Structure and bonding: hybridization, resonance and formal charge

To predict how an organic molecule behaves, you need to know where its electrons are. Are they shared evenly or pulled toward one atom? Are they held between two atoms or spread over several? Is an atom electron-poor and hungry for a pair, or does it carry a lone pair to offer? CHEM-101 introduced Lewis structures, formal charge, VSEPR and hybridization for small molecules. This lesson applies those tools to organic structures and adds the idea that matters most for reactivity: resonance, the delocalization of electrons over several atoms. By the end you should be able to look at a structure and say, for each atom, what its hybridization and geometry are, whether it carries a charge, and where electron density is high or low.

Lewis structures and formal charge

A Lewis structure shows every valence electron as a bond or a lone pair. For organic molecules the rules are simple: hydrogen gets two electrons, and carbon, nitrogen, oxygen and the halogens get an octet. The formal charge on an atom compares the electrons it owns in the structure with the valence electrons of the free atom:

where V is the number of valence electrons of the free atom, N the number of nonbonding electrons on the atom, and B the number of bonding electrons around it. In practice it is faster to compare the number of bonds with the usual valence. A carbon with four bonds is neutral; a carbon with three bonds and no lone pair is a carbocation, with a formal charge of +1; a carbon with three bonds and a lone pair is a carbanion, −1. A nitrogen with four bonds is +1; an oxygen with three bonds and one lone pair, as in the hydronium ion or a protonated alcohol, is +1; an oxygen with one bond and three lone pairs, as in an alkoxide, is −1.

Formal charges are bookkeeping, not real charges. In the ammonium ion the positive charge is spread over the whole ion, and the nitrogen, being more electronegative than hydrogen, actually carries a slight negative partial charge. But formal charges are invaluable for checking structures and, as we shall see, for choosing among resonance forms and for following electrons in mechanisms.

Hybridization and geometry

The shape of a molecule follows from the number of electron domains around each atom, the steric number, which counts bonded atoms plus lone pairs (a double or triple bond counts once). Four domains give a tetrahedral arrangement with angles near 109.5°, three give trigonal planar at 120°, and two give linear at 180°. Valence bond theory describes these arrangements with hybrid orbitals: sp³ for four domains, sp² for three and sp for two. An sp² carbon keeps one unhybridized p orbital perpendicular to its plane, and an sp carbon keeps two, at right angles to each other. Overlap of these p orbitals sideways forms π bonds.

Hybridization also explains trends in bond length, bond strength and acidity. The more s character an orbital has, the closer its electrons are held to the nucleus. An sp orbital is 50 per hundred s, sp² is 33 and sp³ is 25. Bonds made with sp orbitals are shorter and stronger, and a lone pair in an sp orbital is held more tightly, which is why ethyne (pKa about 25) is far more acidic than ethene (about 44) and ethane (about 50).

A π bond is weaker than a σ bond. The C=C bond energy of about 728 kJ/mol is less than twice the C–C single bond, and the energy needed to break only the π bond, measured from the barrier to rotation about the double bond, is about 270 kJ/mol. The π electrons sit above and below the bond axis, farther from the nuclei and more exposed. That is why alkenes react with electrophiles while alkanes do not, a theme of lessons 11 and 12. The π bond also prevents rotation: twisting one end of a double bond by 90° would destroy the p–p overlap, so alkenes can exist as cis and trans isomers, while the ends of a single bond rotate freely.

Polar bonds and electronegativity

Bonds between atoms of different electronegativity are polar. On the Pauling scale carbon is 2.55, hydrogen 2.20, nitrogen 3.04, oxygen 3.44, fluorine 3.98, chlorine 3.16 and bromine 2.96. A C–O or C–Cl bond is polarized with a partial positive charge δ+ on carbon and a partial negative charge δ− on the heteroatom. A carbon bonded to a metal, as in a Grignard reagent, is polarized the other way and carries δ−. These partial charges tell you where reactions happen: nucleophiles attack the δ+ carbon of a C–X bond, and electrophiles attack the δ− carbon of a C–Mg bond. The inductive effect is the pull of electron density through σ bonds by an electronegative atom; it falls off rapidly, by roughly half per bond, and is the main reason chloroacetic acid is a stronger acid than acetic acid (lesson 4).

Resonance

Some molecules cannot be described by a single Lewis structure. The acetate ion, CH₃CO₂⁻, can be drawn with the negative charge on either oxygen, one C=O and one C–O⁻. Neither drawing is correct on its own. Experiment shows that the two C–O bonds are identical, 127 pm long, between a typical C=O (123 pm) and C–O (136 pm), and that the two oxygens carry equal charge. The real ion is a resonance hybrid, a single structure that is a weighted average of the contributing structures, called resonance forms or resonance contributors. The double-headed arrow ↔ between resonance forms does not mean that the molecule flips between them; it means that the true structure lies between them.

Resonance forms differ only in the placement of π electrons and lone pairs; the atoms stay where they are. You move electrons between resonance forms with curved arrows, from a lone pair or a π bond to an adjacent position. A useful set of patterns covers most cases: a lone pair next to a π bond (as in acetate or an enolate), a positive charge next to a π bond (the allyl cation), a negative charge next to a π bond (the allyl anion), a π bond between atoms of different electronegativity (the C=O group, which has a minor resonance form C⁺–O⁻), and alternating π bonds around a ring (benzene).

Not all resonance forms contribute equally. The more stable a form would be on its own, the more it contributes to the hybrid. The rules, in rough order of importance, are:

1. Forms in which every second-row atom has an octet are much more important than forms with an electron-deficient atom.

2. Forms with fewer formal charges are better than forms with more charges, and forms with charge separation are minor.

3. A negative charge is better on the more electronegative atom, and a positive charge on the less electronegative one.

4. Equivalent forms contribute equally, and a molecule with several equivalent forms is especially stabilized.

The extra stability that delocalization brings is the resonance energy. It is large for benzene, about 150 kJ/mol, and for carboxylate ions, and it explains a great deal of organic chemistry: why carboxylic acids are acidic (lesson 4), why allylic and benzylic carbocations form easily (lesson 9), why amides are planar and unreactive, and why conjugated dienes absorb light at longer wavelengths than isolated alkenes.

Molecular orbital view of delocalization

Molecular orbital theory, introduced in CHEM-101 and developed in CHEM-241, describes resonance more naturally. In the allyl system, three adjacent p orbitals combine to make three π molecular orbitals: a bonding orbital spread over all three carbons, a nonbonding orbital with a node at the central carbon and large lobes on the two ends, and an antibonding orbital. In the allyl cation the two π electrons fill only the bonding orbital, and the empty nonbonding orbital is where the positive charge resides: on the end carbons, exactly as the resonance forms predict. The two pictures agree; resonance is the language organic chemists use day to day because it can be drawn quickly with Lewis structures.

Reading skeletal structures for electron density

With these tools you can mark any structure for reactivity. Look for lone pairs (potential nucleophiles or bases), polar bonds with a δ+ carbon (potential electrophiles), π bonds (electron-rich, attacked by electrophiles), formal charges, and delocalization that spreads charge. The C=O group of a ketone, for example, has a δ+ carbon both because oxygen is electronegative and because of the minor resonance form C⁺–O⁻; it is attacked at carbon by nucleophiles. The oxygen has two lone pairs and is weakly basic. This kind of reading becomes automatic with practice and is the basis of all the mechanisms in the second half of the course.

# Formal charge and hybridization from a simple description of each atom.
VALENCE = {'H': 1, 'C': 4, 'N': 5, 'O': 6, 'F': 7, 'Cl': 7, 'Br': 7, 'S': 6}

def formal_charge(element, bonds, lone_pairs):
    """bonds = number of bonds (a double bond counts 2); lone_pairs = pairs."""
    return VALENCE[element] - 2 * lone_pairs - bonds

def hybridization(nbrs, lone_pairs):
    domains = nbrs + lone_pairs
    return {4: 'sp3, tetrahedral', 3: 'sp2, trigonal planar', 2: 'sp, linear'}.get(domains, '?')

atoms = [
    ('C of methane',         'C', 4, 0, 4),
    ('C of a carbocation',   'C', 3, 0, 3),
    ('C of a carbanion',     'C', 3, 1, 3),
    ('N of ammonium',        'N', 4, 0, 4),
    ('O of hydronium',       'O', 3, 1, 3),
    ('O of methoxide',       'O', 1, 3, 1),
    ('C of C=O in acetone',  'C', 4, 0, 3),
    ('O of C=O in acetone',  'O', 2, 2, 1),
    ('N of acetonitrile',    'N', 3, 1, 1),
]
for name, el, bonds, lp, nbrs in atoms:
    fc = formal_charge(el, bonds, lp)
    print(f'{name:22s} FC = {fc:+d}   {hybridization(nbrs, lp)}')

C of methane           FC = +0   sp3, tetrahedral
C of a carbocation     FC = +1   sp2, trigonal planar
C of a carbanion       FC = -1   sp3, tetrahedral
N of ammonium          FC = +1   sp3, tetrahedral
O of hydronium         FC = +1   sp3, tetrahedral
O of methoxide         FC = -1   sp3, tetrahedral
C of C=O in acetone    FC = +0   sp2, trigonal planar
O of C=O in acetone    FC = +0   sp2, trigonal planar
N of acetonitrile      FC = +0   sp, linear

The program uses the shortcut that the steric number is neighbours plus lone pairs. Note the nitrogen of acetonitrile, CH₃C≡N: one neighbour and one lone pair make two domains, so it is sp hybridized and linear, like the carbon it is bonded to. One caution applies to the shortcut: a nitrogen or oxygen whose lone pair is delocalized into a π system, as in an amide, behaves as sp² and planar even though the count suggests sp³, because the lone pair occupies a p orbital to overlap with the π bond.