*Mike Finnis*

- Published in print:
- 2003
- Published Online:
- January 2010
- ISBN:
- 9780198509776
- eISBN:
- 9780191709180
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198509776.003.0006
- Subject:
- Physics, Atomic, Laser, and Optical Physics

This chapter shows how pairwise potentials for simple, s-p bonded metals, can be derived from first-principles. The starting point is jellium, and the ions are specified as pseudopotentials, local or ...
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This chapter shows how pairwise potentials for simple, s-p bonded metals, can be derived from first-principles. The starting point is jellium, and the ions are specified as pseudopotentials, local or non-local. The application of perturbation theory to second order in the pseudopotentials leads to the energy in the form of a density dependent, structure independent term plus a sum of density dependent, pairwise interactions between the ions. With the help of the Hellmann–Feynman theorem a simple physical interpretation is given in terms of interacting, spherically-symmetric pseudoatpms. A simple example using the Ashcroft empty core pseudopotential and the Thomas–Fermi approximation is worked through to illustrate the concepts. The use of a local density as a parameter within the pair potential is discussed.Less

This chapter shows how pairwise potentials for simple, s-p bonded metals, can be derived from first-principles. The starting point is jellium, and the ions are specified as pseudopotentials, local or non-local. The application of perturbation theory to second order in the pseudopotentials leads to the energy in the form of a density dependent, structure independent term plus a sum of density dependent, pairwise interactions between the ions. With the help of the Hellmann–Feynman theorem a simple physical interpretation is given in terms of interacting, spherically-symmetric pseudoatpms. A simple example using the Ashcroft empty core pseudopotential and the Thomas–Fermi approximation is worked through to illustrate the concepts. The use of a local density as a parameter within the pair potential is discussed.

*Mike Finnis*

- Published in print:
- 2003
- Published Online:
- January 2010
- ISBN:
- 9780198509776
- eISBN:
- 9780191709180
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198509776.001.0001
- Subject:
- Physics, Atomic, Laser, and Optical Physics

There is a continuing growth of interest in the computer simulation of materials at the atomic scale, using a variety of academic and commercial computer programs. In all such programs there is some ...
More

There is a continuing growth of interest in the computer simulation of materials at the atomic scale, using a variety of academic and commercial computer programs. In all such programs there is some physical model of the interatomic forces. For a student or researcher, the basis of such models is often shrouded in mystery. It is usually unclear how well founded they are, since it is hard to find a discussion of the physical assumptions that have been made in their construction. The lack of clear understanding of the scope and limitations of a given model may lead to its innocent misuse, resulting either in unfair criticism of the model or in the dissemination of nonsensical results. In this book, models of interatomic forces are derived from a common physical basis, namely the density functional theory. The book includes the detailed derivation of pairwise potentials in simple metals, tight-binding models from the simplest to the most sophisticated (self-consistent) kind, and ionic models. It provides a critical appreciation of the broad range of models in current use, and provides the tools for understanding other variants that are described in the literature. Some of the material is new, and some pointers are given to possible future avenues of model development.Less

There is a continuing growth of interest in the computer simulation of materials at the atomic scale, using a variety of academic and commercial computer programs. In all such programs there is some physical model of the interatomic forces. For a student or researcher, the basis of such models is often shrouded in mystery. It is usually unclear how well founded they are, since it is hard to find a discussion of the physical assumptions that have been made in their construction. The lack of clear understanding of the scope and limitations of a given model may lead to its innocent misuse, resulting either in unfair criticism of the model or in the dissemination of nonsensical results. In this book, models of interatomic forces are derived from a common physical basis, namely the density functional theory. The book includes the detailed derivation of pairwise potentials in simple metals, tight-binding models from the simplest to the most sophisticated (self-consistent) kind, and ionic models. It provides a critical appreciation of the broad range of models in current use, and provides the tools for understanding other variants that are described in the literature. Some of the material is new, and some pointers are given to possible future avenues of model development.