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Related Concept Videos

Potential Energy00:52

Potential Energy

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The energy stored by a structure and location of matter in space is called potential energy. For instance, raising a kettlebell changes its spatial location and increases its potential energy. Similarly, a stretched rubber band contains potential energy which, under certain conditions, can be converted into other forms of energy, such as kinetic energy.
Chemical bonds that form attractive forces between atoms also contain potential energy, called chemical energy. When a chemical reaction...
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Force and Potential Energy in One Dimension01:13

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Force can be calculated from the expression for potential energy, which is a function of position. The component of a conservative force, in a particular direction, equals the negative of the derivative of the corresponding potential energy with respect to the displacement in that direction. For regions where potential energy changes rapidly with displacement, the work done and force is maximum. Also, when force is applied along the positive coordinate axis, the potential energy decreases with...
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Force and Potential Energy in Three Dimensions01:04

Force and Potential Energy in Three Dimensions

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Consider a particle moving under the action of a conservative force that has components along each coordinate axis. Each component of force is a function of the coordinates. The potential energy function U is also a function of all three spatial coordinates. Force in one dimension can be written as the negative ratio of potential energy change to the displacement along that coordinate. For minimal displacement, the ratios become derivatives. If a function has many variables, the derivative only...
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Potential-Energy Criterion for Equilibrium01:16

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Potential energy or potential function plays an essential role in determining the stability of a mechanical system. If a system is subjected to both gravitational and elastic forces, the potential function of the system can be expressed as the algebraic sum of gravitational and elastic potential energy. If the system is in equilibrium and is displaced by a small amount, then the work done on the system equals the negative of the change in the system's potential energy from the initial to...
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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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Equipotential Surfaces and Field Lines01:29

Equipotential Surfaces and Field Lines

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Electric potential can be pictorially represented as a three-dimensional surface. On such a surface, the electric potential is constant everywhere. The equipotential surface is always perpendicular to the electric field lines, and while it is three-dimensional, it can be treated as an equipotential line in a two-dimensional case. These equipotential lines are also always perpendicular to electric field lines. The term equipotential is often used as a noun, referring to an equipotential line or...
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Δ-Machine Learned Potential Energy Surfaces and Force Fields.

Joel M Bowman1, Chen Qu2, Riccardo Conte3

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A new Δ-machine learning method enhances Density Functional Theory (DFT) potential energy surfaces (PESs) to near coupled cluster with singles and doubles (CCSD(T)) accuracy. This approach extends to force fields, improving accuracy for molecular simulations.

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Area of Science:

  • Computational Chemistry
  • Quantum Chemistry
  • Machine Learning

Background:

  • Machine-learned potential energy surfaces (PESs) are advancing for larger molecular systems.
  • Current methods often limit electronic structure theory to below coupled cluster with singles and doubles (CCSD(T)) accuracy.
  • Existing datasets like MD17 use Density Functional Theory (DFT) (PBE) for energies and forces.

Purpose of the Study:

  • To present and demonstrate a Δ-machine learning method for achieving near CCSD(T) accuracy in DFT-based PESs.
  • To extend the Δ-machine learning approach to improve force fields.
  • To develop accurate, ab initio potentials for molecular systems.

Main Methods:

  • Application of a novel Δ-machine learning method to DFT-based PESs.
  • Extension of Δ-machine learning to force fields using many-body corrections.
  • Development of CCSD(T) datasets for 2-body, 3-body, and 4-body interactions in water.

Main Results:

  • Achieved near CCSD(T) accuracy for DFT-based PESs of hydronium, N-methylacetamide, acetyl acetone, and ethanol.
  • Demonstrated the extension of Δ-machine learning to force fields.
  • Developed a new fully ab initio water potential, q-AQUA, using CCSD(T) interaction datasets.

Conclusions:

  • Δ-machine learning is effective in elevating DFT-based PESs to near CCSD(T) accuracy.
  • The method shows promise for improving force fields and developing highly accurate molecular potentials.
  • Specialized techniques may be required for very large systems like 15-atom tropolone to reach CCSD(T) energies.