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lecture31 - 5.61 Physical Chemistry Lecture#31 1 HCKEL...

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1 5.61 Physical Chemistry Lecture #31± HÜCKEL 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 σ and π -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 ½ 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 π x and π y orbitals that were odd with respect to reflection and σ orbitals that were even. In the same way, for planar conjugated systems the orbitals will separate into σ orbitals that are even with respect to reflection
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2 5.61 Physical Chemistry Lecture #31± and π z orbitals that are odd with respect to reflection about z. These π 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 π z orbitals and ignore the σ orbitals. The π z orbitals turn out to be the highest occupied orbitals, with the σ 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 π bonds rather than σ . Thus, at a basic level, we can ignore the existence of the σ -orbitals and deal only with the π -orbitals in a qualitative MO theory of conjugated systems. This is the basic approximation of Hückel 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 π 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 µ th MOs as: N π µ = c i µ p z i i = 1 2) Compute the relevant matrix representations. Hückel makes some radical approximations at this step that make the algebra much simpler without changing the qualitative answer. We have to compute two matrices, H and S which will involve
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