Supercomputational Science pp 235-241 | Cite as

# Energy Minimisation and Structure Factor Refinement Methods

## Abstract

From a computational viewpoint, energy minimization and structure factor refinements of molecules fall into the general area of nonlinear optimization problems. Given a set of independent variables *x* and a specified objective function *F* = *F*(*x*),the task is to find the set of variables *x** for which the function *F* has its minimum value *F*(*x**) = *min*(*F*(*x*)). Clearly, one is interested in a method that delivers the minimum of *F* with the least amount of computational cost. However, there are often many other factors that can determine the method one uses — *e.g*. the amount of computer memory required, whether or not the derivatives of the function can be easily obtained or even if they exist, and indeed also whether the human resources exist to set up and implement the most efficient method.

## Keywords

Conjugate Gradient Method Order Method Simulated Annealing Method Refinement Program Atomic Shift## Preview

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## References and Further Reading

- Nelder J A and Mead R (1965), Computer Journal
**7**, 308Google Scholar - Jack A and Levitt M (1978), Acta Cryst
**A34**, 931CrossRefGoogle Scholar - Kirkpatrick S, Gellat C D and Vecchi M P (1983), Science
**220**, 671PubMedCrossRefGoogle Scholar - Chapter 10 on Minimization and Maximization of Functions: Press W H, Flannery B P, Teukolsky S A and Vetterling W T, ‘Numerical Recipes’ (Cambridge Uni Press), 1987Google Scholar
- The Refinement of Macromolecules. Isaacs N (1982), ‘Computational Crystallography’, Ed. Sayre D, pp 381–397Google Scholar
- Refinement Techniques: Use of the FFT. Isaacs N (1982), ‘Computational Crystallography’, Ed. Sayre D, pp 397–408Google Scholar