Bio-structural Energy Criteria of Functional States in Normal and Pathological Conditions - Progress in Organic and Physical Chemistry: Structures and Mechanisms - page 9

1 1 1

(3)

2

Wn P

q

r ii E

i

P

0

P

(4)

E

r

0

1 1 1

= +

(5)

2

( Wrn )

P q 0

i

*

Z

(6)

q =

*

n

where W i = electron bond energy [4], or ( E i ) = atom ionization energy [5], r i = orbital
radius of i -orbital [6], n i = number of electrons of the given orbital, Z* and n* =
nucleus effective charge and effective main quantum number [7, 8].
Ɋ 0 is called the spatial energy parameter, and Ɋ E = the effective P-parameter. The
effective Ɋ E -parameter has a physical sense of some averaged energy of valence elec-
trons in the atom and is measured in energy units, for example electron volts (eV).
The values of P-parameters are calculated based on the Equations (3) and (6),
some results are given in Table 1. At the same time, the values of parameters during
the orbital hybridization are used (marked with index “H”) [9]. The calculations are
carried out taking into account the possibility of fold bond formation (single, double,
and triple). For carbon atom the covalent radius of triple bond (0.60 Å) nearly equals
its orbital radius of 2Ɋ-orbital (0.59 Å), therefore, the possibility of carbon compound
formation becomes more effective.
And now we will brieÀ y discuss the reliability of such approach. According to the
calculations [3] the values of P E -parameters numerically equal (in the limits of 2%) the
total energy of valence electrons ( U ) by the atom statistic model. Using a well-known
correlation between the electron density ( ) and interatomic potential by atom statistic

model, we can obtain the direct dependence of Ɋ E -parameter upon the electron density
at the distance r i from the nucleus:

β

AP

2/3 0

AP

C

i E

r

i

where Ⱥ = constant.
The rationality of this equation can be con¿ rmed when calculating the electron
density using Clementi's wave functions [10] and comparing it with the value of elec-
tron density calculated via the values of Ɋ E -parameter.
The modules of maximum values of radial part of Ȍ function are correlated with
the values of Ɋ 0 -parameter and the linear dependence between these values is established.