Quantum theory of chiral interactions in cholesteric liquid crystals

The effective chiral interaction between molecules arising from long-range quantum interactions between fluctuating charge moments is analyzed in term s of a simple model of chiral molecules. This model is based on the approxi mations that (a) the dominant excited states of a molecule form a;band whos e width is small compared to the average energy of excitation above the gro und state and (b) biaxial orientational correlation between adjacent molecu les can be neglected. Previous treatments of quantum chiral interactions ha ve been based on a multipole expansion of the effective interaction energy within second-order-perturbation theory. We consider a system consisting of elongated molecules and, although we invoke the expansion in terms of coor dinates transverse to the long axis of constituent molecules, we treat;the longitudinal coordinate exactly. Such an approximation is plausible for mol ecules in real liquid crystals; The macroscopic cholesteric wave vector Q ( Q = 2 pi/P, where P is the pitch) is obtained via Q = h/K-2, where K-2 is t he Frank elastic constant for twist and h is the torque field which we calc ulate from the effective chiral interaction K(IJ)a(I) x a(J).R-IJ, where th e unit vector a(1) specifies the orientation of molecule 1 and R-IJ is the displacement of molecule 1 relative to molecule J. We identify two distinct physical limits depending on whether one or both of the interacting molecu les are excited in the virtual state. When both molecules are excited, we r egain the R-IJ(-8) dependence of kappa(IJ) on intermolecular separation fou nd previously by Van der Meer et at [J. Chem. Phys, 65, 3935 (1976)]. The t wo-molecule, unlike the one-molecule term, can be interpreted in terms of a superposition of pairwise interactions between individual atoms (or local chiral centers) on the two molecules. Contributions to K-IJ when one molecu le is excited in the virtual state are of order R-IJ(-7) for helical molecu les which are assumed not to have a global dipole moment, but whose atoms p ossess a dipole moment. It is shown that for a helical molecule Q can have either the same or the opposite sign as the chiral pitch of an individual m olecule; depending on the details of the anisotropy of the atomic polarizab ility. The one-molecule mechanism can become important when the local atomi c dipoles become sizable, although biaxial correlations (ignored here) shou ld then be taken into account. Our results suggest how the architecture of molecular dipole moments might be adjusted to significantly influence the m acroscopic pitch. [S1063-651X(99)12303-1].