Molecular Shapes

A special notation is used when describing geometries with VSEPR theory. The letter A is used to represent the central atom, X represents bonding pairs of electrons between the central atom and another atom, and E represents lone pairs. So the notation AX₂E₃ means there are two bonding pairs of electrons and three lone pairs of electrons arranged around a central atom, A. The angle formed between two terminal groups (X or E) and the central atom (A) is called the bond angle. Note that the electron-pair geometry includes lone, unbound electron pairs. Lone pairs are not represented in molecular models. Because lone pairs are not shown, the molecular geometry may be different than the electron-pair geometry. The molecular geometry, also called molecular shape, is the shape formed by the central atom, considering only bonding electron pairs.

Consider a molecule with trigonal planar electron-pair geometry with one lone pair of electrons. The molecular geometry of this molecule is bent; it is not trigonal planar. Two atoms are bonded to a central atom at an angle. Furthermore, lone pairs are not constrained by a covalent bond. The electrons in a lone pair have higher energy, which means they can spread out more. Because of the higher energy, lone pairs have a greater repulsive force than bonding pairs. A lone pair–lone pair interaction is the most repulsive (has the highest energy), a bonding pair–bonding pair interaction is the least repulsive (has the lowest energy), and a lone pair–bonding pair interaction is in the middle.

When there is more than one possible location for a lone pair in the molecular geometry, the lone pair settles in the configuration that minimizes the repulsion between the lone pair and other electrons. Consider a central atom with four bonding pairs and one lone pair (AX₄E). For this molecule the lone pair is located in the central plane so that there are two 90° lone pair–bonding electron interactions and two 120° lone pair–bonding electron interactions. If the lone pair were at the tip of the pyramid, there would be three 90° lone pair–bonding interactions and one 120° one. This arrangement would be a higher energy state and would be less stable.

Consider how VSEPR theory predicts the shape of nitrogen triiodide (NI₃). The first step is to draw the Lewis structure for this molecule. The nitrogen atom has five valence electrons, and each iodine atom has seven valence electrons. The Lewis structure reveals that the central atom is nitrogen and that it is surrounded by four electron pairs, which corresponds to a tetrahedral electron-pair geometry. But the molecule has three bonding pairs and one lone pair (a VSEPR notation of AX₃E), so its molecular geometry is not the same as the electron-pair geometry. Instead, the top of the pyramid is occupied by the lone pair, and VSEPR predicts a molecular shape that is trigonal pyramidal with 109.5° bond angles. Note that in reality the bond angles of nitrogen triiodide are slightly less than 109.5° because the forces of repulsion between the two iodine atoms and an iodine atom and a lone pair are different from each other. A more complicated structure is the tetrachloroiodate ion (ICl₄^–). In the case of the tetrachloroiodate ion, the central atom, iodine, has four bonding pairs and two lone pairs, so the structure is AX₄E₂. The iodine atom in this molecule contains an expanded octet. The electron-pair geometry of this structure is octahedral, but the two lone pairs mean that the molecular geometry is different. Remember that lone pair–lone pair interactions are the most repulsive, so the two lone pairs are arranged on opposite sides of the central atom, 180° apart. The molecular structure is therefore square planar, and the bond angles are all 90°. VSEPR theory can also be used to predict molecular geometries of molecules with more than one central atom. The technique is similar, but it is applied to each central atom individually, and the two resulting shapes are simply joined together. Consider the structure of methanol (CH₃OH). There are two central atoms: carbon (C) and oxygen (O). The carbon atom has four bonding pairs of electrons and no lone pairs (AX₄), so the molecular geometry is the same as the electron-pair geometry and is tetrahedral. The oxygen atom has two bonding atoms and two lone pairs (AX₂E₂), so its electron-pair geometry is tetrahedral but its molecular geometry is bent. The structure for the entire molecule can be pictured as a tetrahedron with an angled arm branching off one corner.

A polar covalent bond is a covalent bond in which the electron density is more localized on one end of the bond. One end is slightly positive, and one end is slightly negative. A dipole moment ($\mu$) is a vector quantity that defines the extent of the charge on either side of a polar covalent bond, with the direction that points from the positive side of the bond toward the negative side. The negative side is the more electronegative atom, and the positive side is the less electronegative atom. The dipole moment is the product of the charge ($\delta{+}$ and $\delta{-}$) and distance (d). The distance is simply the bond length. The dipole moment is measured in debyes (D), where $1\;\rm D=3.335641\times10^{-30}\;\rm C\cdot \rm m$.

The polarity of a molecule is related to its shape. Consider the carbon dioxide (CO₂) molecule. Each ${\rm{C{-}O}}$ bond has a dipole moment that has a greater electron density on the oxygen side of the bond, because oxygen is more electronegative than carbon. Schematically, the individual ${\rm{C{-}O}}$bond dipole moments are represented by a crossed arrow that points toward the side of greater negativity. The plus end of the arrow indicates the positively charged side of the molecule, and the tip of the arrow represents the negatively charged side. Because the dipole moments in carbon dioxide are equal in magnitude but opposite in direction, they cancel each other, and $\mu$ is equal to zero when the molecule is considered as a whole. A molecule with a dipole moment equal to zero is called a nonpolar molecule. Carbon dioxide is nonpolar, and VSEPR theory predicts that carbon dioxide is a linear molecule. If the molecule were bent, there would be a net partial charge on the oxygen atoms and the carbon atom, and the dipole moment would not equal zero.
Water, on the other hand, has a central oxygen atom that is more electronegative than the hydrogen atoms bound to it. In this case, the dipole moments are equal in magnitude but have components that point toward each other, so the entire molecule has a dipole moment greater than zero. A polar molecule, such as water, has a specific dipole moment not equal to zero. Because a water molecule is polar, VSEPR theory predicts that it has a bent structure. The two lone pairs and the hydrogen atoms repel each other, resulting in a bend in the shape of the molecule. In a water molecule, there are net partial charges on the two hydrogen atoms and the oxygen atom.