Semiempirical calculations

We tried to calculate all the intermediates starting from the S2 structure (see section 2.3). We have frozen the position of the hydrogen atoms which in the QM/MM model were link atoms. The initial coordinates are taken from the QM/MM S2 minimized structure, and there will be a total of 7 atoms with its position fixed all along the mechanism. The convergence criteria used here is the default in Gaussian98. In general, it took hundreds of steps to reach every stationary point. It can be seen in figure 2.12 that the gas phase model is built by a very weak interactions, then its energy surface is very flat and its stationary points are very difficult to optimize.

Some problems encountered:
Our results obtained using gas phase models are difficult to interpret. We obtain different results when fixing the last hydrogen atom or the last heavy atom (to avoid false rotations). Many reactants and products are found, for example, for the (S)-mandelate reactant the residue His297 may interact with OH group of mandelate or with Glu317. These different structures are obtained during the process of minimization without any other external constraint. A small rotation of some hydrocarbon chain can differentiate two found minima. In comparison with the QM/MM model where we found also several structures, here these structures have significant structural differences. Contrary to the expected, we obtained more significantly different structures in this gas phase model than in the QM/MM model.

The reason of the difficulties may be explained as follows: During the racemization step, the acid-base residues Lys166 and His297, at their respective steps, have to move about 2 Å to be closer to the substrate. In the QM/MM model, for the (S)-mandelate and (R)-mandelate structure the non active residue (His297 and Lys166 respectively) is quite far away from the substrate and not strongly coordinated to any other functional group. This weak interaction situation is very hard to reproduce in a gas phase model. Besides, His297 is too rigid and when it must approximate to the pro-R face of the substrate provokes a movement in the backbone of the protein that is impossible to reproduce freezing the position of an atom in the gas phase model. The acetate that models Glu317 has the same behavior. If we leave free Glu317 we obtain false structures. If we fixe one of its hydrogens we get a too rigid residue whose distance from the substrate should change during the different steps of the mechanism.

Despite of these difficulties we have been able to depict an energy profile for the three mechanisms. The indirect mechanisms I and II reported in section 2.3 have been found also here. We started from a (S2)-like structure, that is, His297 is not coordinated to Glu247 because this interaction is not essential for any of the mechanisms in the racemization.

The results are presented in table 2.7(mec I) and 2.8 (mec II). As we said above, some likely artificial structures have been found and these results have been excluded. However, even among the several intermediates shown in the corresponding tables, the connection cannot be ensured.

Table 2.7: Energies (kcal/mol) and distances (Å) corresponding to the Mechanism I of model 1

Structure	$\Delta$ E	N8-H	C1-H	C7-H	N2-H
S	0	1.77	1.16	2.91	1.00
TS1	20.69	1.75	1.16	2.97	1.00
I1	13.59	1.74	1.17	3.01	1.00
TS2	21.40	1.29	1.42	2.87	1.00
I2	21.85	1.08	1.66	2.45	1.00
TS3	23.79	1.02	1.91	1.98	1.02
I3	18.20	1.01	2.82	1.57	1.14
TS4	18.24	1.01	2.87	1.51	1.19
I4	6.22	1.01	3.25	1.17	1.75
TS5	13.36	1.01	3.19	1.16	1.77
R	-5.64	1.01	2.94	1.16	1.79

Table 2.8: Energies (kcal/mol) and distances (Å) corresponding to the Mechanism II of model 1

Structure	$\Delta$ E	N8-H	C1-H	C7-H	N2-H
S	-1.30	1.77	1.16	3.02	1.03
TS1	19.36	1.75	1.16	3.01	1.00
I1	8.53	1.74	1.17	3.14	1.00
TS2	16.75	1.28	1.42	2.88	1.00
I2	14.76	1.08	1.65	2.70	1.00
TS3	18.38	1.02	2.01	1.97	1.02
I3	14.91	1.01	2.82	1.67	1.08
TS4	16.35	1.01	2.98	1.46	1.26
I4	6.69	1.01	3.20	1.17	1.74
TS5	15.19	1.01	3.15	1.16	1.76
R	-4.52	1.01	2.99	1.16	1.79

The results for the mechanism III are shown in table 2.9. The shallow intermediate found in the QM/MM model after the central TS does not exist in gas phase, however a flat region around the same energy profile zone exist. It has been found another shallow intermediate (I1 in table 2.9) but in this case before the TS of configuration inversion. This structure not reported in the previous QM/MM model will be found by means of the TS search algorithm in the QM/MM model in the following chapter.

Table 2.9: Energies (kcal/mol) and distances (Å) corresponding to the Mechanism III of model 1

Structure	$\Delta$ E	N8-H	C1-H	C7-H	N2-H
S	3.01	1.77	1.16	2.85	1.00
TS1	15.17	1.20	1.48	2.53	1.00
I1	15.10	1.14	1.55	2.49	1.00
TS2	18.57	1.04	1.85	1.93	1.03
R	-6.24	1.01	3.00	1.16	1.79

model 2:
The model 2 in figure 2.13 has been used to calculate the mechanism III with semiempirical methods. This smaller model has also been selected to use it in the DFT calculations and it will be used as a quantum part in the QM/MM free energy calculations of chapter 4.

In model 2 the absence of the Mg cation coordinated to the substrate removes some rigidness to the structure. As a consequence, this shortened selection of the active site is even more flexible and both Lys166 and His297 interact in the (S) and (R) structures, respectively, with the carboxylic group of mandelate. Despite of this fact, using PM3 semiempirical Hamiltonian we have located the central transition state corresponding to the carbon inversion of configuration of mechanism III with very similar characteristics in comparison with the model 1. This fact means that the essential chemistry is already contained in this smaller model and it enables us to use it in the forthcoming chapter 4.