Visualization and thermodynamic encoding of single-molecule partition function projections

Ensemble averaging of molecular states is fundamental for the experimental determination of thermodynamic quantities. A special case occurs for single-molecule investigations under equilibrium conditions, for which free energy, entropy and enthalpy at finite temperatures are challenging to determine with ensemble averaging alone. Here we report a method to directly record time-averaged equilibrium probability distributions by confining an individual molecule to a nanoscopic pore of a two-dimensional metal-organic nanomesh, using temperature-controlled scanning tunnelling microscopy. We associate these distributions with partition function projections to assess real-space-projected thermodynamic quantities, aided by computational modelling. The presented molecular dynamics-based analysis is able to reproduce experimentally observed projected microstates with high accuracy. By an in silico customized energy landscape, we demonstrate that distinct probability distributions can be encrypted at different temperatures. Such modulation provides means to encode and decode information into position–temperature space.