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We present a Gaussian-basis implementation of orbital-free density-functionaltheory (OF-DFT) in which the trust-region image method (TRIM) is used foroptimization. This second-order optimization scheme has been constructed toprovide benchmark all-electron results with very tight convergence of theparticle number constraint, associated chemical potential and electron density.It is demonstrated that, by preserving the saddle-point nature of theoptimization and simultaneously optimizing the density and chemical potential,an order of magnitude reduction in the number of iterations required forconvergence is obtained. The approach is compared and contrasted with a newimplementation of the nested optimization scheme put forward by Chan, Cohen andHandy. Our implementation allows for semi-local kinetic-energy (andexchange-correlation) functionals to be handled self-consistently inall-electron calculations. The all-electron Gaussian-basis setting for thesecalculations will enable direct comparison with a wide range of standardhigh-accuracy quantum-chemical methods as well as with Kohn-Shamdensity-functional theory. We expect that the present implementation willprovide a useful tool for analysing the performance of approximatekinetic-energy functionals in finite systems.

Robust All-Electron Optimization in Orbital-Free Density Functional Theory Using the Trust Region Image Method