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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...

Hybridization of Atomic Orbitals II

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sp3d and sp3d 2 Hybridization

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...

Resonance and Hybrid Structures

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According to the theory of resonance, if two or more Lewis structures with the same arrangement of atoms can be written for a molecule, ion, or radical, the actual distribution of electrons is an average of that shown by the various Lewis structures.
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The Lewis structure of a nitrite anion (NO2−) may actually be drawn in two different ways, distinguished by the locations of the N–O and N=O bonds.

Valence Bond Theory

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Coordination compounds and complexes exhibit different colors, geometries, and magnetic behavior, depending on the metal atom/ion and ligands from which they are composed. In an attempt to explain the bonding and structure of coordination complexes, Linus Pauling proposed the valence bond theory, or VBT, using the concepts of hybridization and the overlapping of the atomic orbitals. According to VBT, the central metal atom or ion (Lewis acid) hybridizes to provide empty orbitals of suitable...

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

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Hybrid functionals with local range separation.

Aliaksandr V Krukau¹, Gustavo E Scuseria, John P Perdew

¹Department of Chemistry, Rice University, Houston, Texas 77005-1892, USA.

The Journal of Chemical Physics

|December 3, 2008

Summary

This summary is machine-generated.

This study introduces locally range-separated hybrids, a new method in density functional theory that uses position-dependent screening for improved electronic structure descriptions. This approach offers greater flexibility and better high-density scaling compared to fixed screening parameters.

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Last Updated: Jun 27, 2026

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Published on: May 27, 2020

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Spatial Separation of Molecular Conformers and Clusters

Spatial Separation of Molecular Conformers and Clusters

Published on: January 9, 2014

Area of Science:

Computational Chemistry
Quantum Chemistry
Materials Science

Background:

Density functional theory (DFT) is a key method for electronic structure calculations.
Range-separated hybrid functionals incorporate exact exchange to improve DFT accuracy.
Current methods use fixed, system-independent screening parameters.

Purpose of the Study:

To develop a novel, more flexible approach to range-separated hybrid functionals.
To improve the description of diverse electronic structures.
To enhance the high-density scaling properties of hybrid functionals.

Main Methods:

Proposed a novel method using a position-dependent screening function for range separation.
Implemented locally range-separated hybrids within a density functional theory framework.
Compared performance against fixed screening parameter approximations.

Main Results:

The locally range-separated hybrids offer substantial flexibility for diverse electronic structures.
The new method satisfies high-density scaling constraints more effectively than fixed screening.
Demonstrated improved accuracy in describing electronic properties.

Conclusions:

Position-dependent screening provides a more adaptable and accurate approach to range-separated hybrids.
Locally range-separated hybrids represent a significant advancement in density functional theory methods.
This method holds promise for more accurate computational chemistry and materials science applications.