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Unformatted text preview: 1 5.61 Physical Chemistry Lecture #31 HCKEL MOLECULAR ORBITAL THEORY In general, the vast majority polyatomic molecules can be thought of as consisting of a collection of two-electron bonds between pairs of atoms. So the qualitative picture of and -bonding and antibonding orbitals that we developed for a diatomic like CO can be carried over give a qualitative starting point for describing the C=O bond in acetone, for example. One place where this qualitative picture is extremely useful is in dealing with conjugated systems that is, molecules that contain a series of alternating double/single bonds in their Lewis structure like 1,3,5-hexatriene: Now, you may have been taught in previous courses that because there are other resonance structures you can draw for this molecule, such as: that it is better to think of the molecule as having a series of bonds of order 1 rather than 2/1/2/1/ MO theory actually predicts this behavior, and this prediction is one of the great successes of MO theory as a descriptor of chemistry . In this lecture, we show how even a very simple MO approximation describes conjugated systems. Conjugated molecules of tend to be planar, so that we can place all the atoms in the x-y plane. Thus, the molecule will have reflection symmetry about the z-axis: z Now, for diatomics, we had reflection symmetry about x and y and this gave rise to x and y orbitals that were odd with respect to reflection and orbitals that were even. In the same way, for planar conjugated systems the orbitals will separate into orbitals that are even with respect to reflection 2 5.61 Physical Chemistry Lecture #31 and z orbitals that are odd with respect to reflection about z. These z orbitals will be linear combinations of the p z orbitals on each carbon atom: z In trying to understand the chemistry of these compounds, it makes sense to focus our attention on these z orbitals and ignore the orbitals. The z orbitals turn out to be the highest occupied orbitals, with the orbitals being more strongly bound. Thus, the forming and breaking of bonds as implied by our resonance structures will be easier if we talk about making and breaking bonds rather than . Thus, at a basic level, we can ignore the existence of the -orbitals and deal only with the -orbitals in a qualitative MO theory of conjugated systems. This is the basic approximation of Hckel theory, which can be outlined in the standard 5 steps of MO theory: 1) Define a basis of atomic orbitals. Here, since we are only interested in the z orbitals, we will be able to write out MOs as linear combinations of the p z orbitals. If we assume there are N carbon atoms, each contributes a p z orbital and we can write the th MOs as: N = c i p z i i = 1 2) Compute the relevant matrix representations.representations....
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This note was uploaded on 09/24/2011 for the course MATH 1090 taught by Professor Greenwood during the Spring '08 term at MIT.
- Spring '08