This chapter discusses the evaluation of momentum distributions and compton profiles for atomic and molecular systems. The Dirac-Fourier transformation of position space wavefunctions and one-particle density matrices are reviewed. The Dirac-Fourier transformation of atomic orbitals is of two types: (1) spherical harmonic orbitals and (2) Cartesian and ellipsoidal Gaussian-type orbitals. Both these types are more commonly used for the construction of atomic and molecular wavefunctions. Evaluation of the momentum density ρ(p) is presented using: (1) spherical harmonic basis functions and (2) Cartesian Gaussian-type functions. The computational access to directional compton profiles is demonstrated for two different schemes. First, the profile is evaluated from the momentum density itself and then it is evaluated from the basis overlap integrals. When one starts from the momentum density ρ(p), there is a further choice between two different methods. One approach is to perform a rotation of the coordinate system once and for all, such that one axis is aligned with the scattering vector. The other method considers each density contribution separately. © 1977 Academic Press Inc.
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