Density functional resonance theory: complex density functions, convergence, orbital energies, and functionals

Aspects of density functional resonance theory (DFRT) [D. L. Whitenack and A. Wasserman, Phys. Rev. Lett. 107, 163002 (2011)], a recently developed complex-scaled version of ground-state density functional theory (DFT), are studied in detail. The asymptotic behavior of the complex density function is related to the complex resonance energy and system's threshold energy, and the function's local oscillatory behavior is connected with preferential directions of electron decay. Practical considerations for implementation of the theory are addressed including sensitivity to the complex-scaling parameter, θ. In Kohn-Sham DFRT, it is shown that almost all θ-dependence in the calculated energies and lifetimes can be extinguished via use of a proper basis set or fine grid. The highest occupied Kohn-Sham orbital energy and lifetime are related to physical affinity and width, and the threshold energy of the Kohn-Sham system is shown to be equal to the threshold energy of the interacting system shifted by a well-defined functional. Finally, various complex-scaling conditions are derived which relate the functionals of ground-state DFT to those of DFRT via proper scaling factors and a non-Hermitian coupling-constant system.     

Fragment occupations in partition Density Functional Theory

The exact ground-state energy and density of a molecule can in principle be obtained via Partition Density Functional Theory (PDFT), a method for calculating molecular properties from Kohn-Sham calculations on isolated fragments. For a given choice of fragmentation, unique fragment densities are found by requiring that the sum of fragment energies be minimized subject to the constraint that the fragment densities sum to the correct molecular ground-state density. We investigate two interrelated aspects of PDFT: the connections between fragment densities obtained via different choices of fragmentation, for which we find "near-additivity", and the nature of their corresponding fragment occupations. Whereas near-integer occupations arise for very large inter-fragment separations, strictly integer occupations appear for small inter-fragment separations. Cases where the fragment chemical potentials cannot be equalized lead to fragment occupations that lock into integers.     

Colored Black Holes

We describe some recent results on solutions of the static, stationary, spherically symmetric solutions of the SU(z) Einstein-Yang/Mills equations. The main result is that any solution which is defined in the far field and has finite (ADM) mass, is defined for all r > 0.