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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.

Molecular Orbital Theory II

Molecular Orbital Theory II

Molecular Orbital Energy Diagrams

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

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...

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Related Experiment Video

Updated: Jun 18, 2025

Three-Dimensional Reconstruction of Orbital Fractures

Three-Dimensional Reconstruction of Orbital Fractures

Published on: May 16, 2025

Orbital optimisation in xTC transcorrelated methods.

Daniel Kats¹, Evelin M C Christlmaier¹, Thomas Schraivogel¹

¹Max Planck Institute for Solid State Research, Heisenbergstr. 1, 70569 Stuttgart, Germany. d.kats@fkf.mpg.de.

Faraday Discussions

|July 29, 2024

Summary

This summary is machine-generated.

We combined bi-orthogonal orbital optimization with transcorrelation (xTC) methods. This improves accuracy for quantum chemistry calculations, offering new possibilities for electronic structure research.

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Area of Science:

Quantum Chemistry
Computational Physics
Electronic Structure Theory

Background:

Transcorrelation (xTC) methods offer accurate solutions for electronic structure problems.
Standard xTC methods can be computationally intensive.
Orbital optimization is crucial for improving the efficiency and accuracy of quantum chemical methods.

Purpose of the Study:

To integrate bi-orthogonal orbital optimization with the xTC framework.
To enable non-iterative perturbation-based methods on the transcorrelated Hamiltonian.
To assess the impact of orbital optimization on truncated methods like distinguishable cluster with singles and doubles.

Main Methods:

Combination of bi-orthogonal orbital optimization and xTC.
Implementation of non-iterative perturbation methods.
Application to distinguishable cluster with singles and doubles.

Main Results:

Demonstrated improved accuracy of the combined methods compared to standard xTC.
Showcased the influence of orbital optimization on other truncated methods.
Provided a detailed discussion of the advantages and disadvantages of orbital optimization within this framework.

Conclusions:

The integration of orbital optimization with xTC enhances computational accuracy.
This approach provides a robust framework for advanced electronic structure calculations.
The study highlights the benefits and limitations of orbital optimization in quantum chemistry.