To gain an understanding of the variational behavior of kinetic energy functionals, we perform a numerical study of the Thomas-Fermi-Dirac-von Weizsacker theory in finite systems. A general purpose Gaussian-based code is constructed to perform energy and geometry optimizations on polyatomic systems to high accuracy. We carry out benchmark studies on atomic and diatomic systems. Our results indicate that the Thomas-Fermi-Dirac-von Weizsacker theory can give an approximate description of matter, with atomic energies, binding energies, and bond lengths of the correct order of magnitude, though not to the accuracy required of a qualitative chemical theory. We discuss the implications for the development of new kinetic functionals.