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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.

The Energies of Atomic Orbitals

The Energies of Atomic Orbitals

In an atom, the negatively charged electrons are attracted to the positively charged nucleus. In a multielectron atom, electron-electron repulsions are also observed. The attractive and repulsive forces are dependent on the distance between the particles, as well as the sign and magnitude of the charges on the individual particles. When the charges on the particles are opposite, they attract each other. If both particles have the same charge, they repel each other.

Atomic Structure

Atomic Structure

Atomic Radii and Effective Nuclear Charge

Atomic Radii and Effective Nuclear Charge

The elements in groups of the periodic table exhibit similar chemical behavior. This similarity occurs because the members of a group have the same number and distribution of electrons in their valence shells.

Electron Configuration of Multielectron Atoms

Electron Configuration of Multielectron Atoms

The alkali metal sodium (atomic number 11) has one more electron than the neon atom. This electron must go into the lowest-energy subshell available, the 3s orbital, giving a 1s22s22p63s1 configuration. The electrons occupying the outermost shell orbital(s) (highest value of n) are called valence electrons, and those occupying the inner shell orbitals are called core electrons. Since the core electron shells correspond to noble gas electron configurations, we can abbreviate electron...

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: Feb 6, 2026

Picometer-Precision Atomic Position Tracking through Electron Microscopy

Picometer-Precision Atomic Position Tracking through Electron Microscopy

Published on: July 3, 2021

Co-crystallization of atomically precise metal nanoparticles driven by magic atomic and electronic shells.

Juanzhu Yan¹, Sami Malola², Chengyi Hu¹

¹State Key Laboratory for Physical Chemistry of Solid Surfaces, Collaborative Innovation Center of Chemistry for Energy Materials, and National & Local Joint Engineering Research Center for Preparation Technology of Nanomaterials, College of Chemistry and Chemical Engineering, Xiamen University, 361005, Xiamen, China.

Nature Communications

|August 24, 2018

Summary

This study co-crystallized two distinct gold-silver nanoclusters, revealing competing atomic and electron shell effects. This breakthrough enables designing new nanocluster systems through co-crystallization.

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Area of Science:

Materials Science
Nanotechnology
Crystallography

Background:

Atomically precise nanoclusters offer tunable properties.
Controlling nanocluster size and structure during synthesis is challenging.
Co-crystallization is a potential strategy for creating complex nanocluster assemblies.

Purpose of the Study:

To report the co-crystallization of two different-sized ligand-stabilized gold-silver nanoclusters.
To investigate the structural and electronic properties of the co-crystallized nanoclusters.
To demonstrate the simultaneous presence of competing atomic and electron shell effects in nanocluster formation.

Main Methods:

X-ray crystallographic analysis was used to characterize the nanoclusters.
Synthesis involved co-crystallization of spherical (AuAg)267(SR)80 and trigonal-prismatic (AuAg)45(SR)27(PPh3)6 nanoclusters.
Structural elucidation of the larger cluster revealed a four-concentric-shell icosahedral structure (Ag@M12@M42@M92@Ag120(SR)80).

Main Results:

Co-crystallization of spherical and trigonal-prismatic nanoclusters in a 1:1 ratio was achieved.
The larger nanocluster exhibited an open electron shell (187 electrons), metallic, plasmonic behavior, and a zero HOMO-LUMO gap.
The smaller nanocluster showed an 18-electron shell closing, a HOMO-LUMO gap, and molecule-like optical properties.

Conclusions:

This work provides the first direct evidence of competing atomic and electron shell closing effects during nanocluster synthesis.
The simultaneous occurrence of these effects leads to the formation of co-crystals with different-sized nanoclusters.
Co-crystallization presents a viable strategy for designing novel nanocluster systems with tailored properties.