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A state function is a thermodynamic property that depends solely on the current state of a system, irrespective of its history or how it arrived at that state. These functions are represented by capital letters, such as U, H, and S, which stand for internal energy, enthalpy, and entropy, respectively.For instance, the value of internal energy depends on the system's state variables and remains unaffected by the process path. This means that whether the system underwent a linear process or a...
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The Debye-Hückel-Onsager equation is a cornerstone of physical chemistry, providing a method to determine the molar conductance (Λm) and molar conductance at infinite dilution (Λ°m) for uni-univalent electrolytes.Uni-univalent electrolytes are electrolytes that dissociate in solution to produce one cation with a +1 charge and one anion with a –1 charge per formula unit.This equation addresses two crucial phenomena: the asymmetry effect and the electrophoretic effect.
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The Debye–Hückel theory, established by Peter Debye and Erich Hückel in 1923, is a fundamental concept in physical chemistry. It provides an understanding of the behavior of strong electrolytes in solution, particularly explaining their deviations from ideal behavior.The theory is based on Coulombic interactions (the attraction or repulsion between charged particles) between ions in solution. In an ionic solution, oppositely charged ions tend to attract each other. This means...
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Related Experiment Video

Updated: Apr 29, 2026

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
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Differentiable but exact formulation of density-functional theory.

Simen Kvaal1, Ulf Ekström1, Andrew M Teale1

  • 1Centre for Theoretical and Computational Chemistry, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway.

The Journal of Chemical Physics
|May 17, 2014
PubMed
Summary

Density-functional theory

Area of Science:

  • Quantum Chemistry
  • Computational Physics

Background:

  • The universal density functional (F) in density-functional theory (DFT) is mathematically complex and non-differentiable, complicating theoretical manipulations.
  • While F and ground-state energy (E) form a conjugate pair via convex analysis, F's non-differentiability poses challenges.
  • Standard Kohn-Sham theory faces issues with noninteracting representability.

Purpose of the Study:

  • To develop a mathematically rigorous and differentiable formulation of density-functional theory.
  • To address the non-differentiability of the universal density functional (F).
  • To provide a robust foundation for Kohn-Sham theory, resolving the noninteracting representability problem.

Main Methods:

  • Application of Moreau-Yosida regularization, a tool from convex analysis.

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  • Construction of pairs of conjugate functionals ((ε)E, (ε)F) for ε > 0.
  • Focus on molecular electronic systems within a finite, large box for technical reasons.

    • Main Results:

    • Regularized functionals ((ε)E, (ε)F) converge pointwise to (E, F) as ε approaches 0.
    • The regularized functional (ε)F is proven to be (Fréchet) differentiable.
    • Physical ground-state energy E(v) is exactly recoverable from the regularized (ε)E(v).

    Conclusions:

    • Moreau-Yosida regularization enables an exact and differentiable formulation of density-functional theory.
    • This approach allows for a rigorous formulation of Kohn-Sham theory, overcoming the noninteracting representability problem.
    • The regularization technique preserves all essential physical information and theoretical concepts of DFT.