Computer Algebra and Materials Physics

A Practical Guidebook to Group Theoretical Computations in Materials Science

  • Akihito Kikuchi

Part of the Springer Series in Materials Science book series (SSMATERIALS, volume 272)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Akihito Kikuchi
    Pages 1-5
  3. Akihito Kikuchi
    Pages 13-17
  4. Akihito Kikuchi
    Pages 39-71
  5. Akihito Kikuchi
    Pages 73-102
  6. Akihito Kikuchi
    Pages 103-118
  7. Akihito Kikuchi
    Pages 119-121
  8. Back Matter
    Pages 123-159

About this book


This book is intended as an introductory lecture in material physics, in which the modern computational group theory and the electronic structure calculation are in collaboration.
The first part explains how to use computer algebra for applications in solid-state simulation, based on the GAP computer algebra package. Computer algebra enables us to easily obtain various group theoretical properties, such as the representations, character tables, and subgroups. Furthermore it offers a new perspective on material design, which could be executed in a mathematically rigorous and systematic way.
The second part then analyzes the relation between the structural symmetry and the electronic structure in C60 (as an example of a system without periodicity). The principal object of the study was to illustrate the hierarchical change in the quantum-physical properties of the molecule, which correlates to the reduction in the symmetry (as it descends down in the ladder of subgroups).
The book also presents the computation of the vibrational modes of the C60 by means of the computer algebra. In order to serve the common interests of researchers, the details of the computations (the required initial data and the small programs developed for the purpose) are explained in as much detail as possible. 


The computational discrete algebra package GAP material simulation and design electronic structure calculation group cohomology Symmetry operations Wyckoff positions group theory

Authors and affiliations

  • Akihito Kikuchi
    • 1
  1. 1.R&D DivisionCanon Inc.TokyoJapan

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