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Mathematical Research in Materials Science Opportunities and Perspectives (1993) / Chapter Skim
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2 ATOMIC SCALE
Pages 5-10

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From page 5...
... This has been the object of solid-state physics theories for crystalline materials, where the nuclei undergo only small-amplitude vibrations about equilibrium positions. However, when the nuclei are permitted to move over more substantial distances, such as in the examples described in 2 above, it is often adequate to treat the nuclear motion in terms of classical equations of motion, with the forces between atoms and molecules calculated using quantum mechanics or, when unavailable, from empirical potential functions.
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From page 6...
... Thus, mathematical approximations are necessary, and this has led to the development of a wide variety of methods, including model Schrodinger equations that contain within them a set of empirical interactions, pseudopotential methods that likewise rely on empirical information or (more recently) on accurate quantum mechanical calculations for atomic systems upon which curves/surfaces are fitted, and the nonempirical density functional and ah initio quantum mechanical methods.
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From page 7...
... A variety of basis sets have proven useful in different cases, but the power of modern computers favors the use of plane waves because the size of the basis set can be increased systematically until convergence is achieved (Thm et al., 1979~. The treatment of dynamical properties, such as conductivity, is generally carried out with semiempirical Hamiltonians, for example, a tight-binding Hamiltonian that is constructed with a localized basis set of atomic orbitals (Khan and Broughton, 1991~.
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From page 8...
... Parallel computers are becoming an important ingredient in the impetus to study larger systems. The current limits are a few hundred atoms for first-principles calculations and several hundred million atoms for conventional molecular dynamics using interatomic potentials.
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From page 9...
... Simulated annealing techniques have enabled the computation of electronically excited potential surfaces in conjunction with molecular dynamics simulations of the nuclear motion. The first thermal simulations combining the full electronic Schrodinger equation and molecular dynamics involve simulations of both ground and electronically excited states of metal atoms solvated in rare 9
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From page 10...
... Electronic structure calculations have been essential in understanding electronic, optical, and transport properties, including elastic constants, conductivities, magnetic properties, and many more. Molecular dynamics is an explanatory mechanism and contributes to determining structural and mechanical properties of complex materials.
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Key Terms

  • molecular dynamics
  • quantum mechanical
  • interatomic potentials
  • functional methods
  • initio quantum

  • electronic structure
  • constituent atoms
  • material properties
  • monte carlo
  • elastic constants

  • functional theory
  • density functionals
  • quantum mechanics
  • conventional molecular
  • fixed positions

  • total energy
  • matrix elements
  • electronically excited
  • dynamical properties
  • electron energy

  • potential energy
  • basis set
  • fast fourier
  • mechanical description
  • structure calculations

  • mechanical methods
  • excited states
  • nuclear motions
  • using quantum
  • pseudopotential methods


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