Chirality-Induced Spin Polarization Places Symmetry Constraints on Biomolecular Interactions
A chiral compound, usually characterized by the presence of an asymmetric carbon center, is a molecule that would be identical to but not superimposable on its mirror image. A "life-size example" would be your hands: they look the same, but you cannot stack your right hand on top of your left hand perfectly! In fact, the term "chirality" is derived from the Greek word meaning hand, and chiral molecules are either right-handed (D) or left-handed (L). The D-molecules and L-molecules of a given compound are called enantiomers.
Chiral molecules are the building blocks of life, and chirality has been highly preserved throughout evolution. For example, all proteins are chiral, and they tend not only to interact with chiral ligands, but specifically with ligands of the same chirality. In contrast, if a chemist were to synthesize an amino acid in the laboratory, s/he would obtain a mixture of both L- and D-amino acids.
In an article in the Proceedings of the National Academy of Science (doi: 10.1073/pnas.1611467114), David Waldeck and colleagues in Israel propose a mechanism for the enantioselectivity (chiral specificity) of non-covalent interactions between chiral molecules. Their study examines how the non-covalent interactions between molecules give rise to enantioselective interaction energies. Non-covalent interactions do not involve the formation of a bond; rather they include electrostatic interactions between permanent or induced dipoles as the electron clouds of the molecules rearrange and the purely quantum exchange interaction as the wavefunctions of the molecules overlap. Their two part study shows experimentally that charge redistribution in chiral molecules is accompanied by spin polarization and it shows theoretically that the exchange interactions for homochiral (both molecules have the same handedness) interactions differ from heterochiral ones.
Hall Voltage and Spin Polarization
In the experimental section, they use a specially-designed Hall effect device to measure the spin polarization of their samples. They applied an electrical voltage to generate an electrostatic field across a monolayer film of molecules and induce a charge polarization. When this charge polarization is accompanied by spin polarization, a Hall voltage develops because of the magnetization created by the spin polarization.
Hall Voltage Measurents
They measured a Hall voltage for their chiral samples (the L- and D- enantiomers); the sign of the Hall potential depends on the handedness (Fig. A), and its magnitudes depends on the molecules length (Fig. B). The Hall signal decays when the spin polarization decays although the device is still charged as long as the gate voltage is on; when turned off, the charge flows in the opposite direction (Fig. C). And finally, the Hall voltage observed with the chiral molecules shows a roughly linear dependence on the applied gate voltage (Fig. D). These data reveal that charge polarization in chiral molecules is accompanied by spin polarization.
Spin Polarization and Enantioselectivity
Having demonstrated that spin polarization occurs during charge displacement in chiral molecules, they considered its implications for the interaction energy between chiral molecules. Although the magnetic interactions are negligible, the spin polarization constrains the symmetry of the wavefunction and therefore the wavefunction overlap between molecules.
This effect on the interaction at short-range emerges from Pauli's exclusion principle. Because they are indistinguishable, electrons can be exchanged, with the only constraint being that electrons with the same spin cannot occupy the same region in space. This exchange interaction stabilizes the overall interaction energy of the system.
Two chiral molecules with the same handedness will also have an identical spin polarization. When two such molecules interact (top), the resulting system is analogous to a singlet, with a pair of electrons with opposite spin. Conversely, if two molecules with different handedness interact (bottom), the resulting system is like a triplet. The homochiral system will be stabilized through the exchange interaction with respect to the heterochiral system, and the interaction between the spins therefore results in an enantioselective interaction.
The authors validated this mechanism by calculating the interaction energy of the model chiral system R*–H3C...CH3–R* as a function of the carbon–carbon distance (Fig. A). The interaction energy of the two molecules with opposite handedness (RS, red curves) is more repulsive than that of the two molecules with the same handedness (SS, blue curves), as shown in the plots of the second-order dispersion energy (Fig. B) and the difference in spin correlation energies (Fig. C).
From these data, the authors point out that the chirality of the molecule is reflected through the interactions, even if the interacting moieties are not chiral. In addition, as the interactions are strictly short range, they are most relevant in biosystems in which molecules are in close contact.
Waldeck says, "This work opens a wholly new perspective on the interaction of chiral molecules. Chemists have known that chirality is important, but almost always try to account for the intermolecular forces of chiral molecules by a combination of the electron charge and the three-dimensional arrangement of a molecule’s atoms. Our work shows that the electron spin has an important role to play because of how it affects the electronic wavefunctions. Classical electrostatics and structure is not capable of capturing this feature, quantum mechanics is required."