Problems . Using Hückel theory, determine the energies of the four pi orbitals of trimethylenemethane (Problem 4-25). . (a) Determine the symmetries of the four pi orbitals of methylenecyclopropene and write the most general pi wave functions which possess these symmetries. 2 Molecular orbital theory CH ₂ 4 Copyrighted mat 299 methylenecyclopropene (b) Set up the secular determinant derived from Hückel theory for this molecule. (c) The roots of the secular determinant are x = -2.170, -0.311, +1.000, and +1.481. Draw an energy level diagram for this molecule and determine the delocalization energy of the neutral species. (d) The wave function for the lowest pi mo is = 0.278p, + 0.612p₂ +0.524p3 + 0.524p4. Using eq. 4-11, solve for the energy of this orbital in terms of a and ß using the approxima- tions of Hückel theory on pages 288-289. Compare your answer to that given by the appropriate root of the secular determinant. By setting up and solving the appropriate simultaneous equations, calculate the coefficients of the pi orbitals of the allyl system. First solve for C₂ and C3 in terms of c, and then normalize each wave function to obtain the coefficients in eq. 4-48. When normalizing the wave functions, remember the Hückel approximation that S₁0 unless i = j.
Problems . Using Hückel theory, determine the energies of the four pi orbitals of trimethylenemethane (Problem 4-25). . (a) Determine the symmetries of the four pi orbitals of methylenecyclopropene and write the most general pi wave functions which possess these symmetries. 2 Molecular orbital theory CH ₂ 4 Copyrighted mat 299 methylenecyclopropene (b) Set up the secular determinant derived from Hückel theory for this molecule. (c) The roots of the secular determinant are x = -2.170, -0.311, +1.000, and +1.481. Draw an energy level diagram for this molecule and determine the delocalization energy of the neutral species. (d) The wave function for the lowest pi mo is = 0.278p, + 0.612p₂ +0.524p3 + 0.524p4. Using eq. 4-11, solve for the energy of this orbital in terms of a and ß using the approxima- tions of Hückel theory on pages 288-289. Compare your answer to that given by the appropriate root of the secular determinant. By setting up and solving the appropriate simultaneous equations, calculate the coefficients of the pi orbitals of the allyl system. First solve for C₂ and C3 in terms of c, and then normalize each wave function to obtain the coefficients in eq. 4-48. When normalizing the wave functions, remember the Hückel approximation that S₁0 unless i = j.
Principles of Modern Chemistry
8th Edition
ISBN:9781305079113
Author:David W. Oxtoby, H. Pat Gillis, Laurie J. Butler
Publisher:David W. Oxtoby, H. Pat Gillis, Laurie J. Butler
Chapter6: Quantum Mechanics And Molecular Structure
Section: Chapter Questions
Problem 64P: For each of the following molecules, construct the MOs from the 2pz atomic orbitals perpendicular...
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solve a, b and c please, sir
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Step 1: Introduction
VIEWStep 2: To determine the symmetries.
VIEWStep 3: Secular determinant derived from Huckel theory for this molecule
VIEWStep 4: Calculation
VIEWStep 5: Energy level diagram and delocalization energy of the neutral species.
VIEWStep 6: To determine the delocalization energy ( DE).
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