exchange_val_hf.F90 24.4 KB
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!     Calculates the HF exchange term 
!
!                                          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
!
!     for the different combinations of n_1 and n_2 and where n' runs only over the valence states.     
!     ( 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
!     expo by exp(-expo*q0**2)=delta  ( delta = small value, e.g., delta = 1d-10 ) .
!     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.)
      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

      SUBROUTINE exchange_valence_hf(&
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                    nk,kpts,nkpt_EIBZ, sym,atoms,hybrid,&
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                    cell, dimension,input,jsp, hybdat, mnobd, lapw,&
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                    eig_irr,results,parent,pointer_EIBZ,n_q,wl_iks,&
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                    it,xcpot, noco,nsest,indx_sest,&
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                    mpi,irank2,isize2,comm,mat_ex)
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      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
#ifdef CPP_MPI
      USE m_mpi_work_dist
      USE m_mpi_tags
#endif
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      USE m_io_hybrid
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      USE m_icorrkeys
      USE m_kp_perturbation
      USE m_types
      IMPLICIT NONE
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      TYPE(t_hybdat),INTENT(IN)   :: hybdat
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      TYPE(t_results),INTENT(IN)   :: results
      TYPE(t_xcpot),INTENT(IN)   :: xcpot
      TYPE(t_mpi),INTENT(IN)   :: mpi
      TYPE(t_dimension),INTENT(IN)   :: dimension
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      TYPE(t_hybrid),INTENT(INOUT)   :: hybrid
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      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

!     - scalars -
      INTEGER,INTENT(IN)      :: it  ,irank2 ,isize2,comm
      INTEGER,INTENT(IN)      :: jsp
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      INTEGER,INTENT(IN)      ::  nk ,nkpt_EIBZ
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      INTEGER,INTENT(IN)      :: mnobd 
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!     - arrays -
      INTEGER,INTENT(IN)      ::  n_q(nkpt_EIBZ)
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      INTEGER,INTENT(IN)      ::  parent(kpts%nkptf)
      INTEGER,INTENT(IN)      ::  pointer_EIBZ(nkpt_EIBZ)
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      INTEGER,INTENT(IN)      ::  nsest(hybrid%nbands(nk)),indx_sest(hybrid%nbands(nk),hybrid%nbands(nk))
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      REAL   ,INTENT(IN)      ::  eig_irr(dimension%neigd,kpts%nkpt)
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      REAL   ,INTENT(IN)      ::  wl_iks(dimension%neigd,kpts%nkptf)
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      TYPE(t_mat),INTENT(INOUT):: mat_ex
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!     - local scalars -
      INTEGER                 ::  iband,iband1,ibando,ikpt,ikpt0
      INTEGER                 ::  i,ic,ix,iy,iz
      INTEGER                 ::  irecl_coulomb,irecl_coulomb1
      INTEGER                 ::  j
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      INTEGER                 ::  m1,m2
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      INTEGER                 ::  n,n1,n2,nn,nn2
      INTEGER                 ::  nkqpt
      INTEGER                 ::  npot
      INTEGER                 ::  ok
      INTEGER                 ::  psize
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      REAL                    ::  rdum
      REAL                    ::  k0
     
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      REAL , SAVE             ::  divergence

      COMPLEX                 ::  cdum,cdum1,cdum2 
      COMPLEX                 ::  exch0
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      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/) )
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      COMPLEX,ALLOCATABLE     ::  phase_vv(:,:)
      COMPLEX                 ::  exchcorrect(kpts%nkptf)
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      COMPLEX                 ::  dcprod(hybrid%nbands(nk),hybrid%nbands(nk),3) 
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      COMPLEX(8)              ::  exch_vv(hybrid%nbands(nk),hybrid%nbands(nk))
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#ifdef CPP_MPI
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      COMPLEX(8)              ::  buf_vv(hybrid%nbands(nk),nbands(nk))
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#endif
      COMPLEX                 ::  hessian(3,3)
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      COMPLEX                 ::  proj_ibsc(3,mnobd,hybrid%nbands(nk))
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      COMPLEX                 ::  olap_ibsc(3,3,mnobd,mnobd)
#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)       
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      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

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      REAL   ,ALLOCATABLE     ::  cprod_vv_r(:,:,:),cprod_cv_r(:,:,:), carr3_vv_r(:,:,:),carr3_cv_r(:,:,:)
      REAL                    ::  carr1_v_r(hybrid%maxbasm1),carr1_c_r(hybrid%maxbasm1)
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#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
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      COMPLEX,ALLOCATABLE     ::  cprod_vv_c(:,:,:),cprod_cv_c(:,:,:), carr3_vv_c(:,:,:),carr3_cv_c(:,:,:)
      COMPLEX                 ::  carr1_v_c(hybrid%maxbasm1),carr1_c_c(hybrid%maxbasm1)
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#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

      LOGICAL                 ::  occup(dimension%neigd)
#ifdef CPP_MPI
      INCLUDE "mpif.h"
      INTEGER                 :: ierr,ierr2,length,rank
      CHARACTER(LEN=MPI_MAX_ERROR_STRING) :: errmsg
#endif
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      IF( initialize ) THEN !it .eq. 1 .and. nk .eq. 1) THEN
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         print *,divergence
         print *,Cell%omtil,kpts%nkpt3,kpts%nkptf
         call calc_divergence(cell,kpts,divergence)
         initialize = .false.
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      END IF
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      ! 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
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      if (mat_ex%l_real) THEn
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         rdum  = hybrid%maxbasm1*hybrid%nbands(nk)*4/1048576.
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      else
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         rdum  = hybrid%maxbasm1*hybrid%nbands(nk)*4/1048576.
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      endif
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      psize = 1
      DO iband = mnobd,1,-1
        ! ensure that the packages have equal size
        IF( modulo(mnobd,iband) .eq. 0 ) THEN
          ! choose packet size such that cprod is smaller than memory threshold
          IF( rdum*iband .le. maxmem ) THEN
            psize = iband
            EXIT
          END IF
        END IF
      END DO

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

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      DO ikpt = 1,nkpt_EIBZ
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        ikpt0 = pointer_EIBZ(ikpt)

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

        ! read in coulomb matrix from direct access file coulomb
#if( !defined CPP_NOSPMVEC && !defined CPP_IRAPPROX )
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        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)
        END IF
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#else
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	call read_coulomb(kpts%bkp(ikpt0),coulomb)
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#endif

        IF( kpts%bkp(ikpt0) .ne. ikpt0 ) THEN
#if( !defined CPP_NOSPMVEC && !defined CPP_IRAPPROX )
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          IF( kpts%bksym(ikpt0) .gt. sym%nop.and..not.mat_ex%l_real ) THEN
            coulomb_mt2_c = conjg(coulomb_mt2_c)
            coulomb_mtir_c= conjg(coulomb_mtir_c)
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          END IF

#else

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          if (.not.mat_ex%l_real) THEN
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          IF( kpts%bksym(ikpt0) .gt. sym%nop ) coulomb = conjg(coulomb)
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       endif
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#endif
        END IF

        DO ibando = 1,mnobd,psize
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        if (mat_ex%l_real) THEN
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#ifdef CPP_IRAPPROX
          CALL wavefproducts_inv(&
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                         1,hybdat,dimension,jsp,atoms,&
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                         lapw,obsolete,kpts,&
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                         nk,ikpt0,mnobd,hybrid, parent,cell, sym,&
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                         nkqpt,cprod_vv)
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#else
          CALL wavefproducts_inv5(&
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                         1,hybrid%nbands(nk),ibando,ibando+psize-1,&
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                         dimension,input,jsp,atoms,&
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                         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
          CALL wavefproducts_noinv(&
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                         1,hybdat,nk,ikpt0,dimension,jsp,&
                         cell,atoms,hybrid, 
                         kpts,&
                         mnobd,&
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                         lapw,sym,&
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                         nkqpt,&
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                         cprod_vv)
#else
          CALL wavefproducts_noinv5(&
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                         1,hybrid%nbands(nk),ibando,ibando+psize-1,&
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                         nk,ikpt0,dimension,input,jsp, &!jsp,&
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                         cell,atoms,hybrid,hybdat, &
                         kpts,&
                         mnobd,&
                         lapw,sym, &
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                         hybrid%nbasp,noco,&
                         nkqpt,cprod_vv_c)
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#endif

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

          ! 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) .ne. ikpt0 ) THEN
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             CALL bra_trafo2(&
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                  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),:,:)
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             ENDIF
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          ELSE
            phase_vv(:,:) = (1d0,0d0)
          END IF

          ! calculate exchange matrix at ikpt0

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          DO n1=1,hybrid%nbands(nk)
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            DO iband = 1,psize
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              IF( ibando + iband - 1 .gt. hybrid%nobd(nkqpt) ) CYCLE
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              cdum  = wl_iks(ibando+iband-1,nkqpt)&
                    * conjg(phase_vv(iband,n1))/n_q(ikpt)

#if( !defined CPP_NOSPMVEC && !defined CPP_IRAPPROX )
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              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))
              endif
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#else
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              if (mat_ex%l_real) THEN
                 carr1_v_r(:n) = matvec( coulomb_r(:nn),cprod_vv_r(:n,iband,n1) )
              ELSE
                 carr1_v_r(:n) = matvec( coulomb_c(:nn),cprod_vv_c(:n,iband,n1) )
              endif
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#endif

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              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
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            END DO
          END DO  !n1
        END DO !ibando
      END DO  !ikpt


      !
      ! 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

      IF ( xcpot%icorr .NE. icorr_hse .AND. xcpot%icorr   .NE. icorr_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
        IF( zero_order ) THEN
          CALL dwavefproducts(  &
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                            dcprod,nk,1,hybrid%nbands(nk),1,hybrid%nbands(nk),.false., atoms,hybrid,&
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                            cell,hybdat, kpts,kpts%nkpt,lapw,&
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                            dimension,jsp,&
                            eig_irr )
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          ! make dcprod hermitian
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          DO n1 = 1,hybrid%nbands(nk)
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            DO n2 = 1,n1
              dcprod(n1,n2,:) = (dcprod(n1,n2,:) &
                              - conjg(dcprod(n2,n1,:)))/2   
              dcprod(n2,n1,:) = -conjg(dcprod(n1,n2,:))
            END DO
          END DO

          IF( ibs_corr ) THEN
            CALL ibs_correction(&
                        nk,atoms,&
                        dimension,input,jsp,&
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                        hybdat,hybrid,&
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                        lapw,kpts,kpts%nkpt,&
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                        cell,mnobd,&
                        sym,&
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                        proj_ibsc,olap_ibsc)
          END IF

        END IF
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        !This should be done with w_iks I guess!TODO
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        occup = .false.
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        DO i=1,hybrid%ne_eig(nk)
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          IF ( results%ef  .ge. eig_irr(i,nk) ) THEN
            occup(i) = .true.
          ELSE IF ( eig_irr(i,nk) - results%ef .le. 1E-06) THEN
             occup(i) = .true.
          END IF
        END DO


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        DO n1 = 1,hybrid%nbands(nk)
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          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

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                  DO iband = 1,hybrid%nbands(nk)
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                    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))
                  END DO

                  ! ibs correction
                  IF( ibs_corr ) THEN 
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                    hessian(i,j) = hessian(i,j) - olap_ibsc(i,j,n1,nn2)/cell%omtil
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                    DO iband = 1,hybrid%nbands(nk)
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                      hessian(i,j) = hessian(i,j) + conjg(proj_ibsc(i,nn2,iband)) * proj_ibsc(j,n1,iband)/cell%omtil
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                    END DO
                  END IF

                END DO
              ELSE

                DO i = 1,3
                  j = i 
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                  DO iband = 1,hybrid%nbands(nk)
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                    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))
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              exch0          = exchcorrect(1)/kpts%nkptf
            END IF


            ! tail correction/contribution from all other k-points (it  goes into exchcorrect )

            ! Analytic contribution

            cdum2 = 0
            !multiply divergent contribution with occupation number;
            !this only affects metals 
            IF ( n1 .eq. nn2 ) THEN
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               cdum2 = fpi_const/cell%omtil * divergence * wl_iks(n1,nk)*kpts%nkptf
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            END IF

            ! due to the symmetrization afterwards the factor 1/n_q(1) must be added

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            IF( n1 .EQ. nn2 ) hybrid%div_vv(n1,nk,jsp) = REAL(cdum2) 
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            exch_vv(nn2,n1)  = exch_vv(nn2,n1) + (exch0 + cdum2)/n_q(1)

          END DO !n2
        END DO !n1
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       END IF ! xcpot%icorr .ne. icorr_hse
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      if (.not.mat_ex%l_real) THEN
         IF(any( abs(aimag(exch_vv)) .gt. 1E-08)) CALL judft_warn('unusally large imaginary part of exch_vv',calledby='exchange_val_hf.F90')
      ENDIF
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      ! write exch_vv in mat_ex
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      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
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      END SUBROUTINE exchange_valence_hf

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      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       = 5d-3
        rrad       = sqrt(-log(5d-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.lt.rrad) THEN
                       found      = .true.
                       divergence = divergence - exp(-expo*knorm2)/knorm2 / kpts%nkptf
                    END IF
                    IF(iz==0) exit
                 enddo
                 
              END DO
           END DO
           n = n + 1
        END DO
      end subroutine calc_divergence
    END MODULE m_exchange_valence_hf