or each of the following molecules, construct the MOS from the 2p, atomic orbitals perpendicular to the plane of the carbon atoms. (a) Cyclobutadiene HC=CH НС—СН HC=CH НС —СH (b) Allyl radical H H H H C=C •C-C, H C-H H C-H H H Indicate which, if any, of these orbitals have identical ener- gies from symmetry considerations. Show the number of electrons occupying each w MO in the ground state, and indicate whether either or both of the molecules are para- magnetic. Assume that the C atoms in the allyl radical are all sp? hybridized. Activate io to S

or each of the following molecules, construct the MOS from the 2p, atomic orbitals perpendicular to the plane of the carbon atoms. (a) Cyclobutadiene HC=CH НС—СН HC=CH НС —СH (b) Allyl radical H H H H C=C •C-C, H C-H H C-H H H Indicate which, if any, of these orbitals have identical ener- gies from symmetry considerations. Show the number of electrons occupying each w MO in the ground state, and indicate whether either or both of the molecules are para- magnetic. Assume that the C atoms in the allyl radical are all sp? hybridized. Activate io to S

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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For each of the following molecules, construct the MOs from the 2pz atomic orbitals perpendicular to the plane of the carbon atoms. (a) Cyclobutadiene HC (b) Allyl radical Indicate which, if any, of these orbitals have identical energies from symmetry considerations. Show the number of electrons occupying each MO in the ground state, and indicate whether either or both of the molecules are paramagnetic. Assume that the C atoms in the allyl radical are all sp2 hybridized.
The ground-state electron configuration of the H; molec- ular ion is (og15)'. (a) A molecule of H absorbs a photon, promoting the electron to the os molecular orbital. Predict what happens to the molecule. (b) Another molecule of H absorbs even more energy promoting the electron to the o,2, molecular orbital. Predict what happens to this molecule.
For monocyclic conjugated polyenes (such as cyclobutadiene and benzene) with each of N carbon atoms contributing an electron in a 2p orbital, Huckel theory gives the fol lowing expression for the energies Ek of the resulting π molecular orbitals Calculate the energies of the 1t molecular orbitals of benzene and cyclooctatetraene. Comment on the presenceor absence of degenerate energy levels. (b) Ca lcu late and compare the delocalization energies of benzene and hexatriene using the expression from the preceding problem. What do you conclude from your results? (c) Calculate and compare the delocalization energies of cyclooctatetraeneand (linear) octatetraene. Are your conclusions for th is pair of molecules the same as for the pair of molecules investigated in part (b)?
Explain why 1og is the ground state for Hi. By combining your answer with the answer to Problem 5, what conclu- sions can you draw about the molecular orbital descrip- tion of the bond in H¿?
β-Carotene is the compound responsiblefor the orange color of carrots and is theprecursor to vitamin A. Judging from theLewis structure shown here, how many πbonds does β-carotene have?
Ketene, CH2=C=O, is an unusual organic molecule that has a singlecarbon atom doubly bonded to two different atoms. Determine thehybridization of both C atoms and the O in ketene. Then, draw a diagramshowing what orbitals are used to form each bond.
6) Given below are the molecule BH3, its character table, and its molecular orbital diagram. By convention, the z-axis lies along the principal rotation axis: (a) What Mulliken symbol represents the symmetry of the MOs I-V? (b) Which of the given atomic orbitals on boron would match the MOS I-V? (c) Depict the in-phase (bonding) and out-of-phase (anti-bonding) of these MOS. B 2p orbitals B 2s orbitals II H 2s orbitals D₂ A, A₂' A," E" 1 1 2 1 1 2 2C, 3C₂ 0₂ 25, 1 1 1 1 1 -1 1 -1 1 -1 0 1 2 -1 -1 30, 1 1 -1 R₂ -1 0 -1 -1 -1 1 1 0 (x, y) (R., R.) x+y²,2² (x²-y, xy) (xz, yz)
TOPIC: QUANTUM, ATOMIC AND MOLECULAR PHYSICIS (a) Using Hückel's method, describe the energy of the molecular orbitals T of cyclobutadiene C4H4, which is a flat molecule made up of a square ring of carbons, as shown in the figure; (b) Do the same for 1,3-butadiene C4H6, which is an elongated planar molecule, as shown in the figure. (c) In both cases, draw an energy diagram indicating the filling of the orbitals and identifying the HOMO and the LUMO. Sketch by hand schematically (using two colors to distinguish the lobes from the 2pz orbitals) the result obtained for the orbitals, identifying them with the corresponding energy. If possible, you can use the Orbital Viewer program to plot the orbitals.
The molecule shown below is called furan. It is represented intypical shorthand way for organic molecules, with hydrogenatoms not shown, and each of the 4 vertices representing acarbon atom.(a) What is the molecular formula for furan? (b) How manyvalence electrons are there in the molecule? (c) What isthe hybridization at each of the carbon atoms? (d) Howmany electrons are in the p system of the molecule? (e) TheC¬C¬C bond angles in furan are much smaller than thosein benzene. The likely reason is which of the following: (i) Thehybridization of the carbon atoms in furan is different fromthat in benzene, (ii) Furan does not have another resonancestructure equivalent to the one above, or (iii) The atoms in afive-membered ring are forced to adopt smaller angles than ina six-membered ring.
4. (a) Use the simple one-electron molecular orbital method, including overlap, to calculate the energies of the molecular orbitals of the hydrogen molecule (H₂) in terms of a, ß and S? (b) Calculate & given that a = -13.6 eV, that S = 0.6, and that the lowest UV absorption energy is 12 eV. (c) Determine the ionisation energy of the bonding molecular orbital in H₂ ? [6 marks]
For each of these contour representations of molecular orbitals,identify (a) the atomic orbitals (s or p) used to constructthe MO (b) the type of MO (s or p), (c) whether the MO isbonding or antibonding, and (d) the locations of nodalplanes.
Construct the molecular-orbital energy level diagramsof (a) ethene and (b) ethyne on the basis that the moleculesare formed from the appropriately hybridized CH2 or CH fragments