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Unformatted text preview: Ch24 Midterm, Winter 2011 Closed Homework. Closed Book. Open Notes and ppts. Time Limit: 4 hours Relevant equations are found on the last page. Please do all of your work on separate paper. 1. Given the following trial wavefunction in polar coordinates: g = G ¡¢£ ¤ a) Use the variational principle to find the value of the parameter α. Use the following Hamiltonian: ℋ = − ℏ ¥ 2¦ § ¨ ¥ © ©¨ ª¨ ¥ © ©¨ « − G ¥ 4¬ ® ¨ b) Calculate the minimized energy. c) Next, calculate the coefficient to normalize the trial wavefunction over all space. d) Using the fact that the Bohr radius is given by: ¯ ® = 4¬ ® ℏ ¥ ¦ § G ¥ Compare your normalized wavefunction to the actual hydrogen 1s orbital wavefunction by plugging α back in. (Give me a sense of how close your values are to the actual 1s value) g°1±² = ª 1 ¬¯ ® ³ « ´/¥ G ¡£/µ ¶ 2. The bonding and antibonding molecular orbitals for H 2 + are given below: a) Label which is bonding and which is antibonding. b) Given the two following energy expressions for H 2 + : · ´ = ¸ ´´ − ¸ ´¥ 1 − ¹ · ¥ = ¸ ´´ + ¸ ´¥ 1 + ¹ Which expression gives the energy of the bonding and antibonding states for H 2 and why? 3. Indicate which atoms are in the same plane in the following peptide molecule and explain why. 4. Using the Walsh Correlation bent....
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 Fall '09
 Variational principle, bound electron, following trial wavefunction, Bohr assumption, following peptide molecule

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