From Intermolecular Poses to Thermodynamics Using Subdivided Spheres

Computing molecular thermodynamic properties is instrumental in multiple scientific disciplines, such as statistical physics, N-body simulations, and molecular docking. However, exact thermodynamic calculations are almost always not feasible. In this work, we introduce a versatile algorithm designed to rapidly compute the two-body partition function, its related thermodynamic properties, and the second virial coefficient for anisotropic nanoparticles and proteins under the rigid-body approximation. Our method involves constructing a quasi-regular grid in the 5D angular space between pairs of arbitrary objects and efficiently scanning the radial-angular space between the rigid molecules. Where available, we find excellent agreement with light and X-ray scattering experiments, as well as with Monte Carlo simulations. Our results suggest a correction to current coarse-grained protein force fields, and we further discover a new, counterintuitive effect of temperature on virial coefficients, caused by a population shift in angular space due to the dielectric response of water. Finally, the grid can serve as an interpolation table for N-body simulations, increasing their performance by orders of magnitude.