electron density that would be derived from these wavefunctions. 5. True or false? a. A probability density can never be negative. b. The wavefunction, ࠵? , can never be negative. c. The wavefunction must be a real function. d. ∫ ࠵?࠵?࠵? 1 21 = 1 for a one-particle, one-dimensional system. e. Electrons orbit around the nucleus of an atom. f. Molecular orbitals are often described using atomic orbitals. g. The most stable way for bonding between atoms to occur is through shared electrons. 6. Determine the reaction energies for the following reactions at 298 o C using PM3. First optimize the molecules, then run a vibrational calculation to get the thermodynamic data. Compare these reaction energies from values taken from the NIST Webbook ( )
To get the reaction energies you need to add the energies for all the product molecules minus the energies of the reactant molecules, or Σν i E i , where ν i is the reaction coefficient. E.g. Δ E reaction = E CH4 + 2E Cl2 - E CCl4 + 2E H2 for part a. The reaction energies are taken from the Webmo output. a. CCl 4 + 2H 2 à CH 4 + 2Cl 2 b. CH 4 à CH 3 + ½ H 2 (CH 3 is a doublet or multiplicity 2) 7. Determine how the timing of a calculation changes with the size of the molecule. First draw the following, CH 3 (CH 2 ) n CH 3 , where n varies from 0 to 15. Then run “Comprehensive Cleanup” while in the Builder screen. Run single point energies for these polymers using PM3. After this, perform the same operation using HF for n = 0 to 5. Plot up the timings as a function of polymer size. How do the two methods compare? At what size do you expect the polymer to take unreasonably long to converge?
- Summer '20