There are two distinct ways to account for valence electrons in molecular structures: oxidation numbers and formal charges. Both methods compare the number of valence electrons (VE) an atom has in its atomic form (i.e. in the periodic table) with the number of valence electrons that are assigned to that atom in the compound according to a specified accounting formula.
FC = VE – LE
Formal charge (FC) is defined as the difference between the number of valence electrons (VE) and the number of Lewis electrons, where the Lewis electron (LE) count includes all unshared electrons on the atom plus the half of all the electrons shared by the atom in the Lewis structure. This accounting scheme assumes that all shared electrons are shared equally, i.e. it explicitly neglects the differences in electronegativity.
If the species is described by resonance structures, the formal charge on a given atom may change from one resonance contributor to another. If all resonance structures are equivalent, the formal charge on a given atom is an average taken over all structures.
ON = VE – CE
Oxidation number (ON) is defined as the difference between the number of valence electrons (VE) and the number of electrons the atom has in the compound (CE). The number of electrons the atom has assigned in the compound (CE) includes all unshared electrons plus half of the electrons shared with atoms of equal electronegativity plus all electrons shared with atoms of lesser electronegativity. This accounting scheme explicitly includes electronegativity differences and assumes that all bonds between atoms of different electronegativity are fully ionic in nature.
An alternative but equivalent way to assign oxidation numbers involves the following rules:
All these rules are the consequences of ON accounting according to the formula above. Thus, F the most electronegative atom must always be assigned all electrons around it and be –1. In oxyanions (such as perchlorate, ClO4–) oxygen is more electronegative than the remaining halogens, resulting in a positive ON for the halogen (+7 in perchlorate, where Cl is formally "stripped" of all its valence electrons by the more electronegative oxygens). Since in the elemental form the atoms are bonded to atoms of the same electronegativity it is not surprising that oxidation numbers are zero. Similarly, in peroxides that have oxygen-oxygen bonds, the oxidation number is –1, rather then typical –2 as now the electrons between the oxygens must be shared for accounting purposes. Hydrogen has lower electronegativity than most non-metals (it has +1 oxidation number in such compounds), but it has higher electronegativity than most metals (it has –1 oxidation number in metallic hydrides).
Electronegativity is defined as the ability of an atom in the molecule to attract electron density to itself. It is expressed on the relative (unitless) scale with F being the most electronegative (4.0) and cesium the least electronegative (0.7). In general, the electronegativity increases from left to right in a period, and from the bottom to the top in the group in the periodic table (there are minor deviations from these trend for transition metals).
For quantitative comparison of electronegativities an appropriate table needs to be consulted. For qualitative comparisons the trends listed above may be used. For the most common non-metals the order of decreasing electronegativity may be conveniently memorized with the help of the following mnemonic, where the atoms symbols are in red for emphasis:
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Dipole moments and real charges
Let's consider a molecule of H–Cl as an example. According to the two electron-accounting schemes, the formal charges on both atoms are zero (equal sharing of bonding electrons), and the oxidation numbers on hydrogen and chlorine are +1 and –1, respectively (a completely ionic bond). Since we have a difference in electronegativity of the elements involved in the bond (3.0 – 2.1 = 0.9) we would expect some electron density shift. We would anticipate chlorine to have some excess of electron density (δ–) and hydrogen to have some deficiency of the electron density (δ+), developing the polarization of the bonding electrons, and indeed of the whole molecule.
Such charge polarization (or in general, molecular polarity) can be quantified by a dipole moment. If two charges of equal magnitude (Q) but opposite sign are separated by distance r, the resulting dipole moment (μ) can be visualized as a vector with the positive end on hydrogen and the negative end on chlorine.
μ = Q r
Dipole moments can be measured experimentally, and are usually expressed in debyes (D). If two charges (–1 and + 1, in units of electron charge) are separated by a distance of 1 Å the resulting dipole moment is 4.79 D. The measured dipole moment for HCl is 1.08 D, and the length of the H–Cl bond (the charge separation distance) is 1.27 Å. If the HCl molecule was purely ionic as indicated by the oxidation-number accounting scheme, the predicted dipole moment would be 6.08 D (1.27 x 4.79). Since the actual dipole moment of HCl is only 1.08 D, we can calculate that only 0.18 (1.08/6.08) of the full electron charge is separated in this molecule, i.e. δ in the picture above is 0.18, or H–Cl bond is 18% ionic (we normally call such bonds polar covalent bonds).
As can be seen from this example, both the formal charges and the oxidation numbers are just "artificial" accounting schemes, none of which reflects the real electron distribution in the molecule accurately. These accounting schemes are very useful in analyzing alternative Lewis structures or redox reactions, but are not adequate in exploring charge separation (polarity) of molecules.
Chemists have developed other ways to present the polarization of electrons in molecules. One that is commonly used paints the artificial surface ("skin") of the volume that contains 95% of electron density of the molecule according to the electrostatic attraction that would be encountered by a probing positive point charge "rolled" on that imaginary surface. Red and orange colors reflect excess of electron density, while blue and green represents area of diminished electron density. These electrostatic potential maps (right in the picture above) are a much fairer representations of true charge distributions than the arbitrary accounting schemes of formal charges (center) or oxidation numbers (left).