Synthesis: Three Models, One Molecule
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You should be comfortable drawing Lewis structures, calculating formal charges, and understanding the basic principles of atomic orbital overlap and molecular orbital energy diagrams.
Why this matters
Chemical bonding is not a single phenomenon but a spectrum of models that each reveal different facets of molecular stability.
Throughout this unit, we have examined chemical bonding through three distinct lenses: the Lewis model, which focuses on electron counting and octet satisfaction; valence bond theory, which emphasises orbital overlap and hybridisation; and molecular orbital theory, which treats electrons as delocalised over the entire molecule. While each model has limitations, their synthesis provides a comprehensive understanding of why molecules have the shapes, reactivities, and properties they do. This final lecture integrates these perspectives to demonstrate how they complement one another in predicting molecular behaviour.
The Complementary Nature of Bonding Models
Imagine trying to describe a complex sculpture. One observer might focus on the geometric arrangement of the pieces (Lewis structures), another on how the pieces are glued together (valence bond theory), and a third on the overall flow and balance of the form (molecular orbital theory). No single description is complete, but together they provide a full picture. In chemistry, the Lewis model gives us a quick, intuitive map of electron distribution and formal charges, helping us predict molecular geometry and reactivity sites. Valence bond theory explains the directional nature of bonds and the concept of hybridisation, which accounts for bond angles and molecular shapes. Molecular orbital theory, meanwhile, offers a quantum-mechanical view that explains phenomena like bond order, magnetic properties, and the stability of molecules that defy simple electron-pairing rules. By using all three models, we gain a robust framework for understanding chemical bonding.
Integrating Lewis Structures and Formal Charge
The Lewis model remains the foundational tool for predicting molecular structure. By counting total valence electrons and distributing them to satisfy the octet rule, we can identify the most stable arrangement of atoms. When multiple structures are possible, formal charge calculations guide us to the best representation. The formal charge on an atom is given by \( FC = V - L - \tfrac{B}{2} \), where \( V \) is the number of valence electrons in the free atom, \( L \) is the number of lone-pair electrons, and \( B \) is the number of bonding electrons. The best Lewis structure minimises the sum of the absolute values of formal charges, \( \sum |FC| \), and places any negative formal charge on the more electronegative atom. This approach is particularly useful for predicting the reactivity of molecules, as atoms with significant formal charges are often the sites of chemical attack.
Valence Bond Theory and Hybridisation
Valence bond theory extends the Lewis model by incorporating the concept of orbital overlap. Atoms form bonds by overlapping their atomic orbitals, creating shared electron density between the nuclei. To explain the observed bond angles in molecules like methane and ammonia, we introduce hybridisation, where atomic orbitals mix to form new hybrid orbitals. For example, in methane, the carbon atom undergoes sp3 hybridisation, forming four equivalent orbitals that point to the corners of a tetrahedron. This model successfully predicts the geometry of many molecules and provides a clear picture of how bonds are formed. However, it has limitations, particularly in explaining the magnetic properties of molecules like oxygen, where it predicts a diamagnetic state that contradicts experimental observations.
Molecular Orbital Theory and Bond Order
Molecular orbital theory offers a more comprehensive view by treating electrons as delocalised over the entire molecule. Atomic orbitals combine linearly to form bonding and antibonding molecular orbitals. The bonding orbital, \( \psi_+ \propto \phi_A + \phi_B \), is lower in energy and has electron density concentrated between the nuclei, stabilising the molecule. The antibonding orbital, \( \psi_- \propto \phi_A - \phi_B \), is higher in energy and has a node between the nuclei, destabilising the molecule. By filling these orbitals according to the aufbau principle and Hund's rule, we can calculate the bond order, \( \text{BO} = \tfrac{n_{\text{bonding}} - n_{\text{antibonding}}}{2} \). A positive bond order indicates a stable molecule, while a zero or negative bond order suggests instability. This model correctly predicts the paramagnetism of oxygen, which has two unpaired electrons in its antibonding orbitals, a feature that the Lewis and valence bond models fail to capture.
The results
Lewis structures and the octet rule
A molecule's total valence electrons can be distributed as bonding pairs (shared between two atoms) and lone pairs (localised on one atom) so that, wherever possible, every main-group atom is surrounded by eight electrons (two, for hydrogen). Where more than one such distribution is possible, the formal charge \(FC=V-L-\tfrac{B}{2}\) (valence electrons \(V\), lone-pair electrons \(L\), bonding electrons \(B\)) on each atom selects the best structure: minimise the magnitude of formal charges, and place any necessary negative formal charge on the more electronegative atom.
Molecular orbital theory
Two atomic orbitals \(\phi_A,\phi_B\) combine linearly into a bonding molecular orbital \(\psi_+\propto\phi_A+\phi_B\) (in-phase, lower energy, electron density concentrated between the nuclei) and an antibonding orbital \(\psi_-\propto\phi_A-\phi_B\) (out-of-phase, higher energy, with a node between the nuclei). Filling these molecular orbitals by the same aufbau and Hund's-rule procedure used for atoms gives a bond order \(\text{BO}=\tfrac{n_{\text{bonding}}-n_{\text{antibonding}}}{2}\), and correctly predicts molecular magnetism — including the paramagnetism of \(\text{O}_2\), which the Lewis/valence-bond picture (this unit's earlier results) cannot explain.
A common misconception is that the Lewis model is "wrong" when it fails to predict magnetic properties. In reality, the Lewis model is a simplified representation that works well for electron counting and reactivity but lacks the quantum-mechanical detail needed to describe electron spin and delocalisation. Molecular orbital theory is not a replacement for the Lewis model but a more sophisticated framework that encompasses its insights while adding predictive power for phenomena like paramagnetism and bond order. C
Worked example
Problem. Apply the MO model to \(\mathrm{O_2}\), the superoxide ion \(\mathrm{O_2^-}\) and the peroxide ion \(\mathrm{O_2^{2-}}\): give each one's bond order and number of unpaired electrons, and compare with the Lewis picture.
- Valence electrons: 12, 13 and 14. Heavy-atom ordering: \(\sigma_{2s}^2\,\sigma_{2s}^{*2}\,\sigma_{2p}^2\,\pi_{2p}^4\), then the extra electrons in \(\pi^*_{2p}\): 2, 3 and 4 respectively.
- Bonding electrons: \(2 + 2 + 4 = 8\) in each. Antibonding: \(2 + 2 = 4\), \(2 + 3 = 5\), \(2 + 4 = 6\).
- Bond orders: \((8-4)/2 = 2\), \((8-5)/2 = 1.5\), \((8-6)/2 = 1\).
- Unpaired electrons (Hund's rule in the two \(\pi^*\) orbitals): 2, 1 and 0. Measured O–O lengths, about 121, 133 and 149 pm, lengthen as the bond order falls.
Units check. Bond orders and electron counts are pure numbers. The Lewis model gets the peroxide single bond right, but only the MO model explains why \(\mathrm{O_2}\) is paramagnetic and why superoxide has an odd bond order of 1.5.
Three quick tests
- In the Lewis structure of nitrate with one N=O and two N–O bonds, what is the formal charge on nitrogen?
Answer
+1: \(FC = 5 - 0 - 8/2 = +1\) (four bonding pairs: one double bond and two single bonds). - Which model is needed to explain why \(\mathrm{O_2}\) sticks to a magnet?
Answer
The MO model: it puts two unpaired electrons in the two degenerate \(\pi^*\) orbitals. Lewis and simple valence-bond pictures pair every electron. - What hybridisation does valence bond theory assign to carbon in \(\mathrm{CO_2}\), and what shape follows?
Answer
sp, giving a linear O=C=O with two \(\pi\) bonds in perpendicular planes; VSEPR (two domains) agrees.
Back to CU-102 →
Every lecture and every result in this unit, with prerequisites and threads.
Lecture notes drafted with a local model and checked line by line by the editor; every number in the worked example was recomputed.