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hw8 - Or use the results of the previous problem to set up...

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Chem 110A 1 Homework 8: Due MONDAY, December 7 This problem set to be turned in on the morning of the Final Exam Chemistry 110A — 2009 Professor McCurdy 1. (Problem 9-4 in McQuarrie and Simon) Determine the normalized wave function for ! " = c 1 s A " 1 s B ( ) This problem is asking you to find the normalization constant, c, in terms of the overlap integral ! * 1 s A " ( r ) ! 1 s B ( r ) d 3 r given in Eq. 9.11. 2. (Problem 9-8 in McQuarrie and Simon) Show that H AA = H BB = ! 1/ 2 + J and that H AB = ! S / 2 + K in the simple molecular-orbital treatment of H 2 + . The quantities J and K are given by Eqs.(9.23) and (9.24). Atomic units are being used in these expressions in the text. 3. (Problem 9-10 in McQuarrie and Simon) Show that for the antibonding orbital of H 2 + the eigenvalue of the simple LCAO treatment is E = E 1 s + J ! K 1 ! S = ! 1 2 + J ! K 1 ! S You can do this one of two ways: Either use the result of problem 1 above take the expectation value of the Hamiltonian, making use of the results in problem 2.
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Unformatted text preview: Or use the results of the previous problem to set up the 2x2 secular determinant and solve the resulting quadratic equation for E. In the latter case, you get two solutions, one for the bonding orbital and one for the antibonding one. 4. (Problem 9-12 in McQuarrie and Simon) Use simple molecular-orbital theory to explain why the dissociation energy of N 2 is treater than that of N 2 + , but that the dissociation energy of O 2 + is greater than that of O 2 . This is a freshman chemistry question about bond order. 5. (Problem 9-23 in McQuarrie and Simon) See your book for the text of the problem. This problem simply asks you to quantify the basic idea behind photoelectron spectroscopy, as shown in Figures 9.16 and 9.17 of the text....
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