Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

Predicting Molecular Geometry

Predicting Molecular Geometry

VSEPR Theory for Determination of Electron Pair Geometries

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...

Hybridization of Atomic Orbitals II

Hybridization of Atomic Orbitals II

sp3d and sp3d 2 Hybridization

Hybridization of Atomic Orbitals I

Hybridization of Atomic Orbitals I

The mathematical expression known as the wave function, ψ, contains information about each orbital and the wavelike properties of electrons in an isolated atom. When atoms are bound together in a molecule, the wave functions combine to produce new mathematical descriptions that have different shapes. This process of combining the wave functions for atomic orbitals is called hybridization and is mathematically accomplished by the linear combination of atomic orbitals. The new orbitals that...

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.

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.

You might also read

Related Articles

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

Sort by

Same author

First-Principles Analysis of Protonation-Induced Electronic Effects in Tetrakis(<i>p</i>-aminophenyl)porphyrin (TAPP).

The journal of physical chemistry. A·2026

Same author

Probing the Ultrafast Photodynamics of Dihydroazulene with In Silico Time-Resolved Photoelectron Spectroscopy and Ultrafast Electron Diffraction.

The journal of physical chemistry. A·2026

Same author

Complete Active Space Self-Consistent Field with GPU-Accelerated Density Fitting.

Journal of chemical theory and computation·2026

Same author

Shadow excited state molecular dynamics with the ΔSCF method.

The Journal of chemical physics·2026

Same author

Accelerating CCSD(T) on Graphical Processing Units (GPUs).

The journal of physical chemistry. A·2026

Same author

Robust and Automated Force Field Parameterization Using Validation Sets and Active Learning.

Journal of chemical theory and computation·2026

Search research articles

Related Experiment Video

Updated: Mar 29, 2026

Rapid in-silico Battery Electrolyte Electrochemical Reaction Generation using 3T-VASP Multi-Scale Energy Minimization

Rapid in-silico Battery Electrolyte Electrochemical Reaction Generation using 3T-VASP Multi-Scale Energy Minimization

Published on: August 22, 2025

Generating Efficient Quantum Chemistry Codes for Novel Architectures.

Alexey V Titov^1,2, Ivan S Ufimtsev², Nathan Luehr²

¹National Center for Supercomputing Applications, University of Illinois at Urbana-Champaign , Urbana, Illinois 61801, United States.

Journal of Chemical Theory and Computation

|November 22, 2015

Summary

This summary is machine-generated.

This study introduces a new GPU-accelerated electronic structure program, TeraChem, featuring d-angular momentum functions. The meta-programming approach optimizes performance for computational chemistry, enhancing GPU capabilities.

More Related Videos

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

Multiscale Sampling of a Heterogeneous Water/Metal Catalyst Interface using Density Functional Theory and Force-Field Molecular Dynamics

Multiscale Sampling of a Heterogeneous Water/Metal Catalyst Interface using Density Functional Theory and Force-Field Molecular Dynamics

Published on: April 12, 2019

Related Experiment Videos

Last Updated: Mar 29, 2026

Rapid in-silico Battery Electrolyte Electrochemical Reaction Generation using 3T-VASP Multi-Scale Energy Minimization

Rapid in-silico Battery Electrolyte Electrochemical Reaction Generation using 3T-VASP Multi-Scale Energy Minimization

Published on: August 22, 2025

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

Multiscale Sampling of a Heterogeneous Water/Metal Catalyst Interface using Density Functional Theory and Force-Field Molecular Dynamics

Multiscale Sampling of a Heterogeneous Water/Metal Catalyst Interface using Density Functional Theory and Force-Field Molecular Dynamics

Published on: April 12, 2019

Area of Science:

Computational Chemistry
Materials Science
Quantum Mechanics

Background:

Electronic structure calculations are crucial for understanding molecular properties.
Graphics Processing Units (GPUs) offer significant computational power for scientific applications.
Existing GPU implementations often lack support for higher angular momentum functions.

Purpose of the Study:

To extend the TeraChem program to include atom-centered Gaussian basis sets with d angular momentum functions.
To develop and implement a meta-programming strategy for optimizing GPU code performance.
To benchmark the performance of the enhanced TeraChem against existing CPU-based codes.

Main Methods:

Utilized a meta-programming strategy with computer algebra systems for equation derivation and code generation.
Generated and empirically tested multiple code fragments to identify optimal variants balancing operations and memory bandwidth.
Implemented mixed precision schemes for stability and accuracy with d functions.
Benchmarked the execution time of self-consistent field (SCF) calculations on GPUs.

Main Results:

Achieved performance comparable to hand-tuned GPU kernels for s and p functions.
Demonstrated stability and accuracy of mixed precision schemes for molecules with d functions.
Showcased significant speedups in SCF calculations compared to mature CPU-based codes.

Conclusions:

The meta-programming and empirical optimization approach effectively enhances GPU performance for electronic structure calculations.
The extended TeraChem program provides a powerful tool for computational chemistry, leveraging GPU architecture.
This methodology is promising for future computational chemistry applications, adapting to evolving computer architectures.