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Molecular AggregationStructure analysis and molecular simulation of crystals and liquids$
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Angelo Gavezzotti

Print publication date: 2006

Print ISBN-13: 9780198570806

Published to Oxford Scholarship Online: January 2010

DOI: 10.1093/acprof:oso/9780198570806.001.0001

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Periodic systems: Crystal orbitals and lattice dynamics

Periodic systems: Crystal orbitals and lattice dynamics

Chapter:
(p.153) 6 Periodic systems: Crystal orbitals and lattice dynamics
Source:
Molecular Aggregation
Author(s):

ANGELO GAVEZZOTTI

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198570806.003.0006

A molecular crystal is an array of molecular objects related by symmetry operations, including pure translation: a system endowed by periodic translational symmetry. This chapter considers atomic orbitals and the crystal orbital approach for the construction of the periodic wavefunction and electron density of a crystal, and for the derivation of its electronic structure, as well as the description of periodic collective molecular oscillations, in an approach which has appropriately been called lattice dynamics. The mathematical description of crystal periodicity is discussed, along with equivalent positions and systematic absences in diffraction patterns, reciprocal space, wave vector, Brillouin zone, Bloch functions, the electronic structure of solids, band structures, electronic density of states, lattice vibrations, periodic vibrations in infinite crystals, and measurement of lattice-vibration frequencies.

Keywords:   atomic orbitals, lattice dynamics, periodic wavefunction, electron density, molecular crystal, electronic structure, molecular oscillations, crystal periodicity, diffraction patterns

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