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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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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...

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Related Experiment Video

Updated: Jun 2, 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

All-Electron BSE@GW Method with Numeric Atom-Centered Orbitals for Extended Periodic Systems.

Ruiyi Zhou¹, Yi Yao^1,2, Volker Blum^2,3

¹Department of Chemistry, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599, United States.

Journal of Chemical Theory and Computation

|January 14, 2025

Summary

This summary is machine-generated.

We present a new all-electron implementation of the Bethe-Salpeter equation at the GW level (BSE@GW) for periodic systems. This method enhances the study of electronic properties in extended materials using numeric atom-centered orbitals.

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Area of Science:

Condensed matter physics
Quantum chemistry
Computational materials science

Background:

Green's function theory is a powerful many-body approach.
The BSE@GW formalism is increasingly used in physics and chemistry.
An all-electron implementation for extended systems is needed.

Purpose of the Study:

To develop and present a new all-electron implementation of the BSE@GW formalism.
To adapt this method for extended periodic systems.
To demonstrate its numerical implementation and convergence properties.

Main Methods:

Developed an all-electron BSE@GW formalism.
Utilized numeric atom-centered orbital basis sets.
Performed convergence tests on basis sets and Brillouin zone sampling.

Main Results:

Successfully implemented the all-electron BSE@GW method for periodic systems.
Demonstrated convergence with respect to numerical parameters.
Provided proof-of-principle examples comparing the new method with existing formalisms.

Conclusions:

The new all-electron BSE@GW method is a viable approach for studying extended periodic systems.
The implementation shows good convergence properties.
This work facilitates advanced electronic structure calculations for materials.