VSEPR Geometry and Molecular Polarity

Counting electron domains around a central atom

VSEPR starts from a correct Lewis structure. Around the central atom, count the electron domains: each lone pair is one domain, and each bond to another atom is one domain whether it is single, double or triple. The total is often called the steric number. A double bond counts once because its electrons occupy the same region of space between the two atoms.

The steric number fixes the electron-domain geometry, the arrangement that keeps the domains farthest apart. Two domains are linear (180°), three are trigonal planar (120°), four are tetrahedral (109.5°), five are trigonal bipyramidal (90° and 120°), and six are octahedral (90°).

A short label keeps track of the count. In AXₘEₙ notation, A is the central atom, m is the number of bonded atoms X, and n is the number of lone pairs E on the central atom. Water is AX₂E₂: two bonded atoms and two lone pairs, steric number 4.

Electron-domain geometry versus molecular shape

Lone pairs take up space, but they are not atoms, so they are invisible in the name of the molecular shape. The molecular geometry describes only where the atoms sit. When there are no lone pairs on the central atom, the two geometries are the same; when there are lone pairs, they differ.

In a trigonal bipyramid the positions are not equivalent: the three equatorial positions are 120° apart and the two axial positions are 90° from the equator. Lone pairs go to equatorial positions first, because an equatorial site has only two neighbors at 90° while an axial site has three.

• Steric number 3: AX₃ trigonal planar; AX₂E bent, angle below 120°.
• Steric number 4: AX₄ tetrahedral; AX₃E trigonal pyramidal; AX₂E₂ bent, angles below 109.5°.
• Steric number 5: AX₅ trigonal bipyramidal; AX₄E seesaw; AX₃E₂ T-shaped; AX₂E₃ linear.
• Steric number 6: AX₆ octahedral; AX₅E square pyramidal; AX₄E₂ square planar.

Why lone pairs compress bond angles

A lone pair is held by only one nucleus, so its electron density spreads wider near the central atom than a bonding pair does. Repulsions therefore follow the order lone pair–lone pair > lone pair–bonding pair > bonding pair–bonding pair, and each added lone pair squeezes the remaining bonds closer together.

The tetrahedral family shows the trend. Methane, CH₄, with no lone pairs, has H–C–H angles of 109.5°. Ammonia, NH₃, with one lone pair, has H–N–H angles a little smaller. Water, with two lone pairs, has an H–O–H angle of 104.5°, the value given in OpenStax Chemistry 2e. Multiple bonds have a similar, smaller effect, because a double bond holds more electron density than a single bond.

VSEPR predicts the direction of these deviations reliably, but not their exact size. When a question asks for an angle in a molecule with lone pairs, answer "slightly less than" the ideal value unless you have measured data.

Worked examples: chlorine trifluoride and xenon tetrafluoride

Chlorine trifluoride, ClF₃. Valence electrons: 7 + 3(7) = 28. Three Cl–F single bonds use 6 electrons, and completing the three fluorine octets uses 3 × 6 = 18, for 24. The remaining 4 electrons go on chlorine as two lone pairs. Chlorine has three bonds and two lone pairs, so it is AX₃E₂ with a steric number of 5 and a trigonal bipyramidal electron-domain geometry.

Both lone pairs take equatorial positions. That leaves one fluorine in the equatorial plane and two in the axial positions, so the atoms form a T shape. The lone pairs push the axial fluorines toward the equatorial one, so the F–Cl–F angles are slightly less than 90°. The three Cl–F bond dipoles do not cancel in a T shape, so ClF₃ is polar.

Xenon tetrafluoride, XeF₄. Valence electrons: 8 + 4(7) = 36. Four Xe–F bonds use 8 electrons and the fluorine lone pairs use 4 × 6 = 24, for 32. The remaining 4 electrons are two lone pairs on xenon. With four bonds and two lone pairs, xenon is AX₄E₂, steric number 6, octahedral electron-domain geometry.

In an octahedron every position is equivalent, so the first lone pair can go anywhere; the second goes directly opposite it, 180° away, to minimize lone pair–lone pair repulsion. The four fluorines then lie in one plane at 90° to their neighbors: square planar. Each Xe–F bond is polar, but opposite bonds point in exactly opposite directions, so the dipoles cancel and XeF₄ is nonpolar.

Adding bond dipoles to find molecular polarity

A bond between atoms of different electronegativity is polar, with a partial negative charge (δ−) on the more electronegative atom. Each bond dipole has a size and a direction, so it behaves like a vector. The molecular dipole moment is the vector sum of all the bond dipoles, usually reported in debyes (1 D ≈ 3.336 × 10⁻³⁰ C·m).

Bond dipoles cancel when identical bonds are arranged symmetrically around the central atom. That happens for AX₂ linear, AX₃ trigonal planar, AX₄ tetrahedral, AX₅ trigonal bipyramidal and AX₆ octahedral molecules when all the X atoms are the same, and also for AX₄E₂ square planar and AX₂E₃ linear shapes, where the lone pairs are arranged symmetrically and each bond points directly opposite an identical bond. Other combinations of shape and substituents generally leave a net dipole.

Worked comparison: sulfur dioxide and sulfur trioxide. SO₂ has 6 + 2(6) = 18 valence electrons; its Lewis structure puts two bonding domains and one lone pair on sulfur (AX₂E), so the molecule is bent. The two S–O dipoles point partly in the same direction, their sum is not zero, and SO₂ is polar. SO₃ has 6 + 3(6) = 24 valence electrons and three bonding domains with no lone pair on sulfur (AX₃), so it is trigonal planar. Three equal dipoles 120° apart sum to zero, and SO₃ is nonpolar even though every bond in it is polar.

Common shape and polarity mistakes

Most errors come from skipping the Lewis structure or from reading the flat drawing on the page as if it were the real shape. A quick routine catches them: draw the Lewis structure, count domains on the central atom, name the electron-domain geometry, remove the lone pairs to name the molecular shape, then add the bond dipoles in three dimensions.

A physical model or a careful wedge-and-dash sketch helps with the last step. If you can rotate the molecule so that one bond dipole has no partner pointing the opposite way, the molecule is polar. If every bond is matched by an identical bond on the opposite side, or by a symmetric set such as three bonds at 120°, it is nonpolar.

• Naming the electron-domain geometry when the question asks for the molecular shape. Water's domains are tetrahedral; its shape is bent.
• Forgetting lone pairs on the central atom, which turns NH₃ into a trigonal planar molecule by mistake.
• Counting a double or triple bond as two or three domains.
• Concluding that a molecule is polar because its bonds are polar, without checking whether the dipoles cancel.
• Judging symmetry from a flat drawing. CH₂Cl₂ looks symmetric on paper but is tetrahedral with two different kinds of bonds, so it is polar.
• Placing lone pairs in axial positions of a trigonal bipyramid, which gives the wrong shape for SF₄, ClF₃ and XeF₂.