The geometry of a molecule determines many of its physical and chemical characteristics, including its polarity, reactivity, and biological function. Molecules are three-dimensional objects with specific shapes that govern how they interact with other substances. Predicting this arrangement of atoms around a central atom is a fundamental goal in chemistry. The steric number provides a simple, yet powerful, mathematical tool that chemists use to quickly predict the shape a molecule will adopt in space.
Defining the Steric Number
The steric number (SN) is a count of the total regions of electron density surrounding the central atom in a molecule. It is calculated as the sum of two components: the number of atoms directly bonded to the central atom and the number of lone pairs of electrons residing on that central atom.
Any atom bonded to the central atom counts as exactly one bonding group, regardless of the type of bond connecting them. For instance, a single bond, a double bond, or a triple bond all count equally as one bonding group for determining the steric number.
The second component is the number of lone electron pairs. Each lone pair on the central atom counts as one non-bonding group of electron density. The calculation focuses exclusively on the central atom because it sets the overall geometry of the molecule.
Step-by-Step Calculation
Calculating the steric number requires visualizing the distribution of valence electrons, typically by drawing the molecule’s Lewis structure. The Lewis structure is the necessary first step, as it reveals the precise number of bonded atoms and the number of lone electron pairs on the central atom.
The calculation begins by identifying the central atom. Next, count the number of atoms bonded directly to this central atom; this number represents the bonding groups. For example, in methane (\(\text{CH}_4\)), the central carbon atom is bonded to four hydrogen atoms, so the count of bonded atoms is four.
The final step is to count the number of lone pairs of electrons on that same central atom. In methane, the central carbon atom has no lone pairs, giving a count of zero. The steric number is found by adding these two values: \(4 \text{ (bonded atoms)} + 0 \text{ (lone pairs)} = 4\).
Consider the water molecule (\(\text{H}_2\text{O}\)), where oxygen is the central atom. Oxygen is bonded to two hydrogen atoms, and the Lewis structure shows two lone pairs of electrons on the oxygen atom. The steric number for oxygen in water is therefore \(2 \text{ (bonded atoms)} + 2 \text{ (lone pairs)} = 4\). Similarly, in ammonia (\(\text{NH}_3\)), the central nitrogen is bonded to three hydrogen atoms and has one lone pair, resulting in a steric number of \(3 + 1 = 4\).
Connecting Steric Number to Molecular Shape
The calculated steric number serves as the basis for predicting the three-dimensional arrangement of electron groups around the central atom, which is the core principle of the Valence Shell Electron Pair Repulsion (VSEPR) theory. VSEPR theory states that regions of electron density will arrange themselves in space to be as far apart as possible to minimize repulsion. The steric number dictates this spatial arrangement.
The number directly corresponds to the molecule’s electron geometry, which is the overall arrangement of all electron groups, both bonding and non-bonding. For instance, a steric number of 2 always results in a linear electron geometry, with the groups separated by \(180^\circ\). A steric number of 3 leads to a trigonal planar electron geometry, with \(120^\circ\) angles, and a steric number of 4 corresponds to a tetrahedral electron geometry, with angles near \(109.5^\circ\).
Steric numbers of 5 and 6 correspond to trigonal bipyramidal and octahedral electron geometries, respectively. While the steric number defines the electron geometry, the molecular geometry—the shape defined only by the atoms—is determined by the distribution of lone pairs within that electron geometry. Lone pairs occupy space and contribute to the repulsion, but they are not visible when describing the final shape of the molecule.
For a molecule with a steric number of 4, if all four groups are bonding atoms (like in \(\text{CH}_4\)), the molecular geometry is also tetrahedral. However, if one group is a lone pair (like in \(\text{NH}_3\)), the shape becomes trigonal pyramidal. If two groups are lone pairs (like in \(\text{H}_2\text{O}\)), the shape is bent or V-shaped. Thus, the steric number provides the foundational electron geometry, and the number of lone pairs dictates the specific variation of the molecular shape.