Spectroscopic Probe of the van der Waals Interaction between Polar Molecules and a Curved Surface

TL;DR

This paper investigates how the van der Waals interaction between a polar molecule and a curved dielectric surface causes measurable shifts in the molecule's rotational energy levels, with potential for experimental observation.

Contribution

It provides a theoretical framework linking surface curvature to molecular energy level shifts via electrostatic interactions, neglecting retardation and dispersion effects.

Findings

Level shifts are temperature-independent.

Shifts depend on surface curvature and are expressible through Green's function derivatives.

Curvature-induced line splitting is experimentally observable.

Abstract

We study the shift of rotational levels of a diatomic polar molecule due to its van der Waals (vdW) interaction with a gently curved dielectric surface at temperature $T$, and submicron separations. The molecule is assumed to be in its electronic and vibrational ground state, and the rotational degrees are described by a rigid rotor model. We show that under these conditions retardation effects and surface dispersion can be neglected. The level shifts are found to be independent of $T$, and given by the quantum state averaged classical electrostatic interaction of the dipole with its image on the surface. We use a derivative expansion for the static Green's function to express the shifts in terms of surface curvature. We argue that the curvature induced line splitting is experimentally observable, and not obscured by natural line widths and thermal broadening.