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Ligand-Mediated Nucleation and Growth of Palladium Metal Nanoparticles
11:54

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Published on: June 25, 2018

Particle number and probability density functional theory and A-representability.

Xiao-Yin Pan1, Viraht Sahni

  • 1Department of Physics, Ningbo University, Ningbo 315211, China.

The Journal of Chemical Physics
|May 6, 2010
PubMed
Summary
This summary is machine-generated.

This study reformulates density functional theory (DFT) by expressing energy as a functional of particle number (N) and probability density (p(r)). This approach establishes the equivalence between A-representable and N-representable probability densities.

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Area of Science:

  • Quantum Chemistry
  • Computational Physics
  • Materials Science

Background:

  • Hohenberg-Kohn density functional theory (DFT) expresses energy as a functional of ground-state electron density, rho(r).
  • The internal energy component, F(HK)[rho], is universal, but knowledge of this functional alone is insufficient for determining total energy.

Purpose of the Study:

  • To reformulate DFT by emphasizing the primacy of particle number (N).
  • To construct a functional theory based on particle number (N) and probability density (p(r)).
  • To establish the relationship between different representability concepts in DFT.

Main Methods:

  • Re-expressing energy E as a nonuniversal functional of N and p(r): E = E[N,p].
  • Defining probability density or p-space with constraints of normalization and non-negativity for each N.
  • Introducing and utilizing the concept of A-representability.

Main Results:

  • Demonstrated the equivalence between the set of functions p(r) in p-space and the A-representable probability density set.
  • Showed, using Harriman and Gilbert constructions, that A-representable and N-representable probability density sets are equivalent.
  • Provided two examples with known exact energy functionals E[N,p].

Conclusions:

  • The particle number N is primary in determining the energy functional.
  • A unified framework is established where probability densities, particle numbers, and energy functionals are interconnected.
  • The findings offer a new perspective on the foundations of density functional theory.