Calculation of Second Virial Coefficients of Small Molecules

Calculation of Second Virial Coefficients of Small Molecules Introduction Second Virial Coefficient (ml/mol) The deviations of a real gas from ideal behavior is experimentally represented using the virial equation of state. The coefficients of this equation are directly related to intermolecular potentials. In particular, the second virial coefficient is related to pairinteractions of molecules. Thus we can evaluate the quality of an intermolecular potential by calculating second virial coefficient and comparing it with experimental data. In this study, we use classical force field CHARMM, and approximate quantum chemical density-functional tight-binding method (DFTB3) with and without empirical dispersion correction (D3), to calculate second virial coefficients at a range of temperatures for small polar and non-polar molecules and compare them with experimental data. Results Methods • Compressibility of a gas Z = p/⍴RT can be expressed as an infinite power series in number density ⍴. Z = 1 + B2(T)⍴ + B3(T)⍴2 + … where B2(T) and B3(T) are second and third virial coefficients, respectively. For example, in Van-Der-Waals Equation of State Temperature (K) Methane (non-polar) Methanol (polar) Nitrous oxide (polar) <...> denotes angular average over molecular orientations, Ω1 and Ω2. The Mayer-f function is dependent on temperature and is a function of u12 , the potential energy between particle 1 and 2. We perform the angular average around each molecule’s center of mass along a radial integration grid. Mayer Function (unitless) • The second virial coefficient is mathematically represented by: Center of mass distance (Å) Conclusions r12 • CHARMM Force Field • Density Functional Tight-Binding theory • Calculating second virial coefficient gives us a qualitative understanding of the pair interaction of molecules. • Comparing DFTB3, DFTB3-D3, and classical CHARMM model, we can conclude that DFTB3-D3 tends to overestimate the short-range interactions. • For non-polar molecules like alkanes and benzene, classical force field underestimates the pair-potential. Whereas for polar molecule methanol, the opposite trend is noticed. • Comparing DFTB3 with and without D3 dispersion, we can comment that dispersion significantly improves long-range attractive part of the potential. The effect of dispersion is most pronounced in polar molecules • At high temperatures, the second virial coefficient gives us an idea of the excluded volume of a gas. The increasing trend of the second virial coefficient aligns with the size of alkanes that we studied.