Doing and Interpreting Semi-Empirical Calculations

Select two of these exercises.

1. Create acetonitrile (CH₃CN) in the SPARTAN builder and set up an AM1 or PM3 semi-empirical calculation. Include printing to the output file of the molecular orbitals, the frequencies, and the Mulliken populations. Add any surfaces you would like to look at, such as the electron density and the HOMO, and optimize the structure. Examine the output file, the vibrational animations, and the orbital pictures and answer the following questions:
   1. What are the energies of the HOMO and the LUMO ?

   2. In which MOs are the two C-N p bonds mostly localized ?

   3. Which MO and which AOs appear to be the locus of the unshared pair on nitrogen ?

   4. What is the calculated stretching frequency of the CN triple bond ?

   5. What is the calculated enthalpy of formation ?

2. We commented that although semi-empirical calculations would not accurately reproduce transition energies for individual UV absorptions, they do better at trends. Examine the series of compounds shown below. The numbers given are the wavelengths of the p to p* transition, and thus should be related to the gap between HOMO and LUMO. How well do AM1 or PM3 (don't do both) calculations reproduce this trend ? (Part of your problem here is to choose a way of defining "how well" in a quantitative manner.) E-mail me a short report.

   

3. Spartan can compute continuum solvation energies using the SM5.4 solvation model. (When an ab initio calculation is selected, Spartan also runs a semi-empirical one to obtain the solvation energy.) Select a simple amino acid. Create both the neutral and the zwitter ion (deprotonate the carboxyl; protonate the amine). Optimize each geometry using the PM3 Hamiltonian. When you set up the calculations, select the "E. Solvation" button.
   • Obviously the zwitterion should have the greater solvation energy. Does it?

   • How do the HOMO and LUMO energies change from the neutral to the zwitterion?

   • Is there any significant difference in the optimized geometry between the two structures?

4. The PM3 module in Spartan has been parameterized for most transition metals. Use the Expert builder to build cis- and trans- Bis-(ethylene)-dichloropalladium in a square planar geometry. You will need to adjust the ethylenes so that they are perpendicular to the plane of the palladium valences. Optimize each isomer.
   • Which is more stable? Why?

   • Optimize ethylene itself with the PM3 module. Compare the gemometries and electrostatic potentials of the ethylenes in the complexes and ethylene itself. What differences do you see? If you've had the organometallics course, rationalixe the differences.