Chemistry Reference
In-Depth Information
which may be further written successively as
1
r
1
−
1
4
πε
0
q
r
1
−
1
4
πε
0
q
r
2
=
q
4
πε
0
1
r
2
q
4
πε
0
·
r
2
−
r
1
Δφ
=
φ
1
−
φ
2
=
=
r
1
r
2
1
4
πε
0
ql
cos
θ
r
2
1
4
πε
0
d
cos
θ
r
2
=
=
(13.17)
when one employed the general expressions for the electrostatic potential
d
·
r
r
3
1
4
πε
0
φ
=
(13.18)
and for the dipole moment
d
·
r
=
d
·
r
·
cos
θ
(13.19)
However, from (13.16) to (13.18) there follows that in general one has the electrostatic
field-potential relationship
E
·
r
=
φ
4
πε
0
d
1
·
r
⇒
E
·
r
=
(13.20)
r
3
leaving with the general electrostatic field-dipole connection too
d
·
E
·
E
4
πε
0
r
3
=
=
α
(13.21)
From Eq. (13.21) one recognizes the polarizability basic formulation
4
πε
0
r
3
R
3
,
ct
α
=
⇔
POL
=
ct
·
=
4
πε
0
(13.22)
allowing further AC-complex polarizability formation as based on the anionic-
cationic summation of the associate radii of action
R
C
=
ct
−
1
/
3
(
POL
1
/
3
POL
1
/
3
R
AC
=
R
A
+
A
+
C
)
(13.23)
which corresponds to the actual projective polarizability formulation for the AC (IL)
complex
POL
1
/
C
)
3
[Å
3
]
(
POL
1
/
A
+
POL
AC
=
(13.24)
On the same analysis line, when one goes to evaluate the total energy of the AC com-
plex, one has to consider also the electrostatic interaction energy which superimposes
to the individual radicalic (atomic or molecular fragments) of A and C subsystems,
to get
q
A
q
C
q
A
q
C
(4
πε
0
)
ct
1
/
3
POL
1
/
3
(4
πε
0
)
R
AC
=
E
AC
=
E
A
+
E
C
−
E
A
+
E
C
−
(13.25)
AC
