High-Precision Calculation of Nanoparticle (Nanocrystal) Potentials of Mean Force and Internal Energies

Abstract

Thermodynamic stability assessment of nanocrystal systems requires precise free energy calculations. This study highlights the importance of meticulous control over various factors, including the thermostat, time step, potential cutoff, initial configuration, sampling method, and overall simulation duration. Free energy computations in dry (solvent-free) systems are on the order of several hundred k B T but can be obtained with consistent accuracy. However, calculation of internal energies becomes challenging, as they are typically much larger in magnitude than free energies and exhibit significant noise and reduced reliability. To address this limitation, we propose a new internal energy estimate that drastically reduces the noise. We also present formulas that enable the optimization of the parameters of the harmonic bias potential for optimal convergence. Finally, we discuss the implications of these findings for the computation of free energies in nanocrystal clusters and superlattices.

Theory and simulation of ligand functionalized nanoparticles – a pedagogical overview

“…The net effect of this complex interplay between ligand splaying, local free volume, and corona interpenetration is the emergence of an attractive potential well between LNPs. 105,107–110 It is here that the starkest contrast between “hard” and “soft” LNPs becomes apparent. Unlike the hard sphere limit, there is an optimal center-to-center separation that arises from the presence of an attractive well between two LNPs.…”

Solvent Isotherms and Structural Transitions in Nanoparticle Superlattice Assembly

“…The excellent agreement between simulation and MOLT-CF reported in Figure c provides evidence that the large (∼500 k B T ) cohesive free energies correspond to actual thermodynamic equilibrium. This is because segment–segment interactions are a fraction of k B T , so bonds among CH 2 and CH 3 break and reform many times over simulation time (see refs , for a more detailed discussion). Moreover, the very large cohesive energy does not hinder structural transitions, such as the bcc-fcc Bain transformation, , because the free-energy barrier between phases is also of the order of k B T …”