Molecular Geometry and Bonding Theories

VSEPR (Valence Shell Electron Pair Repulsion) theory predicts the three-dimensional shape of a molecule by assuming that electron groups around a central atom repel each other and arrange themselves as far apart as possible to minimize repulsion.

An electron group is any region of electron density bonded to the central atom: a single bond, a double bond, a triple bond, or a lone pair. All of these count equally when determining the arrangement. The number of electron groups around the central atom determines the electron-pair geometry — the spatial arrangement of all electron groups, including lone pairs.

To apply VSEPR: (1) draw the Lewis structure, (2) count electron groups on the central atom, (3) identify the electron-pair geometry, and (4) name the molecular geometry based on the positions of the atoms only (ignoring lone pairs in the name).

For a polyatomic ion, account for the overall charge before counting electron groups: add one electron per unit of negative charge or remove one per unit of positive charge to the total valence-electron pool, then build the Lewis structure on that adjusted count. The ICl₄⁻ ion, for example, ends up with 12 valence electrons around iodine (4 bonding pairs + 2 lone pairs = 6 electron groups), giving an octahedral electron-pair geometry and a square-planar molecular geometry once the two lone pairs are placed trans to each other.

The five fundamental electron-pair geometries correspond to 2 through 6 electron groups:

When all electron groups are bonding pairs, the molecular geometry matches the electron-pair geometry. When lone pairs are present, the molecular geometry is a subset: for example, four electron groups with one lone pair give a trigonal pyramidal shape (NH₃), and four groups with two lone pairs give a bent shape (H₂O).

Lone pairs occupy more space than bonding pairs because they are held closer to the nucleus and spread out more broadly. This extra repulsion compresses bond angles below their ideal values. In methane (CH₄), all four groups are bonding and angles are 109.5°. In ammonia (NH₃), one lone pair pushes the three N–H bonds closer together, reducing the angle to about 107°. In water (H₂O), two lone pairs compress the H–O–H angle further to about 104.5°.

For five electron groups, removing bonding pairs in favor of lone pairs produces progressively distorted shapes: seesaw (4 bonds, 1 lone pair), T-shaped (3 bonds, 2 lone pairs), and linear (2 bonds, 3 lone pairs). For six groups: square pyramidal (5 bonds, 1 lone pair) and square planar (4 bonds, 2 lone pairs). Lone pairs preferentially occupy equatorial positions in trigonal bipyramidal systems because equatorial sites have more room.

A molecule is polar if it has a net dipole moment — an overall uneven distribution of electron density. Two conditions must both be met:

1. The molecule must contain polar bonds (bonds between atoms with different electronegativities, producing individual bond dipoles). A bond between two identical atoms (H–H, Cl–Cl) is nonpolar by definition. A bond between two different elements that happen to share the same Pauling electronegativity value is also nonpolar — H and P, for example, are both assigned a Pauling EN of about 2.1, which is why the H–P bond in PH₃ is treated as nonpolar. One distinction worth keeping straight: the ΔEN scale used to classify bonds (nonpolar covalent below ~0.4, polar covalent up to ~1.7, ionic beyond) answers a different question than the one asked here. A pair like Cl–Br (Δχ ≈ 0.2) falls in the “nonpolar covalent” bin on that classification scale, yet the bond still carries a small, real dipole (≈0.6 D) — any nonzero electronegativity difference does. When a problem asks whether a bond is polar, it is asking about the dipole: only identical atoms or same-EN pairs give a truly nonpolar bond.
2. The molecular geometry must be asymmetric so that the individual bond dipoles do not cancel.

Symmetry is the key factor. CO₂ has two polar C=O bonds, but its linear geometry makes the dipoles point in opposite directions and cancel — the molecule is nonpolar. H₂O also has two polar bonds, but its bent shape leaves a net dipole pointing from H toward O — the molecule is polar.

Similarly, CCl₄ (tetrahedral, all identical bonds) is nonpolar because of perfect symmetry, while CHCl₃ (one H replaces a Cl) is polar because the symmetry is broken. Molecular polarity governs many physical properties including boiling point, solubility, and interactions with other molecules.

Hybridization is the mixing of standard atomic orbitals (s, p, d) on a central atom to form a new set of equivalent hybrid orbitals oriented to match the observed molecular geometry. The type of hybridization is determined by the number of electron groups:

The quick rule: count all electron groups (bonding and lone pairs) on the central atom. Two groups = sp, three = sp², four = sp³, and so on. Water has four electron groups (2 bonds + 2 lone pairs), so oxygen is sp³ hybridized even though its molecular shape is bent.

Hybrid orbitals form sigma (σ) bonds — bonds with electron density concentrated directly between the two nuclei along the internuclear axis. Every single bond is a sigma bond, and every double or triple bond contains exactly one sigma bond.

The additional bonds in a double or triple bond are pi (π) bonds, formed by the side-by-side overlap of unhybridized p orbitals. A double bond consists of one σ bond + one π bond. A triple bond consists of one σ bond + two π bonds.

In ethylene (C₂H₄), each carbon is sp² hybridized with three sigma bonds (two C–H and one C–C). The remaining unhybridized p orbital on each carbon overlaps to form the pi bond, locking the molecule into a planar geometry. Pi bonds prevent rotation around the bond axis, which is why geometric (cis/trans) isomerism occurs in molecules with C=C double bonds.

Different atoms can have different hybridizations. When a molecule contains atoms with different electron-group counts, each atom's hybridization is determined independently from its own count. Propyne (H₃C–C≡CH) has an sp³ methyl carbon (4 single bonds → 4 electron groups) and two sp alkyne carbons (each has 2 electron groups along the triple bond axis). Allene (H₂C=C=CH₂) has two sp² terminal carbons (3 electron groups each) and one sp central carbon (2 electron groups). Apply the count-and-match rule per atom, not once per molecule.

Valence-bond theory (the hybridization picture above) is excellent for explaining geometry but cannot easily account for properties like the paramagnetism of O₂ or the existence of one-electron and three-electron bonds. Molecular orbital (MO) theory takes a different starting point: instead of localizing electrons in pairs between two atoms, MO theory combines atomic orbitals from the whole molecule into molecular orbitals that span the entire structure, and then fills those MOs with electrons.

Bonding and antibonding orbitals. When two atomic orbitals on neighboring atoms overlap, they combine in two ways. Constructive overlap concentrates electron density between the two nuclei and lowers the energy of the resulting orbital below the energy of the parent atomic orbitals — this is a bonding molecular orbital. Destructive overlap puts a node between the two nuclei and raises the energy of the resulting orbital above the parents — this is an antibonding orbital, written with an asterisk (e.g., σ*_1s). The number of MOs you produce always equals the number of atomic orbitals you started with: combining two 1s orbitals gives one σ_1s bonding MO and one σ*_1s antibonding MO.

Sigma and pi MOs from p orbitals. When two atoms’ p orbitals overlap end-on along the bond axis, they form a σ bonding MO and a σ* antibonding MO. When the remaining two pairs of p orbitals overlap side-by-side, they form two degenerate π bonding MOs and two degenerate π* antibonding MOs. So combining the 2p subshells of two atoms gives 6 MOs in total: one σ_2p, two π_2p (degenerate), two π*_2p (degenerate), and one σ*_2p.

Filling rules. MOs fill from lowest to highest energy following the same three rules as atomic orbitals: Aufbau (lowest first), Pauli (max two electrons per MO with opposite spins), and Hund (one electron in each degenerate orbital before pairing). For polyatomic ions, adjust the total electron count first — add an electron for each unit of negative charge, remove one for each unit of positive charge.

Bond order. Once the MOs are filled, the strength of the resulting bond is summarized by the bond order:

bond order = ½ (number of bonding electrons − number of antibonding electrons)

A higher bond order means a shorter, stronger bond. A bond order of 1 corresponds to a single bond, 2 to a double bond, 3 to a triple bond. Fractional bond orders are also meaningful (e.g., O₂⁻ has a bond order of 1.5 — weaker than O₂’s double bond, stronger than O₂²⁻’s single bond). When a fully filled bonding subshell is matched by a fully filled antibonding subshell at lower n (for example, all four 1s electrons in a second-row diatomic), those subshells contribute zero net to the bond order and can be excluded from the calculation; counting only the valence (2s and 2p) MOs gives the same answer with less arithmetic.

The 2p ordering switch. For the heavier second-row diatomics — O₂, F₂, Ne₂ — the σ_2p bonding MO sits below the two π_2p bonding MOs, and the standard filling order is σ_2p < π_2p < π*_2p < σ*_2p. For the lighter second-row diatomics — B₂, C₂, N₂ — mixing between the 2s and 2p orbitals raises the σ_2p above the π_2p, so the order is reversed: π_2p fills before σ_2p. Whenever you build an MO diagram for a B/C/N diatomic, swap the σ_2p and π_2p rungs of the ladder.

Carbon monoxide and the heteronuclear precedent. Carbon monoxide (CO) is the one heteronuclear diatomic that appears in this topic, and it is treated as isoelectronic with N₂: both species have 10 valence electrons (5 from each atom in N₂; 4 from carbon plus 6 from oxygen in CO). Because the electron count drives the molecular-orbital pattern, CO uses the reversed B/C/N order — π_2p fills before σ_2p — not the heavier-second-row order. Apply N₂'s MO diagram directly to CO when computing bond order and magnetism. Other heteronuclear diatomics that are not isoelectronic with a B/C/N homonuclear diatomic (HF, HCl, NO) require a more general MO treatment that is outside the scope of this topic.

Magnetism: paramagnetic vs diamagnetic. A species with one or more unpaired electrons in its MO configuration is paramagnetic — it is weakly attracted to a magnetic field. A species with all electrons paired is diamagnetic and is weakly repelled. The classic case is O₂: with 16 electrons filling through (π*_2p)², Hund’s rule places one electron in each of the two degenerate π*_2p orbitals, leaving two unpaired electrons. The valence-bond Lewis structure (a simple O=O double bond with two lone pairs on each oxygen) cannot explain this paramagnetism — it predicts all electrons paired. MO theory gets the right answer because it treats the antibonding electrons explicitly. Bond order: (10 − 6)/2 = 2, matching the double bond seen in the Lewis structure, but with the paramagnetism added on top.

Reading off properties from an MO diagram. Once you have the configuration, the diagram tells you (1) the bond order, (2) whether the species is diamagnetic or paramagnetic, and (3) how the species compares to neighbors when you add or remove electrons. Removing an antibonding electron raises the bond order (cation is more strongly bound); adding an electron to an antibonding orbital lowers the bond order (anion is less strongly bound). This is why O₂⁺ has a bond order of 2.5 (stronger than O₂) while O₂²⁻ has a bond order of 1 (the peroxide single bond, weaker than O₂).

For any molecule, a systematic four-step approach connects Lewis structure to full three-dimensional properties:

1. Draw the Lewis structure to identify bonding pairs, lone pairs, and multiple bonds on the central atom.
2. Count electron groups to determine the electron-pair geometry and hybridization.
3. Identify the molecular geometry by considering only the positions of atoms (excluding lone pairs from the shape name).
4. Assess polarity by checking whether bond dipoles cancel given the molecular geometry.

For example, sulfur dioxide (SO₂): the Lewis structure shows two double bonds and one lone pair on S (3 electron groups). Electron-pair geometry: trigonal planar. Hybridization: sp². Molecular geometry: bent (2 atoms + 1 lone pair). Polarity: the S=O dipoles do not cancel in the bent arrangement, so SO₂ is polar. This integrated approach works for any molecule.

A systematic approach to molecular geometry and polarity:

1. Draw the Lewis structure first. Geometry predictions depend on knowing the number of electron groups.
2. Count electron groups (bonding pairs + lone pairs) around the central atom. Double and triple bonds each count as one group.
3. Determine electron-pair geometry from the total number of electron groups (2 = linear, 3 = trigonal planar, 4 = tetrahedral, 5 = trigonal bipyramidal, 6 = octahedral).
4. Determine molecular geometry by considering only the positions of atoms (not lone pairs).
5. Assess polarity: if all outer atoms are identical and there are no lone pairs on the central atom, the molecule is likely nonpolar. Otherwise, check whether dipole moments cancel.

Common mistakes: counting a double bond as two electron groups, confusing electron-pair geometry with molecular geometry, assuming all tetrahedral molecules are nonpolar (bent and trigonal pyramidal are subsets of tetrahedral electron-pair geometry but are polar), and misidentifying hybridization by not matching it to the electron-pair geometry.