(686a) Computation of Virial Coefficients for Quantum-Mechanical Models Employing the Becke-Johnson Model of Dispersion

The second and third virial coefficients, B₂ and B₃, have long played an important role in the development of classical molecular models for simple fluids because these quantities can be computed rapidly from a model and also extracted reliably from experimental pressure-density-temperature data. Higher-order virial coefficients, the computation of which has been made easier by the advancement of methods such as Mayer-sampling Monte Carlo¹, can be utilized within a truncated virial equation of state to compute low-density properties which can then be compared to experiment.

As integrals over configuration space, virial coefficients are complementary to the assessment tools most often considered in the development of quantum-mechanical models: the location and magnitude of energy minima. Computation of a virial coefficient B_n directly from quantum-mechanical models is uncommon because of the time required to sufficiently explore the required potential energy surface. Rather, B_n is typically computed from classical potentials fit to the quantum-mechanical data. As the potential energy surface becomes more complex, either through the introduction of more molecules or the consideration of rotational or intramolecular degrees of freedom, the fidelity of these fits worsen and become more sensitive to the form of the selected classical model.

An accurate representation of the potential energy surface is essential because slight perturbations are well known to result in dramatic changes to the virial coefficients and the critical point. We are developing approaches to enable efficient computation of virial coefficients directly from quantum-mechanical models. As our first step in this odyssey, we consider argon because its potential energy surface is well studied and has the simplest of spatial dependencies. Unfortunately, the cheapest of quantum-mechanical approaches, density functional theory, is unable to describe the long-range dispersion so essential to noble-gas interactions. To maintain low computational cost, several theories have been developed which include a supplemental dispersion component informed by experimental atomic polarizabilities and semi-empirical dimer energies. Specifically, we consider the Becke-Johnson dispersion model including C₆, C₈, and C₁₀ coefficients² within the framework suggested by Kannemann and Becke (2009)³. To our knowledge, B₂ values have not yet been reported for this model, and computation of higher-order B_n is an especially interesting test because the empirical character of the dispersion model is informed only by dimer data. We detail the variability both in accuracy and time requirements for a selection of different basis sets.

1. A. J. Schultz and D. A. Kofke, "Sixth, seventh and eighth virial coefficients of the Lennard-Jones model," Mol. Phys. 107 (21), 2309-2318 (2009).

2. Erin R. Johnson and Axel D. Becke, "A post-Hartree-Fock model of intermolecular interactions: inclusion of higher-order corrections," J Chem Phys 124 (17), 174104 (2006).

3. Felix O. Kannemann and Axel D. Becke, "Van der Waals Interactions in Density-Functional Theory: Rare-Gas Diatomics," J. Chem. Theory Comput. 5 (4), 719-727 (2009).