Fundamental measure theory for inhomogeneous fluids of nonspherical hard particles

Using the Gauss-Bonnet theorem we deconvolute exactly the Mayer f-function for arbitrarily shaped convex hard bodies in a series of tensorial weight functions, each depending only on the shape of a single particle. This geometric result allows the derivation of a free energy density functional for inhomogeneous hard-body fluids which reduces to Rosenfeld's fundamental measure theory [Phys. Rev. Lett. 63, 980 (1989)10.1103/PhysRevLett.63.980] when applied to hard spheres. The functional captures the isotropic-nematic transition for the hard-spherocylinder fluid in contrast with previous attempts. Comparing with data from Monte Carlo simulations for hard spherocylinders in contact with a planar hard wall, we show that the new functional also improves upon previous functionals in the description of inhomogeneous isotropic fluids.