Things to remember: To run an AMSOL job you will need to have an input file named myfile.dat (where myfile is whatever you want, but .dat is critical). Remember, to create this you need to use the vi editor. You can either create a file directly while in vi, or go into input mode and paste something from the Mac. Once your input file is complete, type amsoli myfile (don't include the .dat suffix) and it will be submitted to run interactively. When the prompt returns, your run is complete (although that doesn't necessarily mean it was successful!) If a job seems to be running a long time, you probably made some sort of mistake (a very bad geometry, for instance), and you should ^C to interrupt the process and look at whatever output file may have been created to see what you did wrong. If everything worked well, you will have a myfile.out and myfile.arc file with the results of the run found therein (the .arc file is very condensed compared to the .out file).

You can look at the output files by using more myfile.out, in which case it will scroll one page at a time, or by using vi, in which case you can use all of the editor commands to move around (be careful not to change the file, though-if you accidentally delete or change something, you can leave the file unaffected by entering :q! when in command mode).

The Problems (do any two of three):

1. Jorgensen et al. reported in JACS 120 (1998) 7637 the synthesis of a tertiary silicenium ion in solution. This assignment is almost certainly wrong (even JACS referees aren't perfect!)-silicenium ions are terrifically unstable compared to carbonium ions. Indeed, the only unambiguously established silicenium ion, tris-mesitylsilicenium (made by Lambert et al.), owes its stability primarily to steric crowding about silicon, not aryl stabilization; triphenylsilicenium cannot be formed in solution. This is in marked contrast to triphenylcarbenium, which is rock stable, and begs the question of: Why doesn't aryl substitution stabilize a silicenium ion like it does a carbenium ion?

To answer this question more fully, let's look at the MOs for phenyl carbonium (PhCH2+) and phenylsilicenium (PhSiH2+). Optimize the structures of these two cations at the AM1 level. To get the MO's you will need to use the keyword VECTORS in your input decks. This causes the program to print out the coefficients for each MO near the end of the file. In the NDDO approximation, recall that the sum of the squares of all coefficients of a MO is 1, so the square of the coefficient tells you the percentage contribution of each AO basis function to a given MO. Sketch the p MO's (how many are there?) noting the percentage contribution of each AO to the MO. To sketch a molecular orbital, you need to adopt a convention for how you shade the orbitals for positive vs. negative coefficients (consistency is all that matters), and you need to make sure that you have the cartesian coordinates for the molecule so you know how the orbitals relate to the atomic positions, and you need to scale your various atomic orbitals according to the MO coefficients, i.e., a big coefficient means lots of that atomic orbital, a small coefficient means just a little bit of that atomic orbital, and finally, of course, you need to know which atom is which in your input deck! [Modern programs will do all of this for you with glitzy graphics, but doing it by hand once or twice is good for the soul and provides more insight into what's going on.] Label your MO's with the calculated MO energy. If any of these p MOs correspond to the HOMO or the LUMO, so label them. Notice anything you think strange about the LUMO energies?

Also report the partial atomic charges on the carbonium carbon and the silicenium silicon. With all your analysis in hand, why is an aryl silicenium ion so much less stable than its analogous carbonium ion?
MO pictures and energies (in eV) and AO contributions can be found on the next page. There are 7 p­type MO's, although number 4 is formally non-bonding. The HOMO and LUMO are 3 and 4, respectively. The LUMO has a negative energy, which is mildly unusual for a neutral (implies that adding an electron would be a favorable process-typical neutrals do not have negative energies for electron affinities) but perfectly reasonable for a cation. Indeed, all of the p-type orbitals have negative energies (eigenvalues) reflecting how much nature hates a charge in the gas phase.

In a nutshell, these two systems differ so significantly because a silicon 3p orbital fails to mix as effectively as a carbon 2p orbital with an attached benzene p system (which is itself, of course, also formed from carbon 2p orbitals). Thus, 76% of the non-bonding LUMO in phenylsilicenium is the silicon p, but only 44% of the same orbital in phenylcarbenium is the carbon p. In other words, charge is more delocalized in the acceptor LUMO. Notice also that since we have all the p orbitals here, the sum of any one AO's contributions to all the p orbitals must be 1. Thus, we can ask how many electrons are on the cationic atom by considering how much its p AO contributes to filled orbitals compared to empty. With carbon, the ratio is 27% filled to 73% empty. With silicon, it is only 15% filled to 85% empty-again, one expects more positive charge to reside on silicon. The Mulliken charges confirm this analysis: charge is 0.13 on carbon but a whopping 1.38 on silicon! (The seemingly much larger difference in charge than in total number of p electrons reflects the importance of s orbitals in the charge analysis.) Concentrated charge causes enormous instability in chemical systems.

Note the interesting inversion in relative energies for p-type orbitals 5 and 6 depending on the nature of the cationic atom. Remember that the two sets of orbital energies are not really on the same scale, since differences in the relative electronegativities of carbon and silicon will be reflected in the absolute energies for adding electrons to the system. Since carbon is more electronegative than silicon, its orbitals are lower in energy than corresponding ones in the other system.

[Some of you, exercising the powerful skepticism that characterizes a scientist, may be wondering how the above problem can prove that Jorgensen and co-workers are wrong. Of course it doesn't-it just suggests why it's so hard to get a stable silicenium ion. We'll defer more convincing proof until we can compute NMR chemical shifts ab initio (next problem set).]

2. Let's return to one of the molecules found in Problem Set 1. For the case of 2-methoxy-1,3-tetrahydropyran, MMX gave a rotational potential consistent with a large anomeric effect. The anomeric effect is a stereoelectronic effect, i.e., it derives from orbital-orbital interactions. Repeat your calculations for this torsional potential at the PM3 level.

AMSOL has a way to simplify the calculation of this potential. Instead of flagging the dihedral angle with a "1" (meaning optimize) flag it with a "-1". A -1 flag means to hold that degree of freedom fixed at whatever the value is in the Z-matrix, optimize everything else, and then repeat that process for every value found on the line(s) following the first blank line after the Z-matrix. All results are provided in a single output file For instance:

AM1

phosphinous acid, rotation coordinate for P-O bond (gas phase)

O

P 1.5 1

H 1.3 1 115. 1

H 1.3 1 115. 1 120. 1 2 1 3

H 1. 1 110. 1 0. -1 3 1 2

30. 60. 90. 120. 150. 180.

would calculate the rotational potential for phosphinous acid (H2POH) by 30 degree intervals starting from zero.

Compare the PM3 potential to the MMX potential. What, if any, are the differences? If there are important differences, what could you do to establish which level of theory (if either) is the more correct?

That comparison is shown graphically below using arbitrary zeroes of energy for the different levels; squares are MMX results, circles are PM3 results. Notice the enormous qualitative difference! Where PM3 says there is a global minimum is roughly where MMX puts the highest barrier on the torsional potential. Secondary minima are also significantly shifted in energy. Yuck.

As to what one might do to try and decide which, if either, is correct, there are any number of possibilities, a few of which are listed below, in rough order of preference.

1) Try to find some reasonably analogous system (dimethoxymethane?) for which experimental data on the torsional potential are available and benchmark both levels of theory against those data.

2) Move on to a higher level of theory to attempt to converge the quantum mechanical results. We'll do this for Problem Set 3 and see if we can come to any conclusions.

3) Try AM1. If AM1 and PM3 disagree significantly, there is more reason to doubt semiempirical theory. Similarly, try a few different force fields. Is there a consensus amongst various lower level theories?

4) Consider the parameterization sets. How carefully were torsions like that found in our test system examined, if at all, as part of the parameterization process?

5) What does the literature have to say, if anything, about these kinds of modeling efforts? Have analogous systems been examined?

6) Trust in your hard-won intuition.

3. Design a problem of your own that uses semiempirical MO theory to illustrate some chemically interesting concept. Write down the problem, and then provide the answer. Note that you do not need to pick something that semiempirical theory performs well for! However, if you create a problem where NDDO theory clearly gives the wrong prediction, provide some discussion in your answer of why the level fails to be accurate. To get more of a feel for typical problems, feel free to drop by the website and look at second problem sets from previous years. Grading will be based on quality of the problem and originality.
Obviously, many answers are possible.