exchange_val_hf.F90 24.7 KB
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!--------------------------------------------------------------------------------
! Copyright (c) 2016 Peter Grünberg Institut, Forschungszentrum Jülich, Germany
! This file is part of FLEUR and available as free software under the conditions
! of the MIT license as expressed in the LICENSE file in more detail.
!--------------------------------------------------------------------------------

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!     Calculates the HF exchange term
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!
!                                          s          s*          s            s*
!                                       phi    (r) phi     (r) phi     (r') phi    (r')
!                         occ.             n_1k       n'k+q       n'k+q        n_2k
!     exchange(n,q)  =  - SUM  INT INT  ------------------------------------------- dr dr'
!                         k,n'                           | r - r' |
!
!                         occ                  s          s    ~        ~       s         s
!                    =  - SUM  SUM  v     < phi      | phi     M    > < M    phi     | phi      >
!                         k,n' I,J   k,IJ      n'k+q      n_1k  q,I      q,J    n_2k      n'k+q
!
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!     for the different combinations of n_1 and n_2 and where n' runs only over the valence states.
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!     ( n_1,n_2:  valence-valence, core-core,core-valence )
!
!
!     At the Gamma point (k=0) v diverges. After diagonalization of v at k=0 the divergence is
!     restricted to the head element I=1. Furthermore, we expand <...> with kp perturbation theory.
!     As a result, the total I=1 element is given by a sum of a divergent 1/k**2-term and an
!     angular dependent term. The former is separated from the numerical k-summation and treated
!     analytically while the latter is spherically averaged and added to the k=0 contribution of
!     the numerical k-summation. (A better knowledge of the integrand's behavior at the BZ edges
!     might further improve the integration.)
!
!     The divergence at the Gamma point is integrated with one of the following algorithms:
! (1) Switching-Off Function
!     In a sphere of radius k0=radshmin/2 a switching-off function g(k)=1-(k/k0)**n*(n+1-n*k/k0)
!     (n=npot) is defined. The 1/k**2 divergence is subtracted from the BZ integral in the form
!     g(k)/k**2 and integrated analytically. The non-divergent rest is integrated numerically.
! (2) Periodic Function (similar to the one used by Massidda PRB 48, 5058)
!     The function  F(k) = SUM(G) exp(-expo*|k+G|**3) / |k+G|**2  is subtracted from the BZ integral
!     and integrated analytically. The non-divergent rest is integrated numerically.
!     The parameter expo is chosen such that exp(-expo*q**3)=1/2
!     with q = radius of sphere with same volume as BZ.
! (3) Periodic Function (same as Massidda's) with expo->0
!     The function  F(k) = lim(expo->0) SUM(G) exp(-expo*|k+G|**2) / |k+G|**2  is subtracted from
!     the BZ integral and integrated analytically. The contribution to the BZ integral including
!     the "tail" is
!     vol/(8*pi**3) INT F(k) d^3k - P SUM(k) F(k)  ( P = principal value ) .
!     For expo->0 the two terms diverge. Therefore a cutoff radius q0 is introduced and related to
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!     expo by exp(-expo*q0**2)=delta  ( delta = small value, e.g., delta = 1*10.0**-10 ) .
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!     The resulting formula
!     vol/(4*pi**1.5*sqrt(expo)) * erf(sqrt(a)*q0) - sum(q,0<q<q0) exp(-expo*q**2)/q**2
!     converges well with q0. (Should be the default.)

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MODULE m_exchange_valence_hf
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   LOGICAL, PARAMETER:: zero_order = .false., ibs_corr = .false.
   INTEGER, PARAMETER:: maxmem = 600
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CONTAINS
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   SUBROUTINE exchange_valence_hf(nk, kpts, nkpt_EIBZ, sym, atoms, hybrid, cell, dimension, input, jsp, hybdat, mnobd, lapw, &
                                  eig_irr, results, parent, pointer_EIBZ, n_q, wl_iks, it, xcpot, noco, nsest, indx_sest, &
                                  mpi, mat_ex)

      USE m_types
      USE m_wrapper
      USE m_constants
      USE m_trafo
      USE m_wavefproducts
      USE m_olap
      USE m_spmvec
      USE m_hsefunctional, ONLY: dynamic_hse_adjustment
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#if defined(CPP_MPI)&&defined(CPP_NEVER)
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      USE m_mpi_work_dist
      USE m_mpi_tags
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#endif
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      USE m_io_hybrid
      USE m_kp_perturbation

      IMPLICIT NONE

      TYPE(t_results), INTENT(IN)    :: results
      TYPE(t_xcpot_inbuild), INTENT(IN)    :: xcpot
      TYPE(t_mpi), INTENT(IN)    :: mpi
      TYPE(t_dimension), INTENT(IN)    :: dimension
      TYPE(t_hybrid), INTENT(INOUT) :: hybrid
      TYPE(t_input), INTENT(IN)    :: input
      TYPE(t_noco), INTENT(IN)    :: noco
      TYPE(t_sym), INTENT(IN)    :: sym
      TYPE(t_cell), INTENT(IN)    :: cell
      TYPE(t_kpts), INTENT(IN)    :: kpts
      TYPE(t_atoms), INTENT(IN)    :: atoms
      TYPE(t_lapw), INTENT(IN)    :: lapw
      TYPE(t_mat), INTENT(INOUT) :: mat_ex
      TYPE(t_hybdat), INTENT(INOUT) :: hybdat

      ! scalars
      INTEGER, INTENT(IN)    :: it
      INTEGER, INTENT(IN)    :: jsp
      INTEGER, INTENT(IN)    :: nk, nkpt_EIBZ
      INTEGER, INTENT(IN)    :: mnobd

      ! arrays
      INTEGER, INTENT(IN)    ::  n_q(nkpt_EIBZ)

      INTEGER, INTENT(IN)    ::  parent(kpts%nkptf)
      INTEGER, INTENT(IN)    ::  pointer_EIBZ(nkpt_EIBZ)
      INTEGER, INTENT(IN)    ::  nsest(hybrid%nbands(nk))
      INTEGER, INTENT(IN)    ::  indx_sest(hybrid%nbands(nk), hybrid%nbands(nk))

      REAL, INTENT(IN)    ::  eig_irr(dimension%neigd, kpts%nkpt)
      REAL, INTENT(IN)    ::  wl_iks(dimension%neigd, kpts%nkptf)

      ! local scalars
      INTEGER                 ::  iband, iband1, ibando, ikpt, ikpt0
      INTEGER                 ::  i, ic, ix, iy, iz
      INTEGER                 ::  irecl_coulomb, irecl_coulomb1
      INTEGER                 ::  j
      INTEGER                 ::  m1, m2
      INTEGER                 ::  n, n1, n2, nn, nn2
      INTEGER                 ::  nkqpt
      INTEGER                 ::  npot
      INTEGER                 ::  ok
      INTEGER                 ::  psize
      REAL                    ::  rdum
      REAL                    ::  k0

      REAL, SAVE             ::  divergence

      COMPLEX                 ::  cdum, cdum1, cdum2
      COMPLEX                 ::  exch0

      LOGICAL, SAVE           ::  initialize = .true.

      ! local arrays
      INTEGER              :: kcorner(3, 8) = reshape((/0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1/), (/3, 8/))
      COMPLEX              :: exchcorrect(kpts%nkptf)
      COMPLEX              :: dcprod(hybrid%nbands(nk), hybrid%nbands(nk), 3)
      COMPLEX              :: exch_vv(hybrid%nbands(nk), hybrid%nbands(nk))
      COMPLEX              :: hessian(3, 3)
      COMPLEX              :: proj_ibsc(3, mnobd, hybrid%nbands(nk))
      COMPLEX              :: olap_ibsc(3, 3, mnobd, mnobd)
      REAL                 :: carr1_v_r(hybrid%maxbasm1), carr1_c_r(hybrid%maxbasm1)
      COMPLEX              :: carr1_v_c(hybrid%maxbasm1), carr1_c_c(hybrid%maxbasm1)
      COMPLEX, ALLOCATABLE :: phase_vv(:, :)
      REAL, ALLOCATABLE :: cprod_vv_r(:, :, :), cprod_cv_r(:, :, :), carr3_vv_r(:, :, :), carr3_cv_r(:, :, :)
      COMPLEX, ALLOCATABLE :: cprod_vv_c(:, :, :), cprod_cv_c(:, :, :), carr3_vv_c(:, :, :), carr3_cv_c(:, :, :)
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#if defined(CPP_MPI)&&defined(CPP_NEVER)
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      COMPLEX             :: buf_vv(hybrid%nbands(nk), nbands(nk))
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#endif

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#if ( !defined CPP_NOSPMVEC && !defined CPP_IRAPPROX )
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      REAL                 :: coulomb_mt1(hybrid%maxindxm1 - 1, hybrid%maxindxm1 - 1, 0:hybrid%maxlcutm1, atoms%ntype)
      REAL                 :: coulomb_mt2_r(hybrid%maxindxm1 - 1, -hybrid%maxlcutm1:hybrid%maxlcutm1, 0:hybrid%maxlcutm1 + 1, atoms%nat)
      REAL                 :: coulomb_mt3_r(hybrid%maxindxm1 - 1, atoms%nat, atoms%nat)
      COMPLEX              :: coulomb_mt2_c(hybrid%maxindxm1 - 1, -hybrid%maxlcutm1:hybrid%maxlcutm1, 0:hybrid%maxlcutm1 + 1, atoms%nat)
      COMPLEX              :: coulomb_mt3_c(hybrid%maxindxm1 - 1, atoms%nat, atoms%nat)
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#else
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      REAL                 :: coulomb_r(hybrid%maxbasm1*(hybrid%maxbasm1 + 1)/2)
      COMPLEX              :: coulomb_c(hybrid%maxbasm1*(hybrid%maxbasm1 + 1)/2)
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#endif

#ifdef CPP_IRCOULOMBAPPROX
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      REAL                 :: coulomb_mtir_r((hybrid%maxlcutm1 + 1)**2*atoms%nat, &
                                             (hybrid%maxlcutm1 + 1)**2*atoms%nat + maxval(hybrid%ngptm))
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#else
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      REAL                 :: coulomb_mtir_r(((hybrid%maxlcutm1 + 1)**2*atoms%nat + maxval(hybrid%ngptm))* &
                                             ((hybrid%maxlcutm1 + 1)**2*atoms%nat + maxval(hybrid%ngptm) + 1)/2)
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#endif

#ifdef CPP_IRCOULOMBAPPROX
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      COMPLEX              :: coulomb_mtir_c((hybrid%maxlcutm1 + 1)**2*atoms%nat, &
                                             (hybrid%maxlcutm1 + 1)**2*atoms%nat + maxval(hybrid%ngptm))
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#else
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      COMPLEX              :: coulomb_mtir_c(((hybrid%maxlcutm1 + 1)**2*atoms%nat + maxval(hybrid%ngptm))* &
                                             ((hybrid%maxlcutm1 + 1)**2*atoms%nat + maxval(hybrid%ngptm) + 1)/2)
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#endif

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      LOGICAL              :: occup(dimension%neigd)
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#if defined(CPP_MPI)&&defined(CPP_NEVER)
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      INCLUDE "mpif.h"
      INTEGER              :: ierr, ierr2, length, rank
      CHARACTER(LEN=MPI_MAX_ERROR_STRING) :: errmsg
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#endif
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      CALL timestart("valence exchange calculation")

      IF (initialize) THEN !it .eq. 1 .and. nk .eq. 1) THEN
         call calc_divergence(cell, kpts, divergence)
         PRINT *, "Divergence:", divergence
         initialize = .false.
      END IF

      ! calculate valence-valence-valence-valence, core-valence-valence-valence
      ! and core-valence-valence-core exchange at current k-point
      ! the sum over the inner occupied valence states is restricted to the EIBZ(k)
      ! the contribution of the Gamma-point is treated separately (see below)

      ! determine package size loop over the occupied bands
      rdum = hybrid%maxbasm1*hybrid%nbands(nk)*4/1048576.
      psize = 1
      DO iband = mnobd, 1, -1
         ! ensure that the packages have equal size
         IF (modulo(mnobd, iband) == 0) THEN
            ! choose packet size such that cprod is smaller than memory threshold
            IF (rdum*iband <= maxmem) THEN
               psize = iband
               EXIT
            END IF
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         END IF
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      END DO

      IF (psize /= mnobd) THEN
         WRITE (6, '(A,A,i3,A,f7.2,A)') ' Divide the loop over the occupied hybrid%bands in packages', &
            ' of the size', psize, ' (cprod=', rdum*psize, 'MB)'
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      END IF
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      ALLOCATE (phase_vv(psize, hybrid%nbands(nk)), stat=ok)
      IF (ok /= 0) STOP 'exchange_val_hf: error allocation phase'
      phase_vv = 0
      IF (ok /= 0) STOP 'exchange_val_hf: error allocation phase'

      if (mat_ex%l_real) THEN
         ALLOCATE (cprod_vv_c(hybrid%maxbasm1, 0, 0), carr3_vv_c(hybrid%maxbasm1, 0, 0))
         ALLOCATE (cprod_vv_r(hybrid%maxbasm1, psize, hybrid%nbands(nk)), stat=ok)
         IF (ok /= 0) STOP 'exchange_val_hf: error allocation cprod'
         ALLOCATE (carr3_vv_r(hybrid%maxbasm1, psize, hybrid%nbands(nk)), stat=ok)
         IF (ok /= 0) STOP 'exchange_val_hf: error allocation carr3'
         cprod_vv_r = 0; carr3_vv_r = 0
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      ELSE
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         ALLOCATE (cprod_vv_r(hybrid%maxbasm1, 0, 0), carr3_vv_r(hybrid%maxbasm1, 0, 0))
         ALLOCATE (cprod_vv_c(hybrid%maxbasm1, psize, hybrid%nbands(nk)), stat=ok)
         IF (ok /= 0) STOP 'exchange_val_hf: error allocation cprod'
         ALLOCATE (carr3_vv_c(hybrid%maxbasm1, psize, hybrid%nbands(nk)), stat=ok)
         IF (ok /= 0) STOP 'exchange_val_hf: error allocation carr3'
         cprod_vv_c = 0; carr3_vv_c = 0
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      END IF
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      exch_vv = 0

      DO ikpt = 1, nkpt_EIBZ

         ikpt0 = pointer_EIBZ(ikpt)

         n = hybrid%nbasp + hybrid%ngptm(ikpt0)
         IF (hybrid%nbasm(ikpt0) /= n) STOP 'error hybrid%nbasm'
         nn = n*(n + 1)/2

         ! read in coulomb matrix from direct access file coulomb
         IF (mat_ex%l_real) THEN
            CALL read_coulomb_spm_r(kpts%bkp(ikpt0), coulomb_mt1, coulomb_mt2_r, coulomb_mt3_r, coulomb_mtir_r)
         ELSE
            CALL read_coulomb_spm_c(kpts%bkp(ikpt0), coulomb_mt1, coulomb_mt2_c, coulomb_mt3_c, coulomb_mtir_c)
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         END IF
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         IF (kpts%bkp(ikpt0) /= ikpt0) THEN
#if( !defined CPP_NOSPMVEC && !defined CPP_IRAPPROX )
            IF ((kpts%bksym(ikpt0) > sym%nop) .and. (.not. mat_ex%l_real)) THEN
               coulomb_mt2_c = conjg(coulomb_mt2_c)
               coulomb_mtir_c = conjg(coulomb_mtir_c)
            END IF
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#else
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            if (.not. mat_ex%l_real) THEN
               IF (kpts%bksym(ikpt0) > sym%nop) coulomb = conjg(coulomb)
            endif
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#endif
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         END IF
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         DO ibando = 1, mnobd, psize
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            IF (mat_ex%l_real) THEN
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#ifdef CPP_IRAPPROX
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               CALL wavefproducts_inv(1, hybdat, dimension, input, jsp, atoms, lapw, obsolete, kpts, nk, ikpt0, &
                                      mnobd, hybrid, parent, cell, sym, noco, nkqpt, cprod_vv)
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#else
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               CALL wavefproducts_inv5(1, hybrid%nbands(nk), ibando, ibando + psize - 1, dimension, input, jsp, atoms, &
                                       lapw, kpts, nk, ikpt0, hybdat, mnobd, hybrid, parent, cell, hybrid%nbasp, sym, &
                                       noco, nkqpt, cprod_vv_r)
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#endif
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            ELSE
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#ifdef CPP_IRAPPROX
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               CALL wavefproducts_noinv(1, hybdat, nk, ikpt0, dimension, input, jsp, cell, atoms, hybrid,
               kpts, mnobd, lapw, sym, noco, nkqpt, cprod_vv)
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#else
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               CALL wavefproducts_noinv5(1, hybrid%nbands(nk), ibando, ibando + psize - 1, nk, ikpt0, dimension, input, jsp, &!jsp,&
                                         cell, atoms, hybrid, hybdat, kpts, mnobd, lapw, sym, hybrid%nbasp, noco, nkqpt, cprod_vv_c)
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#endif
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            END IF
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            ! The sparse matrix technique is not feasible for the HSE
            ! functional. Thus, a dynamic adjustment is implemented
            ! The mixed basis functions and the potential difference
            ! are Fourier transformed, so that the exchange can be calculated
            ! in Fourier space
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#ifndef CPP_NOSPMVEC
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            IF (xcpot%is_name("hse") .OR. xcpot%is_name("vhse")) THEN
               iband1 = hybrid%nobd(nkqpt)

               exch_vv = exch_vv + &
                         dynamic_hse_adjustment(atoms%rmsh, atoms%rmt, atoms%dx, atoms%jri, atoms%jmtd, kpts%bkf(:, ikpt0), ikpt0, &
                                                kpts%nkptf, cell%bmat, cell%omtil, atoms%ntype, atoms%neq, atoms%nat, atoms%taual, &
                                                hybrid%lcutm1, hybrid%maxlcutm1, hybrid%nindxm1, hybrid%maxindxm1, hybrid%gptm, &
                                                hybrid%ngptm(ikpt0), hybrid%pgptm(:, ikpt0), hybrid%gptmd, hybrid%basm1, &
                                                hybrid%nbasm(ikpt0), iband1, hybrid%nbands(nk), nsest, ibando, psize, indx_sest, &
                                                atoms%invsat, sym%invsatnr, mpi%irank, cprod_vv_r(:hybrid%nbasm(ikpt0), :, :), &
                                                cprod_vv_c(:hybrid%nbasm(ikpt0), :, :), mat_ex%l_real, wl_iks(:iband1, nkqpt), n_q(ikpt))
            END IF
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#endif

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            ! the Coulomb matrix is only evaluated at the irrecuible k-points
            ! bra_trafo transforms cprod instead of rotating the Coulomb matrix
            ! from IBZ to current k-point
            IF (kpts%bkp(ikpt0) /= ikpt0) THEN
               CALL bra_trafo2(mat_ex%l_real, carr3_vv_r(:hybrid%nbasm(ikpt0), :, :), cprod_vv_r(:hybrid%nbasm(ikpt0), :, :), &
                               carr3_vv_c(:hybrid%nbasm(ikpt0), :, :), cprod_vv_c(:hybrid%nbasm(ikpt0), :, :), &
                               hybrid%nbasm(ikpt0), psize, hybrid%nbands(nk), kpts%bkp(ikpt0), ikpt0, kpts%bksym(ikpt0), sym, &
                               hybrid, kpts, cell, atoms, phase_vv)
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               IF (mat_ex%l_real) THEN
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                  cprod_vv_r(:hybrid%nbasm(ikpt0), :, :) = carr3_vv_r(:hybrid%nbasm(ikpt0), :, :)
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               ELSE
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                  cprod_vv_c(:hybrid%nbasm(ikpt0), :, :) = carr3_vv_c(:hybrid%nbasm(ikpt0), :, :)
               ENDIF
            ELSE
               phase_vv(:, :) = (1.0, 0.0)
            END IF
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            ! calculate exchange matrix at ikpt0

            call timestart("exchange matrix")
            DO n1 = 1, hybrid%nbands(nk)
               DO iband = 1, psize
                  IF ((ibando + iband - 1) > hybrid%nobd(nkqpt)) CYCLE

                  cdum = wl_iks(ibando + iband - 1, nkqpt)*conjg(phase_vv(iband, n1))/n_q(ikpt)

                  IF (mat_ex%l_real) THEN
                     carr1_v_r(:n) = 0
                     CALL spmvec_invs(atoms, hybrid, hybdat, ikpt0, kpts, cell, coulomb_mt1, coulomb_mt2_r, coulomb_mt3_r, &
                                      coulomb_mtir_r, cprod_vv_r(:n, iband, n1), carr1_v_r(:n))
                  ELSE
                     carr1_v_c(:n) = 0
                     CALL spmvec_noinvs(atoms, hybrid, hybdat, ikpt0, kpts, cell, coulomb_mt1, coulomb_mt2_c, coulomb_mt3_c, &
                                        coulomb_mtir_c, cprod_vv_c(:n, iband, n1), carr1_v_c(:n))
                  END IF

                  IF (mat_ex%l_real) THEN
                     DO n2 = 1, nsest(n1)!n1
                        nn2 = indx_sest(n2, n1)
                        exch_vv(nn2, n1) = exch_vv(nn2, n1) + cdum*phase_vv(iband, nn2)* &
                                           dotprod(carr1_v_r(:n), cprod_vv_r(:n, iband, nn2))
                     END DO !n2
                  ELSE
                     DO n2 = 1, nsest(n1)!n1
                        nn2 = indx_sest(n2, n1)
                        exch_vv(nn2, n1) = exch_vv(nn2, n1) + cdum*phase_vv(iband, nn2)* &
                                           dotprod(carr1_v_c(:n), cprod_vv_c(:n, iband, nn2))
                     END DO !n2
                  END IF
               END DO
            END DO  !n1
            call timestop("exchange matrix")
         END DO !ibando
      END DO  !ikpt
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!   WRITE(7001,'(a,i7)') 'nk: ', nk
!   DO n1=1,hybrid%nbands(nk)
!      DO n2=1,n1
!         WRITE(7001,'(2i7,2f15.8)') n2, n1, exch_vv(n2,n1)
!     END DO
!   END DO

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      ! add contribution of the gamma point to the different cases (exch_vv,exch_cv,exch_cc)
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      ! valence-valence-valence-valence exchange
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      IF ((.not. xcpot%is_name("hse")) .AND. (.not. xcpot%is_name("vhse"))) THEN ! no gamma point correction needed for HSE functional
         IF (zero_order .and. .not. ibs_corr) THEN
            WRITE (6, '(A)') ' Take zero order terms into account.'
         ELSE IF (zero_order .and. ibs_corr) THEN
            WRITE (6, '(A)') ' Take zero order terms and ibs-correction into account.'
         END IF
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         IF (zero_order) THEN
            CALL dwavefproducts(dcprod, nk, 1, hybrid%nbands(nk), 1, hybrid%nbands(nk), .false., atoms, hybrid, &
                                cell, hybdat, kpts, kpts%nkpt, lapw, dimension, jsp, eig_irr)
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            ! make dcprod hermitian
            DO n1 = 1, hybrid%nbands(nk)
               DO n2 = 1, n1
                  dcprod(n1, n2, :) = (dcprod(n1, n2, :) - conjg(dcprod(n2, n1, :)))/2
                  dcprod(n2, n1, :) = -conjg(dcprod(n1, n2, :))
               END DO
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            END DO
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            IF (ibs_corr) THEN
               CALL ibs_correction(nk, atoms, dimension, input, jsp, hybdat, hybrid, lapw, kpts, kpts%nkpt, cell, mnobd, &
                                   sym, proj_ibsc, olap_ibsc)
            END IF
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         END IF
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         !This should be done with w_iks I guess!TODO
         occup = .false.
         DO i = 1, hybrid%ne_eig(nk)
            IF (results%ef >= eig_irr(i, nk)) THEN
               occup(i) = .true.
            ELSE IF ((eig_irr(i, nk) - results%ef) <= 1E-06) THEN
               occup(i) = .true.
            END IF
         END DO
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         DO n1 = 1, hybrid%nbands(nk)
            DO n2 = 1, nsest(n1)!n1
               nn2 = indx_sest(n2, n1)
               exchcorrect = 0
               exch0 = 0

               ! if zero_order = .true. add averaged k-dependent term to the numerical integration at Gamma-point contribution

               ! if we start with a system with a small DFT band gap (like GaAs), the contribution
               ! of the highest occupied and lowest unoccupied state in Hessian is typically
               ! large; a correct numerical integration requires a dense k-point mesh, so
               ! we don't add the contribution exchcorrect for such materials

               IF (zero_order) THEN
                  hessian = 0
                  IF (occup(n1) .and. occup(nn2)) THEN
                     DO i = 1, 3
                        j = i
                        DO iband = 1, hybrid%nbands(nk)
                           IF (occup(iband)) THEN
                              hessian(i, j) = hessian(i, j) + conjg(dcprod(iband, n1, i))*dcprod(iband, nn2, j)
                           END IF
                           hessian(i, j) = hessian(i, j) - dcprod(iband, nn2, i)*conjg(dcprod(iband, n1, j))
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                        END DO
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                        ! ibs correction
                        IF (ibs_corr) THEN
                           hessian(i, j) = hessian(i, j) - olap_ibsc(i, j, n1, nn2)/cell%omtil
                           DO iband = 1, hybrid%nbands(nk)
                              hessian(i, j) = hessian(i, j) + conjg(proj_ibsc(i, nn2, iband))*proj_ibsc(j, n1, iband)/cell%omtil
                           END DO
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                        END IF
                     END DO
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                  ELSE
                     DO i = 1, 3
                        j = i
                        DO iband = 1, hybrid%nbands(nk)
                           IF (occup(iband)) THEN
                              hessian(i, j) = hessian(i, j) + conjg(dcprod(iband, n1, i))*dcprod(iband, nn2, j)
                           END IF
                        END DO
                     END DO
                  END IF
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                  exchcorrect(1) = fpi_const/3*(hessian(1, 1) + hessian(2, 2) + hessian(3, 3))
                  exch0 = exchcorrect(1)/kpts%nkptf
               END IF
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               ! tail correction/contribution from all other k-points (it  goes into exchcorrect )
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               ! Analytic contribution
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               cdum2 = 0
               !multiply divergent contribution with occupation number;
               !this only affects metals
               IF (n1 == nn2) THEN
                  cdum2 = fpi_const/cell%omtil*divergence*wl_iks(n1, nk)*kpts%nkptf
               END IF
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               ! due to the symmetrization afterwards the factor 1/n_q(1) must be added
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               IF (n1 == nn2) hybrid%div_vv(n1, nk, jsp) = REAL(cdum2)
               exch_vv(nn2, n1) = exch_vv(nn2, n1) + (exch0 + cdum2)/n_q(1)
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            END DO !n2
         END DO !n1
      END IF ! xcpot%icorr .ne. icorr_hse
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      IF (mat_ex%l_real) THEN
         IF (any(abs(aimag(exch_vv)) > 1E-08)) CALL judft_warn('unusally large imaginary part of exch_vv', &
                                                               calledby='exchange_val_hf.F90')
      END IF
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!   WRITE(7000,'(a,i7)') 'nk: ', nk
!   DO n1=1,hybrid%nbands(nk)
!      DO n2=1,n1
!         WRITE(7000,'(2i7,2f15.8)') n2, n1, exch_vv(n2,n1)
!      END DO
!   END DO

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      ! write exch_vv in mat_ex
      CALL mat_ex%alloc(matsize1=hybrid%nbands(nk))
      IF (mat_ex%l_real) THEN
         mat_ex%data_r = exch_vv
      ELSE
         mat_ex%data_c = exch_vv
      END IF
      CALL timestop("valence exchange calculation")

   END SUBROUTINE exchange_valence_hf

   SUBROUTINE calc_divergence(cell, kpts, divergence)

      USE m_util, ONLY: cerf
      USE m_types
      USE m_constants

      IMPLICIT NONE

      TYPE(t_cell), INTENT(IN)  :: cell
      TYPE(t_kpts), INTENT(IN)  :: kpts
      REAL, INTENT(OUT) :: divergence

      INTEGER :: ix, iy, iz, sign, n
      logical :: found
      REAL    :: expo, rrad, k(3), kv1(3), kv2(3), kv3(3), knorm2
      COMPLEX :: cdum

      expo = 5*10.0**-3
      rrad = sqrt(-log(5*10.0**-3)/expo)
      cdum = sqrt(expo)*rrad
      divergence = cell%omtil/(tpi_const**2)*sqrt(pi_const/expo)*cerf(cdum)
      rrad = rrad**2
      kv1 = cell%bmat(1, :)/kpts%nkpt3(1)
      kv2 = cell%bmat(2, :)/kpts%nkpt3(2)
      kv3 = cell%bmat(3, :)/kpts%nkpt3(3)
      n = 1
      found = .true.

      DO WHILE (found)
         found = .false.
         DO ix = -n, n
            DO iy = -(n - abs(ix)), n - abs(ix)
               iz = n - abs(ix) - abs(iy)
               DO sign = -1, 1, 2
                  iz = sign*iz
                  k(1) = ix*kv1(1) + iy*kv2(1) + iz*kv3(1)
                  k(2) = ix*kv1(2) + iy*kv2(2) + iz*kv3(2)
                  k(3) = ix*kv1(3) + iy*kv2(3) + iz*kv3(3)
                  knorm2 = k(1)**2 + k(2)**2 + k(3)**2
                  IF (knorm2 < rrad) THEN
                     found = .true.
                     divergence = divergence - exp(-expo*knorm2)/knorm2/kpts%nkptf
                  END IF
                  IF (iz == 0) exit
               END DO
            END DO
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         END DO
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         n = n + 1
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      END DO

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   END SUBROUTINE calc_divergence
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END MODULE m_exchange_valence_hf