Molecular Geometry and Polarity

VSEPR molecular shapes

VSEPR (Valence Shell Electron Pair Repulsion) theory predicts the shape of a molecule from the arrangement of electron domains around the central atom. An electron domain is either a lone pair or a bonding region, and a multiple bond counts as one domain. The domains arrange themselves to be as far apart as possible. The repulsions rank as lone pair–lone pair > lone pair–bonding pair > bonding pair–bonding pair, so lone pairs push bonds closer together. The molecular shape is named by the positions of the atoms only, not the lone pairs.

The number of lone pairs on the central atom of a neutral molecule can be counted with (V - b)/2, where V is the number of valence electrons of the central atom and b is the number of bonds it forms. For SnCl_2, (4-2)/2 = 1, and for NH_3, (5-3)/2 = 1. BeCl_2, BF_3, PF_5 and SF_6 have no lone pair on the central atom, whereas SnCl_2, NH_3 and SF_4 each have one.

The usual shapes are as follows.

• 2 domains: linear, as in BeCl_2.
• 3 domains: trigonal planar with no lone pair (BF_3), or bent with one lone pair (SnCl_2).
• 4 domains: tetrahedral with no lone pair; trigonal pyramidal with one lone pair (NH_3); bent with two lone pairs.
• 5 domains: trigonal bipyramidal. Lone pairs occupy equatorial positions first, giving a seesaw with one lone pair (SF_4), a T-shape with two (ClF_3), and a linear shape with three (XeF_2).
• 6 domains: octahedral with no lone pair (SF_6), square pyramidal with one lone pair (BrF_5), and square planar with two (XeF_4).

Shape also governs symmetry, and symmetry decides chirality. A molecule with a mirror plane is achiral even if it contains stereocentres, as a meso compound does, while a molecule without any mirror plane may be chiral.

Example: for XeF_2, Xe supplies 8 valence electrons and forms 2 bonds, so (8-2)/2 = 3 lone pairs. These occupy the three equatorial positions of the trigonal bipyramid, leaving the two fluorines axial and the molecule linear.

Bond angle trends in molecular geometry

The bond angle is the angle between two bonds that share a central atom. The ideal angle follows from the electron-domain geometry, for example 109.5^\circ for tetrahedral domains. Real angles deviate from this value because lone pairs occupy more space than bonding pairs, and because the nature of the bonds changes the effective repulsion. A pyramidal molecule therefore has bond angles below the ideal tetrahedral value.

Two trends are useful in comparisons. First, going down a group, the bond angle of a hydride usually decreases. The central atom becomes larger, and its bonds use orbitals with less s-character and more nearly pure p-character. In group 15 hydrides the angle falls from about 107.8^\circ in NH_3 to about 93.5^\circ in PH_3, and PH_3 has the smallest angle of PH_3, PF_3, NF_3 and NH_3.

Second, the effect of substituent electronegativity is not the same in every series, so comparisons must be made within one family. In the nitrogen series, NF_3 (102.4^\circ) has a smaller angle than NH_3. In the phosphorus series, PF_3 (97.8^\circ) has a larger angle than PH_3.

• pyramidal — shape with three bonded atoms and one lone pair on the central atom. 예) NH_3 is pyramidal with angles below 109.5^\circ.

Symmetry elements and planes of symmetry

A symmetry element is a geometric feature, such as a plane, axis or centre, about which an operation maps a molecule onto an indistinguishable copy of itself. A mirror plane \sigma maps every atom onto an identical atom. It is labelled \sigma_h if it is perpendicular to the principal axis, \sigma_v if it contains the principal axis, and \sigma_d if it contains the principal axis and bisects the angle between two C_2 axes.

For a planar ring, the molecular plane is a mirror plane only if every substituent lies in that plane or is reflected onto an identical substituent. A substituent above the ring and an identical one below it are interchanged by the ring-plane reflection only if they are equivalent, which they are not when they sit on opposite faces. Each candidate plane must therefore be tested separately, and a plane survives only if every atom and substituent is reflected onto an identical one.

Example: cis-1,2-dichlorocyclobutane, with both chlorines on the same face, belongs to C_{2v} and has two vertical mirror planes. Trans-1,2-dichlorocyclobutane has only a C_2 axis and no mirror plane, so it is chiral.

• improper rotation — an operation S_n combining a rotation with a reflection in the plane perpendicular to the axis. 예) A molecule with only an S_4 axis has no mirror plane but is still a distinct symmetry class.