Kohn-Sham method linear-scaling methods

Linear-Scaling Methods for Solving the Kohn-Sham System... 

Linear-Scaling Methods for the Kohn-Sham Potential and for Numerical Integration... 

The divide-and-conquer method [34,35] was the first Kohn Sham algorithm which delivered linear scaling computational costs that grow linearly with the size of the system. In this technique, one first projects the density matrix onto a basis set, typically... 

Often, the bottleneck in linear-scaling density-functional theory is the evaluation of the Coulomb potential the trade olf between the simple and direct method of integrating Eq. (94) and the more sophisticated linear-scaling approaches is evidenced by the fact that, for moderately large systems, linear-scaling density-functional techniques are often less efficient than direct solution to the Kohn-Sham system. As the size of the system increases beyond 10 to 20 A, however, linear-scaling techniques become essential. 

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