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An ab initio study of TiC: A comparison of different levels of theory including density functional methodsAn optimized Thomas-Fermi theory is proposed which retains the simplicity of the original theory and is a suitable reference theory for Monte Carlo density functional treatments of condensed materials. The key ingredient of the optimized theory is a neighborhood sampled potential which contains effects of the inhomogeneities in the one-electron potential. In contrast to the traditional Thomas-Fermi approach, the optimized theory predicts a finite electron density in the vicinity of a nucleus. Consideration of the example of an ideal electron gas subject to a central Coulomb field indicates that implementation of the approach is straightforward. The optimized theory is found to fail completely when a classically forbidden region is approached. However, these circumstances are not of primary interest for calculations of interatomic forces. It is shown how the energy functional of the density may be constructed by integration of a generalized Hellmann-Feynman relation. This generalized Hellmann-Feynman relation proves to be equivalent to the variational principle of density functional quantum mechanics, and, therefore, the present density theory can be viewed as a variational consequence of the constructed energy functional.

Electron densities obtained from a ground state path integral approach to density functional theory using a primitive Monte Carlo method display large statistical uncertainties when short wavelength fluctuations of the paths are considered directly. An optimized Thomas–Fermi approximation is developed to eliminate these degrees of freedom in a systematic and physically motivated fashion. Beyond improving the precision of the numerical results, this theoretical development permits a simple qualitative discussion of how the calculation pushes electron density into tunneling regions by iteratively renormalizing the Fermi wavelength appropriate to the remaining integrations which involve only long wavelength coordinates.

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A probability distribution for polymer chain end-to-end separation is derived that incorporates the effects of bond stretching and bending. Each bond is represented by a spring with an equilibrium length that can stretch and contract according to a harmonic force law. Such a model is expected to be important for the description of polymeric materials under large deformations. Methods for computing the distribution and related quantities are derived and are shown to be robust and realistic. Computed distributions show noticeable differences from more commonly used models that do not have a dependence on the bond strengths.