Noura Dawass

6 118 S OLUBILITY OF G ASES IN M ONOETHYLENE G LYCOL As opposed to a whole molecule, the strength of interactions of a fractional molecule is varied using a coupling parameter λ . When λ = 0, the fractional molecule acts as an ideal gas molecule and does not interact with the sur- rounding molecules. When λ = 1, the fractional molecule fully interacts with the surrounding molecules. By varying the strength of interactions of the frac- tional molecule with the surrounding molecules, whole molecules can be grad- ually added or removed. Besides the conventional MC thermalization trial moves [22, 23] , trial moves attempting to change λ are required. Shi and Mag- inn [59] derived Metropolis–like acceptance rules for changing the values of λ in the osmotic ensemble. For each solute type, a fractional molecule is used to insert/delete molecules in the simulation box. When λ drops below zero, the fractional molecule is removed and a randomly selected whole molecule is transformed into a fractional molecule. When λ is larger than 1, the fractional molecule is transformed into a whole molecule and a new fractional molecule is inserted [59, 195] . For the solvent, a fractional molecule is used to improve sampling, while keeping the total number of molecules of the solvent fixed. For a fractional molecule of the solvent type, λ trial moves involve changing the val- ues of λ , random reinsertions of the fractional molecule, and identity changes between a fractional molecule and a whole molecule [197] . In CFCMC simula- tions, the system is biased to ensure a flat distribution of the observed probabil- ity of λ . From the probability distribution of λ , the excess chemical potential and hence the Henry coefficient is obtained. For more details the reader is referred to Refs. [59, 60, 196, 197] . S CALING OF THE INTERMOLECULAR INTERACTIONS For each fractional molecule, a weightfunction W ( λ ) is constructed to achieve a flat probability distribution of λ and ensure smooth transitions between λ = 0 and λ = 1 [60] . Essentially, at a certain λ , the value of W ( λ ) counteracts the value of 〈 ∂ U / ∂λ 〉 , which is the average potential energy change with λ . Fluctuations in the value of ∂ U / ∂λ can be large, which can hinder the efficient sampling of the λ space. As a result, a pathway that minimizes the variance of ∂ U / ∂λ has to be chosen [218] . Changes in the values of λ depend on how intermolecular interactions, are scaled when λ is varied [218] (intramolecular interactions are not scaled). Electrostatic interactions are scaled by using a scaling parameter λ el that is a function of λ [196, 219] . For non-bonded LJ interactions, the following soft–core scaling potential is used [218, 220, 221] : u ( r i j , λ ) = 4 ² i j λ a     1 α (1 − λ ) b + ³ r i j σ i j ´ c   12/ c −   1 α (1 − λ ) b + ³ r i j σ i j ´ c   6/ c   (6.1)