({}_{\text{ad}}\), and (D\({}_{3}\)O\({}^{+}\))\({}_{\text{ad}}\) on the Pt or Pd electrode surface: replacing water with heavy water did not effect the charge of the adsorbing particle and, consequently, the energy of its interaction with the surface, as elaborated further.  
In theory, the difference in vibrational bands between H\({}_{2}\)O and D\({}_{2}\)O is defined by a change in the reduced mass of the atoms involved \(\mu_{xx}=m_{x}m_{x}/(m_{x}+m_{x})\), where \(m_{x}\) denotes the mass of the H or D atoms. The expected shift of the vibrational frequency due to H substitution by D can be estimated from \(\
u_{XD}=\
u_{XH}\sqrt{\mu_{XH}/\mu_{XD}}\); one finds \(\
u_{DD}=\
u_{HH}\sqrt{\mu_{HH}/\mu_{DD}}\). Hence, the bands related to D\({}_{2}\)O will be at smaller wavenumbers as compared to those in H\({}_{2}\)O, correspondingly at \(\sqrt{\mu_{HH}/\mu_{DD}}=70.74\%\) of the energy (wavenumber). Such a significant isotopic effect was expected for the interatomic bond in H\({}_{2}\) or D\({}_{2}\) molecules and the OH band at 3000-3600 cm\({}^{-1}\). A certain isotopic effect could be expected if evolution of D\({}_{2}\) went through the formation of a stable chemisorbed compound between D\({}_{ad}\) and the electrode surface, whereas for the weakly adsorbed surface species, the energy of adsorption of charged (H\({}_{2}^{+}\))\({}_{\text{ad}}\) and (D\({}_{2}^{+}\))\({}_{\text{ad}}\) particles in the potential range investigated was, most likely, almost the same, due to the electrostatic nature of the interaction (a spring constant \(k\) of a harmonic oscillator was the same considering mechanical analogy). Due to the same charges and similar size of the adsorbing particles, the isotopic effect was not pronounced.  
From the viewpoint of energetic considerations, SERS spectra reflected the energy of interaction between a particle and electrode surface defined by potential constant \(k\) and the reduced mass \(\mu\). The oscillator frequency \(\omega=\sqrt{k/\mu}\) for small \(k\) and \(\mu\) (in the electron-ion pair, the electron mass dominated \(\mu\)), a small change in vibration energy quanta \(\hbar\omega\) was expected between H and D as observed in the experiment. Since dipole absorption was not Raman active (a negligible polarisability), it was expected that the formation of electron-ion pairs with strong dipole interaction at the interface investigated here had a weak Raman signature, and the use of SERS was essential. The isotopic effect between H\({}_{2}^{+}\) and D\({}_{2}^{+}\) due to the difference in the reduced mass of the (\(+/-\)) ion pair \(\mu=m_{-}m_{+}/\left(m_{-}+m_{+}\right)\) was very small. Indeed, the electron mass in atomic units was \(m_{-}=5.46\times 10^{-4}\); the H\({}_{2}\) mass was 2.1, and the mass on the neutron \(m_{n}=1.009\). The smallest mass \(m_{-}\) defined \(\mu\) and frequency \(\omega\propto\sqrt{1/\mu}\). Reduced mass was only different by 0.014% for H\({}_{2}^{+}\) vs. D\({}_{2}^{+}\) and even less for the H\({}_{3}\)O\({}^{+}\). There was no isotopic effect observed in SERS (Figure 4) according to the expectations discussed above. The appearance of Raman bands at the 15-21 kJ/mol or 1320-1570 cm\({}^{-1}\) wavenumber window leading to hydrogen evolution was consistent with the stepwise reduction mechanism (Figure 1). Microscopic understanding of the hydrogen behaviour at interfaces was essential for the creation of metamaterials with a fast reaction time and detection of hydrogen [38].