Chiral molecules can rotate the plane of polarised light with which they interact. Theoretical methods based on quantum mechanics can be used to predict the rotation angle, based on the atomic configuration of the molecule. For complex molecules, simplified representations of the molecular structure are frequently found to provide accurate accounts of the physics of light rotation. Professor Huajie Zhu at Hebei University of Science and Technology in China has developed a matrix model and found the rules of the various conformers of optical rotation in complex chiral molecules, shedding light on this unexpected result.
The term chirality is used in chemistry to refer to molecules whose atomic structure prevents them from being superposed on their mirror image by translation or rotation. Chiral molecules therefore exist in pairs of mirror images, called enantiomers. Having the same chemical composition and distribution of internal chemical groups, the two enantiomers of the same molecule exhibit the exact same chemical reactivity, except when they interact with other chiral molecules. Intriguingly, most biological molecules involved in life processes, including amino acids in proteins, sugars, and nucleic acids in DNA, are chiral species, which can interact in substantially different ways with metabolites. For instance, the activity of chiral drugs depends strongly on their molecular configuration: only one of the enantiomers can show therapeutic effects, while its mirror image can turn out to be completely unreactive in biological processes.
Optical rotation
Chiral molecules exhibit a characteristic behaviour when they interact with polarised light. Light, which is a form of electromagnetic radiation, propagates in a direction that is perpendicular to the planes of oscillation of the electric and magnetic fields associated with it (which are, themselves, also perpendicular to each other). Light produced by common sources like the Sun, incandescent lamps or flames, is referred to as unpolarised light, and is a mixture of short wave trains in which the electric and magnetic fields oscillate in planes oriented at several different angles. By passing unpolarised light through suitable polarising materials, one specific polarisation can be selected. Chiral molecules have the ability to change the polarisation of light by rotating the plane in which the electric or magnetic field oscillate. The rotation can be to the left or to the right relative to the direction of propagation, depending on the specific enantiomer with which light is interacting.
Chiral molecules have an atomic structure which prevents them from being superimposed on their mirror image.
Stereogenic centres
The origin of the optical activity of chiral molecules is related to the existence within their structures of one or more stereogenic centres (or stereocentres). In most organic molecules, these are carbon atoms bonded to four substituent groups in a tetrahedral arrangement. The two enantiomers of the same molecule are related by a simple interchange in the bonding positions of two of the four substituents. ‘The relationship between a chiral centre and its optical rotation,’ says Professor Huajie Zhu at Hebei University of Science and Technology, ‘has long been a very important part of stereochemistry research. Determining the specific optical rotation remains a crucial tool for exploring the configuration of chiral molecules.’
Predicting optical rotation
Many methods have been developed to link molecular structure and optical rotation, including chemical degradation of target molecules, total synthesis and physical methods, such as X-ray crystallography, circular dichroism (CD), vibrational CD (VCD), nuclear magnetic resonance (NMR) and magneto-optical rotation measurements. Empirical and semi-empirical rules have also been developed as part of these efforts. These experimental methods suffer from drawbacks caused by the large quantity of samples required in the measurements or by difficulties in obtaining single crystals of sufficient quality for X-ray structure determination.
“Determining the specific optical rotation remains a crucial tool for exploring the configuration of chiral molecules.”
More recently, computational approaches based on quantum mechanics have been applied to study optical rotation in chiral molecules with relatively rigid backbones, with considerable success. The complexity of these methods, however, makes it very difficult to assess, prior to a calculation, the level of theory required to obtain consistently accurate results over different classes of molecules. Besides, phenomena like solvation (the process whereby molecules of a solvent associate with molecules of a solute), which are known to play a role in the optical activity of chiral molecules, cannot always be taken into account straightforwardly in these types of calculations.
A matrix model of optical rotation
The focus of the work of Zhu and colleagues has been on developing a rigorous but intuitive mathematical model that predicts both the magnitude and the direction of the optical rotation of a chiral molecule, potentially also taking into account the effects of the environment surrounding the molecule, for instance the presence of a solvent or changes in temperature.
Diagram conceptualising the rotation of a chiral molecule.
The model requires a preliminary knowledge of the structure of the molecule, which can be obtained either from experimental measurements or from quantum-mechanical calculations. The substituent groups bonded to a stereogenic centre are then represented in terms of a relatively small set of model parameters. These include a comprehensive mass for each of the four substituents, which, in general, differ from the molecular weight and is determined from the setup of the quantum-mechanical calculations. Other parameters include the substituent radius, which accounts not only for the substituent’s size, but also for the occurrence of different internal conformations, the electronegativity of the substituent, which quantifies the tendency of a chemical group to attract or repel electrons on the stereogenic centre, and the symmetry number, which accounts for the asymmetry of a given substituent.
The matrix model thus incorporates key physical characteristics of each substituent group bonded to a stereogenic centre, which are used to predict the direction and magnitude of a molecule’s specific rotation. Multiple stereogenic centres can also be included in the calculations, which allows one to study molecules of sizes and complexities well beyond those treatable with fully quantum-mechanical calculations.
Molecular conformations
Typical chiral molecules exhibit high flexibility, which is caused by the tendency of each substituent at the stereogenic centre to rotate around bonds. This gives rise to a large number of molecular conformers, each of which can in principle contribute to the overall optical rotation. In the matrix model, the coexistence of individual conformers and their population are accounted for in terms of the substituent radius, which can be interpreted as an effective radius encoding information on conformer rotations. Once the matrix elements have been computed, the optical rotation (relative to a chosen axis) can simply be estimated from the determinant of the matrix (with a proportionality constant k0) accounting for external effects, including temperature, the presence of a solvent and the wavelength of the polarised light.
Zhu’s matrix model has important implications for our understanding of optical rotation. RDVector/Shutterstock.com
Sampling molecular configurations
The matrix model has been used successfully to study optical rotation in large sets of flexible chiral linear molecules, and its accuracy has been shown to match that of high-level quantum mechanical calculations. It has also been applied to molecules containing more than one stereogenic centre and to complex molecules in which substituents at the same stereogenic centre interact with each other. The physical significance of the model parameters (comprehensive mass, radius, electronegativity, and symmetry number) has been analysed in detail.
“The concept of ‘conformer pairs’ has constructed the fundamental basis for using simplified models of complex chiral molecules.”
At variance with quantum-mechanical calculations, whose complexity limits their application to molecules composed of a relatively rigid chiral compounds, or a chiral compound with short chain substituents, or small flexible groups. It requires simplifications in the structure of the substituents if a chiral molecule has a long flexible chain. The matrix model can in principle account for the structural details of the substituents, as well as for the existence of long chain groups that means there are large number of potential conformers, and to study their relative contributions to the overall optical rotation.
Conformational flexibility
As the size and complexity of the substituents increase, the number of possible molecular conformers can rapidly overwhelm the capabilities of computational methods. In quantum-chemical calculations, chiral compounds with long and flexible substituents are often represented using shortened and relatively rigid model substituents. In most situations, this approach provides estimates of optical rotation in excellent agreement with experimental data, but it leaves the question open as to why such a drastically oversimplified representation of the substituent structure can account for the coexistence of large numbers of conformers.
christo mitkov christov/Shutterstock.com
Conformer pairs
By studying a series of chiral linear aliphatic alcohols with long and flexible substituents, Zhu and collaborators have used the matrix model to clarify the role of different conformers in the optical rotation properties of these molecules. ‘Although many different conformers contribute simultaneously to the optical activity’, explains Zhu, ‘the majority of them form conformer pairs, which are mirror-like images of each other and rotate light in opposite directions. Their collective contribution to optical rotation is, therefore, very small. By contrast, it is the most stable optically active conformer that plays the leading role and largely determines the optical rotation properties of the molecule.’
The concepts of conformer pairs and the most stable conformer concluded from wave-function theory offer a powerful and innovative means of understanding the origin of optical rotation in chiral molecules and linking it to their molecular structure. They also largely concur with the matrix model. For instance, it has been shown using the matrix model that the molecules at the stereocenter (an atom with four attachments which are different from one another) have the smallest possible contact radius used in calculations. In the case of long-carbon chain substituents, this corresponds to a small constant (0.8 Å) plus the radius of their zig-zag geometry of the substituent. This is a highly important result, which makes it possible to correlate an easily accessible model of a molecule with its complex original structure. Further, to extend the use of simplified models using methods such as CD or VCD may involve very similar principles as optical rotation study, paving the way for important future discoveries.
Particle-wave duality
The agreement between structurally simplified quantum-mechanical calculations and the statistical conformer sampling approach of Zhu’s matrix model has important implications for our understanding of the physics of optical rotation in complex molecules. Both particle and wave characteristics of polarised light and the electrons of a chiral molecule manifest themselves in optical rotation experiments. Quantum-mechanical calculations, which describe the coupling of the wavefunctions of light and electrons, and the particle-based matrix method provide two complementary approaches to modelling optical rotation in chiral molecules.
What are the most promising future developments and improvements of the matrix method that you have developed to predict optical rotation in chiral molecules? The particle-based matrix method and the new concept of conformer pairs provide the answers to the use of simplification of a complex molecule mentioned above. Both construct the fundamental base to use of simplified models used in quantum-mechanical calculations. This method may have the possible uses in further development of new equipment in optical rotation, namely, absolute configuration study. For example, the novel rotational interference and diffraction fringes, if possible polarized light is used. Different rotation values may mean different fringe patterns which may exhibit more details about the stereogenic centres of chiral compounds.
References
Zhao, D, Ren, J, Xiong, Y et al (2019) Conformer pair contributions to optical rotations in a series of chiral linear aliphatic alcohols. Chemical Research in Chinese Universities, 35, 109-119.
Zhu, H.J, Ren, J, Pittman Jr, C, (2007) Matrix model to predict specific optical rotations of acyclic chiral molecules. Tetrahedron, 63, 2292-2314.
Zhu, H. J. (2015) Organic Stereochemistry—experimental and computational methods, Wiley-VCH, Verlag GmbH & Co. KGaA, Chapters 2 to 6.
Professor Huajie Zhu studies optical rotation in complex chiral molecules.
Funding
The National Nature Scientific Foundation of China (#21877025)
The Joint Key Medical Joint Project from Science and Technology Committee of Hebei Province (#H2020201029)
Collaborators
Thanks to Prof Charles U Pittman, Jr. for his assistances in the study.
Bio
Professor Zhu obtained his BS and MS degrees from Wuhan University in 1990, and PhD from Kunming Institute of Botany of CAS in 1996. His research involves the original discovery of particle functions of chiral optical rotation; determination of absolute configuration using theoretical methods; asymmetric catalytic reactions; antitumor and antivirus compounds, like chiral alkaloids.
Dr Huajie Zhu
Contact
#26, Yuxiang Street
Chemical and Pharmaceutical Engineering
Hebei University of Science and Technology
Shijiazhuang, 050018
Hebei
China
