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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...

Molecular Orbital Theory II

Molecular Orbital Theory II

Molecular Orbital Energy Diagrams

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

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.

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Analyzing Melts and Fluids from Ab Initio Molecular Dynamics Simulations with the UMD Package

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Toward Efficient GW Calculations Using Numerical Atomic Orbitals: Benchmarking and Application to Molecular Dynamics

Peter Koval¹, Mathias Per Ljungberg¹, Moritz Müller¹

¹Donostia International Physics Center , Paseo Manuel de Lardizabal 4 , 20018 Donostia-San Sebastián , Spain.

Journal of Chemical Theory and Computation

|July 19, 2019

Summary

This study introduces an efficient computational method using numerical atomic orbitals for Hedin's GW approximation, enabling accurate modeling of large molecules. The approach reveals significantly stronger electron-phonon couplings compared to standard DFT-GGA methods.

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Area of Science:

Computational Chemistry
Quantum Mechanics
Materials Science

Background:

The GW approximation is a powerful tool for calculating electronic properties of materials.
Traditional plane-wave basis sets can be computationally expensive for large systems.
Numerical atomic orbitals offer a potentially more cost-effective alternative.

Purpose of the Study:

To implement and benchmark an efficient GW approximation using numerical atomic orbitals.
To assess the accuracy and cost-effectiveness of this approach for molecular systems.
To investigate electron-phonon couplings in complex molecules.

Main Methods:

Implementation of the GW approximation with numerical atomic orbitals and pseudopotentials.
Utilized a contour deformation technique and one-shot quasiparticle energy extraction.
Tested on G2/97 and acceptor molecule test sets, and applied to a photochromic compound using ab initio molecular dynamics.

Main Results:

The numerical atomic orbital-based GW method demonstrates good performance and basis set convergence.
Electron-phonon couplings computed with GW were found to be approximately twice as large as those from DFT-GGA.
Frozen-phonon calculations corroborated the enhanced electron-phonon coupling findings.

Conclusions:

The developed GW method using numerical atomic orbitals provides an efficient and accurate approach for electronic structure calculations.
This method accurately captures electron-phonon interactions, offering insights into molecular dynamics and properties.
The findings suggest this approach is suitable for modeling large molecules and complex phenomena.