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