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Like most ``energy-band methods``, the LAPW method is a procedure for solving the Kohn-Sham equations for the ground state density, total energy, and (Kohn-Sham) eigenvalues (energy bands) of a many-electron system (here a crystal) by introducing a basis set which is especially adapted to the problem.
electric field gradients, isomer shifts, hyperfine fields, NMR chemical shifts, NMR Knight shifts
x-ray emission and absorption spectra, electron energy loss spectra
optical properties
fermi surfaces
The coefficients Alm, Blm, and Clm, are determined by the requirements that $\phi^{LO}$ should be normalized and has zero value and slope at the sphere boundary.
This adaptation is achieved by dividing the unit cell into (I) non-overlapping atomic spheres (centered at the atomic sites) and (II) an interstitial region. In the two types of regions different basis sets are used:
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