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Debye–Huckel–Onsager Conductance Equation01:28

Debye–Huckel–Onsager Conductance Equation

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. According to this equation,...
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The ideal gas law is an approximation that works well at high temperatures and low pressures. The van der Waals equation of state (named after the Dutch physicist Johannes van der Waals, 1837−1923) improves it by considering two factors.
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The ionization-constant expression for a solution of a weak acid can be written as:

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Related Experiment Video

Updated: May 22, 2026

Multiscale Sampling of a Heterogeneous Water/Metal Catalyst Interface using Density Functional Theory and Force-Field Molecular Dynamics
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Multiscale Sampling of a Heterogeneous Water/Metal Catalyst Interface using Density Functional Theory and Force-Field Molecular Dynamics

Published on: April 12, 2019

Projected Hartree-Fock theory.

Carlos A Jiménez-Hoyos1, Thomas M Henderson, Takashi Tsuchimochi

  • 1Department of Chemistry, Rice University, Houston, Texas 77005, USA.

The Journal of Chemical Physics
|May 8, 2012
PubMed
Summary

Projected Hartree-Fock (PHF) theory offers a new computational approach for quantum chemistry. This variation after projection method provides high-quality wavefunctions but is not size-consistent in the thermodynamic limit.

Area of Science:

  • Quantum Chemistry
  • Computational Chemistry
  • Theoretical Physics

Background:

  • Projected Hartree-Fock (PHF) theory, a method for determining N-electron wavefunctions with correct quantum numbers, has a historical significance in quantum chemistry.
  • The method involves variational determination of a broken symmetry Slater determinant followed by projection, but its active development appears to have ceased decades ago.

Purpose of the Study:

  • To derive and implement a novel "variation after projection" Projected Hartree-Fock (PHF) theory.
  • To explore the applicability and performance of this new PHF methodology in quantum chemical calculations.
  • To assess the quality of the wavefunctions and the energy characteristics of the developed PHF approach.

Main Methods:

  • Development of a "variation after projection" Projected Hartree-Fock (PHF) theory using distinct techniques.

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  • Implementation of the PHF methodology with modest mean-field computational cost and relatively simple expressions.
  • Application to both collinear and non-collinear spin cases, incorporating symmetry breaking and restoration (complex conjugation, point group).

    • Main Results:

    • Benchmark applications to molecular dissociation curves and singlet-triplet energy splittings demonstrate high-quality multireference character of PHF wavefunctions.
    • The derived PHF methodology exhibits computational efficiency and flexibility in handling various symmetries.
    • Numerical evidence indicates that PHF energy is not lower than broken-symmetry Hartree-Fock (HF) in the thermodynamic limit.

    Conclusions:

    • The implemented "variation after projection" PHF theory provides accurate multireference wavefunctions with manageable computational expense.
    • The method is versatile, applicable to diverse quantum chemical problems including spin-related phenomena and molecular symmetries.
    • Projected Hartree-Fock (PHF) theory lacks size consistency and extensivity, limiting its energy advantage over simpler methods in the thermodynamic limit.