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Direct Minimisation

  Traditionally the Kohn Sham equations given by Equation 2.5 were solved by a self consistent iteration. This requires expensive matrix diagonalisation for each iteration at a cost of operations where is the number of plane waves.

A more efficient approach involves the direct minimisation of the total energy functional (Equation 2.2). This was first suggested by Car and Parrinello in 1985, who proposed minimisation by a molecular dynamics treatment of the electronic degrees of freedom [7]. This approach scales as where is the number of bands. The direct minimisation approach used in the CASTEP/CETEP codes uses a conjugate gradient technique to minimise the Kohn-Sham functional [8]. The use of a plane wave basis set and Fast Fourier Transform algorithms lead to a scaling of for the majority of the calculation, although for large systems the cost of maintaining orthogonality between the orbitals, , dominates. Furthermore, the conjugate gradients approach leads to a much faster convergence in practice than the molecular dynamics approach.



Mr. Matthew D. Segall
Fri Jul 21 15:33:30 BST 1995