8.6 Appendix: Electronegativity (χ)
227
8.6.6 Electronegativity Equalization (Sanderson 1983a, b)
In the following, it is assumed that Sanderson’s electronegativiy scale is used. It is
given in Table 8.9.
The electronegativity is assumed to be a property of the atom. Actually, it depends
on the atomic structure when atoms combine. Consider a diatomic molecule AB.
When the bond is formed, the initially more electronegative atom acquires more than
half share of the bonding electrons, i.e., it gains a partial negative charge, whereas
the other atom gets a partial positive charge. The effect of the partial negative charge
is to diminish the effective nuclear charge, to increase the atomic radius, and to
diminish the electronegativity. For the atom with a partial positive charge, the contrary
happens. The consequence of these electron transfers is that the electronegativities
are equalized throughout the molecule, and the electronegativity of the bonded atoms,
χ M is the geometric mean of electronegativities χ I of all component atoms
χ M =
n
i=1
χ i
1 / n
(8.25)
where n is the number of atoms of the molecule.
8.6.7 Partial Atomic Charge
A partial charge is a non-integer charge value on an atom (in elementary charge unit)
due to the asymmetric distribution of electrons in chemical bonds. They are used in
molecular mechanics to compute the electrostatic interaction energy (see (2.47) in
Sect. 2.16.2). They are also useful for a qualitative understanding of the structure: It is
the goal of this chapter. Finally, because chemical reactions often occur by attack on
some reagent on the more positive or more negative site in a molecule, it is interesting
to have reliable predictions of atom charges. The difficulty is that assigning charges
to individual atoms is arbitrary and various methods have been proposed. Among the
orbital-based charges, there is the AIM method (see Sect. 2.18) and the natural bond
orbital (NBO) charges (Reed et al. 1985). A more recent method, charge model 5
(CM5), is described by Marenich et al. (2012).
The electronegativity equalization, (7.5), permits to estimate the partial charge δ i
on atom i
δ i =
χ M − χ i
χ i
(8.26)
χ i is the charge that the atom i would have undergone if it had acquired a unit
charge. It may be estimated with the following equation
227
8.6.6 Electronegativity Equalization (Sanderson 1983a, b)
In the following, it is assumed that Sanderson’s electronegativiy scale is used. It is
given in Table 8.9.
The electronegativity is assumed to be a property of the atom. Actually, it depends
on the atomic structure when atoms combine. Consider a diatomic molecule AB.
When the bond is formed, the initially more electronegative atom acquires more than
half share of the bonding electrons, i.e., it gains a partial negative charge, whereas
the other atom gets a partial positive charge. The effect of the partial negative charge
is to diminish the effective nuclear charge, to increase the atomic radius, and to
diminish the electronegativity. For the atom with a partial positive charge, the contrary
happens. The consequence of these electron transfers is that the electronegativities
are equalized throughout the molecule, and the electronegativity of the bonded atoms,
χ M is the geometric mean of electronegativities χ I of all component atoms
χ M =
n
i=1
χ i
1 / n
(8.25)
where n is the number of atoms of the molecule.
8.6.7 Partial Atomic Charge
A partial charge is a non-integer charge value on an atom (in elementary charge unit)
due to the asymmetric distribution of electrons in chemical bonds. They are used in
molecular mechanics to compute the electrostatic interaction energy (see (2.47) in
Sect. 2.16.2). They are also useful for a qualitative understanding of the structure: It is
the goal of this chapter. Finally, because chemical reactions often occur by attack on
some reagent on the more positive or more negative site in a molecule, it is interesting
to have reliable predictions of atom charges. The difficulty is that assigning charges
to individual atoms is arbitrary and various methods have been proposed. Among the
orbital-based charges, there is the AIM method (see Sect. 2.18) and the natural bond
orbital (NBO) charges (Reed et al. 1985). A more recent method, charge model 5
(CM5), is described by Marenich et al. (2012).
The electronegativity equalization, (7.5), permits to estimate the partial charge δ i
on atom i
δ i =
χ M − χ i
χ i
(8.26)
χ i is the charge that the atom i would have undergone if it had acquired a unit
charge. It may be estimated with the following equation