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! Copyright (C) 2021 J. K. Dewhurst, S. Sharma and E. K. U. Gross.

! This file is distributed under the terms of the GNU General Public License.

! See the file COPYING for license details.


!BOP

! !ROUTINE: k_tfvw_sp

! !INTERFACE:


subroutine k_tfvw_sp(n,rhoup,rhodn,gup2,gdn2,dtdru,dtdrd,dtdgu2,dtdgd2)

! !INPUT/OUTPUT PARAMETERS:

!   n      : number of density points (in,integer)

!   rhoup  : spin-up charge density (in,real(n))

!   rhodn  : spin-down charge density (in,real(n))

!   gup2   : |grad rhoup|^2 (in,real(n))

!   gdn2   : |grad rhodn|^2 (in,real(n))

!   dtdru  : dtauup/drhoup (out,real(n))

!   dtdrd  : dtaudn/drhodn (out,real(n))

!   dtdgu2 : dtauup/d(|grad rhoup|^2) (out,real(n))

!   dtdgu2 : dtaudn/d(|grad rhodn|^2) (out,real(n))

! !DESCRIPTION:

!   Calculates the derivatives of the spin-polarised kinetic energy density

!   $\partial\tau^{\uparrow}/\partial\rho^{\uparrow}$,

!   $\partial\tau^{\downarrow}/\partial\rho^{\downarrow}$,

!   $\partial\tau^{\uparrow}/\partial|\nabla\rho^{\uparrow}|^2$ and

!   $\partial\tau^{\downarrow}/\partial|\nabla\rho^{\downarrow}|^2$.

!   This is done by noting the relation for the kinetic energy functional

!   [G. L. Oliver and J. P. Perdew, {\it Phys. Rev. A}

!   {\bf 20}, 397 (1979)]

!   $$ T[\rho^{\uparrow},\rho^{\downarrow}]=\tfrac{1}{2}T[2\rho^{\uparrow}]

!    +\tfrac{1}{2}T[2\rho^{\downarrow}] $$

!   and taking, for example,

!   $$ \tau^{\uparrow}(\rho^{\uparrow},|\nabla\rho^{\uparrow}|^2)

!   =\tfrac{1}{2}\tau(2\rho^{\uparrow},4|\nabla\rho^{\uparrow}|^2), $$

!   where the gradient expansion of the unpolarised kinetic energy density is

!   used for $\tau$. See the routines {\tt k\_tfvw1}, {\tt ggamt\_4},

!   {\tt ggair\_4}, {\tt potxcmt}, and {\tt potxcir}.

!

! !REVISION HISTORY:

!   Created December 2021 (JKD)

!EOP

!BOC

implicit none

! arguments

integer, intent(in) :: n

real(8), intent(in) :: rhoup(n),rhodn(n)

real(8), intent(in) :: gup2(n),gdn2(n)

real(8), intent(out) :: dtdru(n),dtdrd(n)

real(8), intent(out) :: dtdgu2(n),dtdgd2(n)

! local variables

integer i

do i=1,n

  call k_tfvw1(2.d0*rhoup(i),4.d0*gup2(i),dtdru(i),dtdgu2(i))

  dtdgu2(i)=2.d0*dtdgu2(i)

end do

do i=1,n

  call k_tfvw1(2.d0*rhodn(i),4.d0*gdn2(i),dtdrd(i),dtdgd2(i))

  dtdgd2(i)=2.d0*dtdgd2(i)

end do


end subroutine

!EOC


k_tfvw1
elemental subroutine k_tfvw1(rho, grho2, dtdr, dtdgr2)
Definition k_tfvw1.f90:10

k_tfvw_sp
subroutine k_tfvw_sp(n, rhoup, rhodn, gup2, gdn2, dtdru, dtdrd, dtdgu2, dtdgd2)
Definition k_tfvw_sp.f90:10