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Keywords:

  • density functional theory;
  • ensemble density theory;
  • electronic structure theory;
  • exchange and correlation energy;
  • kinetic energy;
  • coulomb interaction energy;
  • atoms molecules and solids

Abstract

Formal properties of ensemble density functionals are examined. Expressions for the difference between energy functionals where the particle number differs by one are constructed in terms of their first functional derivatives for the universal energy functional, the electron–electron repulsion energy functional, and the interacting kinetic energy functional. Equations that must be satisfied by second and higher order functional derivatives are derived. It is also shown that the shape of equation image and equation image, the functional derivatives of the mutual electron–electron repulsion, and kinetic energy, respectively, are separately particle number independent for particle numbers between successive integers. © 2013 Wiley Periodicals, Inc.