Extensive Accuracy Test of the Force-Field-Based Quasichemical Method PAC–MAC

Abstract

We present a comprehensive evaluation of the recently developed pair configuration to molecular activity coefficient (PAC−MAC) method. PAC−MAC is a force-fieldbased quasichemical method for rapid calculation of binary phase diagrams. The accuracy of the method is tested by comparing the calculated excess mixing free energy with experimental data for 1092 binary mixtures. The root mean squared error (RMSE) is shown to be 0.15 k B T. Furthermore, a comparison with UNIFAC and molecular simulations is performed. UNIFAC shows a significantly higher accuracy (RMSE: 0.07 k B T), whereas molecular simulations lead to comparable results. The accuracy of both molecular simulations as well as PAC−MAC depends highly on the used force field. The binary parameters of UNIFAC are optimized using experimental miscibility data, whereas the force field parameters are not. Therefore, a better performance of UNIFAC is expected. A concise data set shows the capacity of PAC− MAC in predicting results obtained using Monte Carlo simulations.

Accuracy Test of the OPLS-AA Force Field for Calculating Free Energies of Mixing and Comparison with PAC-MAC

“…30 Figure 4 shows comparable results for the subset of 1053 binary mixtures. Of note is that Figure 4 is almost the same as Figure 9 from our previously published paper.…”

“…In a previous publication, the total observed RMSE of PAC-MAC is proven to be 0.153 k B T , with a correlation coefficient of 0.695, for the calculation of excess free energies in comparison with experimental data. 30 Figure 4 shows comparable results for the subset of 1053 binary mixtures. Of note is that Figure 4 is almost the same as Figure 9 from our previously published paper.…”

“…In PAC-MAC, the expression for the free energy of mixing is based on the quasi-chemical approximation of Guggenheim 24,39 and is given byThe 5 contributing free energy terms in eq 12 are given by the entropy of mixing of an ideal solution ( F id ), a modified Staverman–Guggenheim correction term ( F SG ), 30,40 the combinatorial expression according to the quasi-chemical approximation ( F comb ), the entropic contribution due to inhomogeneities in the occupation of the molecular surface ( F vac ), and the total intermolecular energy ( F int ). The expressions of the free energy terms in eq 12 are, for a binary mixture containing molecules A and B , given byin which x I , φ I , and y I are respectively the mole, volume, and coordination fraction of component I ∈ { A , B } in the mixture, z represents the average coordination number, x i IJ is the fraction of pair configuration i between molecules I and J in the mixture, A j I represents the surface area of surface panel j in component I , ⟨ A i ⟩ I is the average occupied area in an interaction on molecule I , x J,I vac represents the unoccupied area fraction of surface panel j on molecule I , and x vac is the total unoccupied surface fraction of a molecule.…”

“…For more information concerning the PAC-MAC method, we refer to two previously published articles. 29 , 30 …”

Cluster-Based Thermodynamics of Interacting Dice in a Lattice

“…These form the basis of a number of so-called quasichemical models, starting with Guggenheim [ 1 , 2 , 3 ] and continuing with more recent models that are frequently used in chemical engineering applications, like UNIFAC [ 4 , 5 ], GEQUAC [ 6 ], MOQUAC [ 7 ], COSMO-RS resp. COSMOTHERM [ 8 , 9 , 10 , 11 , 12 ], and PAC-MAC [ 13 , 14 , 15 , 16 ]. One common simplifying assumption used in quasichemical models is that surface segments are decoupled, and only the number densities of surface fragments are used.…”