We recently presented a new method for developing exchange-correlation functionals using ab initio numerical exchange-correlation potentials and accurate total energies. A preliminary functional was presented. In this paper we refine the functional expansion and demonstrate that significantly improved atomization energies can be obtained by amending the fitting procedure to include atomization energies rather than total molecular energies. A new functional is presented that provides an improved description of simple first-row hydrogen abstraction reactions compared to conventional continuum density functionals, This improvement is achieved without introducing any fraction of exact orbital exchange.