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- Three of the four molecular orbitals for cyclobutadiene are pictured here. Place them in order of increasing energy. (See Figures 9.13, 9.15, 9.16, and 9.18 and the relation of orbital energy and nodes.)arrow_forwardConsidering only the molecular orbitals formed by combinations of the 2s atomic orbitals, how many molecular orbitals can be formed by 1000 Li atoms? In the lowest energy state, how many of these orbitals will be populated by pairs of electrons and how many will be empty?arrow_forwardSuppose that a molecular orbital has the (unnormalized) form 0.727A + 0.144B. Find a linear combination of the orbitals A and B that is orthogonal to this combination and determine the normalization constants of both combinations using S = 0.117. Show full and complete procedure, indicating where and how you are using the value of Sarrow_forward
- Show the secular determinant with x substitution for the compound. Calculate its Huckel Molecular orbital levels, wave function, as well as the electron density and bond orders of all carbons.arrow_forwardFor 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)?arrow_forwardDraw the π-molecular orbitals for benzene, indicate the nodal planes and designate the proper energy corresponding to these orbitals.arrow_forward
- Calculate the Hückel molecular orbital energies of the planar radical (i.e., one nonpaired electron) CH2CHCH2•.Derivethe molecular wavefunction and sketch the molecular orbitals for the lowest energy state. Hint:LCAO-MO principle, use p"(i=1-3) as atomic orbitals.What is the first/minimal electronic excitation energy? Hint:HOMO to LUMO transition.arrow_forwardProvide a diagram which depicts the relative energies of the pi molecular orbitals of benzene. Show which molecular orbitals are filled in benzene's ground state.arrow_forwardDeduce the parities of the six π-orbitals of benzene.arrow_forward
- How do you write the Huckel determinant for the pi electrons of butadiene? How would you find the energies of the molecular orbitals?arrow_forward4. Sketch the Hückel molecular orbitals for 1,3,5-hexatriene. Be sure to identify the HOMO and LUMO levels, the number of nodes present at each psi level, and the electrons present in each orbital. 1,3,5-hexatrienearrow_forwardSet up the secular determinants for the homologous series consisting of ethene, butadiene, hexatriene, and octatetraene and diagonalize them by using mathematical software. Use your results to show that the π molecular orbitals of linear polyenes obey the following rules: • The π molecular orbital with lowest energy is delocalized over all carbon atoms in the chain. • The number of nodal planes between C2p orbitals increases with the energy of the π molecular orbital.arrow_forward
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