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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 =CH₂ L Copyrighted mat 299 3 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 = 0.278p₁ + 0.612p₂ + 0.524p, + 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. C3 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 S₁ = 0 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 =CH₂ L Copyrighted mat 299 3 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 = 0.278p₁ + 0.612p₂ + 0.524p, + 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. C3 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 S₁ = 0 unless i = j.

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ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
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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. Copyrighted mate Molecular orbital theory 299 Dat ECH2 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 v = 0.278p, + 0.612p, + 0.524p, + 0.524p.. 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 c, and c, 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 Sij = 0 unless i = j. Transition Metal Complexes is section we will consider only the most common idealized structure of sition metal complexes in which the metal is surrounded by six ligands ie vertices of an octahedron (Fig. 4-57). We suppose that each ligand some kind of sigma orbital pointing at the transition metal, and that e is no pi bonding between the metal and ligands. The characters of the id sigma orbitals and the transition metal s, p, and d valence shell tals are given in Table 4-18. As one example of how these characters are ined, the complete C, matrix for the metal d orbitals is given in eq. 4-52. 0 0 1 *p dy 1 dyz dyy 0 1 dxy (4-52) = d2;2-x²-y? 0 0 0 d 2;2-x - y? 0 0 0 - -}
Transcribed Image Text: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. Copyrighted mate Molecular orbital theory 299 Dat ECH2 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 v = 0.278p, + 0.612p, + 0.524p, + 0.524p.. 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 c, and c, 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 Sij = 0 unless i = j. Transition Metal Complexes is section we will consider only the most common idealized structure of sition metal complexes in which the metal is surrounded by six ligands ie vertices of an octahedron (Fig. 4-57). We suppose that each ligand some kind of sigma orbital pointing at the transition metal, and that e is no pi bonding between the metal and ligands. The characters of the id sigma orbitals and the transition metal s, p, and d valence shell tals are given in Table 4-18. As one example of how these characters are ined, the complete C, matrix for the metal d orbitals is given in eq. 4-52. 0 0 1 *p dy 1 dyz dyy 0 1 dxy (4-52) = d2;2-x²-y? 0 0 0 d 2;2-x - y? 0 0 0 - -}
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