My momentum of describing early attempts to use optical rotation to correlate absolute configuration of small molecules such as glyceraldehyde and lactic acid with their optical rotations has carried me to L-Malic acid (below labelled as (S)-Malic acid).
The measured optical rotatory dispersion curve at low wavelengths is shown below (dashed line for Malic acid, solid line for Lactic acid). A sign inversion occurs <220nm to negative rotations. [1]‡ I decided to explore how modern theory of both conformational analysis and chiroptical calculation performs for this small molecule at these wavelengths.
You need good tools to investigate the conformational space of even a small molecule such as malic acid. I used Gaussview 6 with the GMMX plugin.† This identifies rotatable bonds and uses molecular mechanics to optimise all unique conformations which are located up to 3.5 kcal/mol above the lowest energy one. Using this procedure for malic acid produces 17 conformations! The geometry of each was then re-optimised at the following level: B3LYP+GD3BJ dispersion correction, Def2-TZVPP basis and using a superfinegrid pruned to 175,974 for first-row atoms (the default grid is 99,590 in the Gaussian 16 program) to avoid any significant incurrence of rotational dependence of the computed energy. Extra tight convergence criteria for the SCF and 2-electron integrals (12 and 14 respectively in the Gaussian definition) were also selected. A solvent correction for ethanol was also included and the free energy calculated.♥ Once the geometries were obtained, the optical rotations were calculated using ωB97XF/Def2-TZVPP/SCRF=ethanol (DOI: 110.14469/hpc/6510) and the results inserted into a spreadsheet (which is available for you to inspect for yourself).
To summarise.
Wavelength | ~Observed rotation, ° | Calculated rotation, ° |
---|---|---|
260 | +250 | +194 |
230 | +1500 | +318 |
220 | +900 | +385 |
215 | +400 | +631 |
205 | -2660 | -1778 |
Given all these errors, and the observation that I have not plotted a complete range of wavelengths in order to determine the maximum and minimum values in the ORD curve, the final agreement with experiment is actually not that bad! Perhaps however it is easy to see why ORD is rarely used nowadays to assign absolute configuration using computations, given this combination of interacting errors. Perhaps the greatest value in performing these calculations is actually to give some sense of a reality check on the computed conformational analysis itself, with its calculated Boltzmann populations!
‡This also confirms that the rotation of L-Lactic acid is positive (+) for wavelengths down to 220nm, below which the sign also inverts to a negative rotation. Kuhn’s assertion of absolute configuration of lactic acid is nonetheless proven correct, although he only had access to the much less useful value of the rotation at 589nm.[2] †The free Avogadro program can also perform this task.♥The calculations also include the VCD or vibrational circular dichroism responses for each conformation. I have thus far avoided the task of applying the Boltzmann populations to the VCD spectra for 1cm-1 increments to reveal the expected spectrum.
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