We reformulate the strong-interaction limit of electronic density functional theory in terms of a classical problem with a degenerate minimum. This allows us to clarify many aspects of this limit, and to write a general solution, which is explicitly calculated for spherical densities. We then compare our results with previous approximate solutions and discuss the implications for density functional theory.

Genomic plasticity enables adaptation to changing environments, which is especially relevant for pathogens that engage in "arms races" with their hosts. In many pathogens, genes mediating virulence cluster in highly variable, transposon-rich, physically distinct genomic compartments. However, understanding of the evolution of these compartments, and the role of transposons therein, remains limited. Here, we show that transposons are the major driving force for adaptive genome evolution in the fungal plant pathogen Verticillium dahliae. We show that highly variable lineage-specific (LS) regions evolved by genomic rearrangements that are mediated by erroneous double-strand repair, often utilizing transposons. We furthermore show that recent genetic duplications are enhanced in LS regions, against an older episode of duplication events. Finally, LS regions are enriched in active transposons, which contribute to local genome plasticity. Thus, we provide evidence for genome shaping by transposons, both in an active and passive manner, which impacts the evolution of pathogen virulence.

Abstract:The exchange-correlation energy in Kohn-Sham density functional theory can be expressed exactly in terms of the change in the expectation of the electron-electron repulsion operator when, in the many-electron Hamiltonian, this same operator is multiplied by a real parameter λ varying between 0 (Kohn-Sham system) and 1 (physical system). In this process, usually called adiabatic connection, the one-electron density is kept fixed by a suitable local one-body potential. The strong-interaction limit of density functional theory, defined as the limit λf∞, turns out to be like the opposite noninteracting Kohn-Sham limit (λf0) mathematically simpler than the physical (λ ) 1) case and can be used to build an approximate interpolation formula between λf0 and λf∞ for the exchange-correlation energy. Here we extend the systematic treatment of the λf∞ limit [Phys. Rev. A 2007, 75, 042511] to the next leading term, describing zero-point oscillations of strictly correlated electrons, with numerical examples for small spherical atoms. We also propose an improved approximate functional for the zero-point term and a revised interpolation formula for the exchange-correlation energy satisfying more exact constraints.