Atomic-Scale Theory of Stark Shift in Optical Transitions of Organic Molecules under Inhomogeneous Electric Fields

When molecules are exposed to external static electric fields, their optical transitions shift in energy, which is a phenomenon known as the DC Stark effect. Conventionally, the Stark effect is treated under the assumption of field homogeneity at the molecular scale, allowing for interpretations of the energy shifts based on the changes of the molecular dipole moment and polarizability. However, in realistic environments featuring defects and nanoscale heterogeneities, molecules experience strongly inhomogeneous electric fields that vary on the submolecular scale, rendering standard selection rules and dipole-based models inadequate. Here, we develop a generalized theory of the Stark effect that accounts for such atomic-scale field inhomogeneities. We demonstrate that the total Stark shift can be decomposed into linear and quadratic contributions, which, when treated locally, break the conventional dipolar selection rules and are sensitive to specific microscopic molecular properties. Furthermore, we show that these effects should be accessible in a well-controlled manner in the current experimental setups. Specifically, we consider a realistic configuration in which the atomically sharp tip of a light-assisted scanning-tunneling microscope (STM) generates highly localized electric fields. We show that spatial variations in the linear Stark shift provide maps with subnanometric spatial resolution of photoinduced charge redistribution for representative molecular dyes, exhibiting high sensitivity to molecular composition and chemical functionalization. Additionally, the quadratic contribution probes the spatial distribution of the changes in the polarizability upon excitation. These results establish nanoscale Stark shift spectroscopy as a robust method for studying excited-state properties in strongly inhomogeneous electric fields characteristic of STM, defects, interfaces, and molecular nanostructures.