This problem set may be difficult to finish with the time you have remaining on your Cray accounts. I recommend that you work entirely on one problem before beginning the other (all are worth the same number of points). Once your account is closed, you will not be able to log in to see your files, so copy out the information you need as it becomes available.

A practical reminder: To run a job, you're input file should be called myfile.dat. Simply issue the command qrun myfile.dat and the script will take care of the rest. If you want to look at an output deck while a job is running, you can either VI myfile.out or more myfile.out.

A nomenclature reminder: the notation x/y//w/z means level of theory x using basis set y at a geometry optimized at level of theory w with basis set z. E.g., MP4/6-311G**//HF/6-31G* means the geometry was optimized at the HF/6-31G* level but the energy (and/or other properties) are being calculated at the MP4/6-311G** level.

Some quick notes/reminders with respect to Gaussian94:

1. Always include the keyword: scf=direct.
   

2. Always specify freq=noraman for frequency calculations.
   

3. To find transition states in the absence of a symmetry constraint, use at least the keywords fopt=(ef,ts,z-matrix)

4. You can save a lot of time by using useful information from previous calculations stored in the checkpoint file. Plan your calculations to try to save time.
   
   1. Keywords guess=read and geom=checkpoint get the wave function and the geometry, respectively, from the last completed calculation. So, if you have just done an optimization, and want to follow-up with a frequency calculation, you will certainly want to use these keywords. Note: Frequencies must be calculated using the same level of theory with which the geometry was optimized!
      

   2. If you just optimized a geometry at one level of theory, and want to repeat that optimization at a different level, include readfc in the fopt=() keyword. E.g., fopt=(readfc,z-matrix). This causes the program to read the force constants from the previous calculation, which speeds up the geometry optimization.

The Problems: (note that there is an appendix to simplify the compilation of some answers-report absolute energies in au to 5 decimal places, relative energies in kcal/mol to 1 decimal place, bond lengths in ångstroms to 3 decimal places, and valence and dihedral angles in degrees to 1 decimal place-written comments should still be provided separately)

1. Last problem set, we (painfully) examined the inversion barriers for ammonia and fluoroammonia. What is the inversion barrier for ammonia as calculated at the CCSD(T)/cc-pVTZ//MP2/cc-pVDZ level? Does the inclusion of triple excitations have much effect? Correct the CCSD(T) barrier for zero-point vibrational energy. Correct for thermal vibrational enthalpy. Finally, correct for all free-energy effects. (To do these last items, a frequency calculation will be required for the optimized geometry). Fill this information in Table 1. How does this barrier compare to the estimate from AM1? Without knowledge of the experimental value, what factors remain that might cause any deviation between the calculated value and experiment.

2. FOOF (fluorine peroxide) is an odd molecule, to say the least, but DuPont thinks it is fascinating (oxyTeflon^®?) Using the cc-pVDZ basis set, calculate the structure for FOOF at the RHF, MP2, and BPW91 (a density functional) levels and record your results in Table 2. What level of theory appears to be most accurate compared to experiment? Take the total time for your calculation (printed at the bottom of the output file) and divide by the number of geometry optimization steps to get a rough estimate of the time per step for each level of theory. Report this time, and comment on whether this makes any theory seem more attractive than an analysis based purely on agreement with experimental structure. (If one of your jobs runs out of time (after 6 minutes), note the number of steps so you can keep track before you restart).

3. Find a transition state where the reaction coordinate is not symmetric. That is, a case where one cannot use symmetry to impose a particular constraint on the transition state structure (like ammonia inversion necessarily being planar-an example of an unconstrained case is the tautomerization of ammonia N-oxide to hydroxylamine from last year's Problem Set 3 (also on server Dionysus), which you can not use). Verify your calculation by reporting the imaginary frequency for the transition state structure. Print out a picture (Chem-3D or your favorite drawing program) of the transition state structure and, using the imaginary vector, describe what the imaginary mode looks like (if you want, you can print out pictures of the structure distorted by the displacements listed in the output, or you can just say something like "the hydrogen is moving to eclipse the sulfur while the oxygen-manganese bond lengthens"). Pick any ab initio level of theory you want.

Table 1. Ammonia inversion barrier (absolute energies in au, barrier height in kcal/mol).

NH3 structure	MP2/cc-pVDZ	CCSD(T)/cc-pVTZ//MP2/cc-pVDZ	H0	H298a	G298a
pyramidal
planar
barrier height

^a Note that the default for Gaussian94 is 298 K, so all thermochemical information is provided for this temperature without you needing to specify any additional input.

Table 2. Details of FOOF calculations with cc-pVDZ basis set.

Level	rFO, Å	rOO, Å	Angle FOO, deg	wFOOF, deg	time per geometry step, sec
RHF
MP2
DFT
expt.	1.575	1.217	109.5	87.5

If you'd like to download the Microsoft Word version of this document, click here: ProbSet3.doc