Bio-structural Energy Criteria of Functional States in Normal and Pathological Conditions - Progress in Organic and Physical Chemistry: Structures and Mechanisms - page 15

P
P

2

Then: γ = = (n+1) 13(ɚ)

1

In the same way, for “singular” systems (with similar values of functions) of two-
dimensional harmonic oscillator the energy of stationary states is found as follows:

ε = h ν (n+1)

By this model the maximum of interactions corresponds to the principle of algebraic
addition of P-parameters Equations (7) and (8). When n = 0 (basic state), we have Ɋ 2
= Ɋ 1 , or: the maximum of structure interaction occurs if their P-parameters are equal.
This postulate and Equation (13(ɚ)) are used as basic conditions for the formation of
stable structures [13].
Hydrogen atom, element No 1 with orbital 1S 1 de¿ nes the main energy criteria of
structural interactions (their “ancestor”).
Table 1 shows its three Ɋ E -parameters corresponding to three different character-
istics of the atom.

TABLE 2 Calculation of molecular EN.

W
(eV)

r i
(Å)

q 2
(eVÅ)

P 0
(eVÅ)

R K
(Å)

P 0 /3Rn
(eV)

X
(Batsanov)

Atom Orbital

1 2 3 4 5 6 7 8 9

Li 2S 1 5.3416 1.586 5.8902 3.475 1.33 0.87 0.98

Be 2S 1 8.4157 1.040 13.159 5.256 1.13 (Ɇ) 1.55 1.52

B 2Ɋ 1 8.3415 0.770 21.105 4.965 0.81 2.04 2.03

ɋ 2Ɋ 1 11.792 0.596 35.395 5.868 0.77 2.54 2.56

N 2Ɋ 1 15.445 0.4875 52.912 6.5903 0.74 2.97 3.05

O 2Ɋ 1 17.195 0.4135 71.383 6.4660 0.66 3.27 3.42

F 2S 2 2Ɋ 5 50.809 0.64 3.78 3.88

Na 3S 1 4.9552 1.713 10.058 4.6034 1.54 1.00 0.98

Ɇg 3S 1 6.8859 1.279 17.501 5.8588 1.6 (Ɇ) 1.22 1.28

Ⱥl 3Ɋ 1 5.7130 1.312 26.443 5.8401 1.26 1.55 1.57