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Degree of Unsaturation

Degree of Unsaturation

The degree of unsaturation (U), or index of hydrogen deficiency (IHD), is defined as the difference in the number of pairs of hydrogen atoms between the compound and the acyclic alkane with the same number of carbon atoms. Each double bond or ring costs two hydrogen atoms compared to a saturated analog and results in one degree of unsaturation.
The degree of unsaturation for hydrocarbons is U = (2C + 2 − H) / 2, where C is the number of carbon atoms and H is the number of hydrogen atoms.

Atomic Structure

Atomic Structure

Atomic Mass

Atomic Mass

Atoms — and the protons, neutrons, and electrons that compose them — are extremely small. For example, a carbon atom weighs less than 2 × 10−23 g. When describing the properties of tiny objects such as atoms, we use appropriately small units of measure, such as the atomic mass unit (amu). The amu was originally defined based on hydrogen, the lightest element, then later in terms of oxygen. Since 1961, it has been defined with regard to the most abundant isotope of carbon, atoms of which...

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.

The Quantum-Mechanical Model of an Atom

The Quantum-Mechanical Model of an Atom

Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra.

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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Related Experiment Video

Updated: Jan 30, 2026

Picometer-Precision Atomic Position Tracking through Electron Microscopy

Picometer-Precision Atomic Position Tracking through Electron Microscopy

Published on: July 3, 2021

Atomically Precise Expansion of Unsaturated Silicon Clusters.

Kinga I Leszczyńska¹, Volker Huch¹, Carsten Präsang¹

¹Krupp-Chair of Inorganic and General Chemistry, Saarland University, Campus Saarbrücken C41, 66123, Saarbrücken, Germany.

Angewandte Chemie (International Ed. in English)

|January 12, 2019

Summary

Researchers expanded stable silicon clusters by adding one atom at a time, enabling systematic scaffold modification for catalysis and materials science applications.

Keywords:

anions cluster compounds main group elements silicon subvalent compounds

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Last Updated: Jan 30, 2026

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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:

Cluster chemistry
Materials science
Heterogeneous catalysis

Background:

Small- to medium-sized clusters are crucial in heterogeneous catalysis and chemical vapor deposition.
Manipulating stable clusters is limited to ligand periphery, hindering scaffold variation.

Purpose of the Study:

To achieve deliberate expansion of stable unsaturated silicon clusters.
To enable systematic variation of cluster scaffolds for property tuning.

Main Methods:

Utilized a consecutive reduction and electrophilic silicon source approach.
Employed lithium/naphthalene as the reducing agent.
Used decamethylsilicocene as the electrophilic silicon source.

Main Results:

Successfully expanded a six-vertex silicon cluster to seven and then eight vertices.
Demonstrated precise, one-atom expansion of the silicon cluster core.
Showcased the potential for infinite, controlled cluster growth.

Conclusions:

Developed a novel method for stepwise silicon cluster expansion.
Opened avenues for designing tailored silicon cluster scaffolds.
Facilitated systematic studies of cluster properties by scaffold modification.