Quantum Theory of Structure: Crystals and Quasicrystals, Melts and Glasses

  • Jürgen Hafner
Part of the NATO ASI Series book series (NSSB, volume 319)


A quantum theory of structure, i.e. a prediction of the spatial distribution of the atoms in the condensed phases of matter on a quantum-mechanical basis, remains one of the great challenges of condensed-matter physics. The challenge is a triple one. The first task consists in the reduction of the many-ion-many-electron Hamiltonian to an effective one-particle form. This may be achieved using the Born-Oppenheimer or adiabatic approximation 1 for the decoupling of the ionic and electronic degrees of freedom and using the local density approximation2 to reduce the many-electron Schrödinger equation to the one-electron LDA-Schrodinger equation. The second problem is to solve the LDA-Schrödinger equation with the accuracy required for the prediction of structural energy differences. Even with advanced computational methods and using the most powerful supercomputers, this accuracy can be achieved only for systems with a maximum of 200 inequivalent atomic sites. To go beyond this limit requires simplifications. Chemists describe bonding in terms of the σ, π, and δtransfer integrals resulting from the overlap of the angular-dependent valence orbitals 3. At the reduced accuracy of a Tight-Binding-Huckel approximation systems with some ten thousand atoms may be modelled quite successfully. In materials science and metallurgy, atoms are traditionally considered as soft spheres interacting through pair- or embedded-atom potentials 4. The simplicity of the interatomic force law allows to simulate the properties of ensembles with up to a million of atoms.The third problem arises from the lack of a comprehensive scheme for enumerating and classifying all possible solid-state structures.


Metallic Glass Lave Phase Liquid Structure Interatomic Force Pair Force 
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© Springer Science+Business Media New York 1994

Authors and Affiliations

  • Jürgen Hafner
    • 1
  1. 1.Institut für Theoretische PhysikTechnische Universität WienWienAustria

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