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Van der Waals Interactions01:24

Van der Waals Interactions

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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.
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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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Thus far, the ideal gas law, PV = nRT, has been applied to a variety of different types of problems, ranging from reaction stoichiometry and empirical and molecular formula problems to determining the density and molar mass of a gas. However, the behavior of a gas is often non-ideal, meaning that the observed relationships between its pressure, volume, and temperature are not accurately described by the gas laws. 
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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...
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Intermolecular forces (IMF) are electrostatic attractions arising from charge-charge interactions between molecules. The strength of the intermolecular force is influenced by the distance of separation between molecules. The forces significantly affect the interactions in solids and liquids, where the molecules are close together. In gases, IMFs become important only under high-pressure conditions (due to the proximity of gas molecules). Intermolecular forces dictate the physical properties of...
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The Source of Some Empirical Density Functionals van der Waals Forces.

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Minnesota functionals, widely used in chemistry, achieve high accuracy by exploiting basis set incompleteness. This physics-defying behavior distorts electron densities and suggests future functionals should satisfy the Hellmann-Feynman theorem.

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Area of Science:

  • Computational Chemistry
  • Quantum Chemistry
  • Materials Science

Background:

  • Density functional approximations (DFAs) are essential in chemistry for their balance of accuracy and computational cost.
  • Minnesota functionals are highly parameterized DFAs known for exceptional accuracy in thermochemistry and weak interactions.
  • However, their underlying physical mechanisms and potential limitations require further investigation.

Purpose of the Study:

  • To investigate the origin of the high accuracy of Minnesota functionals, particularly in describing weak medium-range interactions.
  • To determine if the performance of these functionals is linked to artifacts or physical principles.
  • To provide guidance for the development of future density functional approximations.

Main Methods:

  • Analysis of the performance of various Minnesota functionals.
  • Investigation of the role of basis set incompleteness in the functionals' accuracy.
  • Evaluation of the electron density distortion and adherence to fundamental theorems like the Hellmann-Feynman theorem.

Main Results:

  • The remarkable accuracy of many Minnesota functionals in reproducing weak interactions stems from exploiting basis set incompleteness.
  • This exploitation leads to a physics-defying behavior and can cause distortions in calculated electron densities.
  • The Hellmann-Feynman theorem is often violated, indicating a potential artifact rather than true physical accuracy.

Conclusions:

  • The accuracy of Minnesota functionals in certain areas is an artifact of basis set incompleteness, not necessarily robust physical modeling.
  • Future development of highly parameterized density functionals, including neural network-based approaches, should prioritize adherence to fundamental theorems like the Hellmann-Feynman theorem.
  • Satisfying the Hellmann-Feynman theorem should be a key criterion for parameterization to ensure physically meaningful results.