Bond order is a fundamental concept in chemistry that quantifies the number of chemical bonds existing between a pair of atoms in a molecule. This numerical value measures the degree of covalent bonding, typically represented by an integer for simple bonds, but sometimes a fraction. Understanding bond order offers a direct indication of a molecule’s inherent stability and its overall structure. Calculating this value allows chemists to characterize the nature of a chemical connection and predict a molecule’s behavior and properties.
Calculating Bond Order Using Simple Valence Structures
The most straightforward method for determining bond order applies to molecules where electrons are localized between two atoms, represented by a single Lewis structure. This approach is based on counting the shared electron pairs between the two atoms. A single bond results in a bond order of one, a double bond yields two, and a triple bond results in three.
For example, the diatomic nitrogen molecule (\(\text{N}_2\)) features a triple bond, giving it a bond order of three. The oxygen molecule (\(\text{O}_2\)) is represented by a double bond, corresponding to a bond order of two. The bond order is always an integer, which directly reflects the number of lines drawn between the atoms in the Lewis structure.
This counting technique is suitable for molecules without electron delocalization, providing an accurate assessment of the bond character. This method establishes the foundational understanding of bond order before moving to more complex systems where simple counting is insufficient.
Determining Bond Order in Averaged Structures
When a molecule or ion exhibits resonance, the electrons are delocalized over three or more atoms, meaning no single Lewis structure accurately represents the true bonding arrangement. In these averaged structures, the bond order is a fractional value that represents the average bonding character across all equivalent resonance forms. To calculate this value, one must first draw all possible contributing resonance structures.
The calculation requires summing the total number of bonds between the atoms in question across all resonance structures. This total bond count is then divided by the number of equivalent resonance structures. The averaging formula is: Bond Order = (Total number of bonds in all structures) / (Number of resonance structures).
Consider the carbonate ion (\(\text{CO}_3^{2-}\)), which has three equivalent resonance structures. Across the three structures, there is a total of four bonds shared among the three carbon-oxygen positions. Dividing the four total bonds by the three resonance structures yields a carbon-oxygen bond order of \(4/3\), or approximately \(1.33\). This fractional bond order indicates a bond character between a single and a double bond, reflecting the equal sharing of electron density across all three equivalent bonds in the actual ion.
Molecular Orbital Theory and Bond Order
For certain molecules, particularly diatomic species or charged ions, relying solely on Lewis structures can be insufficient. Molecular Orbital (MO) Theory provides a more sophisticated approach, defining bond order based on the arrangement of electrons in molecular orbitals rather than localized bonds. This theory explains that when atomic orbitals combine, they form an equal number of new molecular orbitals, categorized as either bonding or anti-bonding.
Bonding orbitals are lower in energy than the original atomic orbitals and concentrate electron density between the nuclei, stabilizing the molecule. Anti-bonding orbitals are higher in energy and destabilize the molecule by placing electron density outside the region between the nuclei. The MO theory formula for bond order quantifies the net stabilization: \(\text{BO} = \frac{1}{2} (\text{Number of electrons in bonding orbitals} – \text{Number of electrons in anti-bonding orbitals})\).
This method is necessary for understanding molecules like \(\text{O}_2\), which Lewis structures incorrectly predict to be diamagnetic. MO theory calculates the bond order of \(\text{O}_2\) as two, but the electron configuration reveals two unpaired electrons in the anti-bonding orbitals, correctly explaining its observed paramagnetic behavior. When the number of electrons in bonding and anti-bonding orbitals is equal, the bond order is zero, indicating that a stable bond will not form.
The Physical Significance of Bond Order
Once calculated, the bond order provides insight into the physical properties of the chemical bond. The bond order is directly related to bond strength, which is the energy required to break the bond. A higher bond order signifies a greater number of shared electron pairs, resulting in a stronger attraction between the atoms and a higher bond dissociation energy.
The bond order is also inversely correlated with bond length, the distance between the nuclei of the two bonded atoms. As the bond order increases, the greater electron density pulls the nuclei closer together, causing the bond length to decrease. For instance, a carbon-carbon triple bond (BO=3) is shorter and stronger than a carbon-carbon double bond (BO=2), which is shorter and stronger than a carbon-carbon single bond (BO=1). Fractional bond orders, such as \(1.5\) in benzene, correlate to bond lengths and strengths that fall between those of a single and a double bond.