Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Kinetic Energy for a Rigid Body01:13

Kinetic Energy for a Rigid Body

215
Imagine a solid object involved in a general planar movement, with its center of mass pinpointed at a spot labeled G. The object's kinetic energy relative to an arbitrary point A can be quantified for each of its particles - the ith particle in this case. This measurement is achieved through the employment of the relative velocity definition. The position vector, known as rA, extends from point A to the mass element i.
215
Free Energy Changes for Nonstandard States03:25

Free Energy Changes for Nonstandard States

11.4K
The free energy change for a process taking place with reactants and products present under nonstandard conditions (pressures other than 1 bar; concentrations other than 1 M) is related to the standard free energy change according to this equation:
 
where R is the gas constant (8.314 J/K·mol), T is the absolute temperature in kelvin, and Q is the reaction quotient. This equation may be used to predict the spontaneity of a process under any given set of conditions.
Reaction Quotient...
11.4K
The Quantum-Mechanical Model of an Atom02:45

The Quantum-Mechanical Model of an Atom

42.4K
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.
42.4K
First Law: Particles in Two-dimensional Equilibrium01:18

First Law: Particles in Two-dimensional Equilibrium

5.1K
Recall that a particle in equilibrium is one for which the external forces are balanced. Static equilibrium involves objects at rest, and dynamic equilibrium involves objects in motion without acceleration; but it is important to remember that these conditions are relative. For instance, an object may be at rest when viewed from one frame of reference, but that same object would appear to be in motion when viewed by someone moving at a constant velocity.
Newton's first law tells us about...
5.1K
Equilibrium Conditions for a Particle01:23

Equilibrium Conditions for a Particle

1.2K
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.
To understand the concept of equilibrium, let us first consider the forces acting on an object. When different forces act on an object, they can...
1.2K
First Law: Particles in One-dimensional Equilibrium01:10

First Law: Particles in One-dimensional Equilibrium

6.9K
Newton's first law of motion states that a body at rest remains at rest, or if in motion, remains in motion at constant velocity, unless acted on by a net external force. It also states that there must be a cause for any change in velocity (a change in either magnitude or direction) to occur. This cause is a net external force. For example, consider what happens to an object sliding along a rough horizontal surface. The object quickly grinds to a halt, due to the net force of friction. If...
6.9K

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Multistate coupled diabatic neural network potential for the quantum non-adiabatic photofragmentation of CH<sub>2</sub><sup></sup>.

Physical chemistry chemical physics : PCCP·2026
Same author

Accurate Chemistry Collection: Coupled cluster atomization energies for broad chemical space.

Scientific data·2026
Same author

Chemical Space Exploration with Artificial "Mindless" Molecules.

Journal of chemical information and modeling·2025
Same author

Quantum dynamics and cooling kinetics of BN- anions via buffer gases in ion traps.

The Journal of chemical physics·2025
Same author

Understanding the destruction of CH<sup>+</sup> with atomic hydrogen at low temperatures: a non-adiabatic dynamical study.

Physical chemistry chemical physics : PCCP·2025
Same author

Highly accurate real-space electron densities with neural networks.

The Journal of chemical physics·2025

Related Experiment Video

Updated: Jul 11, 2025

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
11:03

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

8.6K

Variational principle to regularize machine-learned density functionals: The non-interacting kinetic-energy

Pablo Del Mazo-Sevillano1,2, Jan Hermann2,3

  • 1Departamento de Química Física Aplicada, Universidad Autónoma de Madrid, Módulo 14, 28049 Madrid, Spain.

The Journal of Chemical Physics
|November 16, 2023
PubMed
Summary
This summary is machine-generated.

This study introduces a novel deep neural network method to train kinetic-energy density functionals. The approach shows excellent results for one-dimensional systems and atomic systems, advancing density functional theory (DFT) applications.

More Related Videos

Author Spotlight: Streamlining Visual Dynamics to Simplify Molecular Dynamics Simulations Using Gromacs
05:00

Author Spotlight: Streamlining Visual Dynamics to Simplify Molecular Dynamics Simulations Using Gromacs

Published on: August 9, 2024

1.3K
Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
08:04

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids

Published on: May 27, 2020

8.5K

Related Experiment Videos

Last Updated: Jul 11, 2025

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
11:03

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

8.6K
Author Spotlight: Streamlining Visual Dynamics to Simplify Molecular Dynamics Simulations Using Gromacs
05:00

Author Spotlight: Streamlining Visual Dynamics to Simplify Molecular Dynamics Simulations Using Gromacs

Published on: August 9, 2024

1.3K
Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
08:04

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids

Published on: May 27, 2020

8.5K

Area of Science:

  • Computational Chemistry
  • Quantum Mechanics
  • Machine Learning

Background:

  • Density Functional Theory (DFT) relies on the Kohn-Sham approach for non-interacting kinetic energy calculation.
  • Accurate kinetic-energy functionals are crucial for unlocking DFT's full potential but remain challenging due to their non-local nature.
  • Existing approximations for kinetic-energy functionals have had limited success compared to exchange-correlation functionals.

Purpose of the Study:

  • To develop and test a new, efficient regularization method for training density functionals using deep neural networks.
  • To specifically focus on improving the accuracy of the kinetic-energy functional within DFT.
  • To demonstrate the generalizability of the proposed machine learning approach to other DFT functionals, such as exchange-correlation.

Main Methods:

  • Implementation of a novel regularization technique for training deep neural networks.
  • Application of the method to train kinetic-energy density functionals.
  • Testing the trained functionals on one-dimensional systems (hydrogen chain, non-interacting electrons) and atomic systems (first two periods).

Main Results:

  • The proposed regularization method achieved excellent performance in training kinetic-energy functionals for the tested systems.
  • Demonstrated successful generalization by training an exchange-correlation functional using the same machine learning approach.
  • Provided insights into the contrasting characteristics of kinetic-energy and exchange-correlation functionals from a machine learning perspective.

Conclusions:

  • The deep neural network-based regularization method offers an efficient and promising avenue for developing accurate density functionals.
  • This approach shows significant potential for advancing the capabilities of DFT calculations, particularly for kinetic energy.
  • The study highlights the applicability and adaptability of machine learning techniques in quantum chemistry and materials science.