Answer Happy

2. For each molecule, sketch (approximately) the space MOs resulting from your analysis in order of increasing energy. 3. By invoking what you know about a very simple model problem that we've used in this class, explain why it is not surprising that butadiene has the larger gap. 4. Consider the lowest energy triplet state (in which both electrons are spin up) of the hydrogen molecule for a bond distance of 0.75 bohr. Inspired by mean field theory, you decide to construct as your approximate wave function a Slater determinant in which the two molecular orbitals are the + and - linear combinations of the hydrogen atom 1s orbitals centered on each of the two nuclei. Assuming both electrons lie on the inter-nuclear axis and that one of them is held fixed 1/6 of the way in between the nuclei, evaluate the probabilities of finding the other electron 0/9, 1/9, 2/9, ..., up to 8/9 of the way in between the nuclei relative to finding it at the far nucleus (i.e. at 9/9). Explain what you see in your results. Hint: When computing relative probabilities (i.e. ratios of probabilities), the normalization of the wave function does not matter. Also, remember that the probability function for the position is just the square of the wave function.