Background:
Summary of Methods Used
Simple Example:
Theory
The Vibrations
Research Topics:
Fatty Acid Methyl Esters (FAMEs)
School of Chemistry
The Queen's University of Belfast
Fatty Acid Methyl Esters (FAMEs)
The next few pages will aim to give an introduction into my research using DFT methods to study FAMEs.
Saturated fatty acid methyl esters (FAMEs) have the general molecular formula CH3(CH2)nCOOCH3 (see Figure below for structure and numbering) and are commonly used as model compounds for the much more complex triglycerides that are found in edible fats and oils. We are interested in using vibrational spectroscopy for the non-destructive characterisation of foodstuffs, studies that are aimed, ultimately, at providing quality indicators for both raw and processed foodstuffs. To this end, we have embarked on detailed experimental and computational studies of extended series of model compounds, such as the fatty acid methyl esters discussed here, to determine the extent to which we can characterise complex foodstuffs on the basis of rich but highly complex and structured Raman spectra.
This simple picture shows the molecule C5H10O2. However, we have found that the nomenclature of these FAMEs can become confusing, often different conformers are referred to as cis or trans and there are instances of these terms being used to label exactly opposite conformers when used by different researchers. The terms 'syn and anti', 'staggered and eclipsed', 's-trans and s-cis' and 'E and Z' are also widely used in the literature, in many cases without any clear definition of what is meant. So we use a simple system of describing the conformations which uses the torsion angles of the molecules' backbones, so that we can define the conformation of the FAME shown above by three torsions, T0, T1 and T2. Of course, this is not a complete description because, in addition to the Tn torsions of the backbone, there can also be rotations of the methyl groups (i.e. C-H torsions with respect to the backbone), but we have found that only a few calculations are needed to establish a pattern which allows the lowest energy methyl C-H torsion angles to be chosen by inspection.
All the details concerning the procedures that I followed to do the DFT calculations and the surprising complexity of this apparently straightforward molecule can be found in my paper which is available from J. Mol. Struct. THEOCHEM.
Briefly; I did calculations on a variety of conformers of the homologous series of FAMEs, starting with methyl acetate, through to C21H42O2.
Among other things, I was able to generate a spectrum from the calculations of the C5H10O2 FAME that was in excellent agreement with the experimentally observed Raman spectrum. This used the Sadlej basis set optimised for electric properties.8 Clicking on the thumbnail below will link you to a bigger picture of these spectra, the larger picture is 56kb in size.
There appears to be a systematic decrease in the intensities of the bands in the observed spectra versus the calculated values with increasing cm-1 but this disagreement is due to the fall off in the spectral response of the detector at higher cm-1 rather than a systematic error in the calculations. In addition to giving accurate relative band intensities, the calculations with the Sadlej pVTZ basis set also yield, without scaling, band positions that are marginally better than the scaled 6-31G(d) values obtained in the conventional way (RSD= 9.1 vs 12.6 cm-1).
So, what we found was that conventional B3LPY DFT methods with the 6-31G(d) basis set are well established in predicting the geometries, physical properties and vibrational spectra of small organic molecules.
In the compounds we have studied so far, the DFT methods show that the lowest energy conformer has a simple (all-trans) structure but there are other conformers, with different torsions about the backbone, which lie reasonably close in energy to the global minimum. The possibility of higher-lying conformers contributing to the Raman spectra would be expected to complicate assignment of observed Raman bands.
To resolve this problem, we have used the DFT methods to predict the vibrational spectra of the various conformers as well as their energies. Although an excellent fit between calculated and experimental frequencies (RSD= 12.6 cm-1) can be obtained by scaling predictions from the economical 6-31G(d) basis set, the agreement between predicted and observed intensities is much less satisfactory. This would not normally be a problem because even if the predicted intensities are not accurate, they are good enough to relate predicted to observed bands.
However, in some of these FAMEs it was necessary to include contributions from more than one conformer to account for 'extra' bands observed in the experimental Raman spectra before a complete set of vibrational assignments could be made. This leads to some degree of uncertainty because the relative contributions which each of the conformers make to the final simulated spectrum is set by relative band intensities that are not well predicted in the calculations.
The easiest way to resolve this uncertainty, and therefore to confirm the validity of the approach followed with the 6-31G(d) basis set, was to find a basis set that gave accurate Raman intensities. The Sadlej pVTZ basis set proved to be ideal, giving intensities very close to their observed values and simulated spectra (summed from two different conformers) that were in quantitative agreement with experiment.
Furthermore, because this basis set also gave acceptably accurate vibrational frequencies (RSD= 9.1 cm-1) after scaling only the carbonyl frequency, the results could be used to test the validity of the scaling factors used for the 6-31G(d) calculations. We found that the unscaled Sadlej pVTZ, and the scaled 6-31G(d) calculations did indeed give the same vibrational mode assignments for all bands in the experimental data.
The work completed to date provides the foundation for calculations on longer-chain FAMEs (which are closer to those found as triglycerides in edible fats and oils) because it shows that scaled 6-31G(d) calculations give equally accurate frequency predictions, and the same vibrational mode assignments, as the very CPU-expensive Sadlej pVTZ basis set calculations which would be prohibitively time-consuming for FAMEs with chains greater than 14 carbon atoms.
On the next page I show some of the vibrational motions of these molecules. I've picked out the ones that either look really good or are very helpful in understanding the spectroscopy of these FAMEs
