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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.

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...

Hybridization of Atomic Orbitals II

Hybridization of Atomic Orbitals II

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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.

Molecular Orbital Theory I

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Molecular Orbital Theory II

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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

Implementation of exact exchange with numerical atomic orbitals.

Honghui Shang¹, Zhenyu Li, Jinlong Yang

¹Hefei National Laboratory for Physical Sciences at Microscale, University of Science and Technology of China, Hefei, Anhui 230026, China.

The Journal of Physical Chemistry. A

|January 15, 2010

Summary

This summary is machine-generated.

A new method for calculating Hartree-Fock exact exchange was implemented in the SIESTA code using numerical atomic orbitals. This approach accurately computes electron repulsion integrals for various systems, matching established software results.

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Area of Science:

Computational physics
Quantum chemistry
Materials science

Background:

Accurate calculation of electronic structure is crucial for understanding material properties.
Existing methods for exact exchange can be computationally expensive.

Purpose of the Study:

To implement and validate a method for calculating Hartree-Fock-type exact exchange within the SIESTA code.
To utilize a localized numerical atomic orbital basis set for efficiency.

Main Methods:

Implementation of exact exchange calculation in SIESTA.
Calculation of electron repulsion integrals via Poisson's equation and real-space numerical integration.
Utilizing interpolating scaling functions.

Main Results:

Successful implementation of the exact exchange method in SIESTA.
Accurate results obtained for both isolated and periodic systems.
Good agreement with established computational packages like Gaussian03 and Crystal06.

Conclusions:

The implemented method provides a reliable and efficient way to compute exact exchange in SIESTA.
This advancement enables more accurate electronic structure calculations for a wide range of materials.