Electronic Structure, Bonding and Resonance in Organic Compounds

Organic chemistry is, at bottom, the chemistry of one element — carbon — and the small set of heteroatoms (nitrogen, oxygen, sulfur, halogens) that decorate it. Everything that follows in this block, from why a leaving group leaves to why one ring carbon of benzene is attacked in preference to another, is a direct consequence of where the electrons sit and how freely they can move. This opening chapter builds the electronic vocabulary — hybridization, $\sigma$ and $\pi$ bonds, formal charge, electronegativity, and above all resonance — on which every mechanism in this course will be drawn.

The single most important skill introduced here is the curly arrow: a notation for electron movement, not atom movement. An organic mechanism is nothing more than a sequence of curly arrows, each one starting at a source of electron density (a lone pair, a $\sigma$ bond, a $\pi$ bond) and ending at a sink (an atom that can accept electron density, or a bond that forms). Mastering what counts as a legitimate arrow — and what does not — is the prerequisite for every reaction mechanism in this course.

1. Atomic Orbitals and Hybridization at Carbon

A ground-state carbon atom has the electron configuration $1s^2\,2s^2\,2p_x^1\,2p_y^1$, with two unpaired electrons — yet carbon is almost never divalent in a stable organic compound. The resolution is orbital hybridization: the one $2s$ and three $2p$ orbitals mix mathematically to produce new, degenerate hybrid orbitals, each with a fixed proportion of $s$ and $p$ character, oriented to minimize electron-pair repulsion (consistent with VSEPR).

• $sp^3$ hybridization mixes all four valence orbitals ($2s + 3p$, i.e. 25% $s$ and 75% $p$ character) into four equivalent $sp^3$ orbitals, pointing to the corners of a tetrahedron ($109.5^\circ$ apart). This is the hybridization of a saturated carbon — methane, ethane, every carbon bonded to four single bonds.
• $sp^2$ hybridization mixes the $2s$ orbital with only two of the three $2p$ orbitals, giving three coplanar $sp^2$ orbitals at $120^\circ$, with one unhybridized $p$ orbital left perpendicular to that plane. This is the hybridization of every doubly-bonded carbon — alkenes, carbonyl carbons, aromatic ring carbons.
• $sp$ hybridization mixes the $2s$ orbital with one $2p$ orbital, giving two collinear $sp$ orbitals ($180^\circ$ apart) and two unhybridized $p$ orbitals, mutually perpendicular and both perpendicular to the $sp$ axis. This is the hybridization of a triply-bonded or cumulated-double-bonded carbon — alkynes, nitriles, the central carbon of an allene.

Key distinction. The number of $\sigma$ bonds plus lone pairs on an atom fixes its hybridization — not the number of atoms drawn around it in a skeletal formula. A carbon with two single bonds and one double bond ($3$ attachments, trigonal) is $sp^2$; a carbon with one single bond and one triple bond, or two double bonds, ($2$ attachments, linear) is $sp$.

The same logic extends to nitrogen and oxygen: an amine nitrogen with three $\sigma$ bonds and one lone pair is $sp^3$ (pyramidal, lone pair in the fourth $sp^3$ orbital); a carbonyl oxygen is $sp^2$ (its $\sigma$ bond to carbon and its two lone pairs occupy the three in-plane $sp^2$ orbitals, while the unhybridized $p$ orbital forms the $\text{C=O}$ $\pi$ bond).

2. $\sigma$ Bonds and $\pi$ Bonds

A covalent bond forms when two atomic orbitals overlap and the resulting molecular orbital is populated by two electrons of opposite spin. Organic structures are built almost entirely from two bond types, distinguished by the symmetry of that overlap:

• A $\sigma$ bond forms by head-on, end-to-end overlap of two orbitals (two $sp^3$ orbitals, an $sp^2$ and a hydrogen $1s$, etc.) along the internuclear axis. The resulting electron density is cylindrically symmetric about that axis, which permits essentially free rotation about a single $\sigma$ bond (subject only to small steric/electronic preferences, as Chapter 3 develops for conformational analysis).
• A $\pi$ bond forms by side-on overlap of two parallel, unhybridized $p$ orbitals, above and below the plane containing the attached $\sigma$ framework. The electron density lies in two lobes, not along the internuclear axis, and rotation about a $\pi$ bond is not free: twisting the $p$ orbitals out of alignment breaks the overlap and costs the full $\pi$-bond energy. This is why alkene cis/trans (or $E/Z$) geometry is configurationally locked at room temperature.

A carbon–carbon double bond is therefore one $\sigma$ bond (from head-on $sp^2$–$sp^2$ overlap) plus one $\pi$ bond (from side-on $p$–$p$ overlap); a triple bond is one $\sigma$ bond plus two mutually perpendicular $\pi$ bonds, built from the two unhybridized $p$ orbitals of each $sp$ carbon.

Key distinction. $\sigma$ bonds are stronger than $\pi$ bonds (better orbital overlap along the axis) — which is why, when a $\pi$ bond reacts (as in electrophilic addition, Chapter 6), the $\sigma$ framework survives untouched and only the weaker, more exposed $\pi$ electrons are attacked.

3. Lewis Structures and Formal Charge

A correct Lewis structure is the non-negotiable starting point of every mechanism: get the lone pairs and formal charges wrong, and every curly arrow drawn afterwards is wrong too. Formal charge on an atom is calculated by comparing its valence electron count to the number it "owns" in the structure:

Worked example. Consider the nitrogen of the ammonium ion, $\text{NH}_4^+$. Nitrogen contributes $5$ valence electrons in its free-atom group. In $\text{NH}_4^+$ it has zero lone-pair (non-bonding) electrons and four $\sigma$ bonds, i.e. $8$ bonding electrons:

consistent with the overall $+1$ charge of the ion, which must reside on nitrogen since every hydrogen (one bond, no lone pairs: $1 - 0 - \tfrac{1}{2}(2) = 0$) is neutral.

Worked example. The oxygen of the hydroxide ion, $\text{OH}^-$, has $6$ valence electrons, three lone pairs ($6$ non-bonding electrons) and one $\sigma$ bond ($2$ bonding electrons):

again consistent with the ion's overall charge.

4. Electronegativity and Bond Polarity

Electronegativity is the tendency of an atom to draw shared electron density toward itself. Across a bond between two different elements, the pair is not shared equally: the bond is polarized toward the more electronegative atom, which carries a partial negative charge ($\delta^-$) while its partner carries a partial positive charge ($\delta^+$). For the elements that matter most in organic chemistry, electronegativity increases in the order

(Pauling scale). A $\text{C-O}$ bond is therefore polarized $\overset{\delta^+}{\text{C}}-\overset{\delta^-}{\text{O}}$, a $\text{C-Cl}$ bond $\overset{\delta^+}{\text{C}}-\overset{\delta^-}{\text{Cl}}$, and a $\text{C-H}$ bond only very weakly polarized (and, by convention, essentially non-polar). This single idea — that a carbon attached to an electronegative atom carries a partial positive charge — is the reason that carbon becomes an electrophile (an electron-pair acceptor) in nucleophilic substitution (Chapter 4) and nucleophilic addition to carbonyls (Chapter 9): the incoming nucleophile (an electron-pair donor) is attracted to exactly that $\delta^+$ carbon.

Key distinction. Electronegativity differences create polarity within a single bond; an atom's willingness to donate a whole lone pair, or to stabilize a negative charge once formed, is a related but separate question of basicity and acidity, developed fully in Chapter 2.

5. Curly Arrows: the Grammar of Mechanism

A curly arrow always represents the movement of one electron pair (a full-headed arrow) or, less commonly in this course, a single electron (a fish-hook, half-headed arrow, reserved for radical mechanisms in Chapter 13). Three rules govern every legitimate arrow:

1. The arrow starts at the electron source: a lone pair, a $\sigma$ bond, or a $\pi$ bond — never at a positive charge, and never at a hydrogen atom with no lone pair to offer.
2. The arrow ends at the electron sink: an atom that gains a lone pair or negative charge, or the midpoint of a bond being formed.
3. Charges and bonds must balance. Every arrow tail removes electron density from where it starts (a lone pair becomes a bond; a bond becomes a lone pair or breaks entirely) and every arrowhead adds it to where it lands; the formal charges of the whole structure before and after must be consistent with these individual electron movements.

Worked example — a two-step curly-arrow sequence. Hydroxide attacks the carbonyl carbon of acetaldehyde, $\text{CH}_3\text{CHO}$. Step 1: a lone pair on the oxygen of $\text{OH}^-$ (the nucleophile, electron-rich) is drawn as an arrow starting on that lone pair and ending at the carbonyl carbon (the electrophile, $\delta^+$ because it is double-bonded to the more electronegative oxygen). Simultaneously, a second arrow starts on the $\text{C=O}$ $\pi$ bond and ends on the oxygen atom, because that carbon cannot accept a fifth bond — the $\pi$ electrons must be pushed onto oxygen as a new lone pair, converting the neutral carbonyl oxygen into an alkoxide oxygen bearing a formal $-1$ charge. The product is the tetrahedral alkoxide $\text{CH}_3\text{CH}(\text{O}^-)(\text{OH})$. This exact two-arrow pattern — nucleophile's lone pair in, $\pi$ bond's electrons out onto the more electronegative atom — recurs throughout Chapter 9.

6. Resonance: Delocalized Electron Distributions

Many real molecules and ions cannot be represented by a single Lewis structure without implying a false asymmetry. Resonance structures are alternative, equally valid Lewis structures that differ only in the placement of electrons (never of atoms); the real molecule is a single entity, the resonance hybrid, whose true electron distribution is a weighted blend of all contributing structures, connected to one another by curly arrows that move only $\pi$ electrons or lone pairs — never $\sigma$ bonds, which fix the atomic skeleton.

Rules for drawing valid resonance structures:

• Only electrons move (lone pairs and $\pi$ electrons); atomic positions and $\sigma$-bond connectivity never change between resonance structures.
• Every structure must be a legitimate Lewis structure in its own right: correct electron count, no atom (besides H) with more than an octet for second-row elements.
• The net formal charge of the whole species is identical in every resonance structure.
• Curly arrows connecting one resonance structure to the next follow the same source/sink rules as mechanistic arrows (Section 5).

Worked example — the carboxylate ion. Deprotonated acetic acid, $\text{CH}_3\text{COO}^-$, is drawn with one $\text{C=O}$ and one $\text{C-O}^-$. A curly arrow starts on the lone pair of the negatively charged oxygen and moves in to form a new $\text{C=O}$ $\pi$ bond; a second arrow starts on the original $\text{C=O}$ $\pi$ bond and moves out onto the carbonyl oxygen, converting it into the new $\text{O}^-$. The net effect is the mirror-image structure, with the double bond and the negative charge now sitting on the other oxygen. Because these two structures are related by a symmetry operation and have identical energy, they contribute equally to the hybrid: the true carboxylate ion has two equivalent $\text{C-O}$ bonds, each of intermediate length between a single and a double bond, and the negative charge is shared equally, $-\tfrac{1}{2}$ on each oxygen. This delocalization is also why carboxylic acids are dramatically more acidic than alcohols (Chapter 2): the negative charge of the conjugate base is spread over two electronegative oxygens instead of being localized on one.

Worked example — the allyl cation. Ionization of an allylic substrate (for example, loss of water from a protonated allylic alcohol) gives the allyl cation $\text{CH}_2=\text{CH-CH}_2^+$. A curly arrow from the $\text{C=C}$ $\pi$ bond onto the adjacent empty $p$ orbital of the cationic carbon moves the double bond over by one position and relocates the positive charge to the far end: $^+\text{CH}_2-\text{CH=CH}_2$. Both resonance structures place positive charge on a terminal $sp^2$ carbon with an empty $p$ orbital aligned for overlap with the $\pi$ system, and (being related by the molecule's symmetry) contribute equally; the true allyl cation has its positive charge shared equally between $\text{C1}$ and $\text{C3}$, with partial $\pi$ bonding across all three carbons. This is why allylic and benzylic cations are markedly more stable than ordinary, non-delocalized carbocations of the same substitution class — a fact exploited repeatedly in $S_N1$ and $E1$ mechanisms (Chapters 4–5).

6.1 Ranking resonance structures by relative importance

Not all contributing structures are equally important to the hybrid. In rough order of priority:

1. Structures with more covalent bonds (and fewer formal charges) contribute more.
2. Among charged structures, those placing negative charge on the more electronegative atom (and positive charge on the less electronegative atom) contribute more.
3. Structures with separated charges of opposite sign on adjacent atoms contribute very little and can usually be discounted unless no better alternative exists.
4. Structures that preserve a full octet on every second-row atom are strongly preferred over those that do not.

7. Common Exam Pitfalls

• Drawing a curly arrow starting from a positive charge or a hydrogen atom. An arrow tail must sit on an actual pair of electrons (a lone pair, $\sigma$ bond or $\pi$ bond); a cation has no electrons to donate from the charge itself, and a bare $\text{H}^+$ offers nothing either — it is always the recipient of an arrowhead.
• Treating resonance structures as if they were in rapid equilibrium, with the molecule "flickering" between them. They are not separate species at all — the hybrid is a single, static (though delocalized) electron distribution; only the drawing changes, never the molecule.
• Moving atoms instead of electrons when drawing resonance. If a hydrogen or any other atom changes position between two structures, they are not resonance structures of the same species — they are different compounds, or a genuine reaction has occurred (e.g. a proton transfer), and a reaction arrow ($\rightarrow$) is needed, not a resonance double-headed arrow ($\leftrightarrow$).
• Forgetting that formal charge must be conserved overall across a set of resonance structures, even as its location moves from atom to atom.
• Confusing hybridization with bond order. A carbon can be $sp^2$ while bearing only single bonds in a localized drawing (e.g. a carbanion stabilized by an adjacent carbonyl) if it needs an empty or filled $p$ orbital aligned with a neighbouring $\pi$ system — hybridization is dictated by geometry and orbital availability, not merely by the bond orders written on the page.
• Assuming longer or more resonance structures always mean more stability. A minor contributor with separated, poorly placed charges (Section 6.1, rule 3) barely stabilizes the hybrid at all; what matters is the quality, not just the quantity, of the contributing structures.

Summary

• Carbon's valence orbitals hybridize to $sp^3$ (tetrahedral, four $\sigma$ bonds), $sp^2$ (trigonal planar, one $\pi$ bond) or $sp$ (linear, two $\pi$ bonds), fixed by the number of attached groups plus lone pairs.
• A $\sigma$ bond (end-on overlap, free rotation) is stronger than a $\pi$ bond (side-on overlap, no free rotation); double and triple bonds are one $\sigma$ bond plus one or two $\pi$ bonds respectively.
• Formal charge, $\text{FC} = V - N - \tfrac{1}{2}B$, must be assigned correctly before any mechanism can be drawn.
• Electronegativity polarizes bonds ($\overset{\delta^+}{\text{C}}-\overset{\delta^-}{\text{X}}$ for $\text{X}$ more electronegative than C), creating the electrophilic carbons attacked by nucleophiles throughout this course.
• A curly arrow moves one electron pair from a legitimate source (lone pair, $\sigma$ bond, $\pi$ bond) to a legitimate sink; getting the tail and head right is the foundation of every mechanism in this block.
• Resonance structures are alternative electron-placements of one real, delocalized hybrid — connected by curly arrows that move only $\pi$ electrons and lone pairs, never atoms — and are ranked by bond count, charge placement on appropriate electronegativity, and avoidance of adjacent like or unlike separated charges.
• Delocalization (allylic, benzylic, carboxylate-type) measurably stabilizes a structure and underlies the acidity trends of Chapter 2 and the carbocation stability trends of Chapters 4–5.