Thursday, July 29, 2010

Amide hydrolysis, revisited

Fig4-29
Figure 4.29. Sketch of hydrolysis reaction of several amides together with their experimentally observed half-lives. The free energies of activation are computed via Equations (4.30) and (4.31). (Adapted from N. M. Hernandes et al 2008. Journal of Organic Chemistry 73: 6413–6416.)
From Molecular Modeling Basics CRC Press, 2010
January, 2011 update: The figure in the book is missing an N atom in structures 4 and 5

Figure 4.30a and b shows the TS geometries for the hydrolysis of 1 and 3 computed at the PM3 level of theory, together with the normal modes associated with the imaginary frequencies (2336i and 239i cm–1, respectively).




Figure 4.30a. PM3 geometries of the TSs for hydrolysis of compound 1 (Figure 4.29), and the normal modes associated with the imaginary frequencies.
Click on the picture for an interactive version.
From Molecular Modeling Basics CRC Press, 2010





Figure 4.30b. PM3 geometries of the TSs for hydrolysis of compound 3 (Figure 4.29), and the normal modes associated with the imaginary frequencies.
Click on the picture for an interactive version.
From Molecular Modeling Basics CRC Press, 2010

As I show in the book, the predicted activation free energy of 1 is 4.2 kcal/mol higher than the activation free energy for the hydrolysis of 3. The source of the difference is roughly half electronic (1.9 kcal/mol) and half thermodynamic (2.3 kcal/mol). The explanation for the latter is the loss of translational entropy associated with hydrolysis of 1, but it is not obvious why the electronic activation energy should be lower.

For example, one might imagine that it would be energetically unfavorable to fold the chain of 3 into a ring due to some kind of strain when forming the transition state. This can be tested by studying the hydrolysis of 2 (Figure 4.29), which should have roughly the same amount of ring-strain associated with the reaction.

Indeed, the free energy of activation for hydrolysis of 2 is considerably higher than that for 3, and due entirely to an increased electronic activation energy.  This points toward the importance of the amine group in the middle of the chain in lowering the electronic barrier for 3-hydrolysis, presumably by stabilizing the partially positive –NH3+-like portion of the TS (Figure 4.31).




Figure 4.31. 0.002 au isodensity surface with superimposed molecular electrostatic potential of the TS for hydrolysis of 3. The maximum potential value is 0.05 au, and the level of theory is M06/6-31G(d). The orientation is the same as Figure 4.30.
Click on the picture for an interactive version.
From Molecular Modeling Basics CRC Press, 2010

It might be tempting to ascribe the more open TS structure in 3 compared to 1 (Figure 4.30) to ring-strain, but the TS for “methanolysis” of 1 is equally open (Figure 4.32). This is presumably due to steric hindrance of the methanol methyl group and the carbonyl oxygen.




Figure 4.32. PM3 geometries of the TSs for methanolysis of compound 1 (Figure 4.29), and the normal modes associated with the imaginary frequencies.
Click on the picture for an interactive version.
From Molecular Modeling Basics CRC Press, 2010

I will discuss how to find the TS structure for the hydrolysis of 1 in a future post.  I have already discussed how to find the TS structure for the hydrolysis of 3 here and hereThis post describes how to verify that the TS connects the correct reactants and product, and this post describes the relationship between half lives and activation free energy.

Sunday, July 25, 2010

Melting: a simple model


Figure 4.26. PM3 optimized structure of the V-shaped water timer. Shown also is the normal mode corresponding to the lowest vibrational frequency (36 cm–1).
Click on the picture for an interactive version.
From Molecular Modeling Basics CRC Press, 2010

While the lowest energy conformation of three water molecules is the ring structure (Figure 4.17), there is another minimum (at least on the PM3 potential energy surface - Figure 4.26) that is 7.7 kcal/mol higher in (electronic) energy.

The free energy difference between the cyclic and V-shaped structure is zero at around 480 K. This can be considered a very simple model for melting (i.e., the T at which higher enthalpy conformations are most probable because of entropy). The entropic term has two basic contributions: there are more higher-energy structures (they are more disordered so there are more ways to make them: e.g. there are 3 identical V-shaped structures), which lowers the conformational free energy, and the structures are “floppier” (they have more low-frequency vibrational modes), which lowers the vibrational free energy.



Figure 4.28a. Structure of one of the water clusters found by Maeda and Ohno. The coordinates are taken from their supplementary materials. (From S. Maeda and K. Ohno, 2007. Journal of Physical Chemistry A. 111: 4526–4534.)
Click on the picture for an interactive version.
From Molecular Modeling Basics CRC Press, 2010

Of course, this is a hypothetical melting transition because the cyclic “ice” structure already sublimates at 285 K. The main reason for the high melting temperature is the small number of higher-enthalpy conformations, which increases quickly with the number of water molecules. For example, for water octamer [(H2O)8] a study by Maeda and Ohno found 164 different conformations, and only seven of these can be classified as some variant of the lowest-enthalpy cubic conformation (Figure 4.28a), while the rest are more disordered (e.g., Figure 4.28b). The study estimates that the temperature at which the cubic and more disordered structures become equally probable (i.e., the melting temperature) is around 280–320 K, which is significantly closer to the melting temperature of bulk ice of 273 K. The uncertainty in the estimate of Tmelt comes from the difficulty in estimating the effect of BSSE and anharmonic effects.



Figure 4.28b. Structure of one of the water clusters found by Maeda and Ohno. The coordinates are taken from their supplementary materials. (From S. Maeda and K. Ohno, 2007. Journal of Physical Chemistry A. 111: 4526–4534.)*
Click on the picture for an interactive version.
From Molecular Modeling Basics CRC Press, 2010
* The Jmol structure does not correspond exactly to the picture.  When making the figure I forgot to write down which of the 164 structures I used for this figure.  Still, the point is the same.