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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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The Quantum-Mechanical Model of an Atom

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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.

Valence Bond Theory and Hybridized Orbitals

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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.
A σ bond (single bond in a Lewis structure) is a covalent bond in which the electron density is...

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Related Experiment Video

Updated: Dec 30, 2025

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids

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Embedding Methods for Quantum Chemistry: Applications from Materials to Life Sciences.

Leighton O Jones¹, Martín A Mosquera¹, George C Schatz¹

¹Department of Chemistry , Northwestern University , Evanston , Illinois 60208 , United States.

Journal of the American Chemical Society

|January 29, 2020

Summary

This summary is machine-generated.

Quantum mechanical embedding methods offer reduced computational costs for large molecular systems. This perspective reviews QM:MM and QM:QM approaches, highlighting applications and future directions for computational chemistry.

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Area of Science:

Computational Chemistry
Quantum Mechanics

Background:

Quantum mechanical embedding methods promise to revolutionize molecular calculations.
These methods aim to reduce computational costs and improve scaling for large systems.

Purpose of the Study:

To provide a perspective on the field of quantum mechanical embedding methods.
To categorize and review existing methods, focusing on QM:MM and QM:QM approaches.

Main Methods:

Categorization of embedding methods into QM:MM and QM:QM streams.
Review of literature, underpinning theories, and author contributions.
Highlighting current applications in materials and life sciences.

Main Results:

Discussion of advantages and disadvantages of QM:MM and QM:QM methods.
Presentation of select examples spanning materials and life sciences.
Identification of future prospects and outlook for embedding theories.

Conclusions:

Embedding methods are crucial for advancing computational chemistry for large systems.
Standardized test cases are recommended for cross-comparison of embedding theories.
The field is rapidly evolving with significant potential for future development.