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The electrochemical transformation of a drinking water into the positively charged one by means of the galvanic cell with the quasi-equilibrium anode and with the strongly polarized cathode is considered. These electrodes intensively produce hydroxyl radicals in the stream of pure water by the electric current in the cell. The mole fraction [OH] of the active and short-living radicals is nearly equal to the mole fraction [H3O+] of hydroxonium ions. These species form the positively charged pair as a hydrated cluster ()()+222nHOHOin liquid water. It is shown that such water is characterized by high concentration of the charged particles [(H2O)+2]~10-7 and by the shift of oxidation-reduction potential (ORP) into the positive region ORP > 1.0 V.
Simple water is described as a dielectric with the wide band gap, gε, equal to 6.9eV , It is the energy difference between the highest molecular orbital occupied by electrons and the lowest unoccupied molecular orbital. At the same time, there are two allowed local energy levels in the band gap of liquid water as occupied-by-electrons, εOH, hydroxide ion, OH–, and the vacant one, εH3O, of the hydroxonium ion, H3O+. These levels are located symmetrically nearby the band-gap middle with the energy difference between them of 1.75eV . Such the model allows eliminating the inconsistencies of electrochemical properties of these well known charged particles  by means of the band theory of water .
So, one can use Fermi level, Fε, as an oxidation-reduction potential (ORP) [4,5] which indicates the tendency of liquid water to donate or accept the proton. When Fermi level is high, liquid water will donate protons, i.e. that is an antioxidant. Opposite, water will accept protons and will become the oxidant when Fermi level is low . Since electrons cannot occupy the same quantum states, they have to occupy the ones that can accept them. If it is not happening, all the local quantum states (as oxidants) are inactive due to high Fermi level in the band gap of liquid water. For activating oxidizing agents, Fermi level is to shift down at least to the electron level of these agents and this is possible only when water becomes hyper-stoichiometric, H2O1–z (z < 0).
From this rule, one can easily get the difference between pH and ORP of liquid water. The first can be changed in stoichio metric water, H2O, by adding equivalent amount of anions and cations into liquid water. The second can be modified without
changing pH by electro-oxidizing of pure liquid water. In as much as just a little non-stoichiometry of H2O1–z, is required (|z| < 10–10) for this and ORP will be sensitive to external conditions and may be changed without visible varying a composition of aqueous solution .
At the same time, such water can get the positive electrical charge that gives several unique properties of drinking water responsible for the health benefits: antibacterial and clearing action becomes curative. It is important to correctly estimate a scale of this tendency for generating electro-positive drinking water in practice. This estimate is the subject of the given work.
Allowed local electronic levels in the band gap of liquid water, εH3O and εOH, can be vacant and occupied by electrons like impurity levels in the band gap of solid dielectric. The molecular carriers of these levels are the attributive species of water as the occupied-by-electrons hydroxide ion, OH–, and the vacant one of hydroxonium ion, H3O+. They are obtained by the chemical reaction of dissociation :
and their mole fractions [H3O+], [OH–] as the inherent water species satisfy the ratio 
with the dissociation constant Kw =10–14 M2 at T =298 K. Their electronic levels, εH3O and εOH, are symmetrically to the band-gap middle which is Fermi level, Fsε, of stoi chiometric water, H2O, (Figure 1a) . In non-stoi chiometric water, H2O1–z, Fermi level, εF , is the single-valued characteristic of ORP :
where e is the charge of electron and SHE ε = –6.21eV  is
Fermi level of the Standard Hydrogen Electrode (SHE) 
One can see that ORP becomes negative when Fermi level is
shifted to the donor level,
εH3O . Then, this level will be occupied
by electrons forming the hydroxonium radicals, H3O, as strongest
antioxidants. This transforms water into hypo-stoichiometric
state, H2O1–z, (z>0). Opposite in the hyper-stoichiometric water
(z<0), Fermi level is shifted to the acceptor level, εOH , making
the positive ORP and forming hydroxyl radicals, OH, as strongest
So, Fermi level, εF(8) , in hypo-stoichiometric water H2O1–z
(z>0) is defined by the electron population of the donor level,
εH3O , as a molar fraction
KH2 is the
constant of H2 dissociation in water for forming hydroxonium
radicals, H3O, as hydrated hydrogen atoms, 2 H ⋅ H O , by reaction
Fermi level, F(9) ε , in hyper-stoichiometric water (z<0)
is defined by hole population of the acceptor level, εOH , as
O2 K and
H2O2 K are the constants of O2 dissociation in water with forming
hydrogen peroxide, H2O2, as hydrated oxygen atom, 2 HH O and its
The states of liquid water in Figure 1b with Fermi levels:
F(8) ε and F(9) ε are obtained by the standard reactions :
at [H3O+] = [OH–] = 10–7 M, [H2] = 1.6•10–3 M, [O2] = 2.7•10–4
M, H2 P =
O2 P = 1 atm, T = 298 K and
H2 K ~ 2•10–19 M,
O2 K ~
H2O2 K ~ 6•10–7 M  giving [H3O] •~ 2•10–11 M for
the reaction (8) and [OH] ~ 8•10–13 M for (9) .
It means that the electron level,
εH3O , is mostly vacant as
hydroxonium ions, H3O+, due to F(8) ε is below
εH3O (see Figure
1b, left) and the energy level, εOH , is fully occupied by electrons
as hydroxide ions since this Fermi level is essentially above
εOH . Fermi level, F(9) ε , is slightly above the electron level, εOH
. Therefore it contains holes (the thin dotted blue line in Figure
1b, right) as hydroxyls (OH) but the energy level,
εH3O , is fully
vacant as hydroxonium ions, H3O+, since F(9) ε is essentially
Forcedly shifted Fermi level, εF , in the band gap of liquid
water is determined rigorously by the ratios of mole fractions:
[H3O+]/[H3O] and [OH]/[OH–], of the vacant species (H3O+, OH)
and the occupied-by-electrons ones (H3O, OH–) for the energy
εH3O and εOH , in the band gap of liquid water. These
ratios are given by Fermi–Dirac statistics which can be simplified
to Maxwell–Boltzmann distribution of electrons and holes in the
corresponding energy levels :
Then, submitting [H3O+], [H3O] of the electrode (8) into (10)
and [OH], [OH–] of the electrode (9) into (11), we have obtained
εH3O – εOH = 1.75eV out of the well-known requirement
of the chemical stability of liquid water: F(8) ε – F(9) ε = 1.23eV
. So, εH3O = –5.58eV and εOH = –7.32eV.
Thus, consideration of liquid water in the frame of band
theory shows that varying its ORP is the immediate result of
Fermi level shift in the band gap. Water becomes an antioxidant,
i.e. hypo-stoi chiometric, H2O1–z, with z>0 when Fermi level is
shifted to the level εH3O which is occupied by electrons and
hydroxonium radicals (H3O) are formed. Opposite, in hyperstoichiometric
water (z<0), Fermi level is shifted to the level
εOH which is occupied by holes and forms hydroxyls. Therefore
water becomes oxidant.
Now, we can obtain the dependence of Fermi level on the
of non-stoi chiometric water, H2O1–z as the graph represented
in Figure 2 .
One can see that the region of chemical water stability
(-1×10-13≤z≤4×10-13 ) is shifted to the hypo-stoichiometric state,
H2O1–z (z>0), which is achieved easier by least shifting of Fermi
level from the band-gap middle to the donor level, εH3O , as well
as the hyper-stoichiometric one, H2O1–z (z<0), is achieved by a
little variation of z to the acceptor level, εOH . At the same time,
Fermi level is shifted in the band gap about 1eV.
Forced oxidizing of liquid water (shifting εF down) can be
carried out by the electrochemical cell with the voltage of ~ 2V
between the strongly polarized cathode and the anode at quasiequilibrium
with water  under obvious condition :
at fa >> fc . Here index “c” denotes cathode and “a” – anode,
fi is the specific surface of distributed i-electrode, and
divergence of electric field in this electrode. At these conditions,
the external potential applied to the cathode intensively
Hydroxide ions are discharged to hydroxyls by quasiequilibrium
anodic reaction 
in the bulk anode region (Figure 3). Here, the hydroxonium
radicals, H3O, diffused out of the cathode layer donate electrons
to hydroxyl radicals by reaction
All this forms the positive charge in liquid water near the
cathode (Figure 3) with the ratio
In contrast to (12) here, the index z of non-stoichiometric
water, H2O1–z, is defined by formula 
We have obtained in  the z-depended graphs of these
species as shown in Figure 4. One can see the equal mole
fractions of hydroxonium ions and hydroxyls.
Thus, the ratio (18) indicates the strong acidic reaction of
the chemically stable hypo-stoi chiometric water containing the
large mole fraction of hydroxyls ([OH] ~ 10–7M) as strongest
oxidants (see Table 1).
Oxidation potential of chemical oxidants  .
In this case, the hydroxyl radicals quickly form the solvated
acceptors for electrons by reaction
in the bulk of electrochemical cell due to their very short lifetime
(only few nanoseconds) .
The quick response of Fermi level to changing of the water
non-stoichiometry, z, takes place in the stoi chiometric state
(z=0). Just therefore, a little additive of oxidant in pure water
changes oxidation-reduction potential (Fermi level) appreciably.
Such the effect may be gotten also by electric oxidizing of pure
water in the electrochemical cell with strongly polarized cathode
and the anode in equilibrium with the aqueous medium under
the condition (13).
The advantages of this approach are the high efficiency of
oxidation reaction, the simplicity of the procedure, low cost,
and there is no need for special sorbents because pure water
itself becomes the agent for oxidizing pollutants. Such water can
contain the large concentration of the charged particles [(H2O)+2]~10-7 M and the oxidation-reduction potential can be in the
positive region ORP > 1.0 V.
Author thanks the Russian Foundation of Basic Research
(RFBR) for supporting this work (grant # 16-08-00029a) and
appreciates his colleagues at active discussing all the aspects of