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4.4 -Charge Distribution

Partial atomic charges in -systems are calculated by generating all valence bond (resonance) structures for this system and then weighting them on the basis of -orbital electronegativities and formal considerations (PEPE = Partial Equalization of -electronegativity).

First the -system of a molecular structure is determined and those atoms are identified that are starting points of +M or -M effects. The various resonance structures are then generated starting at the acceptor or donor atoms. One or more topological weights are assigned to the various resonance structures that depend on the changes in the valence bond structure and in the formal charges of the atoms at both ends of a resonance structure. These topological weight factors have been optimized from sets of data on 13C NMR shifts of twelve monosubstituted benzene derivatives, 13C NMR shifts of twelve carbon atoms in nine substituted pyridines, and C-1s ESCA shifts of eleven carbon atoms in seven fluorinated olefines.

shift of charge
topological weight = 1

separation of charge
topological weight = 0.5

If the positive and the negative charge are on adjacent atoms the topological factor has only a value of 0.25

recombination of charge
topological weight = 1.0

Scheme 3. Example for the topological weight factor

The total topological weight factor Wt consists of three parts:
Wt = fQ fB fA

In the next step, the resonance structures are weighted based on consideration of their electronic nature. The electronic weight We of each resonance structure is derived from -electronegativities and the electrostatic influences of neighbouring atoms:
We = + fe qN

The -electronegativities are dependent on atom type, hybridisation state and -charge. The following equation is applied:

= a + b q + c q2

Using the product of the topological and the electronic weight the effect of each resonance structure on the charge equalization process is calculated. The charge is moved along the various -system to the atoms of the resonance structures thereby changing their electronegativity. Therefore, the process of weighting the structures and shifting electron density has to be repeated in several cycles with decreasing amounts of charge being shifted.

Values calculated
The following quantities are obtained by the PEPE procedure:

q,A (QPI (A)): -charge on atom A

,A (ENPI (A)): -electronegativity of atom A

q,AB (DQPI (AB)): Difference on the -charges on atoms A and B

,AB (ENPI (A)): Difference in the -electronegativities of atoms A and B of a bond

LP,A (ENLP (A)): Lone pair electronegativity of atom A

Example

 

charge separation

charge separation of
atoms bonded directly

charge separation of
atoms bonded directly

   

decrease of the number
of covalent bonds

decrease of the
number of covalent
bonds

wt

0.5

0.1625

0.1625

Scheme 4. Determination of topological weights

Changes of -charges:

atom number

1

2

3

 

6.690

8.568

3.747

Cycle 1

q

-0.01

-0.004

0.005

 
         

6.720

8.290

3.977

Cycle 2

q

0.003

-0.026

0.022

 
         
         

6.895

7.301

4.802

Cycle 8

q

0.022

-0.119

0.097

 

Contribution of the various resonance structures:

 

R1: 213

R1: 12

R1: 21

 

charge shifted

-0.005

0.001

-0.001

cycle 1

 

-0.017

-0.005

0.005

cycle 2

 

-0.016

-0.004

0.004

cycle 3

 

-0.014

-0.004

0.004

cycle 4

         
 

-0.010

-0.002

0.002

cycle 8

Scheme 5. Process of charge equalization including electronic weighting

Results
The -charges calculated by the PEPE method for various heterocycles containing nitrogen atoms were compared with values from a Mulliken population analysis of ab initio STO-3G wave functions.
pyridine derivatives:
Pyridine and 2- and 4-hydroxy pyridine derivatives show similar -charge patterns. The nitrogen and the carbon atoms at the 3- and 5- position have negative charges in the range of 0 and -0.125 e and the atoms at the 2-,4- and 6- position have positive charges in the range of 0 and +0.125. The results of the STO-3G and the PEPE-calculations correspond with each other to a reasonable degree.

R

N1

C2

C3

C4

C5

C6

O

 

H

-0.13

0.07

-0.03

0.06

-0.03

0.07

-

ab initio

 

-0.08

0.02

-0.00

0.04

0.02

0.00

-

PEPE

2-OH

0.13

0.06

-0.09

0.07

-0.08

0.04

0.131

ab initio

 

-0.11

0.02

-0.13

0.05

-0.01

0.02

0.051

PEPE

3-OH

-0.01

-0.09

0.03

-0.03

0.02

-0.05

0.115

ab initio

 

-0.08

0.00

0.00

0.02

0.00

0.01

0.044

PEPE

4-OH

-0.07

0.04

-0.12

0.07

-0.08

0.04

0.125

ab initio

 

-0.10

0.02

-0.01

0.03

-0.01

0.02

0.057

PEPE

Table 8. Comparison of -charges in pyridine derivatives calculated by PETRA and
STO-3G, respectively
(ab initio values from: J. E. Del Bene, J. Comp. Chem. 2, 251-260 (1981))

pyrimidine derivates
PEOE -charges of pyrimidines, which are substituted at the 4-position, a show well agreement with the corresponding values from a Mulliken population analysis of STO-3G wave functions (see next page):

R

N1

C2

N3

C4

C5

C6

 

H

-0.04

0.01

-0.04

0.03

0.01

0.03

ab initio

 

-0.08

0.04

-0.08

0.06

0.00

0.06

PEPE

Me

-0.06

0.03

-0.07

0.07

-0.02

0.04

ab initio

 

-0.08

0.04

-0.08

0.06

0.00

0.06

PEPE

NH2

-0.12

0.05

-0.15

0.09

-0.09

0.06

ab initio

 

-0.11

0.04

-0.12

0.06

-0.03

0.06

PEPE

OH

-0.09

0.05

-0.14

0.06

-0.05

0.06

ab initio

 

-0.10

0.04

-0.11

0.05

-0.01

0.06

PEPE

F

-0.07

0.04

-0.10

0.03

-0.04

0.06

ab initio

 

-0.09

0.04

-0.11

0.05

-0.01

0.06

PEPE

CH=CH2

-0.16

0.03

-0.07

0.05

-0.01

0.04

ab initio

 

-0.09

0.04

-0.10

0.06

0.00

0.06

PEPE

CHO

-0.04

0.02

-0.05

0.03

0.02

0.04

ab initio

 

-0.07

0.04

-0.08

-0.05

0.02

0.06

PEPE

CN

-0.03

0.03

-0.04

-0.01

0.03

0.05

ab initio

 

-0.07

0.04

-0.08

0.04

0.01

0.07

PEPE

Table 9 Comparison of -charges in pyrimidine derivatives calculated by PETRA and
STO-3G, respectively
(ab initio values from: J. E. Del Bene, J. Comp. Chem. 2, 251-260 (1981))

Scope and Limitations
The dependence of the -electronegativity on charge is parameterized for the following atoms.

(The functions are dependent on the hybridization states)

Applications
A detailed discussion will be given in the next section using the results of the calculations on both the - and -charges.

References

  1. Pi-Charge Distributions from Molecular Topology and Pi-Orbital Electronegativity
    M. Marsili, J. Gasteiger
    Croat. Chem. Acta
    53, 601-614 (1980)
  2. Berechnung der Ladungsverteilung in konjugierten Systemen durch eine Quantifizierung des Mesomeriekonzeptes
    Gasteiger, H. Saller
    Angew. Chem.
    97, 699-701 (1985)
    Angew. Chem. Intern. Ed. Engl.
    24, 687-689 (1985)

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