A Minimalist Model of Single Molecule Spectroscopy in a Dynamic Environment Studied by Metadynamics

In this paper we develop a minimalist model of single molecule spectroscopy in a dynamic environment. Our model is based upon a lattice system consisting of a probe molecule embedded in an Ising-model like environment. We assume that the probe molecule interacts with the Ising spins via a dipole-dipole potential, and calculate free energy curves and lineshapes of the system. To investigate fluctuation behavior of the system we exploit the metadynamics sampling method. In particular, using the method, we calculate the free energy curve of magnetization of the lattice and that of the transition energy of the probe molecule. Furthermore, we compare efficiencies of three different sampling methods used; unbiased, umbrella, and metadynamics sampling methods. Finally, we explore the lineshape behavior of the probe molecule as the system undergoes a phase transition from a sub-critical and to a super-critical temperature. We show that the transition energy of a probe molecule is broadly distributed due to the heterogeneous, local environments.