Sign inversions in optical rotation as a function of wavelength (ORD spectra)

I have been discussing some historical aspects of the absolute configuration of molecules and how it was connected to their optical rotations. The nomenclature for certain types of molecules such as sugars and less commonly amino acids includes the notation (+) to indicate that the specific optical rotation of the molecule has a positive (rather than a negative) value. What is rarely mentioned is the implicit wavelength at which the rotation is measured. Historically polarimeters operated at the so-called sodium Fraunhofer D-line (588.995nm, hence the name [α]D) and only much more recently at the mercury e-line (546.073nm). The former was used for uncoloured organic molecules, since it was realised early on that colour and optical rotation did not mix well. Here I take a closer look at this aspect by constructing the hypothetical molecule shown below.

The rational behind this choice is that it is (a) based on indigo, which is deep blue in colour and (b) has a bridge of four methylene groups added to make it (axially) asymmetric. The calculated UV/Vis spectrum (ωB97XD/Def2-SVP/SCRF=water, FAIR DOI: 10.14469/hpc/6457) is shown below and you can see the very intense absorption at 535nm (corresponding to a visually blue colour).

The electronic circular dichroism version of this spectrum (simply the difference in absorbance between left and right polarised light instead of absorbance by unpolarised light) is shown below, and this form of chiroptical spectroscopy in large measure replaced the use of specific optical rotations as a means of assigning absolute configurations from the 1960s onwards. Note that the large peak at 535nm is replaced by a much smaller one (the Cotton effect) in the ECD spectrum.

Now I show the original optical rotation as a function of wavelength in 10nm increments. At 589nm ([α]D) it is negative (-1364°), but what on earth is going on at a wavelength of ~535nm, which as you can see above is the value of the first electronic excitation?

An expansion in 0.2nm increments shows more clearly what is happening. The negative value suddently shoots down to -1,200,000°, frankly an absurd value, before discontinuously reversing sign to a positive value of 75,000°. At exactly the value of the electronic absorption it is zero. Most people seeing this happen would conclude that the mathematics derived from the solutions of the quantum mechanical equations is resulting in an unphysical discontinuity. It is in fact the result of the behaviour of the electric and magnetic dipole moment vectors, and it CAN be seen experimentally, albeit never in quite such extreme form![1] The sign of the optical rotation CAN invert, but in this very strange manner whereby if it starts as negative, it first becomes infinitely negative before passing through zero and becoming infinitely positive and finally settling down to a normal positive value. The reason by the way why the “blip” in the ORD spectrum above is +ve, but -ve in the expansion below is “digital resolution”, with the top trace having too coarse a resolution to capture the detail. Now the reason why optical rotation measurement at 589nm becomes clear; it avoids any inversions caused by this effect for the majority of less-coloured molecules. However, if you do have a molecule that were to absorb at 589nm itself, the sodium D-line is the last wavelength you would want to use to measure its optical rotation!

So the notation (+) or (-) used to describe the sign of the specific rotation of a chiral molecule might give the misleading impression that it is a characteristic of the molecule at all wavelengths used to measure it. The rotation can change sign an impressive number of times as the wavelength changes! Does anyone know of any coloured pharmaceutical drugs that are available as pure enantiomers?  It would be fun to repeat the above on such a molecule.


  1. M.S. Andrade, V.S. Silva, A.M. Lourenço, A.M. Lobo, and H.S. Rzepa, "Chiroptical Properties of Streptorubin B: The Synergy Between Theory and Experiment", Chirality, vol. 27, pp. 745-751, 2015.

2 Responses to “
Sign inversions in optical rotation as a function of wavelength (ORD spectra)

  1. Bob McMeeking says:

    I have (for a number of reasons) been thinking about carotinoids. They may not have proven use as drugs, but have been certainly advocated as dietary supplements, etc. Beta-carotene is itself non-chiral, but the likes of Astaxathin and Zeaxathin can be, and they have been well studied. Have you done any ORD calculations on these systems?

    The world could be your lobster!

  2. Henry Rzepa says:

    Greetings Bob,

    What would the point of interest be about Astaxathin or Zeaxathin? Is their absolute configuration uncertain? Has their ORD been measured, etc?

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