Kohn linear scaling techniques

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. 

X-ray crystallography for detection of metalloproteins accuracy problems, 66 determination of geometric parameters DFT-the Hohenberg-Kohn theorem approach, 67 QM/S techniques, 67 QSOR approach, Karplus relationship, 67 refinement of, linear-scaling quantum chemical methods, 66-67... 

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... 

The LSDA approach requires simultaneous self-consistent solutions of the Schrbdinger and Poisson equations. This was accomplished using the Layer Korringa-Kohn-Rostoker technique which has many useful features for calculations of properties of layered systems. It is, for example, one of only a few electronic structure techniques that can treat non-periodic infinite systems. It also has the virtue that the computational time required for a calculation scales linearly with the number of different layers, not as the third power as most other techniques. 

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