  The potential of mean force (PMF) between two nano crystals (NCs) represents
an effective interaction potential that can be used to study the assembly of
NCs to various superstructures. For a given temperature, the effective
interaction is obtained best from molecular dynamics simulations. Based on a
density functional approach, this study proposes three methods of predicting
the PMF for any temperature based on a single molecular dynamics simulation for
one temperature. The three methods construct the PMF by considering the ligands
as an ideal gas, as hard-sphere chains, or as Lennard-Jones interaction sites.
To apply this methodology, the density of the interaction centers must be
extracted from the simulation data. For the ideal gas model, a straightforward
sampling procedure with a fixed lattice in space leads to free energies that
are too large in order to consistently explain the simulation data for
different temperatures. Naive sampling does not account for the small momenta
added to the NCs when coupled to a thermostat. A method is proposed that
corrects for the unphysical steps during the simulation. The ideal gas
contribution computed for the corrected density is significantly smaller than
the one obtained from naive sampling and can thus explain the temperature
dependence of the PMF correctly. For the hard-sphere chain model, where a
weighted density is used, the correction of the particle density is not
essential. However, the PMF calculated based on the corrected density confirms
our approach. All three models predict PMF curves in very good agreement with
simulation results, but they differ in the number of input parameters and the
computational effort. Based on the modeling results, we predict the existence
of an additional attractive force at small distances of the NCs - a depletion
force.
