_{1}

^{*}

Studying liquid water in a frame of band theory shows that varying a reduction-oxidation (RedOx) potential of aqueous solution can be identified as shifting Fermi level in its band gap. This medium becomes the reductive one when Fermi level is shifting to the conduction band due to populating hydroxonium level (H
_{3}O
^{+}/ H
_{3}O) by electrons and transforming water in a hypo-stoichiometric state,
H_{2}O_{1-│X│}
. Opposite in the hyper-stoichiometric one
H_{2}O_{1+│X│}
Fermi level is shifting to the valence band due to populating hydroxide level OH/OH^{-} by holes and the aqueous solution becomes the oxidative one. The energy difference between these electronic levels is estimated of 1.75 eV. It is shown that the standard half-reactions and the typical aqueous electrodes fix their RedOx potential only by the electrons and holes populations ([H_{3}O],[OH]) of these local electronic levels in the band gap of non-stoichiometric water in the corresponding solutions.

The electronic properties of liquid water and its solutions have been studied by different research groups [

The main difficulty in producing reliable theoretical predictions of the electronic properties of liquid water lies in the necessary compromise between the level of accuracy at which the system can be described and the thorough sampling of the phase-space, as required for converged computational quantities [

Several strategies have been considered to simplify the study of disordered systems: use of clusters of increasing size to model the liquid, “mean-field” approaches, use of periodically repeated small unit cells, and hybrid approaches, which use different combinations of quantum and classical methods to describe the two subsystems [

Allowed local electronic states have to be in the band gap of liquid water similar to impurity levels in the band gap of solid insulators occupied and not occupied by electrons [

The electronic properties of water are extremely interesting since water can influence many electrochemical processes with dissolved constituents of aqueous solution by their actively participating in these processes [

In the frame of electronic band theory, these inherent constituents of liquid water can be described as local carriers of vacant

As seen in

ium-radical concentration,

gen molecule in water up to

ter is controlled by hole population of the energy level,

where

at

The forcedly variable Fermi level,

the concentrations:

electrons

where T is Kelvin temperature, and ^{–5} eV/K.

So, we submit the values of

Equations and obtain:

the non-stoichiometric states of liquid water are the confines of its thermodynamic stability.

From the well known requirement of

where

and one can show that the hypo-stoichiometric state, ^{–6} is achieved in acidic solution

tion band.

Opposite, the hyper-stoichiometric one, ^{–6} is achieved in basic solution

At the same time, Fermi level is mostly sensitive to the non-stoichiometry amount, x, in the hypo-stoi- chiometric basic solution and in the hyper-stoichiometric acidic one because the concentrations of hydroxonium and hydroxide ions as inherent water species have to be in the ratio [

with the dissociation constant K_{w} = 10^{–14} M^{2} at T = 298 K. Reduction-Oxidation (RedOx) potential of an aqueous solution is measured by Standard Hydrogen Electrode (SHE) with the half-reaction [

Directly identifying this electrode by means of congruous Fermi level,

For illustrating this identification, we consider the following half-reactions [

in addition to the half-reaction (10) which is characterized by

is shown above for the half-reaction (2). We obtain

limited hydroxonium level population:

Similarly, we can find the RedOx of Standard Oxygen Electrode (11). Substituting

gives

For (12), we also have _{OH} − ε_{F(12)} = 0.113 eV_{ }and Fermi level equal to

Finally, we can find the RedOx potential of the Electrode (13) in the basic solution with

and

The electronic band structure of spatially-separated different aqueous electrodes is essentially differed from the one of an electric contact between them via an ion-exchanging membrane shown in

One can see that, the electrochemical cell generates the negative voltage relative to the standard hydrogen electrode when Fermi levels of these electrodes are equated. Here, in the specific case of Standard Electrodes (10) and (12), the SHE has the positive charge and the band-gap model of liquid water allows visualizing correctly the deformed electronic energy levels of aqueous solutions near the ion-exchanging membrane.

Using this method for identifying the RedOx potentials of the following half-reactions [

we can assay the effect of

From the Equation (9), we obtain

exponential proportion between the values of hydrated dissociation energy of

solution [

reaction (14) inasmuch as

Opposite, the Standard Electrode (15) of two oxidants as gaseous oxygen and liquid hydrogen peroxide is characterized by the negative effect of this combination. Indeed, for RedOx = 0.695 V of this electrode, Fermi

level is equal to

mono-oxidant electrodes (12) and (14) accordingly. It implies that gaseous oxygen and liquid hydrogen peroxide force out each other from water because the actual concentration of hydroxide radicals in it as the electrode (15)

is reduced up to

ally does not involve in the half-reaction (15) and free oxygen is reduced only up to hydrogen peroxide.

The liquid water is considered in the frame of electronic band theory with accentuating the guessed energy levels,

ions

In this model, the specific concentration of hydroxonium radicals,

given

solution.

It is shown that such the variation of Fermi level allows describing the typical half-reactions and aqueous electrodes. For this, only two allowed electronic levels in the band gap of liquid water,

cupied

At the same time, the forced transformation of liquid water in the hypo-stoichiometric state,

example, by its electric reduction is realized when Fermi level,

Opposite, the hyper-stoichiometric water,

dissociated and hydrated oxidants: half-oxygen,

shown that two-oxidant solution of

Such theoretical approach closely relates the electrochemistry of aqueous solutions with the specification of electron population of allowed levels in the band gap of liquid water.

Author is pleased to the Russian foundation of basic research (RFBR) for supporting this work (grant # 13-08-00826a).