(a) Calculate the energies of the two ? molecular orbitals of ethylene (these are the HOMO and LUMO in the full molecular orbital diagram shown in class). Since each carbon atom contributes one ? electron, two electrons are considered for ethylene in this simple model. What is the total energy then? (b) Calculate the energies of the ? molecular orbitals of benzene and cyclooctatetraene. Remember each atom contributes one ? electron to the simplified Hückel MO system. What is the spin multiplicity of the ground state for each molecule? (c) Calculate and compare the delocalization energies of benzene and hexatriene. The delocalization energy is the difference between the total energy of a molecule and the "supposed" energy if all double bonds are separated into individual ethylene molecules. Between benzene and hexatriene, which has higher delocalization energy? Interpret your result. (d) Calculate and compare the delocalization energies of cyclooctatetraene and octatetraene. Are your conclusions for this pair of molecules the same as for the pair in (c)? Interpret your result.
Added by John M.
Close
Step 1
The energies of these orbitals can be calculated using the Huckel molecular orbital method, which gives the following energies: E(ψ1) = α + β E(ψ2) = α - β Here, α is the energy of an isolated p-orbital, and β is the resonance integral between adjacent Show more…
Show all steps
Your feedback will help us improve your experience
Sri K and 86 other Chemistry 101 educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
(a) Give the secular equations for the coefficients cA and cB in the wavefunction Ψ = cAΦA + cBΦB. Where A and B are the atomic orbital wavefunctions of atom A and atom B respectively. (b) Determine the energies of the bonding and antibonding molecular orbitals from the secular equations in terms of the Coulomb integrals, resonance integral, and overlap integral. (c) What are the energies of the bonding and antibonding molecular orbitals for a homonuclear diatomic molecule? (d) What are the energies of the bonding and antibonding molecular orbitals for a heteronuclear diatomic molecule, in which the difference in the energy of the interacting atomic orbitals is large? Hint: apply the zero overlap approximation. (e) Calculate the energies of the bonding and antibonding molecular orbitals for XeF. The ionization energy of Xe (5p) and F (2p) electrons are 12.1 eV and 17.4 eV, respectively. Use β = -1.5 eV and S = 0.
Sri K.
For monocyclic conjugated polyenes (such as cyclobutadiene and benzene) with N carbon atoms each contributing an electron in a 2p orbital, simple Hückel theory gives the following expression for the energies Ek of the resulting π molecular orbitals: Ek = α + 2β cos(2kπ / N) k = 0, ±1, ±2, ..., +N/2 for even N; k = 0, ±1, ±2, ..., ±(N-1)/2 for odd N. For a linear conjugated polyene with N carbon atoms each contributing an electron in a 2p orbital, Hückel theory gives: Ek = α + 2β cos(kπ / (N+1)) k = 1, 2, ..., N. (a) Calculate the energies of the π molecular orbitals of cyclooctatetraene and benzene. Comment on the presence or absence of degenerate energy levels. (b) The delocalization energy is the difference between the total π-electron binding energy and the binding energy of the corresponding isolated double bonds. In Hückel theory it is given by Edeloc = Eπ - n(α + β), where Eπ is the total π-electron binding energy and n is the total number of π electrons. Calculate and compare the delocalization energies of benzene and hexatriene. What do you conclude about the relative stability of these molecules from your results? (c) Calculate and compare the delocalization energies of cyclooctatetraene and octatetraene. How do your conclusions for this pair of molecules match up with your conclusions for the pair of molecules in part b?
Adi S.
The energy-level diagram in Figure 9.36 shows that the sideways overlap of a pair of $p$ orbitals produces two molecular orbitals, one bonding and one antibonding. In ethylene there is a pair of electrons in the bonding $\pi$ orbital between the two carbons. Absorption of a photon of the appropriate wavelength can result in promotion of one of the bonding electrons from the $\pi_{2 p}$ to the $\pi_{2 p}^{*}$ molecular orbital. (a) What would you expect this electronic transition to do to the carbon-carbon bond order in ethylene? (b) How does this relate to the fact that absorption of a photon of appropriate wavelength can cause ready rotation about the carbon-carbon bond, as described in the "Chemistry and Life" box and shown in Figure $9.30 ?$
Recommended Textbooks
Chemistry: Structure and Properties
Chemistry The Central Science
Chemistry
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD