Visualization and thermodynamic encoding of single-molecule partition functions

Abstract

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 provide a method to access single-molecule thermodynamics, by confining an individual molecule to a nanoscopic pore of a two-dimensional metal-organic nanomesh, where we directly record finite-temperature time-averaged statistical weights using temperature-controlled scanning tunneling microscopy. The obtained patterns represent a real space equilibrium probability distribution. We associate this distribution with a partition function projection to assess spatially resolved thermodynamic quantities, by means of computational modeling. The presented molecular dynamics based Boltzmann weighting model is able to reproduce experimentally observed molecular states 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 or to realize nanoscopic thermal probes.