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Abstract The dipole moments and the polarizabilities in the excited states of some pyridinium ylides were estimated using the results of the statistic cell model proposed by
Takehiro Abe.
Keywords dipole moment and polarizabilities, cycloimmonium ylids
INTRODUCTION
Pyridinium ylids [1] are dipolar molecules in the ground electronic state. They have a visible electronic absorption band that appear by an intramolecular charge transfer (ICT) from the carbanion to the heterocycle. This band is very sensitive at the solvent nature. A study about the solvent influence on the ICT visible band offers information on the ylid electric parameters modifications by passing from the ground state to its excited state.
THEORETICAL ASPECTS
Takehiro Abe statistic cell model of a pure liquid [2] permits to express the spectral shifts in function of the microscopic parameters both of the solvent and of the spectrally active molecule. In this model a spectrally active molecule is surrounded by concentric solvatation spheres containing identic, spherical solvent molecules. The spheres containing solvent molecules have their centers on the solvatation sphere surface (Fig.1). p r v
R
R u u v(2) v(1)
2
1 r u
R u v(p)
Fig.1 The arrangement of the molecules in Abe model.

The p-th solvatation sphere radius can be expressed as function of the radius of the spheres that represent solvent and solute molecules, r u and r v respectively:
R uv ( p )
 r u

( 2 p

1 ) r v
(1)
The system of the spheres is considered in two electronic states:
ground state (g) in which all the molecules are in their ground electronic state
excited state (e) corresponding to the ground state of the solvent molecules and to the excited electronic state of the central, spectrally active molecule.
The chosen states correspond to the experimental check of the model, by spectral means. The used liquids for spectral recordings may be transparent in the absorption range of the spectrally active molecule. Durring spectra recordings, the solvent molecules do not change their electronic state.
In liquid state, the molecules interact. The solvatation energies in the states participating to the electronic charge transitions are:
W
W g e


W
W e
0 g
0 

W
W e g
(
( u u
)
)


W
W g g
(
( v v
)
)
(2) where W
0 represent the energies in the ground and excited states of the system, for its g , e gaseous state; W g , e
( u ) - interaction energies between the central molecule (in the two states of the transition) and the solvent molecules surrounding it; W g
( v ) -the interaction energy between the solvent molecules. The energies in the gaseous state of the system can be express by the following terms:
W
W g e
0
0

W g

W e
(
( u ) u )

W g

W g
( v )
( v )
(3)
W g
W
0 e
0 hc
ν v
W e
(u) + W g
(v) hc ν l
W e
Gaseous state
W g
(u) + W g
(v)
Solution
W g
Fig.2 The electronic shifts by passing from gaseous to liquid solution.
From Fig.2 and the relations (2) and (3), it results that spectral shift by passing from gaseous state to the binary solutions is proportional with the difference between the solvatation energies of the spectrally active molecule in the two electronic states of the transition. hc (
 l
  v
)

W e
( u )

W g
( u ) (4)

Taking into account Van der Waals interactions, Abe expressed the spectral shift by the relation (5): hc (
 l
  v
)
   p
R

6 uv ( p )
2
3 kT
 g
2
( v )

 e
2
( u )
  g
2
( u )

  g
( v )

 e
2
( u )
  2 g
( u )

  2 g
( v )

 e
( u )
  g
9 u )

  p
R

6 uv ( p )
3
2
I g
( v )
 g
( v )
I g
I g
( v )

( u )

I g hc
 l
( u )
 hc
 l
 e
( u )

3
2
I g
( v )
 g
( v )
I g
( u )
I g
( v )

I g
( u ) l
 e
( u )

Relation (5) has been obtained in the hypothesis of the additivity of the orientation, induction and dispersion energies of the pairs of molecules. In this relation the index “u” reffers to the spectrally active molecules and “v”- to the solvent ones; g and e describe the ground and the excited states of the molecules and

is the wave number in the maximum of the pyridinium ylids electronic absorption band, measured in liquid solution (l) and în vaporous state (0);
 represents the dipole moment and

- the polarizability. C is a constant dependent on the molecular weights and on the densities of the molecules [2]: hcC
   p

6
R uv ( p )
 n ( 1 )

6
R uv ( 1 )
 n ( 2 )

6
R uv ( p )

...
 n ( p )

6
R uv ( p )

 
16

9
3
N
2
A


 v
M v


2




 




M
 u u


1 / 3



M
 v v


1 / 3




4






M
 u u


1 / 3

3


M v
 v


1 / 3




4

...


(6)
The radius of a solvent and solute molecule was express in (6) as function on molar mass and density of the corresponding substance.
In order to estimate the dipole moments and polarizabilities in the excited state of
 pyridinium ylids, a formula resulting from (5) and (6) has been used:

2 e
( u )
 
2 g
( u )


T
1
( v , u )
 e
( u )

T
2
( v , u )
 g
( u )

 l

C
 v 
0 where:
T
1
( v , u )


2 g
( v )

3
2 I g
I g
( v )

I g
( v )

I g
( u )

( u )
 hc
 hc
 l l

2
 g
2
( v )
  g
( v )
 g
( v )
3 kT
(7)
(8)
T
2
( v , u )


2 g
( v )

2
3
2 I g
I g
( v ) I g
( v )

I g
( u )
( u )
 g
( v )
 g
2
( v )
  g
( v )
3 kT
(9) and
T
3
( v , u )

 l
  v (10)
C
The terms T i
(v,u), i=1,2,3 can be computed using the microscopic parameters both of the ylid and solvent and the wavenumbers of the ICT band. So, relation (7) permits to estimate, by regressional method, the dipole moments and the polarizabilities of the pyridinium ylids.
RESULTS AND DISCUSSIONS
The studied ylids were: pyridinium acetyl benzoyl methylid (Y
1
); pyridinium anilido benzoyl methylid (Y
2
); pyridinium dicarbetoxy methylid (Y
3
).The ionization potential and the value of the dipole moment in the ground state of pyridinium ylid was estimated by PM3.

The visible electronic absorption band of the studied pyridinium ylids was recorded in aprotic solvents with known parameters mentioned above.
Nr
Table 1 The solvent parameters and the wavenumbers in the ICT visible band
Solvent

(D) 10
25 
I(eV)

M

(cm
-1
)
(g/cm
3
) (g/mol) Y
1
Y
2
Y
3
1 n-Heptan 0 136.1 10.35 0.68 100.2 22600 22150 22080
2 Cyclohexane 0
3 CCl
4
0
4 Dioxan 0
108.5 11.00 0.78
105 9.72 1.59
94.4 9.52 1.42
5 Mesitilen 0 161.2 8.76 0.86
6 Chloroform 1.05 82.3 11.50 1.49
7
8
Methanol
Methyl acetate
9 Ethanol
1.62 32.6 10.97 0.70
1.67 69.9 10.51 0.97
1.69 50.6 10.70 0.79
10 Aceton 2.80 63.9 9.89.
9.77
0.79
11 Acetophenon 3.94 143.7 12.39 1.03
12 Acetonitrile 4.25 44.0 0.79
84.2
88.1
76.1
32.0
74.1
46.1
58.1
120.1
41.1
22550 20970 21910
153.8 22610 20970 21900
23830
120.2 23100 21730 22410
24630
24500
24330
26760
24480
24720
24600
22350
22470
24400
23030
24400
23240
22990
23560
22950
23280
25230
23400
24970
23450
23370
23750
Table 2 The parameters

Nr Ylid
 g g
,

, M and I of the studied ylids
(D)

(g/cm
3
) M (g/mol)
1
3
Y
Y
1
2 Y
2
3
5.6
5.9
4.1
1.41
1.76
1.53
239
253
293
I g
(eV)
8.96
8.72
8.93
The terms T i
(v,u), i=1,2,3 was estimated using the microscopic parameters both of the ylid and solvent and the wavenumbers of the ICT band from Tables 1 and 2.
Using a Multireg BASIC program [5], both the dipole moments in the excited state and the polarizabilities in the ground and the excited states of pyridinium ylids were estimated.
Table 3 Dipole moments
 e
(u) and polarizabilities
 g
Nr Ylid 
2 e
( u )
  g
2
( u )
 g
( u ) 10
25

( u )
 e
( u ) of the studied ylids e
( u ) 10
25
 e
( u ) (D)
1
2
3
Y
1
Y
2
Y
3
-36.76
-22.61
-22.35
48.4
66.4
34.1
40.0
41.4
13.1
2.32
3.49
1.91
The obtained data (Table 3) reflect that, in the intramolecular charge transfer process, the dipole moment of pyridinium ylids decreases and changes its sens, concomitantly with an decrease of the molecular polarizability. The values for the dipole moments of pyridinium ylids are in good agreement with the values obtained in [4] for some pyridazinium ylids.
REFERENCES
1. I.Zugravescu and M.Petrovanu, N Ylid Chemistry, Acad.Press, London, 1976
2.
Takehiro Abe, Bull.Chem.Soc.Japan, 38,1314, 1965; 39, 936, 1966
3.
G.Henrion, A.Henrion and R.Henrion, Beispiele Zur Datenanalyse mit BASIC
Programmen, Berlin, 264-282, 1988
4.
D.Dorohoi, G.Surpateanu and L.Gheorghies, Balkan Phys.Letters, 6(3), 198, 1998