| Summary: | We have implemented a new grid-free density-functional technique for exchange-correlation potentials of $\rho\sp{1/3}$ form (X$\alpha$ potentials). The nonanalytic potential is fitted to integrable functions by solving a set of nonlinear equations, rather than by fitting on a three-dimensional grid of points. This completely analytical method produces smooth energy surfaces and exact energy gradients. The method is found to be several times faster computationally in single-point calculations than a comparable grid-based method with a moderate number of grid points and to be more than an order of magnitude faster for geometry optimizations. The performance of the method is demonstrated on the umbrella inversion of ammonia (NH$\sb3),$ the isoelectronic series of ethane $\rm(C\sb2H\sb6),$ hydrazine $\rm(N\sb2H\sb4),$ and hydrogen peroxide $\rm(H\sb2O\sb2),$ and the water-gas shift reaction (WGSR: $\rm CO+H\sb2O\to CO\sb2+H\sb2).$
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