By David J. Singh
The 1st version of this ebook, released in 1994, supplied an exposition of the LAPW approach and its dating with different digital constitution techniques, in particular Car-Parrinello established planewave tools. considering booklet of that publication, the LAPW procedure has been remodeled from a really good approach used regularly via researchers working their very own selfmade types, to a favored, accepted procedure, the place such a lot clients run typical codes to enquire ma terials of curiosity to them. this is often a thrilling improvement since it opens the door to common use of first ideas calculations in different components of condensed topic physics and fabrics technology. The optimistic effect of this on clinical growth is already turning into transparent. additionally because of this pattern, the nice majority of researchers utilizing the LAPW approach aren't any longer at once in volved within the improvement of LAPW codes. still, it continues to be very important to appreciate how the LAPW strategy works, what its barriers are, and the way its parameters ascertain the quahty and potency of calculations. The scientist with an knowing of the way the strategy works has a transparent virtue. This version is an up to date and improved remedy of the LAPW procedure, together with descriptions of key advancements within the LAPW technique seeing that 1994, similar to p half neighborhood orbitals, the APW-i-LO procedure, LDA+U calculations and non-collinear magnetism, in addition to a lot of the cloth from the 1st version.
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Extra info for Planewaves, Pseudopotentials, and the LAPW Method
The eigenvectors can be transformed efficiently between real and momentum space using fast Fourier transform (FFT) methods. Exploiting this to operate the potential in real space and the kinetic energy in momentum space, the computational cost of operating the Hamiltonian on an eigenvector is dominated by the 0(n(,log2(nb)) cost per band of the FFTs and as a result this part of the calculation scales with the number of atoms as 0(iV^logA'^). g. Ref. , for details), the prefactor of the remaining O(N^) term is much smaller than in conventional diagonalization based methods.
Because of the high order of this error, the LAPWs form a good basis set over a relatively large energy region, so that all valence bands may typically be treated with a single set of Eg. In the few instances for which this is not possible, the energy region of interest may be divided into a few (very rarely more than 2) windows and separate solutions carried out for each (see Chapter 5). This is an enormous simplification over the standard APW method. In the LAPW method accurate energy bands (at a given k-point) are obtained with a single diagonalization, while in the APW method one is needed for each band.
The advent of ab initio molecular dynamics using the Car-Parrinello (CP) method  has resulted in a considerable leap in the capability of planewave based density functional methods, and application of these approaches has permitted the solution of numerous previously intractable problems. But even now, few substantial applications of these ideas to nonplanewave based methods have been reported. Why? We think that it is safe to say that the real reasons for the early dominance of planewave methods relate less to computational efficiency than to human efficiency.