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These are the first thoughts on how to represent Wavefunctions.
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### Basis set ###
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There are two main basis set types: atom centered and absolute
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Atomic basis set can always be represented as a radial function and an l value that specifies which spherical harmonics $Y_m^l$ are used for the radial part.
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For the radial part one could store just numerical values on a logarithmic grid and still have enough accuracy. This is natural for fhi-aims.
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As long as no mixed basis set are used I think fhi aims integrals can be used to calculate any derived quantity wanted.
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Plane waves are normally defined through a cutoff, but in practice FFT have to be calculated on a real space grid of a given size.
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This size should be stored. Real space grid, keep all coefficients, while plane waves normally in the reciprocal space use a spherical cutoff.
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While one can try to recover the core electrons from a pseudo potential calculation (as it is done for NMR) in general it is difficult.
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In approaches like GAPW the density in pane waves can be seen as a projection of the total density, which shows that the inversion (plane waves -> all atoms in general might need a self consistent optimization. It is possible that for given pseudopotentials this might be simpler (especially if the projectors are known).
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The fitting of pseudopotentials using scalar relativistic solutions (so that the unrelativistic solution is close to the relativistic one) murkies further the things.
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Wavelets can be refined close to the atom, but such basis set are not considered.
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If Numerical orbitals are used for all representations some approach migtht be envisaged (using the potential values as stating point?). |
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