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Related Concept Videos

π Molecular Orbitals of the Allyl Radical01:27

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.
Angular Momentum01:21

Angular Momentum

Angular momentum characterizes an object's rotational motion and is defined as the moment of its linear momentum about a specified point O. When a particle moves along a curved path in the x-y plane, the scalar formulation calculates the magnitude of its angular momentum, utilizing the moment arm (d), representing the perpendicular distance from point O to the line of action of the linear momentum. Despite being scalar in formulation, angular momentum is inherently a vector quantity. Its...
Atomic Orbitals02:44

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 Cation and Anion01:18

π Molecular Orbitals of the Allyl Cation and Anion

An allyl group is a three-carbon conjugated system where the sp³-hybridized allylic carbon is bonded to a CH=CH2 group via a single bond. Allyl anions can be obtained by treating propene with a strong base that can deprotonate methyl groups. Allyl cations are formed as intermediates during substitution reactions involving allylic halides. In both cases, the hybridization of the allylic carbon changes from sp3 to sp2, giving rise to a carbon chain with three sp2-hybridized carbons, each with an...
MO Theory and Covalent Bonding02:40

MO Theory and Covalent Bonding

The molecular orbital theory describes the distribution of electrons in molecules in a manner similar to the distribution of electrons in atomic orbitals. The region of space in which a valence electron in a molecule is likely to be found is called a molecular orbital. Mathematically, the linear combination of atomic orbitals (LCAO) generates molecular orbitals. Combinations of in-phase atomic orbital wave functions result in regions with a high probability of electron density, while...
Molecular Orbital Theory I02:35

Molecular Orbital Theory I

Overview of Molecular Orbital Theory

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Updated: Jun 4, 2026

Liquid-cell Transmission Electron Microscopy for Tracking Self-assembly of Nanoparticles
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Liquid-cell Transmission Electron Microscopy for Tracking Self-assembly of Nanoparticles

Published on: October 16, 2017

The Angular Localization Function (ALF): A Practical Tool to Measure Solvent Angular Order with Molecular Density

Maïwenn Souetre1, Benjamin Rotenberg1,2, Guillaume Jeanmairet1,2

  • 1Sorbonne Université, CNRS, Physico-Chimie des Électrolytes et Nanosystèmes Interfaciaux, PHENIX, Paris F-75005, France.

The Journal of Physical Chemistry. B
|June 3, 2026
PubMed
Summary
This summary is machine-generated.

Researchers developed the Angular Localization Function (ALF) to analyze solvent structure. This new method quantifies local angular order, offering deeper insights into molecular interactions and solvent behavior.

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Last Updated: Jun 4, 2026

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08:39

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Published on: October 16, 2017

Spatial Separation of Molecular Conformers and Clusters
10:37

Spatial Separation of Molecular Conformers and Clusters

Published on: January 9, 2014

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry
12:11

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

Published on: April 8, 2020

Area of Science:

  • Computational chemistry
  • Physical chemistry
  • Materials science

Background:

  • Molecular density functional theory (DFT) computes solvent density around solutes.
  • Interpreting the detailed solvent structure from DFT is challenging.
  • Current analyses often neglect angular information of solvent molecules.

Purpose of the Study:

  • Introduce a new function, the Angular Localization Function (ALF).
  • Quantify local angular order and entropy of solvent molecules.
  • Enhance the interpretation of molecular solvent structure.

Main Methods:

  • Derived ALF from the ideal free energy functional.
  • Analyzed solvent structure for water, octanol, and clay minerals (talc, fluorotalc, pyrophyllite) in water.
  • Connected ALF to established statistical functions.

Main Results:

  • ALF provides a local measure of angular order.
  • Demonstrated ALF's utility in characterizing solvent orientation around solutes and surfaces.
  • Showcased ALF's complementary information to polarization and charge density.

Conclusions:

  • ALF offers a novel way to analyze solvent orientational distribution.
  • ALF serves as a valuable visualization tool, similar to the Electronic Localization Function (ELF).
  • The method reveals subtle effects of solute structure on water interactions.