The stabilization of the positive and the negative charge obtained in the polar breaking of a bond is calculated from the - and lone pair-electronegativity values of the atoms that are in conjugation to the atoms obtaining the charges.

The search for the atoms that can stabilize a positive or a negative charge does not start at the atoms of the bond that is broken. Rather, the search is initiated the other way round, starting at the atoms that have the potential of stabilizing charges through the resonance effects (source atoms). Then, the atoms of those bonds are marked that will be in conjugation to the source atoms.

The following types of source atoms are considered:

- donor atoms (bearing a free electron pair)
- acceptor atoms (being able to accept an electron pair)
- alkyl groups at multiple bonds (hyperconjugation effect)
- alkyl groups at donor atoms (hyperconjugation effect).

Resonance stabilization is a bond property since it is a bond that is being broken to generate charges. As there are two directions for breaking a bond in a polar manner, each bond is investigated twice:

A bond is characterized by the indices of the two atoms A, B comprising the bond. The convention is that the first atom obtains the positive charge.

A value, R^{-}, is calculated for stabilizing the negative charge and another value, R^{+}, for stabilizing the positive charge. Furthermore, both values are combined into an additional value, R^{}, for resonance stabilization of the charges at both atom centers.

See Figure 7 for details.

**Figure 7. The generation of resonance structures on breaking a bond**

The numerical value for the stabilization of a negative charge, R^{-}, is obtained from all those atoms, i, that will stand in resonance to the negative center:

The summation goes over all atoms, i, of the resonance structures. The parameter f is a fading factor which is set to 1.0 if the intervening bonds are aromatic, otherwise f = 0,67. The variable n is the number of bonds between the negative center and the atom, i, (source atom) that, can take over this negative charge in a resonance structure.

The value for the stabilization of the positive charge, R^{+}, is obtained by the following equation:

Again, the summation runs over all atoms, i, of the various resonance structures, f is the fading factor having the same values as above, and n is the topological distance between the positive center and the atom, i, that can take over the positive charge.

The constant, c, was set to a value of 26.63 eV under the assumption that a CC-double bond can stabilize a positive or a negative charge at an adjacent CH_{2}-group to the same extent. In other words, allyl resonance in the cation and in the anion is assumed to have the same stabilizing effect.

The value of the combined effect, R^{+/-}, is obtained simply by adding R^{+} and R^{-} of the inverse bond.

__Values Calculated__
**R ^{+}_{AB} (PSTAB (A,B)):**

Extent of resonance stabilization of a positive charge on A when the bond A-B is broken in a polar manner.

**R ^{-}_{AB} (NSTAB (A,B)):**

Amount of resonance stabilization of a negative charge on A when the bond A-B is heterolytically broken

**R ^{+/-}_{AB} (STABRES (A,B)):**

Amount of resonance stabilization of a positive charge on A and a negative charge on B.

__Results__

The parameter on resonance stabilization is empirical in nature. To establish its importance comparison has to be made with physical or chemical data. No property has yet been found that is directly related to this concept of resonance stabilization. However, the values calculated for resonance stabilization have been very useful in many multi-parameter correlation (see applications).

__Applications__

The parameter for resonance stabilization has been found to be extremely useful in many applications. Particularly, when studying data on chemical reactivity, this parameter is quite often the singly most important influence. However, as already mentioned, nearly all applications found so far involve multi-parameter equations.

Ionization potentials are data that should, and have indeed been found to give useful applications for the parameter on resonance stabilization of positive charges. Since, on ionization, a positive charge is generated in a molecule and must somehow be accommodated. Any effect contributing to a stabilization of this positive charge should lower the value of the ionization potential.

In fact, it was found that the values for ionization from lone pair or -orbitals over the entire range of organic compounds could be reproduced well if these compounds are ordered into five different classes:

- aromatic compounds
- carbonyl compounds
- olefines and acetylenes
- olefines and acetylenes with heterodynes in conjugation
- compounds with unconjugated lone pair electrons (heteroatoms).

For each one of these five classes multiparameter equations have been developed, each one of the first four involving the parameter, R^{+}, for resonance stabilization of a positive charge. Here, the study on ionization potentials of alkenes is presented in more detail to develop an understanding of how the resonance parameter can be used.

Ionization from the highest occupied molecular orbital (HOMO) of an olefin leads to a radical cation that can be described by two resonance structures. Thus, this ionization is formally quite similar to the process that is used for the definition of the parameter for resonance stabilization:

(Remember, the first index of an atom pair specifies that atom of a bond that receives the positive charge).

The fact that two resonance structures are necessary for describing the ionized HOMO indicates that both resonance parameters R^{+}_{1,2} and R^{+}_{2,1} should be used for reproducing the ionization potential. In fact, we used the average, , of these two parameters as a measure of stabilization of the positive charge in the HOMO by resonance (or, to be the more exactly here: hyperconjugation, as only alkylsubstituted alkenes were investigated).

In addition to this stabilization mechanism, the stabilization of a positive charge by the polarizability effect (vide infra), as expressed by the parameter _{b} for the double bond, had to be used. The final equation obtained by multilinear regression analysis of the ionization potential of 56 alkenes was:

(1)

This equation can reproduce the ionization potentials of these compounds with a standard deviation of 0.11 eV (regression coefficient, r = 0.980).

**Figure 8. Calculation of Ionization Potentials of alkenes by equation 1**

The largest deviations are found for ethylene itself as the first member of the series, and for strained alkenes, cyclopropene e. g.

Parameters for resonance stabilization of charges produced on polar breaking of bonds have been found useful in many studies of data on chemical reactivity. In these cases it is always useful to write down explicitly the mechanism of a reaction. This allows one to deduce the correct resonance parameter that should be used.

For example, the rate determining step of the hydrolysis of amides under basic conditions is:

Thus, the CO-double bond is broken in the rate determining step, suggesting that the following resonance parameter should be used:

In fact, this parameter was found to be of good modelling power for the calculation of rate data on hydrolysis of amides under basic catalysis.

__Reference__

H. Saller, *Dissertation*, TU München, 1985

The resonance variables R^{+}, R^{-}, R^{+/-} have be shown to be powerful in estimating the resonance stabilization. Nevertheless, it has to be beared in mind that there is no real physical foundation of them. Since the calculation of R^{+} bases on the reziprocal values of the -electonegativity resulting in the unit [1/eV] while R^{-} is given in [eV] all three descriptors have another unit although they have the same physical meaning.

Furthermore, in fact, the energy of resonance stabilization in allylic cations and anions is not equal and this assumption means to be a simplification.

Thus, another variable has been developed for quantifying the delocalisation of charges. Analogues to the resonance variable they are called delocalization variables D^{+}, D^{-} and D^{+/-}.

D^{+/-} gives the mesomeric stabilization of the positive and negative charge in the fragments resulting from a heterolytic bond cleavage.

D^{+/-} is depending on the direction in which the bond is broken:

A B - bond to be broken in heterolytic manner

For calculating and the following equations are applied:

f_{j} - donor potential of the atom or bond typ j

m - number of the atom or bond typ j

g_{j} - acceptor potential of the atom or bond typ j

k - number of the atom or bond typ j

- -electronegativity of the charge center A with the charge

- residual -electronegativity of source of stabilization X_{i}

- donor and acceptor potential of the -system

The stabilization of the charges on the fragments is predicted from charge distribution of the compound in the ground state before breaking the bond. The -electronegativity serves as a measure for the delocalization potential of the atoms being part of the -system and is obtained by the PEPE-procedure (see 4.4)

The -electronegativity of the charge centre is calculated by distributing the formal charge one moiety in the -system the other in the -system. This leads to updated total charges which are used in calculating _{} by the known polynomial of degree 2:

1a. 1b.

2.

3.

The factors and give the total donor/acceptor potential of the bond and atom typs of the -system in the considered structures.

The bond and atom parameters f_{j} and g_{j} are standardized to the C-C double bond which is set arbitrary to 1.

f_{j} was derived from 219 different substituted allylic compounds by considering the proton affinities calculated by AM1:

Bond |
f |
Atom |
f | |

aro |
0.5 |
NR |
2.6 | |

C=C |
1.0 |
OR |
2.3 | |

C=O |
0.4 |
SR |
1.7 | |

C=S |
0.4 |
PR |
0.5 | |

C=N |
0.6 |
F |
0.9 | |

N=C |
1.4 |
Cl |
0.6 | |

CC |
1.0 |
Br |
0.1 | |

CN |
0.6 |
J |
-0.2 | |

NC |
1.4 |
Me-X |
0.6 | |

Me-X=X |
0.7 |

**Table 12. Atom and bond parameter for calculating D ^{+}**

For the determination of g_{j} a dataset of 37 gas phase acidities was taken:

bond |
g |

aro |
0.6 |

C=C |
1.0 |

C=O |
2.2 |

S=O |
1.2 |

N=O |
3.0 |

CN |
2.9 |

**Table 13. Atom and bond parameter for calculating D ^{-}**

In addition, two exeptional cases have to be considered:

for the stabilization of an aromatic or an antiaromatic system which was formed by a heterolytic bond cleavage the factors and must be modified by addition of a further factor f_{aro}=g_{aro}=2 in case of aromaticity or substruction in case of antiaromaticity, respectively.

If an atom changes its hybridisation state to sp the f and g parameters are fixed to f_{vic}=g_{vic}=0.5 due to the formation of an orthogonal -system.

__Values calculated:__

**D ^{+}_{AB}(PDELOC(A-B)):**

Extent of delocalization stabilization of a positive charge on A when the bond A-B is broken in a polar manner.

**D ^{-}_{AB}(NDELOC(A-B)):**

Extent of delocalization stabilization of a negative charge on A when the bond A-B is broken in a polar manner.

**D ^{-}_{AB}(NDELOC(A-B)):**

Amount of delocalization stabilization of a positive charge on A and a negative charge on B.

__Example:__

As example should serve the electrophilic aromatic substitution of mono substituted benzene derivatives. It is well known that donor groups activate the ortho and para position while the meta position is activated by acceptors.

This fact should be quantified by the delocalization variable D^{+}.

For calculating D^{+} all formal bond cleavages of aromatic -bonds have to be considered which are resulting in a positive charge in ortho or para position of the reaction centre. By summing up all D^{+} parameters for every broken bond D^{+}_{aro,position} could be obtained:

__Stabilization of the positive charge in the -complex__

__Prediction from the ground state__

**Figure 9. Determination of the delocalization variable D ^{+}_{aro} in the -complex**

Table 14 shows the calculated values for some mono substituated benzene derivatives compared to benzene.

The different donor potential of the different subtituents can be cleary seen.

compound |
|||

benzene |
38.0 |
38.0 |
38.0 |

nitrobenzene |
36.9 |
46.2 |
36.9 |

methoxybenzene |
95.3 |
38.7 |
95.3 |

chlorobenzene |
48.4 |
38.2 |
48.4 |

**Table 14. D ^{+}_{aro} of ortho, meta and para position of some selected benzene derivatives**

__Reference__

Angela Fröhlich, *Dissertation*, TU München, 1993