Chemistry 8003: Computational Chemistry

Midterm Answers

1. Listed below are a number of different theoretical models. This problem consists of a series of properties you would like to calculate for various molecular systems. For each property, explain what level or levels of theory might be most useful. If there is more than one possibility for a useful level, describe which, if any, you think would be best and explain your answer. If there are any levels that would clearly not be applicable for calculation of the property (perhaps because they are physically incapable of its calculation), list them and explain why. Finally, it is conceivable you might use multiple methods, and you are free to describe that, together with your rationale, as well. Be concise but detailed in your explanations.

a) Lowest energy structure for cyclodecane (25 points). C10 H20

MM3 is probably the best choice, because the force field was specifically parameterized for problems like hydrocarbon conformational analysis. The OPLS force field might also work, but it was developed for proteins and dynamics simulations, so there is less likelihood that it will be robust. Semiempirical models are not, as a rule, very good for conformational analysis problems like this one. Moreover, there are potentially dozens if not hundreds of possible minima, and it would be computationally intensive to try to find them all at the semiempirical level.

b) UV spectrum (i.e., energies to reach excited electronic states) of iron-oxo porphyrin (25 points).

Fe-oxo por

Only the ZINDO model has parameters that can handle iron reasonably. Moreover, it was specifically developed for spectroscopic studies, so it is ideal for this case. Note that even if iron parameters were available for the force field methods, they would still not be useful for spectroscopy, since they are not quantum mechanical in nature, and know nothing about orbital energies, excited states, etc.

c) Calculation of the gas-phase activation energy for the atmospherically important reaction HO* + HOO* -> H2O + O2 (25 points).

The listed force field methods have not been parameterized for transition states, so they would not be useful in calculating the activation barrier (i.e., the energy of the transition state less the energy of the reactants). Of the semiempirical methods, AM1 and PM3 are more likely to be useful since both handle interatomic (and hence intermolecular) interactions with more flexibility than the older INDO method. Although they are the best choice, however, that is no guarantee that they will give reasonable results. Certainly, it is difficult to predict a priori whether one will be better than the other.

d) "Flexibility" of chymotrypsin in aqueous solution (a typical way to measure this is to examine the mean-square-displacement of the a-carbons in the peptide backbone from their average positions during the course of a dynamics simulation) (25 points).

Since the mean-square-displacement of the a-carbons in the peptide backbone must be measured as a time average, this calculation requires molecular dynamics. Dynamics on large molecules with semiempirical methods is extremely time-consuming (if not outright impossible) and they are not very good for conformational energetics in any case. Of the two force fields, OPLS was specifically designed for proteins and simulations (OPLS stands for Optimized Potentials for Liquid Simulations) so it would definitely be the better choice.

e) Gas-phase dipole moment for the lowest energy structure of the sugar D-lyxose (25 points).

D-lyxose

There are two parts to this problem. First, one must get the lowest energy structure of lyxose, and then one must calculate the dipole moment. For the latter property, semiempirical methods are expected to be better because the dipole moment is an electronic property and force fields don't treat electrons explicitly (although it is possible that you could get lucky from calculating simply the dipole moment derived from all of the force-field partial atomic charges). AM1 and PM3 are better for dipole moments than an INDO method, but it is not clear that either is to be preferred over the other.

As for the structural problem, theinability of AM1 and PM3 to do very well with hydrogen-bonded systems is worrisome. AM1 does marginally better with intramolecular hydrogen bonds based on limited literature data (this was mentioned in class) so of all the semiempirical methods, it might be expected to be the best. However, the force fields might well do better than the quantum mechanical methods for this problem. We discussed the paper by French et al. that showed MM3 to be well suited to sugar conformational analysis.

As a result, the best approach might be to optimized the lowest-energy geometry with MM3 and then do a single-point AM1 or PM3 calculation of the dipole moment at the MM3 geometry.

f) Pictures of the p orbitals for pyridine (25 points). Pyr

Again, the force field methods are useless since they are not quantum mechanical and hence know nothing about molecular orbitals. Of the semiempirical methods, it is a bit difficult to know which to choose. On the one hand, ZINDO is ideal for spectroscopy, and getting the p orbital energy levels right would seem to be correlated with getting their "shapes" right. On the other hand, the pi orbitals are delocalized, and AM1 and PM3 should more accurately describe the Coulomb interactions between electrons in the p orbitals on different atoms, e.g., the <pNpN|pCpC> Coulomb integral. Any reasonably defended answer will be considered.

2. Implicit in the above problem was that none of the properties being calculated was available experimentally. Given that, explain how you might assess the quality of the answers you get from your calculations in different instances. You don't have to do this on a molecule by molecule basis! Rather, I am looking for some general discussion of how you decide on the trustworthiness of your results. A good answer will provide some hypothetical situations for discussion (e.g., I could do x and compare to y and if situation z were to be true I would draw conclusion w, etc.) and/or include specific examples which may or may not be derived from the above problems (50 points).

Although I will be looking for a bit of expansion on these points, the ideal answer is essentially the following:

The only benchmarks available for theoretical results are either trustworthy experimental data or other theoretical results from a higher level that is unimpeachable (the latter is usually hard to get, since if you could do the calculation at the higher level, you wouldn't be wasting your time wondering about your lower level results). But, the premise of the question is that the experimental result is unknown (otherwise, again, why waste your time with the calculation?)

It may be, however, that some other property of the molecule in question is known experimentally. E.g., you might want to calculate the structure of a molecule for which the dipole moment is known. In that case, it is worthwhile to calculate the observed property at the same level of theory and see how you do. One might call this "extrapolation in the property direction".

Alternatively, the property you are interested in might be known experimentally for a closely related molecule/system. In that instance, you would repeat your calculation for the known system and the same level of theory and see how it does. This could be called "extrapolation in the molecular direction".

The degree to which you have to go in either or both directions before you can make contact with experiment (or very-high-level theory) should dictate how comfortable you are with your computational results. There are subtleties in these extrapolations, as well. For instance, are X-ray crystal data always relevant to gas-phase calculations (put more generally, are the experimental conditions relevant to the theoretical ones)? There are no cut and dried analyses.