We present an analysis and extension of our constraint-based approach to orbital-free ͑OF͒ kinetic-energy ͑KE͒ density functionals intended for the calculation of quantum-mechanical forces in multiscale moleculardynamics simulations. Suitability for realistic system simulations requires that the OF-KE functional yield accurate forces on the nuclei yet be computationally simple. We therefore require that the functionals be based on density-functional theory constraints, be local, be dependent at most upon a small number of parameters fitted to a training set of limited size, and be applicable beyond the scope of the training set. Our previous "modified-conjoint" generalized-gradient-type functionals were constrained to producing a positive-definite Pauli potential. Though distinctly better than several published generalized-gradient-approximation-type functionals in that they gave semiquantitative agreement with Born-Oppenheimer forces from full Kohn-Sham results, those modified-conjoint functionals suffer from unphysical singularities at the nuclei. Here we show how to remove such singularities by introducing higher-order density derivatives and analyze the consequences. We give a simple illustration of such a functional and a few tests of it.

Erratum: Properties of constraint-based single-point approximate kinetic energy functionals [Phys. Rev. B 80, 245120 (2009)]

Effective, explicitly density-dependent (i.e., orbital-free) approximations to the Kohn-Sham kinetic energy functional T s remain elusive. In the course of developing such functionals in collaboration with Frank Harris, various issues have arisen that have gone unaddressed. We consider four of them here: positivity of the KS kinetic energy density, supposed requirements on its functional dependence, the use of cutoffs to insure positivity, and the role of the Coulomb virial theorem in the asymptotic analysis of T s .

The need to perform a numerical integration of the exchange-correlation functional because of its nonanalyticity severely complicates the accurate application of local-density functional methods to molecules and clusters. The optimal choice of grid points for this integration and the estimation of the error made by the choice are subtle considerations. In particular, because the position and/or weighting of each grid point must change when the nuclear positions change, these errors are most noticeable when different geometries are compared. We have determined a method of grid point selection and weighting that reduces these errors. We have also determined a simple method of estimating the extent of the error made in the particular density of points used for the grid. These results are illustrated for a selection of small molecules.

We have calculated the equilibrium geometries and elastic properties of transition-metal superlattices (Cu-Ni, Cu-Pd, and Cu-Au) over a range of composition modulation wavelengths for both slab-layered systems (with alternating equal-width slabs of the constituents) and for systems with a sinusoidally modulated composition. The energies and equilibrium geometries were obtained with the embeddedatom method and the elastic constants were determined both by considering appropriate sums over the dynamical matrix and by calculating the energy of specific deformations of the unit cell. No enhancements of the elastic constants or moduli were found for any of the systems considered, in agreement with recent experimental results.

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