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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.

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Electronic Structure of Atoms

Electronic Structure of Atoms

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...

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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Updated: Jul 5, 2025

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

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Published on: May 27, 2020

Self-interaction corrected SCAN functional for molecules and solids in the numeric atom-center orbital framework.

Sheng Bi^1,2,3, Christian Carbogno¹, Igor Ying Zhang^2,4

¹The NOMAD Laboratory at the FHI of the Max-Planck-Gesellschaft and IRIS-Adlershof of the Humboldt-Universität zu Berlin, Faradayweg 4-6, D-14195 Berlin-Dahlem, Germany.

The Journal of Chemical Physics

|January 18, 2024

Summary

This study introduces a stable self-interaction correction (SIC) method to improve density-functional approximations (DFAs) like SCAN. The new approach enhances accuracy for ionization potentials, charge-transfer energies, and bandgaps in molecules and solids.

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Area of Science:

Computational Chemistry
Materials Science
Quantum Mechanics

Background:

Semilocal density-functional approximations (DFAs) suffer from self-interaction error (SIE).
The Perdew-Zunger self-interaction correction (PZ-SIC) method aims to mitigate SIE but is numerically unstable.
Accurate electronic structure calculations are crucial for predicting material and molecular properties.

Purpose of the Study:

To develop a numerically stable and efficient implementation of the PZ-SIC method.
To mitigate the self-interaction error in the SCAN functional.
To improve the accuracy of calculated electronic properties for molecules and solids.

Main Methods:

Introduced a novel constraint for self-consistent localization of SIC orbitals, inspired by Edmiston-Ruedenberg localization.
Implemented the constrained PZ-SIC method within the all-electron numeric atom-centered orbitals code FHI-aims.
Tested the method on various molecules and solids to assess its performance for electronic properties.

Main Results:

Achieved efficient and stable convergence for self-consistent PZ-SIC calculations in both molecules and solids.
Demonstrated significant mitigation of SIE in the SCAN functional, improving accuracy for ionization potentials, charge-transfer energies, and bandgaps.
Showed that the method does not improve properties already accurately described by SCAN, such as cohesive energies and lattice constants.

Conclusions:

The developed constrained PZ-SIC method offers a stable and practical approach to correct self-interaction error in DFAs.
This advancement improves the predictive power of electronic structure calculations for specific properties.
Highlights the ongoing need for next-generation DFAs with broader applicability and inherent accuracy.