Enhanced Chiral Discriminatory van der Waals Interactions Mediated by Chiral Surfaces

Abstract

We predict a discriminatory interaction between a chiral molecule and an achiral molecule which is mediated by a chiral body. To achieve this, we generalize the van der Waals interaction potential between two ground-state molecules with electric, magnetic and chiral response to non-trivial environments. The force is evaluated using second-order perturbation theory with an effective Hamiltonian. Chiral media enhance or reduce the free interaction via many-body interactions, making it possible to measure the chiral contributions to the van der Waals force with current technology. The van der Waals interaction is discriminatory with respect to enantiomers of different handedness and could be used to separate enantiomers. We also suggest a specific geometric configuration where the electric contribution to the van der Waals interaction is zero, making the chiral component the dominant effect.PACS numbers: 34.20. Cf, 33.55.+b,42.50.Nn Introduction. Casimir and van der Waals (vdW) forces are electromagnetic interactions between neutral macroscopic bodies and/or molecules due to the quantum fluctuations of the electromagnetic field [1][2][3]. In particular, the attractive vdW potential between two electrically polarisable particles was first derived by Casimir and Polder using the minimal-coupling Hamiltonian [2]. Molecules can also exhibit magnetic [4][5][6][7] and chiral polarisabilities [4,8,9] and their contribution to the vdW force can be repulsive.The aim of this work is the study of the interaction between chiral molecules in the presence of a chiral magneto-dielectric body. Chiral molecules lack any center of inversion nor plane of symmetry. Hence they exist as two distinct enantiomers, left-handed and righthanded, which are related to space inversion. Due to their low symmetry they have distinctive interactions with light. In a chiral solution the refractive indices for circularly polarized light of different handedness are different. Hence a chiral solution can rotate the plane of polarization of light with an angle related to the concentration of the solution (optical rotation) [10][11][12], or absorb left-and right-circularly polarised light at different rates (circular dichroism) [13]. All of these phenomena are related to the optical rotatory strength, defined in terms of electric (d nk ) and magnetic (m nk ) dipole moment matrix elements [14]:

Perspective: Quantum Hamiltonians for optical interactions

“…In both the migration of energy and the van der Waals dispersion interaction, the starting point in the calculation is the PZW Hamiltonian. Expression of the interaction Hamiltonian in terms of multipole moments coupled to Maxwell fields is also advantageous when evaluating phenomena involving chiral species [115], often demanding relaxation of the electric dipole approximation and the inclusion of effects due to magnetic dipole and electric quadrupole coupling. A more complete understanding of these processes will lead to design principles that are expected to give rise to the development of new nano-materials for light-harvesting technologies and photovoltaics.…”

Medium-assisted van der Waals dispersion interactions involving chiral molecules

“…Interaction component Retarded limit non-retarded limit electric-electric [49] −R −7 −R −6 electric-paramagnetic [58] +R −7 +R −4 electric-diamagnetic [50] −R −7 −R −4 electric-chiral [64] ±R −8 ±R −5 paramagnetic-paramagnetic [58] −R −7 −R −6 paramagnetic-diamagnetic [50] +R −7 +R −6 paramagnetic-chiral [64] ±R −8 ±R −5 diamagnetic-diamagnetic [50] −R −7 −R −6 diamagnetic-chiral [65] ±R −8 ±R −6 chiral-chiral [53] ±R −9 ±R −6…”

Quantum formulation for nanoscale optical and material chirality: symmetry issues, space and time parity, and observables

“…One of the main or implicit motivations for several of the recent studies in this area is the prospect of achieving, by optical means, a separation of particles-especially chiral molecules-of opposite handedness [7,10,43,[98][99][100][101][102][103][104][105][106][107][108][133][134][135][136][137][138][139][140][141][142][143][144][145]. Certainly such a capacity might have important commercial applications-notably in the pharmaceutical industry, where oppositely handed compounds can deliver drastically different effects.…”