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Atomic Orbitals

Atomic Orbitals

An atomic orbital represents the three-dimensional regions in an atom where an electron has the highest probability to reside. The radial distribution function indicates the total probability of finding an electron within the thin shell at a distance r from the nucleus. The atomic orbitals have distinct shapes which are determined by l, the angular momentum quantum number. The orbitals are often drawn with a boundary surface, enclosing densest regions of the cloud.

Electronic Structure of Atoms

Electronic Structure of Atoms

An atom comprises protons and neutrons, which are contained inside the dense, central core called the nucleus, with electrons present around the nucleus. Taking into account the wave–particle duality of electrons and the uncertainty in position around the nucleus, quantum mechanics provides a more accurate model for the atomic structure. It describes atomic orbitals as the regions around the nucleus where electrons of discrete energy exist, characterized by four quantum...

VSEPR Theory

VSEPR Theory

Valence shell electron-pair repulsion theory (VSEPR theory) enables us to predict the molecular structure around a central atom from an examination of the number of bonds and lone electron pairs in its Lewis structure. The VSEPR model assumes that electron pairs in the valence shell of a central atom will adopt an arrangement that minimizes repulsions between these electron pairs by maximizing the distance between them. The electrons in the valence shell of a central atom form either bonding...

Valence Bond Theory and Hybridized Orbitals

Valence Bond Theory and Hybridized Orbitals

According to valence bond theory, a covalent bond results when: (1) an orbital on one atom overlaps an orbital on a second atom, and (2) the single electrons in each orbital combine to form an electron pair. The strength of a covalent bond depends on the extent of overlap of the orbitals involved. Maximum overlap is possible when the orbitals overlap on a direct line between the two nuclei.
A σ bond (single bond in a Lewis structure) is a covalent bond in which the electron density is...

VSEPR Theory and the Basic Shapes

VSEPR Theory and the Basic Shapes

Overview of VSEPR Theory

The Quantum-Mechanical Model of an Atom

The Quantum-Mechanical Model of an Atom

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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Related Experiment Video

Updated: May 30, 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

The design space of E(3)-equivariant atom-centred interatomic potentials.

Ilyes Batatia^1,2, Simon Batzner³, Dávid Péter Kovács¹

¹Engineering Laboratory, University of Cambridge, Cambridge, UK.

Nature Machine Intelligence

|January 29, 2025

Summary

Machine learning revolutionized molecular dynamics simulations by creating new interatomic potentials. A unified mathematical framework connects atomic cluster expansion and Neural Equivariant Interatomic Potentials (NequIP), leading to simplified, accurate models like BOTnet.

Keywords:

Atomistic models Computational chemistry Computational methods Molecular dynamics

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Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

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Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

Published on: April 8, 2020

Area of Science:

Computational Materials Science
Computational Chemistry
Machine Learning

Background:

Machine learning has significantly advanced molecular dynamics simulations.
New architectures for machine learning interatomic potentials have emerged rapidly.
Atomic cluster expansion and Neural Equivariant Interatomic Potentials (NequIP) are notable recent developments.

Purpose of the Study:

To construct a unifying mathematical framework for existing machine learning interatomic potential models.
To provide a tool for systematically exploring the design space of these models.
To analyze critical design choices in NequIP through ablation studies.

Main Methods:

Developed a mathematical framework unifying atomic cluster expansion and NequIP.
Extended atomic cluster expansion into a multi-layer architecture.
Interpreted linearized NequIP as a sparsification of a polynomial model.
Conducted ablation studies on NequIP focusing on in- and out-of-domain accuracy and extrapolation.

Main Results:

The framework unifies atomic cluster expansion and NequIP.
Ablation studies identified critical design choices for NequIP accuracy.
A simplified model, BOTnet (body-ordered tensor network), was developed.
BOTnet demonstrates interpretable architecture and maintains accuracy on benchmark datasets.

Conclusions:

A unified framework provides insights into machine learning interatomic potentials.
BOTnet offers a simplified, accurate, and interpretable alternative.
Understanding design choices is crucial for developing high-accuracy potentials.