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Coordination Number and Geometry

Coordination Number and Geometry

For transition metal complexes, the coordination number determines the geometry around the central metal ion. Table 1 compares coordination numbers to molecular geometry. The most common structures of the complexes in coordination compounds are octahedral, tetrahedral, and square planar.

Symmetry

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Polar Coordinates

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The polar coordinate system represents points using a distance from a central point (the pole) and an angle from a reference direction (the polar axis). Unlike rectangular coordinates, polar coordinates are ideal for graphing curves with radial symmetry or periodic behavior.Some general forms of graphs in polar coordinates include the following:Equation of a Circle (Centered at the Pole):A graph where the radius remains constant for all angles traces a circle centered at the pole:Equation of a...

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The spirograph is a versatile tool for visualizing the relationship between geometry and mathematical representation. In particular, it demonstrates how polar coordinates offer an alternative framework for describing curves in comparison to Cartesian coordinates. Instead of specifying a point by its horizontal and vertical displacements (x, y), polar coordinates use a radius r, the distance from the origin, and an angle θ, measured counterclockwise from the polar axis. This system is...

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Related Experiment Video

Updated: Jun 25, 2026

Self-assembly of Complex Two-dimensional Shapes from Single-stranded DNA Tiles

Self-assembly of Complex Two-dimensional Shapes from Single-stranded DNA Tiles

Published on: May 8, 2015

A dodecameric porphyrin wheel

Xiaobin Peng¹, Naoki Aratani, Akihiko Takagi

¹Department of Chemistry, Graduate School of Science, Kyoto University, Core Research for Evolutional Science and Technology, Japan Science and Technology Agency, Sakyo-ku, Kyoto 606-8502, Japan.

Journal of the American Chemical Society

|April 9, 2004

Summary

Researchers created a dodecameric porphyrin wheel using silver(I)-promoted coupling. Scanning tunneling microscopy and femtosecond transient anisotropy measurements revealed efficient energy hopping along the porphyrin array.

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Area of Science:

Supramolecular Chemistry
Materials Science
Photophysics

Background:

Porphyrins are versatile macrocyclic compounds with applications in catalysis, sensing, and light-harvesting.
Constructing complex porphyrin architectures is crucial for developing advanced functional materials.
Understanding energy transfer dynamics in ordered porphyrin systems is key to optimizing their performance.

Purpose of the Study:

To synthesize a novel dodecameric porphyrin wheel structure.
To investigate the structural and electronic properties of the porphyrin wheel.
To probe the energy transfer dynamics within the assembled porphyrin array.

Main Methods:

Synthesis of a linear porphyrin dodecamer.
Silver(I)-promoted intramolecular coupling to form the porphyrin wheel.
Scanning tunneling microscopy (STM) for structural visualization.
Femtosecond transient anisotropy measurements for energy transfer studies.

Main Results:

Successful preparation of a dodecameric porphyrin wheel.
Direct visualization of the porphyrin wheel structure using STM.
Observation of efficient energy hopping along the porphyrin array.
Quantitative analysis of energy transfer rates.

Conclusions:

The Ag(I)-promoted coupling is an effective method for constructing porphyrin macrocycles.
The dodecameric porphyrin wheel exhibits efficient intramolecular energy transfer.
This study provides insights into the design of novel porphyrin-based light-harvesting systems.