Theoretical Methods for Free Energy Calculations

The most widely used method for calculating the formation free energy is the classical nucleation theory (CNT) [12-16] based on thermodynamics. The molecular clusters are treated as spherical droplets of bulk liquid having sharp boundaries 

Classical density functional theory (DFT) [18,19] treats the cluster formation free energy as a functional of the average density distributions of atoms or molecules. The required input information is an intermolecular potential describing the substances at hand. The boundary between the cluster and the surrounding vapor is not anymore considered sharp, and surface active systems can be studied adequately. DFT discussed here is not to be confused with the quantum mechanical density functional theory (discussed below), where the equivalent of the Schrodinger equation is expressed in terms of the electron density. Classical DFT has been used successfully to uncover why and how CNT fails for surface active systems using simple model molecules [20], but it is not practically applicable to real atmospheric clusters if the molecules are not chain-like, the numerical solution of the problem gets too burdensome, unless the whole molecule is treated in terms of an effective potential. 

Classical interaction potentials for molecular systems can be pairwise or take manybody interactions into account, molecules can be rigid or flexible, and both stretching and torsion motions can be considered [28]. Polarizability can be introduced, but for example for water this does not seem to make the potentials mimic reality unambiguously better. The potentials, also called force fields, are fitted to reproduce certain sets of properties, and can fail to reproduce other characteristics. The potentials suffer from problems with transferability for example a water-sulfuric acid potential developed for the two-component mixture does not necessarily describe the interaction between water and sulfuric acid in a three-component mixture of water, sulfuric acid and ammonia. Also, potentials created for bulk liquid do not always work for surface layers or small clusters. 

DFT methods while their accuracy is significantly lower, they are seldom used anymore. 

Atmospherically relevant molecular clusters often contain strongly acidic or basic molecules e.g. sulfuric acid and ammonia), which gives rise to various dif- 

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