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Gauss's Law: Problem-Solving

Gauss's Law: Problem-Solving

Gauss's law helps determine electric fields even though the law is not directly about electric fields but electric flux. In situations with certain symmetries (spherical, cylindrical, or planar) in the charge distribution, the electric field can be deduced based on the knowledge of the electric flux. In these systems, we can find a Gaussian surface S over which the electric field has a constant magnitude. Furthermore, suppose the electric field is parallel (or antiparallel) to the area...

Gauss's Law

Gauss's Law

If a closed surface does not have any charge inside where an electric field line can terminate, then the electric field line entering the surface at one point must necessarily exit at some other point of the surface. Therefore, if a closed surface does not have any charges inside the enclosed volume, then the electric flux through the surface is zero. What happens to the electric flux if there are some charges inside the enclosed volume? Gauss's law gives a quantitative answer to this question.

Predicting Molecular Geometry

Predicting Molecular Geometry

VSEPR Theory for Determination of Electron Pair Geometries

Gauss's Law: Planar Symmetry

Gauss's Law: Planar Symmetry

A planar symmetry of charge density is obtained when charges are uniformly spread over a large flat surface. In planar symmetry, all points in a plane parallel to the plane of charge are identical with respect to the charges. Suppose the plane of the charge distribution is the xy-plane, and the electric field at a space point P with coordinates (x, y, z) is to be determined. Since the charge density is the same at all (x, y) - coordinates in the z = 0 plane, by symmetry, the electric field at P...

Gauss's Law in Dielectrics

Gauss's Law in Dielectrics

Consider a polar dielectric placed in an external field. In such a dielectric, opposite charges on adjacent dipoles neutralize each other, such that the net charge within the dielectric is zero. When a polar dielectric is inserted in between the capacitor plates, an electric field is generated due to the presence of net charges near the edge of the dielectric and the metal plates interface. Since the external electrical field merely aligns the dipoles, the dielectric as a whole is neutral. An...

Maxwell-Boltzmann Distribution: Problem Solving

Maxwell-Boltzmann Distribution: Problem Solving

Individual molecules in a gas move in random directions, but a gas containing numerous molecules has a predictable distribution of molecular speeds, which is known as the Maxwell-Boltzmann distribution, f(v).
This distribution function f(v) is defined by saying that the expected number N (v1,v2) of particles with speeds between v1 and v2 is given by

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Related Experiment Video

Updated: Oct 24, 2025

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

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

Published on: May 27, 2020

Gaussian Process Regression for Materials and Molecules.

Volker L Deringer¹, Albert P Bartók², Noam Bernstein³

¹Department of Chemistry, Inorganic Chemistry Laboratory, University of Oxford, Oxford OX1 3QR, United Kingdom.

Chemical Reviews

|August 16, 2021

Summary

Gaussian process regression (GPR) is a powerful machine learning technique for computational materials science and chemistry. This review covers GPR for interatomic potentials and other properties, highlighting its applications and future directions.

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Last Updated: Oct 24, 2025

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

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Published on: May 27, 2020

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Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level

Published on: September 26, 2016

Area of Science:

Computational materials science and chemistry
Machine learning applications in scientific research

Background:

Gaussian process regression (GPR) is a versatile machine learning method.
Its application in computational science is rapidly expanding.
Key areas include atomistic property regression and interatomic potential development.

Purpose of the Study:

To introduce Gaussian process regression (GPR) methods for computational materials science and chemistry.
To review the construction of interatomic potentials (force fields) within the Gaussian Approximation Potential (GAP) framework.
To discuss the fitting of scalar, vectorial, and tensorial quantities using GPR.

Main Methods:

Focus on regression of atomistic properties using GPR.
Detailed discussion on constructing interatomic potentials (force fields) via the Gaussian Approximation Potential (GAP) framework.
Exploration of fitting arbitrary scalar, vectorial, and tensorial quantities.

Main Results:

Methodological aspects of data generation, representation, and regression are critically examined.
Validation strategies for data-driven models are reviewed.
A wide range of applications in chemistry and materials science are surveyed, demonstrating GPR's utility.

Conclusions:

Gaussian process regression (GPR) is a rapidly growing field with significant impact.
The review provides a comprehensive overview of GPR in materials science and chemistry.
Future developments and a vision for the methodology are outlined.