Computational techniques, momentum density

The Fourier transforms of Eq. (51) can be performed in closed form for most commonly used basis sets. Moreover, formulas and techniques for the computation of the spherically averaged momentum density, isotropic and directional Compton profiles, and momentum moments have been worked out for both Gaussian- and Slater-type basis sets. Older work on the methods and formulas has been summarized in a review article by Kaijser and Smith [79]. A bibliography of more recent methodological work can be found in another review article [11]. Advantages and disadvantages of various types of basis sets, including many unconventional ones, have been analyzed from a momentum-space perspective [80-82]. Section 19.7 describes several illustrative computations chosen primarily from my own work for convenience. 

As the study of the electron momentum density and the Fermi surface by the positron annihilation techniques is rather indirect, it is important to perform the experimental investigations in close relation with a strong computational approach. The first valuable quantity to estimate is the positron density distribution in the lattice unit cell it will indicate which electronic states might be observed experimentally. One has then to evaluate the electron momentum density as seen by the positron. From this, the... 

In this section, we briefly summarize the major theoretical techniques employed in contemporary pseudopotential calculations. The approach involves the use of initio pseudopotentials3 7 to compute the electron-core interactions and local density function-als° for evaluating electron-electron interactions. Several different basis sets can be used to solve the electron wave equation. The particular choice is determined by the system of interest. Finally, the total energies and forces are calculated using a momentum space scheme. 

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