(Digital Presentation) The Intermediate Electron Bond. Half-Reactions and the Electronic Structure of Atoms
Authors: Chernomorskii Alexandr I. 
Published: August 2024

The transfer of electrons ne from the intermediate state (Ox1 ← ne → Ox2) is associated with formation of a chemical bond with one Ox-form. Consequently, chemical bonds of electrons with Ox - forms should be formed Ox + ne
+ H2O→ Red or broken Red + H2O → Ox + ne in half-reactions. Then, there should be concluded some electronic state and bond without a specific chemical component. This electronic bond was determined as a definite coulomb bond, intermediate from metallic to non-metallic specific bonds. Ionization potential of intermediately bound electrons is determined
I

interm.
= 5.19 eV [1-4].

The chemical energy released in half-reactions-interactions is spent at once on separation of formed oppositely charged electrons and ions, polarization of water molecules of formed intermediate complexes. External potential differences appear between charged particles (double layers). Electrons and ions acquire electrochemical potentials, and electrochemical equilibriums are established.

Exchange of formed electrons with electrons of electrodes stabilizes half-reactions. At that, a contact potential drop (not associated with interaction) appears in the electrode surface. However, only potential drops in double layers need to be taken into account. The rates of half-reactions-interactions change with changes in potential drops in double layers during electrical polarization.

An important determination of ionization energy
I

interm.
= 5.19 eV based on the found linear relationships between the first ionization potentials
I
of elements (related to the main groups) and their reversal covalent atomic radii 1/
r

atom (Fig. 1). The linear relations cross when
I
interm.
= 5.19 eV at 1/
r

atom = 0.35 Ằ-1 (
r

atom = 2.79 Ằ). It is concluded, that a specific electron bond formation with wave overlap begins with
r

atom = 2.79 Ằ at
I
interm.
= 5.19 eV. Taking
r
interm.
= 2.79 Ằ, ionization potential
I

interm.
was calculated as coulomb energy of attraction between electron and polarized positive charge on Ox - form [2 - 4]

I

interm.
=-
e

2/
r

interm.
= - (4.8.10-10 e.s.u.)2 / 1.6.10-12 erg/eV
.

r

interm.

.10-8 cm =
= - 14.4
.
10-8eV.cm/2.79.10-8cm = - 5.19 eV (1)

According to linear relations (Fig.1), for similar elements, the first ionization potentials
I
are equal

I

=
5.19 eV + Δ
I
(2)
when energies of formation of specific electronic bonds Δ
I
are changed by quanta. The quantum linear oscillator model is applied

Δ
I

= (Δ
n
+ ½)

h

ν

o

(3)
where
h
is Plank constant, ν
o

is the natural frequency of electron - wave, Δ
n
are numbers of quantum jumps, Δ
I

= ½

hν

o

is the point zero energy [4,5].
It is concluded, that quantum jumpsΔ
n
= 8 -
n
= 1, 2, 3... should be counted from the orbital
n
= 8 on which electron localization and specific bonding is absent (8th period is absent in the Periodic System). However, the coulomb non-specific electronic bonding (
I

interm.
= 5.19 eV) must be preserved (Figh.1). Indeed, the first ionization potentials of elements of the 7th period are ~ 5 eV (5.17 eV for Ac).

Therefore, Δ
n
= 1, Δ
n
= 2, Δ
n
= 3 ... correspond to one, two, three electron jumps necessary to reach the localization orbital related to the 7th, 6th, 5th .... (and so on) periods. First, using these Δ
n
, close natural frequencies ν
o

of electron waves were calculated for similar atoms as

ν
o

=
I
- 5.19 eV / (Δ
n
+ ½)

h
(4)
For example, calculated
ν

o

are for
I
(0.364.1015 s-1),
Br
(0.358.1015 s-1),
Cl
(0.344.1015 s-1),
F
(0.347 .1015 s-1).

Using even the average natural frequency (0.35.1015 s-1), the first ionization potentials
I
(close to reference) were then calculated as the sums (Eqn.2).

I =
5.19 eV + Δ
I =
5.19 eV + (Δ
n
+ ½)

hν

o

(5)
for most of elements. For example, for elements of the 7th main groups:
I
10.3 eV (10.4 eV),
Br
11.75 eV (11.8 eV),
Cl
13.1 eV (13.0 eV), F 17.5 eV (17.4 eV). Emission wavelengths are also determined [4].

Therefore, the quantum-mechanical oscillator model can be applied to electron localization in atoms and to formation and breaking of specific chemical electron bonds with Ox - forms in half-reactions. In both cases, electron - waves pass to (or from) the intermediate state
I

interm.
= 5.19 eV corresponding to the absence of specific bond formation.

References

A.I Chernomorskii, Russian Journal of Physical Chemistry, 55(2)1981.

A.I. Chernomorskii, Thermodynamics of Electrodes (FAN,Tashkent,1993);

A.I Chernomorskii, Journal of The Electrochemical Society, 2021, 168, 116514

A.I Chernomorskii, The intermediate electron bond and half-reactions (Scientific Resources, N-Y) (1999).

P. Atkins, Julio de Paula, Physical Chemistry (W.H. Freeman and company,2006).

Figure 1