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Related Concept Videos

Thermodynamic Potentials01:26

Thermodynamic Potentials

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Thermodynamic potentials are state functions that are extremely useful in analyzing a thermodynamic system. They have dimensions of energy. The four important thermodynamic potentials are internal energy, enthalpy, Helmholtz free energy, and Gibbs free energy. These thermodynamic potentials can be expressed using two of the following variables: pressure, volume, temperature, and entropy. These two variables are expressed as the rate of change of the thermodynamic potential with respect to other...
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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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Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra.
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Van der Waals Interactions01:24

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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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Real Gases: Effects of Intermolecular Forces and Molecular Volume Deriving Van der Waals Equation04:01

Real Gases: Effects of Intermolecular Forces and Molecular Volume Deriving Van der Waals Equation

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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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When an object is in equilibrium, it is either at rest or moving with a constant velocity. There are two types of equilibrium: static and dynamic. Static equilibrium occurs when an object is at rest, while dynamic equilibrium occurs when an object is moving with a constant velocity. In both cases, there must be a balance of forces acting on the object.
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Updated: Oct 25, 2025

Multiscale Sampling of a Heterogeneous Water/Metal Catalyst Interface using Density Functional Theory and Force-Field Molecular Dynamics
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General Many-Body Framework for Data-Driven Potentials with Arbitrary Quantum Mechanical Accuracy: Water as a Case

Eleftherios Lambros1, Saswata Dasgupta1, Etienne Palos1

  • 1Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California 92093, United States.

Journal of Chemical Theory and Computation
|August 9, 2021
PubMed
Summary
This summary is machine-generated.

We developed a framework for data-driven many-body potential energy functions (MB-QM PEFs) for accurate molecular simulations. Density-corrected functionals improve accuracy, especially for water clusters, overcoming limitations of generalized gradient approximation functionals.

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Area of Science:

  • Computational Chemistry
  • Quantum Mechanics
  • Materials Science

Background:

  • Developing accurate potential energy functions (PEFs) is crucial for molecular simulations.
  • Quantum mechanical (QM) methods offer high accuracy but are computationally expensive.
  • Many-body (MB) approaches can bridge the gap between accuracy and computational cost.

Purpose of the Study:

  • To present a general framework for data-driven many-body QM PEFs (MB-QM PEFs).
  • To develop and validate MB-QM PEFs for water interactions using various QM methods.
  • To identify and address limitations of existing methods, particularly density functional approximations.

Main Methods:

  • Development of a general framework for MB-QM PEFs.
  • Derivation of MB-QM PEFs for water from density functional theory (DFT) and Møller-Plesset perturbation theory (MP2).
  • Systematic analysis of MB contributions to interaction energies in water clusters.
  • Application of density-corrected DFT (DC-DFT) to improve PEF accuracy.

Main Results:

  • MB-QM PEFs generally preserve the accuracy of the parent QM calculations.
  • Generalized gradient approximation (GGA) functionals show deviations due to density-driven errors.
  • DC-DFT functionals provide a more consistent representation of MB contributions.
  • A MB-DFT PEF derived from DC-PBE-D3 accurately reproduces ab initio results for water clusters.

Conclusions:

  • The developed MB-QM PEF framework enables accurate simulations of molecular interactions.
  • DC-DFT offers a viable solution to overcome limitations of GGA functionals in MB formalisms.
  • The MB-QM PEF approach is promising for high-accuracy computational chemistry and materials science applications.