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Construction and Systematical Symmetric Studies of a Series of Supramolecular Clusters with Binary or Ternary Ammonium Triphenylacetates
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Minimum Vertex-type Sequence Indexing for Clusters on Square Lattice.

Longguang Liao1, Yu-Jun Zhao1,2, Zexian Cao3

  • 1Department of Physics, South China University of Technology, Guangzhou, 510640, China.

Scientific Reports
|March 26, 2017
PubMed
Summary
This summary is machine-generated.

A new minimum vertex-type sequence method efficiently indexes clusters for fast comparison. This orientation-independent approach offers advantages over traditional methods for mathematics and materials science applications.

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Area of Science:

  • Mathematics and Computer Science
  • Materials Science
  • Artificial Intelligence

Background:

  • Effective cluster indexing is crucial for structure comparison and congruence checks across various scientific fields.
  • Existing methods like coordinate-based and distance-matrix approaches have limitations in efficiency and data handling.

Purpose of the Study:

  • To introduce a novel indexing scheme for clusters on a square lattice.
  • To enable fast and reliable structure comparison and congruence checks.
  • To provide an orientation-independent method with a one-to-one correspondence to the cluster.

Main Methods:

  • Development of the minimum vertex-type sequence concept.
  • Assigning integer labels to atom vertex types within a cluster.
  • Utilizing this sequence for structural comparison and congruence verification.

Main Results:

  • The minimum vertex-type sequence is orientation independent and uniquely represents each cluster.
  • Comparison involves only one data type, with a maximum of n pairs to compare (n = cluster size).
  • Demonstrated advantages over traditional coordinate-based and distance-matrix methods.

Conclusions:

  • The minimum vertex-type sequence provides an effective and efficient indexing scheme for clusters.
  • The method is easily generalizable to other high-symmetry lattices.
  • This work facilitates cluster indexing and searching, potentially inspiring new indexing schemes for large clusters.