Ab initio metadynamics determination of temperature-dependent free-energy landscape in ultrasmall silver clusters

Ab initio metadynamics enables the extraction of free-energy landscapes having the accuracy of first-principles electronic structure methods. We introduce an interface between the PLUMED code that computes free-energy landscapes and enhanced-sampling algorithms and the Atomic Simulation Environment (ASE) module, which includes several ab initio electronic structure codes. The interface is validated with a Lennard-Jones cluster free-energy landscape calculation by averaging multiple short metadynamics trajectories. We use this interface and analysis to estimate the free-energy landscape of Ag₅ and Ag₆ clusters at 10, 100, and 300 K with the radius of gyration and coordination number as collective variables, finding at most tens of meV in error. Relative free-energy differences between the planar and non-planar isomers of both clusters decrease with temperature in agreement with previously proposed stabilization of non-planar isomers. Interestingly, we find that Ag₆ is the smallest silver cluster where entropic effects at room temperature boost the non-planar isomer probability to a competing state. The new ASE-PLUMED interface enables simulating nanosystem electronic properties under more realistic temperature-dependent conditions.