Summary of the DFT calculations
The work has consisted of mainly two parts:
i)
ii)
Optimization of the structures; reactants, intermediate and products.
Search for the TS for the different reaction path.
The calculations have been performed with the ADF package and with the B3LYP [1] and
SSB-D [2] functionals. The default functional, VWN [3], was used for optimization purposes.
The basis set is DZP for all calculations.
The work has been conducted with methyl groups on both the amine and in the alfa position
of the hydroxyl acid, unless otherwise noted.
i)
Optimization of the structures:
The work started with the use of a solvent model, to account for the nature of the experiments,
and also for the treatment of the ionic nature of the starting material. This was done with the
COSMO model implemented in the ADF program package and with toluene as the specific
solvent. Toluene was used because it is available as a subkey within COSMO and because of
the similarities with xylene which are used in in experiments.
With COSMO, problems with imaginary frequencies for structures that were expected to be in
an energy minimum occurred. At the same time it was after discussion concluded that the salt
form of the reactants is not part of the reaction, and that the real starting structure is the nonionic form with protonated acid group. Because of this, solvation was set aside, and in the
following all calculation are done in the gas phase.
Geometry optimization in gas phase was done for the various structures, and frequencies were
calculated with numerical methods. The results are summarized in table 1 with energies for
the different structures.
Table 1: Energies for the different structures.
B3LYP
Energy
(a.u)
Energy
(kcal/mol)
Relative MetaGGA
energy SSB-D
Start
-4,44584769
-2789,81
0,7 Start
Ketene
-4,39017583
-2754,88
35,63 Ketene
Enolate
-4,36907069
-2741,63
48,88 Enolate
Product (S) -4,44670798
-2790,35
Product (R) -4,44695613
-2790,51
Energy (a.u)
Energy
(kcal/mol)
Relative
energy
-3,85792056
-2420,88
48,95
0,16 Product (S)
-3,93475808
-2469,1
0,73
0 Product (R)
-3,93592001
-2469,83
0
Further on, optimization were also done on tartaric acid and on the ketene and enolate of
tartaric acid. This was done to get a picture of the relative energies for the “real” structures.
The results are summarized in table 2 with energies and the name of the belonging .xyz and
.inp files.
Table 2: Energies and filenames for the different structures based on tartaric acid, with the
VWN functional.
VWN
Energy (a.u)
Energy (kcal/mol)
Relative energy
Start
-5,25176696
-3295,53
19,18
Startb
-5,2416461
-3289,18
25,53
Ketene
-5,19635292
-3260,76
53,95
Enolate
-5,21346876
-3271,5
43,21
Product
-5,28232618
-3314,71
0
It is important to note that only relative energies are relevant.
For every structure in table 1 and 2, the IR spectra were calculated, and the structures had no
imaginary frequencies. It can therefore be concluded that these structures are in an energy
minimum.
When the geometry of the ketene was optimized, it was observed addition of the amine to the
ketene. This structure can look like the expected TS, and in addition, it showed one imaginary
frequency in a frequency run. This happened for both the tartaric acid and the simplified
structure.
For the total structure, ther following was observed:
Length of amide bond: 1,5737 Å in the observed structure and 1,3467 Å in the product.
The optimized structure for the enolate showed the preference for the anime hydrogen bonded
to the two hydroxy group. The amine ended up on the same side as the proton transfer
happened, as can be observed in figure 1 and enol.xyz. This may facilitate a fast transfer of
the proton, and therefore no racemization can occur.
Figure 1; Optimized structure of the enolate.
ii)
Climbing Image Nudged Elastic Band (CINEB)
For location of the TS for the different pathways the CINEB method in the ADF package was
used.
It is assumed that the direct addition and the last step in the enolate mechanism is the same.
This leads to four different steps that need to be evaluated.
i)
Direct addition
ii)
Enolate formation
enolform.inp
iii)
Ketene formation
cinebc,6,78.xyz; 1,8827 Å (Not optimized)
iv)
Addition to ketene
In conclusion, the CINEB method gave some structures that could resemble TS, but it never
converged. If it is to be used, it must be worked out more properly.
Summary
The relative energies for the simplified structures show that the ketene is lower in energy than
the enolate. Partly, this can be indicative for that the ketene pathway is more favorable for
explaining the racemization.
More important is the optimized structure of the enolate that shows that the amine is
positioned so that the proton will go back to the same side as it came off. This will produce
the same stereo chemistry.
The amine shows an tendency in geometry optimizations to attack the ketene, leading to an
product/TS like structure. That can mean that the ketene and the product/TS is relatively close
in energy.
References:
[1]: P.J. Stephens, F.J. Devlin, C.F. Chabalowski and M.J. Frisch, Ab Initio Calculation of
Vibrational Absorption and Circular Dichroism Spectra Using Density Functional Force
Fields. Journal of Physical Chemistry 98, 11623 (1994)
[2] M. Swart, M. Solà and F.M. Bickelhaupt, A new all-round DFT functional based on spin
states and SN2 barriers, Journal of Chemical Physics 131, 094103 (2009)
[3] S.H. Vosko, L. Wilk and M. Nusair, Accurate spin-dependent electron liquid correlation
energies for local spin density calculations: a critical analysis. Canadian Journal of Physics
58 (8), 1200 (1980)