Skip to content

Commit

Permalink
Made a first pass through the real epsilon calculator; restructructur…
Browse files Browse the repository at this point in the history 
…ed the imag part calculator.
  • Loading branch information
@nakib
nakib committed Jul 1, 2024
1 parent f546ac5 commit 59b9cf4
Showing 1 changed file with 86 additions and 50 deletions.
136 changes: 86 additions & 50 deletions src/screening.f90
View file
Original file line number Diff line number Diff line change
Expand Up @@ -59,7 +59,7 @@ pure elemental real(r64) function finite_element(w, wl, w0, wr)
!! Triangular finite elements.
!!
!! w Continuous sampling variable
!! w_stencil 3-point stencil
!! wl, w0, wr 3-point stencil left, center, respectively

real(r64), intent(in) :: w
real(r64), intent(in) :: wl, w0, wr
Expand Down Expand Up @@ -95,7 +95,8 @@ subroutine calculate_Hilbert_weights(w_disc, w_cont, eps, Hilbert_weights)

!Grid spacing of "continuous" variable
dw = w_cont(2) - w_cont(1)


!TODO Need to handle the edges
do i = 2, n_disc - 1
Phi_i = finite_element(w_cont, w_disc(i - 1), w_disc(i), w_disc(i + 1))
do j = 1, n_disc
Expand All @@ -104,82 +105,117 @@ subroutine calculate_Hilbert_weights(w_disc, w_cont, eps, Hilbert_weights)
(w_disc(j) + w_cont)/((w_disc(j) + w_cont)**2 + eps))
!TODO Would be nice to have a compsimps function instead of
!a subroutine.
call compsimps(integrand, dw, Hilbert_weights(i, j))
call compsimps(integrand, dw, Hilbert_weights(j, i))
end do
end do
end subroutine calculate_Hilbert_weights

subroutine Re_head_polarizability_3d_T(Reeps_T, Omegas, Im_part_T, Hilbert_weights_T)
!! Real part of the head of the bare polarizability of the 3d Kohn-Sham system using
!! Hilbert transform for a given set of temperature-dependent quantities.
!!
!! Here we calculate the diagonal in G-G' space. Moreover,
!! we use the approximation G.r -> 0.
!!
!! Reeps_T Real part of bare polarizability
!! Omega Energy of excitation in the electron gas
!! Imeps_T Imaginary part of bare polarizability
!! Hilbert_weights_T Hilbert transform weights

real(r64), allocatable, intent(out) :: Reeps_T(:)
real(r64), intent(in) :: Omegas(:)
real(r64), intent(in) :: Im_part_T(:)
real(r64), intent(in) :: Hilbert_weights_T(:, :)

allocate(Reeps_T(size(Omegas)))

!TODO Can optimize this sum with blas
Reeps_T = matmul(Hilbert_weights_T, Im_part_T)
end subroutine Re_head_polarizability_3d_T

real(r64) function Im_polarizability_3d(Omega, q_indvec, el, pcell_vol, T)
!! Imaginary part of bare polarizability of the 3d Kohn-Sham system using
subroutine Im_head_polarizability_3d(Imeps, Omegas, q_indvec, el, pcell_vol, T)
!! Imaginary part of the head of the bare polarizability of the 3d Kohn-Sham system using
!! Eq. 18 of Shishkin and Kresse Phys. Rev. B 74, 035101 (2006).
!!
!! Here we calculate the diagonal in G-G' space. Moreover,
!! we use the approximation G.r -> 0.
!!
!! Imeps Imaginart part of bare polarizability
!! Omega Energy of excitation in the electron gas
!! q_indvec Wave vector of excitation in the electron gas (0-based integer triplet)
!! el Electron data type
!! pcell_vol Primitive unit cell volume
!! T Temperature (K)

real(r64), intent(in) :: Omega, pcell_vol, T
real(r64), intent(in) :: Omegas(:), pcell_vol, T
integer(i64), intent(in) :: q_indvec(3)
type(electron), intent(in) :: el

real(r64), allocatable, intent(out) :: Imeps(:)

!Locals
integer(i64) :: m, n, ik, ikp, ikp_window, k_indvec(3), kp_indvec(3)
integer(i64) :: m, n, ik, ikp, ikp_window, iOmega, nOmegas, k_indvec(3), kp_indvec(3)
real(r64) :: overlap, ek, ekp
procedure(delta_fn), pointer :: delta_fn_ptr => null()

nOmegas = size(Omegas)

allocate(Imeps(nOmegas))

!Associate delta function procedure pointer
delta_fn_ptr => get_delta_fn_pointer(tetrahedra = .true.)

Imeps = 0.0
do iOmega = 1, nOmegas
!Below, we will sum out m, n, and k
do m = 1, el%numbands
do ik = 1, el%nwv
ek = el%ens(ik, m)

!Apply energy window to initial electron
if(abs(ek - el%enref) > el%fsthick) cycle

!Calculate index vector of final electron: k' = k + q
k_indvec = nint(el%wavevecs(ik, :)*el%wvmesh)
kp_indvec = modulo(k_indvec + q_indvec, el%wvmesh) !0-based index vector

!Multiplex kp_indvec
ikp = mux_vector(kp_indvec, el%wvmesh, 0_i64)

!Below, we will sum out m, n, and k, accumulating the result into aux.
Im_polarizability_3d = 0.0
do m = 1, el%numbands
do ik = 1, el%nwv
ek = el%ens(ik, m)

!Apply energy window to initial electron
if(abs(ek - el%enref) > el%fsthick) cycle

!Calculate index vector of final electron: k' = k + q
k_indvec = nint(el%wavevecs(ik, :)*el%wvmesh)
kp_indvec = modulo(k_indvec + q_indvec, el%wvmesh) !0-based index vector

!Multiplex kp_indvec
ikp = mux_vector(kp_indvec, el%wvmesh, 0_i64)

!Check if final electron wave vector is within FBZ blocks
call binsearch(el%indexlist, ikp, ikp_window)
if(ikp_window < 0) cycle

do n = 1, el%numbands
ekp = el%ens(ikp_window, n)

!Apply energy window to final electron
if(abs(ekp - el%enref) > el%fsthick) cycle

!This is |U(k')U^\dagger(k)|_nm squared
!(Recall that U^\dagger(k) is the diagonalizer of the electronic hamiltonian.)
overlap = (abs(dot_product(el%evecs(ikp_window, n, :), el%evecs(ik, m, :))))**2

Im_polarizability_3d = Im_polarizability_3d + &
(Fermi(ek, el%chempot, T) - &
Fermi(ekp, el%chempot, T))*overlap* &
delta_fn_ptr(ekp - Omega, ik, m, &
el%wvmesh, el%simplex_map, &
el%simplex_count, el%simplex_evals)
!Check if final electron wave vector is within FBZ blocks
call binsearch(el%indexlist, ikp, ikp_window)
if(ikp_window < 0) cycle

do n = 1, el%numbands
ekp = el%ens(ikp_window, n)

!Apply energy window to final electron
if(abs(ekp - el%enref) > el%fsthick) cycle

!This is |U(k')U^\dagger(k)|_nm squared
!(Recall that U^\dagger(k) is the diagonalizer of the electronic hamiltonian.)
overlap = (abs(dot_product(el%evecs(ikp_window, n, :), el%evecs(ik, m, :))))**2

Imeps(iOmega) = Imeps(iOmega) + &
(Fermi(ek, el%chempot, T) - &
Fermi(ekp, el%chempot, T))*overlap* &
delta_fn_ptr(ekp - Omegas(iOmega), ik, m, &
el%wvmesh, el%simplex_map, &
el%simplex_count, el%simplex_evals)
end do
end do
end do
end do
!Recall that the resolvent is already normalized in the full wave vector mesh.
!As such, the 1/product(el%wvmesh) is not needed in the expression below.
Im_polarizability_3d = Im_polarizability_3d*pi*sign(1.0_r64, omega)*el%spindeg/pcell_vol

!Zero out extremely small numbers
if(abs(Im_polarizability_3d) < 1.0e-30_r64) Im_polarizability_3d = 0.0_r64
end function Im_polarizability_3d
do iOmega = 1, nOmegas
!Recall that the resolvent is already normalized in the full wave vector mesh.
!As such, the 1/product(el%wvmesh) is not needed in the expression below.
Imeps(iOmega) = &
Imeps(iOmega)*pi*sign(1.0_r64, Omegas(iOmega))*el%spindeg/pcell_vol

!Zero out extremely small numbers
if(abs(Imeps(iOmega)) < 1.0e-30_r64) Imeps(iOmega) = 0.0_r64
end do
end subroutine Im_head_polarizability_3d

!!$ subroutine calculate_RPA_dielectric_3d(el, crys, num)
!!$ !! Dielectric function of the 3d Kohn-Sham system in the
Expand Down

0 comments on commit 59b9cf4

Please sign in to comment.