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Related Concept Videos

The Kinetic Model of Gases01:24

The Kinetic Model of Gases

The kinetic model of gases explains the properties of a perfect gas using three main assumptions: molecules move in ceaseless random motion, their size is negligible compared to the distances between them, and they do not interact except during perfectly elastic collisions. The total energy of a gas is the sum of the kinetic energies of all its constituent molecules. The pressure exerted by the gas arises from the continual bombardment of the container walls by billions of colliding molecules.
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Related Experiment Video

Updated: Jul 18, 2026

Multiscale Sampling of a Heterogeneous Water/Metal Catalyst Interface using Density Functional Theory and Force-Field Molecular Dynamics
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Time-dependent density-functional theory beyond the adiabatic approximation: insights from a two-electron model

C A Ullrich1

  • 1Department of Physics and Astronomy, University of Missouri, Columbia, Missouri 65211, USA.

The Journal of Chemical Physics
|December 28, 2006
PubMed
Summary

This study reveals that the exact extension of the local density approximation in time-dependent density-functional theory (TDDFT) introduces dissipation due to memory effects. This nonadiabatic TDDFT approach is accurate for large systems but fails for finite ones.

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Last Updated: Jul 18, 2026

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Area of Science:

  • Computational Physics
  • Quantum Mechanics
  • Materials Science

Background:

  • Time-dependent density-functional theory (TDDFT) is a powerful tool for studying electron dynamics.
  • The adiabatic local-density approximation (ALDA) is commonly used in TDDFT but has limitations.

Purpose of the Study:

  • To investigate the nonadiabatic behavior of TDDFT beyond the ALDA.
  • To understand the origin of dissipation in electron dynamics.
  • To compare TDDFT with and without ALDA against accurate numerical solutions.

Main Methods:

  • Studied the dynamics of two interacting electrons in a 2D quantum strip.
  • Employed time-dependent density-functional theory (TDDFT) both within and beyond the adiabatic local-density approximation (ALDA).
  • Compared TDDFT results with numerical solutions of the time-dependent Schrödinger equation.

Main Results:

  • Demonstrated that nonadiabatic TDDFT introduces dissipation through multiple particle-hole excitations.
  • Showed that the nonadiabatic extension of ALDA fails for finite systems.
  • Confirmed the accuracy of nonadiabatic TDDFT in the thermodynamic limit.

Conclusions:

  • The exact extension of LDA into the dynamical regime leads to dissipative electron dynamics.
  • Nonadiabatic TDDFT is crucial for accurately describing electron dynamics in finite systems.
  • The ALDA approximation breaks down for small systems, necessitating more advanced TDDFT methods.