exchange_val_hf.F90 23.6 KB
Newer Older
1 2 3 4 5 6
!--------------------------------------------------------------------------------
! 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.
!--------------------------------------------------------------------------------

7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51
!     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.)

52
MODULE m_exchange_valence_hf
53

54 55
   LOGICAL,PARAMETER:: zero_order=.false.,ibs_corr=.false.
   INTEGER,PARAMETER:: maxmem=600
56

57
CONTAINS
58

59 60
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,&
61
                               mpi,mat_ex)
62

63 64 65 66 67 68 69 70
   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
71
#if defined(CPP_MPI)&&defined(CPP_NEVER)
72 73
   USE m_mpi_work_dist
   USE m_mpi_tags
74
#endif
75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92
   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
Matthias Redies's avatar
Matthias Redies committed
93
   TYPE(t_hybdat),        INTENT(INOUT) :: hybdat
94 95

   ! scalars
96
   INTEGER,               INTENT(IN)    :: it
97 98 99 100 101 102 103 104 105 106 107
   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))
Daniel Wortmann's avatar
Daniel Wortmann committed
108 109

 
110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125
   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
Daniel Wortmann's avatar
Daniel Wortmann committed
126
     
127
   REAL , SAVE             ::  divergence
128

129 130
   COMPLEX                 ::  cdum,cdum1,cdum2 
   COMPLEX                 ::  exch0
Daniel Wortmann's avatar
Daniel Wortmann committed
131
 
132 133 134 135 136 137
   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) 
138
   COMPLEX              :: exch_vv(hybrid%nbands(nk),hybrid%nbands(nk))
139 140 141 142 143 144 145 146
   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(:,:,:)
147 148


149
#if defined(CPP_MPI)&&defined(CPP_NEVER)
150
   COMPLEX             :: buf_vv(hybrid%nbands(nk),nbands(nk))
151 152
#endif

153 154 155 156 157 158
#if ( !defined CPP_NOSPMVEC && !defined CPP_IRAPPROX )
   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)
159
#else
160 161
   REAL                 :: coulomb_r(hybrid%maxbasm1*(hybrid%maxbasm1+1)/2)
   COMPLEX              :: coulomb_c(hybrid%maxbasm1*(hybrid%maxbasm1+1)/2)
162 163 164
#endif

#ifdef CPP_IRCOULOMBAPPROX
165 166
   REAL                 :: coulomb_mtir_r((hybrid%maxlcutm1+1)**2*atoms%nat,&
                                          (hybrid%maxlcutm1+1)**2*atoms%nat+maxval(hybrid%ngptm))
167
#else
168 169
   REAL                 :: coulomb_mtir_r(((hybrid%maxlcutm1+1)**2*atoms%nat +maxval(hybrid%ngptm)) *&
                                          ((hybrid%maxlcutm1+1)**2*atoms%nat +maxval(hybrid%ngptm)+1)/2)
170 171 172
#endif

#ifdef CPP_IRCOULOMBAPPROX
173 174
   COMPLEX              :: coulomb_mtir_c((hybrid%maxlcutm1+1)**2*atoms%nat,&
                                          (hybrid%maxlcutm1+1)**2*atoms%nat+maxval(hybrid%ngptm))
175
#else
176 177
   COMPLEX              :: coulomb_mtir_c(((hybrid%maxlcutm1+1)**2*atoms%nat +maxval(hybrid%ngptm)) *&
                                          ((hybrid%maxlcutm1+1)**2*atoms%nat +maxval(hybrid%ngptm)+1)/2)
178 179
#endif

180
   LOGICAL              :: occup(dimension%neigd)
181
#if defined(CPP_MPI)&&defined(CPP_NEVER)
182 183 184
   INCLUDE "mpif.h"
   INTEGER              :: ierr,ierr2,length,rank
   CHARACTER(LEN=MPI_MAX_ERROR_STRING) :: errmsg
185
#endif
Matthias Redies's avatar
Matthias Redies committed
186
   CALL timestart("valence exchange calculation")
Daniel Wortmann's avatar
Daniel Wortmann committed
187
     
188 189 190 191 192
   IF(initialize) THEN !it .eq. 1 .and. nk .eq. 1) THEN
      call calc_divergence(cell,kpts,divergence)
      PRINT *,"Divergence:",divergence
      initialize = .false.
   END IF
Daniel Wortmann's avatar
Daniel Wortmann committed
193
   
194 195 196 197 198 199
   ! 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
Matthias Redies's avatar
Matthias Redies committed
200
   rdum  = hybrid%maxbasm1*hybrid%nbands(nk)*4/1048576.
201 202 203 204 205 206
   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
207 208
            psize = iband
            EXIT
209
         END IF
210
      END IF
211 212 213 214 215 216 217 218 219 220 221 222
   END DO

   IF(psize.ne.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)'
   END IF
   ALLOCATE( phase_vv(psize,hybrid%nbands(nk)),stat=ok )
   IF(ok.ne.0) STOP 'exchange_val_hf: error allocation phase'
   phase_vv=0
   IF(ok.ne.0) STOP 'exchange_val_hf: error allocation phase'

   if (mat_ex%l_real) THEN
223
      ALLOCATE( cprod_vv_c(hybrid%maxbasm1,0,0), carr3_vv_c(hybrid%maxbasm1,0,0))
224 225 226 227 228 229
      ALLOCATE( cprod_vv_r(hybrid%maxbasm1,psize,hybrid%nbands(nk)),stat=ok )
      IF( ok .ne. 0 ) STOP 'exchange_val_hf: error allocation cprod'
      ALLOCATE( carr3_vv_r(hybrid%maxbasm1,psize,hybrid%nbands(nk)),stat=ok )
      IF( ok .ne. 0 ) STOP 'exchange_val_hf: error allocation carr3'
      cprod_vv_r = 0 ; carr3_vv_r = 0 
   ELSE
230
      ALLOCATE( cprod_vv_r(hybrid%maxbasm1,0,0), carr3_vv_r(hybrid%maxbasm1,0,0))
231 232 233 234 235 236
      ALLOCATE( cprod_vv_c(hybrid%maxbasm1,psize,hybrid%nbands(nk)),stat=ok )
      IF( ok .ne. 0 ) STOP 'exchange_val_hf: error allocation cprod'
      ALLOCATE( carr3_vv_c(hybrid%maxbasm1,psize,hybrid%nbands(nk)),stat=ok )
      IF( ok .ne. 0 ) STOP 'exchange_val_hf: error allocation carr3'
      cprod_vv_c = 0 ; carr3_vv_c = 0
   END IF
Daniel Wortmann's avatar
Daniel Wortmann committed
237
         
238
   exch_vv = 0
239

240
   DO ikpt = 1,nkpt_EIBZ
241

242
      ikpt0 = pointer_EIBZ(ikpt)
243

244 245 246
      n  = hybrid%nbasp + hybrid%ngptm(ikpt0)
      IF( hybrid%nbasm(ikpt0).ne.n) STOP 'error hybrid%nbasm'
      nn = n*(n+1)/2
247

248 249 250 251 252 253
      ! 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)
      END IF
254

255
      IF(kpts%bkp(ikpt0).ne.ikpt0) THEN
256
#if( !defined CPP_NOSPMVEC && !defined CPP_IRAPPROX )
257
         IF((kpts%bksym(ikpt0).gt.sym%nop).and.(.not.mat_ex%l_real)) THEN
Daniel Wortmann's avatar
Daniel Wortmann committed
258
            coulomb_mt2_c = conjg(coulomb_mt2_c)
259 260
            coulomb_mtir_c = conjg(coulomb_mtir_c)
         END IF
261
#else
262 263 264
         if (.not.mat_ex%l_real) THEN
            IF( kpts%bksym(ikpt0) .gt. sym%nop ) coulomb = conjg(coulomb)
         endif
265
#endif
266
      END IF
267

268
      DO ibando = 1, mnobd, psize
269

270
         IF (mat_ex%l_real) THEN
271
#ifdef CPP_IRAPPROX
272 273
            CALL wavefproducts_inv(1,hybdat,dimension,input,jsp,atoms,lapw,obsolete,kpts,nk,ikpt0,&
                                   mnobd,hybrid,parent,cell,sym,noco,nkqpt,cprod_vv)
274
#else
275 276 277
            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)
278
#endif
279
         ELSE
280
#ifdef CPP_IRAPPROX
281 282
            CALL wavefproducts_noinv(1,hybdat,nk,ikpt0,dimension,input,jsp,cell,atoms,hybrid, 
                                     kpts,mnobd,lapw,sym,noco,nkqpt,cprod_vv)
283
#else
284 285
            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)
286
#endif
287
         END IF
288

289 290 291 292 293
         ! 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
294
#ifndef CPP_NOSPMVEC
295
         IF (xcpot%is_name("hse").OR.xcpot%is_name("vhse")) THEN
Daniel Wortmann's avatar
Daniel Wortmann committed
296
            iband1  = hybrid%nobd(nkqpt)
297 298 299 300 301 302 303 304 305 306

            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
307 308
#endif

309 310 311 312 313 314 315 316 317 318 319 320 321 322
         ! 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
            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)
            IF (mat_ex%l_real) THEN
               cprod_vv_r(:hybrid%nbasm(ikpt0),:,:) = carr3_vv_r(:hybrid%nbasm(ikpt0),:,:)
            ELSE
               cprod_vv_c(:hybrid%nbasm(ikpt0),:,:) = carr3_vv_c(:hybrid%nbasm(ikpt0),:,:)
            ENDIF
         ELSE
323
            phase_vv(:,:) = (1d0,0d0)
324
         END IF
325

326
         ! calculate exchange matrix at ikpt0
Matthias Redies's avatar
Matthias Redies committed
327 328
   
         call timestart("exchange matrix")
329
         DO n1=1,hybrid%nbands(nk)
330
            DO iband = 1,psize
331 332 333
               IF((ibando+iband-1).gt.hybrid%nobd(nkqpt)) CYCLE

               cdum  = wl_iks(ibando+iband-1,nkqpt) * conjg(phase_vv(iband,n1))/n_q(ikpt)
334

335 336 337 338 339 340 341 342 343
               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
344

345 346 347 348 349 350 351 352 353 354 355 356 357
               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
358
            END DO
359
         END DO  !n1
Matthias Redies's avatar
Matthias Redies committed
360
         call timestop("exchange matrix")
361 362
      END DO !ibando
   END DO  !ikpt
363

364 365 366 367 368 369 370
!   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

371
   ! add contribution of the gamma point to the different cases (exch_vv,exch_cv,exch_cc)
372

373 374 375 376 377 378 379 380 381 382 383 384 385 386 387
   ! valence-valence-valence-valence exchange

   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

      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)

         ! make dcprod hermitian
         DO n1 = 1, hybrid%nbands(nk)
388
            DO n2 = 1,n1
389 390
               dcprod(n1,n2,:) = (dcprod(n1,n2,:) - conjg(dcprod(n2,n1,:)))/2   
               dcprod(n2,n1,:) = -conjg(dcprod(n1,n2,:))
391
            END DO
392 393 394 395 396 397 398
         END DO

         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
      END IF
Daniel Wortmann's avatar
Daniel Wortmann committed
399
        
400 401 402 403
      !This should be done with w_iks I guess!TODO
      occup = .false.
      DO i=1,hybrid%ne_eig(nk)
         IF (results%ef.ge.eig_irr(i,nk)) THEN
404
            occup(i) = .true.
405 406 407 408
         ELSE IF ((eig_irr(i,nk)-results%ef).le.1E-06) THEN
            occup(i) = .true.
         END IF
      END DO
409

410 411
      DO n1 = 1, hybrid%nbands(nk)
         DO n2 = 1, nsest(n1)!n1
412 413
            nn2 = indx_sest(n2,n1)
            exchcorrect = 0
414 415 416
            exch0 = 0

            ! if zero_order = .true. add averaged k-dependent term to the numerical integration at Gamma-point contribution
417 418 419 420 421 422

            ! 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 

423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441
            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))
                     END DO

                     ! 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
                     END IF
442
                  END DO
443 444 445 446 447 448 449 450
               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
451
                  END DO
452
               END IF
Daniel Wortmann's avatar
Daniel Wortmann committed
453
 
454 455
               exchcorrect(1) = fpi_const/3 * (hessian(1,1)+hessian(2,2)+hessian(3,3))
               exch0 = exchcorrect(1)/kpts%nkptf
456 457 458 459 460 461 462 463 464
            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 
465
            IF (n1.eq.nn2) THEN
Daniel Wortmann's avatar
Daniel Wortmann committed
466
               cdum2 = fpi_const/cell%omtil * divergence * wl_iks(n1,nk)*kpts%nkptf
467 468 469 470
            END IF

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

471
            IF(n1.EQ.nn2) hybrid%div_vv(n1,nk,jsp) = REAL(cdum2) 
472 473
            exch_vv(nn2,n1)  = exch_vv(nn2,n1) + (exch0 + cdum2)/n_q(1)

474 475 476
         END DO !n2
      END DO !n1
   END IF ! xcpot%icorr .ne. icorr_hse
477 478


479
   IF (mat_ex%l_real) THEN
480 481 482
      IF(any(abs(aimag(exch_vv)).gt.1E-08)) CALL judft_warn('unusally large imaginary part of exch_vv',&
                                                            calledby='exchange_val_hf.F90')
   END IF
483

484 485 486 487 488 489 490
!   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

491 492 493 494 495 496 497
   ! 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
Matthias Redies's avatar
Matthias Redies committed
498
   CALL timestop("valence exchange calculation")
Daniel Wortmann's avatar
Daniel Wortmann committed
499
     
500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515
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
Daniel Wortmann's avatar
Daniel Wortmann committed
516
        
517 518 519 520
   INTEGER :: ix,iy,iz,sign,n
   logical :: found
   REAL    :: expo,rrad,k(3),kv1(3),kv2(3),kv3(3),knorm2
   COMPLEX :: cdum
Daniel Wortmann's avatar
Daniel Wortmann committed
521
        
522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557
   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
            END DO 
         END DO
      END DO
      n = n + 1
   END DO

END SUBROUTINE calc_divergence

END MODULE m_exchange_valence_hf