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Hybridization of Atomic Orbitals I

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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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¹H NMR: Long-Range Coupling

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Van der Waals Equation

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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.
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Related Experiment Video

Updated: Jun 18, 2026

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

Long-range corrected double-hybrid density functionals.

Jeng-Da Chai¹, Martin Head-Gordon

¹Department of Chemistry, University of California, Berkeley, Berkeley, California 94720, USA. jdchai@phys.ntu.edu.tw

The Journal of Chemical Physics

|November 10, 2009

Summary

This summary is machine-generated.

We introduce omegaB97X-2, a new long-range corrected double-hybrid density functional. It offers high accuracy for chemical properties and improves calculations for systems with self-interaction errors.

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Area of Science:

Computational Chemistry
Quantum Chemistry
Theoretical Chemistry

Background:

Previous long-range corrected (LC) hybrid functional, omegaB97X, has limitations.
Need for improved density functional theory (DFT) methods for accuracy.

Purpose of the Study:

Extend the applicability of omegaB97X.
Develop a new LC double-hybrid density functional, omegaB97X-2.
Enhance accuracy for thermochemistry, kinetics, and noncovalent interactions.

Main Methods:

Incorporated nonlocal electron correlation inspired by second-order Moller-Plesset perturbation theory.
Developed omegaB97X-2, a long-range corrected double-hybrid density functional.
Optimized the functional at the complete basis set limit and with a smaller basis set.

Main Results:

omegaB97X-2 demonstrates high accuracy for thermochemistry and kinetics.
The functional accurately predicts noncovalent interactions.
Significant improvement observed for systems with severe self-interaction errors, like radical cations.

Conclusions:

omegaB97X-2 offers a significant advancement in DFT methods.
The new functional provides reliable predictions for a wide range of chemical problems.
High fraction of exact Hartree-Fock exchange contributes to improved performance.