computing betas and qs for NCPP/USPP/PAW PseudoPotentials - - PowerPoint PPT Presentation

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computing betas and qs for ncpp uspp paw pseudopotentials
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computing betas and qs for NCPP/USPP/PAW PseudoPotentials - - PowerPoint PPT Presentation

Dec 07, 2022 182 likes •481 views

computing betas and qs for NCPP/USPP/PAW PseudoPotentials Periodic potential Periodic potential Periodic potential Periodic potential Periodic potential crystal structure factor atomic form factor ab initio Norm Conserving

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computing betas and qs for NCPP/USPP/PAW PseudoPotentials

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Periodic potential

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Periodic potential

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Periodic potential

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Periodic potential

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Periodic potential

atomic form factor crystal structure factor

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ab initio Norm Conserving PseudoPotentials semilocal form where projects over L = l(l+1)

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ab initio Norm Conserving PseudoPotentials semilocal form is local with a Coulomb tail is local in the radial coordinate, short ranged and l-dependent where projects over L = l(l+1)

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An example: Mo l-dependent potential

Hamann, schlueter & Chiang, PRL 43, 1494 (1979)

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An example: Mo

Hamann, schlueter & Chiang, PRL 43, 1494 (1979)

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ab initio Norm Conserving PseudoPotentials

  • Kleinman-Bylander fully non-local form
  • semilocal form
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ab initio Norm Conserving PseudoPotentials

  • Kleinman-Bylander fully non-local form

is local with a Coulomb tail are localized radial functions such that the transformed pseudo acts in the same way as the original form on the reference confjg.

  • semilocal form ...

One has

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ab initio Norm Conserving PseudoPotentials Kleinman-Bylander fully non-local form

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ab initio Norm Conserving PseudoPotentials Kleinman-Bylander fully non-local form

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ab initio Norm Conserving PseudoPotentials Kleinman-Bylander fully non-local form

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with

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Ultra Soft PseudoPotentials

where the “augmentation charges” are are projectors are atomic states (not necessarily bound) are pseudo-waves (coinciding with beyond some core radius)

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Ultra Soft PseudoPotentials

where leading to a generalized eigenvalue problem Orthogonality with USPP:

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Ultra Soft PseudoPotentials

where There are additional terms in the density, in the energy, in the hamiltonian in the forces, ...

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with

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The betas and qs functions can be computed in reciprocal space as described above. Alternatively they can be computed directly in real-space interpolating from the radial grid to the fgt grid. If the kinetic energy cutofg used is not converged enough the two procedure ARE NOT the same. In our experience the G-space treatment is more relieable.