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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.

π Molecular Orbitals of the Allyl Radical

π Molecular Orbitals of the Allyl Radical

Allyl radicals are three-carbon conjugated systems. They are readily formed as intermediates in halogenation reactions of alkenes involving the addition of halogen to the allylic carbon instead of the double bond. As seen in allyl cations and anions, each of the three sp2-hybridized carbon atoms in allyl radicals has an unhybridized p orbital. These orbitals combine to give three π molecular orbitals.
The allyl systems have identical molecular orbitals but differ in the number of π electrons.

Radicals: Electronic Structure and Geometry

Radicals: Electronic Structure and Geometry

This lesson delves into the geometry of a radical, which is influenced by the electronic structure of the molecule. The principle is similar to that of a lone pair, where the unpaired electron influences the geometry at the radical center.
Accordingly, the structure of a trivalent radical lies between the geometries of carbocations and carbanions. An sp2-hybridized carbocation is trigonal planar, while an sp3-hybridized carbanion is trigonal pyramidal. Here, the difference in geometry is...

Radical Reactivity: Overview

Radical Reactivity: Overview

Radicals, the highly reactive species, gain stability by undergoing three different reactions. The first reaction involves a radical-radical coupling, in which a radical combines with another radical, forming a spin‐paired molecule. The second reaction is between a radical and a spin‐paired molecule, generating a new radical and a new spin‐paired molecule. The third reaction is radical decomposition in a unimolecular reaction, forming a new radical and a spin‐paired molecule. These three...

Radical Formation: Addition

Radical Formation: Addition

Radicals can be formed by adding a radical to a spin-paired molecule. This is typically observed with unsaturated species, where the addition of a radical across the π bond leads to the production of a new radical by dissolving the π bond. For example, the addition of a Br radical to an alkene yields a carbon-centered radical.
Similar to charge conservation in chemical reactions, spin conservation is implicit for radical reactions. Accordingly, the product formed must possess an unpaired...

Molecular Orbital Theory I

Molecular Orbital Theory I

Overview of Molecular Orbital Theory

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Related Experiment Video

Updated: Jun 3, 2026

Isolating Free Carbenes, their Mixed Dimers and Organic Radicals

Isolating Free Carbenes, their Mixed Dimers and Organic Radicals

Published on: April 19, 2019

Diradicals and diradicaloids in natural orbital functional theory.

Xabier Lopez¹, Fernando Ruipérez, Mario Piris

¹Kimika Fakultatea, Euskal Herriko Unibertsitatea and Donostia International Physics Center (DIPC), Donostia, Euskadi, Spain. xabier.lopez@ehu.es

Chemphyschem : a European Journal of Chemical Physics and Physical Chemistry

|April 8, 2011

Summary

Natural orbital functional (NOF) theory, specifically PNOF4, accurately describes diradicals and diradicaloids by correctly handling near-degeneracy effects. This computational method shows promise for simulating these challenging molecular systems.

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Area of Science:

Computational Chemistry
Quantum Chemistry
Theoretical Chemistry

Background:

Diradicals and diradicaloids exhibit near-degeneracy effects, making them challenging to simulate accurately.
Natural Orbital Functional (NOF) theory offers a potential approach to address these challenges.

Purpose of the Study:

To investigate the electronic structure and energetics of diradicals and diradicaloids using NOF theory.
To evaluate the performance of PNOF3 and PNOF4 implementations for systems with diradical character.
To compare NOF results with wave-function methods like CASSCF.

Main Methods:

Application of Piris NOF (PNOF) theory, specifically PNOF3 and PNOF4.
Study of paradigmatic diradical (trimethylenmethane) and diradicaloid (imino-allyl, oxyallyl) systems.
Analysis of natural orbital occupation numbers to determine diradical character.
Investigation of energetics relative to cyclic isomers.

Main Results:

PNOF4 provides a promising description of diradicals and diradicaloids.
The method correctly captures trends in natural orbital occupation numbers.
PNOF4 accurately reproduces near-degeneracy effects, aligning with CASSCF results.

Conclusions:

PNOF4 is a promising computational method for accurately treating diradicals and diradicaloids.
The method's ability to handle near-degeneracy effects makes it suitable for these delicate molecular systems.