! computation of the film-case Yukawa potential for the preconditioning of the charge density residual
! Computation of the film-case Yukawa potential for the preconditioning of the charge density residual
! 1. part: The pseudo-charge density is used for the vacuum and interstitial potentials.
! 4. part: The MT potential is calculated at the end.
! These two parts do not change compared to the bulk case.
! 2. and 3. part: The vacuum and interstitial potentials are calculated by integration of the product of the charge density and
! the 1D Green function with respect to z (from minus infinity to infinity). The integrals for both potentials are split in 4:
! the seperating points are the boundaries of the slab and the point where the integration variable z' equals the point z where we
! want to evaluate the potential for. For the contribution from the vacuum charge density we do a numerical integration. For the
! contribution from the slab charge density we have analytical expressions of the integrals.
contains
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@@ -65,8 +75,8 @@ module m_VYukawaFilm
psq,rhtxy,rht,&
VVxy,VVz,alphm)
! 1. part: compute the contribution from the interstitial charge density to the vacuum potential as a function of q_xy and z
! 2. part: compute the contribution from the vacuum charge density to the vacuum potential as a function of q_xy and z by numerical integration
! 1. part: Compute the contribution from the interstitial charge density to the vacuum potential as a function of q_xy and z (analytic expression for integral)
! 2. part: Compute the contribution from the vacuum charge density to the vacuum potential as a function of q_xy and z by numerical integration
! 1. part: compute the contribution from the interstitial charge density to the interstitial potential (largest part) as a function of q_xy and z
! 2. part: add the contribution from the vacuum charge density to the interstitial potential, which had already been computed earlier for the vacuum potential
! 3. part: compute the coefficients V^I(q_xy,q_z) from the function V^I(q_xy,z) by a 1D Fourier transform: V^I(q_xy,z) = sum_{q_z} V^I(q_xy,q_z) * exp( ImagUnit * q_z * z )
! main parts:
! 1. part: Compute the contribution from the interstitial charge density to the interstitial potential as a function of q_xy and z (analytic expression for integral)
! 2. part: Add the contribution from the vacuum charge density to the interstitial potential, which had already been computed earlier for the vacuum potential
! 4. part: Compute the coefficients V^I(q_xy,q_z) from the function V^I(q_xy,z) by a 1D Fourier transform: