Energy Minimisation and Structure Factor Refinement Methods
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.
KeywordsConjugate Gradient Method Order Method Simulated Annealing Method Refinement Program Atomic Shift
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References and Further Reading
- Nelder J A and Mead R (1965), Computer Journal 7, 308Google 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