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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.

Electron Orbital Model

Electron Orbital Model

Orbitals are the areas outside of the atomic nucleus where electrons are most likely to reside. They are characterized by different energy levels, shapes, and three-dimensional orientations. The location of electrons is described most generally by a shell or principal energy level, then by a subshell within each shell, and finally, by individual orbitals found within the subshells.
The first shell is closest to the nucleus, and it has only one subshell with a single spherical orbital called the...

Molecular Orbital Theory I

Molecular Orbital Theory I

Overview of Molecular Orbital Theory

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...

The Energies of Atomic Orbitals

The Energies of Atomic Orbitals

In an atom, the negatively charged electrons are attracted to the positively charged nucleus. In a multielectron atom, electron-electron repulsions are also observed. The attractive and repulsive forces are dependent on the distance between the particles, as well as the sign and magnitude of the charges on the individual particles. When the charges on the particles are opposite, they attract each other. If both particles have the same charge, they repel each other.

Nuclear Overhauser Enhancement (NOE)

Nuclear Overhauser Enhancement (NOE)

Irradiation of a spin-active nucleus causes an increase or decrease in the signal intensity of neighboring nuclei that are not necessarily chemically bonded or involved in J-coupling. This phenomenon, called the Nuclear Overhauser Enhancement (NOE), results from through-space interactions between the nuclear spins. The NOE effect decreases with increasing internuclear distance and is generally not observed beyond 4 angstroms. In NOE, dipole-dipole interactions between neighboring...

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Related Experiment Video

Updated: Oct 27, 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

Nuclear-electronic orbital methods: Foundations and prospects.

Sharon Hammes-Schiffer¹

¹Department of Chemistry, Yale University, New Haven, Connecticut 06520, USA.

The Journal of Chemical Physics

|July 23, 2021

Summary

This summary is machine-generated.

The nuclear-electronic orbital (NEO) approach quantizes nuclei alongside electrons, enabling accurate quantum chemistry simulations. This method inherently captures nuclear quantum effects for diverse chemical and biological systems.

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Last Updated: Oct 27, 2025

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

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Published on: April 8, 2020

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Published on: July 27, 2018

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Published on: October 12, 2019

Area of Science:

Quantum Chemistry
Computational Chemistry
Molecular Dynamics

Background:

Incorporating nuclear quantum effects and non-Born-Oppenheimer behavior into simulations is a significant challenge.
Accurate modeling of molecular systems requires accounting for quantum mechanical properties of nuclei.

Purpose of the Study:

To provide an overview of the foundational nuclear-electronic orbital (NEO) methods.
To explore the prospects of NEO methods for future developments in computational chemistry.

Main Methods:

The nuclear-electronic orbital (NEO) approach treats specified nuclei quantum mechanically on the same level as electrons.
Utilizes wave function and density functional theory methods.
Enables nonequilibrium nuclear-electronic dynamics simulations beyond the Born-Oppenheimer approximation.

Main Results:

The NEO approach inherently includes nuclear delocalization and zero-point energy.
Accurately describes molecular energies, geometry optimizations, reaction paths, and dynamics.
Provides accurate descriptions of excited electronic, vibrational, and vibronic states, nuclear tunneling, and nonadiabatic dynamics.

Conclusions:

The NEO approach offers a powerful framework for including nuclear quantum effects and non-Born-Oppenheimer dynamics.
Its conceptual simplicity and computational efficiency enhance accessibility for diverse chemical and biological systems.
NEO methods serve as crucial building blocks for advancing quantum simulations.