10: Bonding in Polyatomic Molecules

The concept of a molecular orbital is readily extended to provide a description of the electronic structure of a polyatomic molecule. Indeed molecular orbital theory forms the basis for most of the quantitative theoretical investigations of the properties of large molecules. In general a molecular orbital in a polyatomic system extends over all the nuclei in a molecule and it is essential, if we are to understand and predict the spatial properties of the orbitals, that we make use of the symmetry properties possessed by the nuclear framework.

• 10.1: Hybrid Orbitals Account for Molecular Shape
The shape and bonding valecies of polyatomic molecules can be accounted for by hybrid orbitals. Molecular orbitals are formed from linear combinations of atomic orbitals which are similar in energy. These atomic orbitals could come from di erent atoms, or from the same atom. For example, the 2 sand 2patomic orbitals are very close energetically. When a linear combo of more than one atomic orbital from the same atom is formed, we have a hybrid orbital
• 10.2: Hybrid Orbitals in Water
The goal of applying Valence Bond Theory to water is to describe the bonding in H2O and account for its structure (i.e., appropriate bond angle and two lone pairs predicted from VSEPR theory).  This means applying a localize two-atom bonding approach, which requires introducing hybrid orbitals to describe the experimentally observed bent structure.
• 10.3: Why is BeH₂ Linear and H₂O Bent?
Walsh correlation diagram is a plot of molecular orbital energy as a function of some systematic change in molecular geometry. For example, the correlation between orbital energies and bond angle for an $$AH_2$$ molecule. The geometry of a molecule is determined by which possible structure is lowest in energy. We can use the Walsh diagram to determine the energy trends based on which orbitals are occupied.
• 10.4: Photoelectron Spectroscopy
A photoelecton spectrum can show the relative energies of occupied molecular orbitals by ionization. (i.e. ejection of an electron). A photoelectron spectrum can also be used to determine energy spacing between vibrational levels of a given electronic state. Each orbital energy band has a structure showing ionization to different vibrational levels.
• 10.5: The $$\pi$$-Electron Approximation of Conjugation
Molecular orbital theory has been very successfully applied to large conjugated systems, especially those containing chains of carbon atoms with alternating single and double bonds. An approximation introduced by Hü​ckel in 1931 considers only the delocalized p electrons moving in a framework of $$\pi$$-bonds. This is, in fact, a more sophisticated version of a free-electron model.
• 10.6: Butadiene is Stabilized by a Delocalization Energy
Delocalization energy is intrinsic to molecular orbital theory, since it results from breaking the two-center bond concept. This is intrinsic to molecular orbital theory with the molecular orbitals spreading further than just one pair of atoms. However, within the two-center theory of valence bond theory, the delocalization energy results from a stabilization energy attributed to resonance.
• 10.7: Benzene and Aromaticity
The previous sections addressed the $$\pi$$ orbitals of linear conjugated system. Here we address conjugated systems of cyclic conjugated hydrocarons with the general formula of $$C_nH_n$$ where n is the number of carbon atoms in the ring. The molecule from this important class of organic molecule that you are most familiar with is benzene ($$C_6H_6$$) with n=6, although many other molecules exist like cyclobutadiene ($$C_4H_4$$ with n=4).
• 10.E: Bonding in Polyatomic Molecules (Exercises)
These are homework exercises to accompany Chapter 10 of McQuarrie and Simon's "Physical Chemistry: A Molecular Approach" Textmap.