Related Experiment Video
Updated: May 13, 2026
06:37
Analyzing Melts and Fluids from Ab Initio Molecular Dynamics Simulations with the UMD Package
Published on: September 17, 2021
Interatomic methods for the dispersion energy derived from the adiabatic connection fluctuation-dissipation theorem
Alexandre Tkatchenko1, Alberto Ambrosetti, Robert A DiStasio
1Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, 14195 Berlin, Germany.
The Journal of Chemical Physics
|March 1, 2013
Summary
Dispersion energy calculations in density functional theory are rigorously derived from quantum mechanics using the adiabatic connection fluctuation-dissipation theorem. This provides a more accurate and efficient method for many-body dispersion energy computations.
Area of Science:
- Quantum Chemistry
- Computational Physics
- Materials Science
Background:
- Interatomic pairwise methods are widely used for dispersion energy in density functional theory.
- These methods are often perceived as lacking rigorous quantum mechanical derivation for multi-atom systems.
Purpose of the Study:
- To demonstrate a rigorous quantum mechanical derivation for pairwise interatomic dispersion energy.
- To establish an efficient method for calculating many-body dispersion energy.
- To clarify the origin of short-range damping functions in dispersion calculations.
Main Methods:
- Utilizing the adiabatic connection fluctuation-dissipation (ACFD) theorem.
- Applying the random-phase approximation (RPA) and full-potential approximation.
- Employing Hamiltonian diagonalization for quantum harmonic oscillators.
Main Results:
- Pairwise interatomic dispersion energy is shown to emerge from the second-order ACFD expansion.
- Hamiltonian diagonalization is proven equivalent to ACFD-RPA correlation energy for specific systems.
- The origin of switching functions is linked to screened Coulomb potentials.
Conclusions:
- The ACFD formula provides a rigorous foundation for dispersion energy calculations.
- Hamiltonian diagonalization offers an efficient route to many-body dispersion energy.
- This work deepens the understanding of approximations in pairwise dispersion methods and guides future developments.
Related Concept Videos
01:24Van der Waals Interactions
Atoms and molecules interact with each other through intermolecular forces. These electrostatic forces arise from attractive or repulsive interactions between particles with permanent, partial, or temporary charges. The intermolecular forces between neutral atoms and molecules are ion–dipole, dipole–dipole, and dispersion forces, collectively known as van der Waals forces.
03:13Intermolecular Forces
Atoms and molecules interact through bonds (or forces): intramolecular and intermolecular. The forces are electrostatic as they arise from interactions (attractive or repulsive) between charged species (permanent, partial, or temporary charges) and exist with varying strengths between ions, polar, nonpolar, and neutral molecules. The different types of intermolecular forces are ion–dipole, dipole–dipole, hydrogen bonds, and dispersion; among these, dipole–dipole, hydrogen bonds, and dispersion...
03:13Intermolecular Forces
Atoms and molecules interact through bonds (or forces): intramolecular and intermolecular. The forces are electrostatic as they arise from interactions (attractive or repulsive) between charged species (permanent, partial, or temporary charges) and exist with varying strengths between ions, polar, nonpolar, and neutral molecules. The different types of intermolecular forces are ion–dipole, dipole–dipole, hydrogen bonds, and dispersion; among these, dipole–dipole, hydrogen bonds, and dispersion...
01:18Adiabatic Processes for an Ideal Gas
When an ideal gas is compressed adiabatically, that is, without adding heat, work is done on it, and its temperature increases. In an adiabatic expansion, the gas does work, and its temperature drops. Adiabatic compressions actually occur in the cylinders of a car, where the compressions of the gas-air mixture take place so quickly that there is no time for the mixture to exchange heat with its environment. Nevertheless, because work is done on the mixture during the compression, its...
01:27The Molecular Nature of Internal Energy
The internal energy of a molecule is determined by its degrees of freedom, including translational, rotational, and vibrational motions. In addition to these kinetic activities, the energy of molecules is also shaped by electronic energy, intermolecular forces, and the rest-mass energy of electrons and nuclei. These factors collectively influence the energy state of the molecules. The equipartition theorem of classical mechanics provides insight into this energy distribution. It posits that the...
02:39Entropy
Salt particles that have dissolved in water never spontaneously come back together in solution to reform solid particles. Moreover, a gas that has expanded in a vacuum remains dispersed and never spontaneously reassembles. The unidirectional nature of these phenomena is the result of a thermodynamic state function called entropy (S). Entropy is the measure of the extent to which the energy is dispersed throughout a system, or in other words, it is proportional to the degree of disorder of a...