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1 : : !!****m* ABINIT/m_paw_sym
2 : : !! NAME
3 : : !! m_paw_sym
4 : : !!
5 : : !! FUNCTION
6 : : !! This module contains several routines related to the use of symmetries in the PAW approach.
7 : : !!
8 : : !! COPYRIGHT
9 : : !! Copyright (C) 2018-2026 ABINIT group (MG)
10 : : !! This file is distributed under the terms of the
11 : : !! GNU General Public License, see ~abinit/COPYING
12 : : !! or http://www.gnu.org/copyleft/gpl.txt .
13 : : !!
14 : : !! SOURCE
15 : :
16 : : #if defined HAVE_CONFIG_H
17 : : #include "config.h"
18 : : #endif
19 : :
20 : : #include "abi_common.h"
21 : :
22 : : MODULE m_paw_sym
23 : :
24 : : use defs_basis
25 : : use m_abicore
26 : : use m_errors
27 : :
28 : : use m_crystal, only : crystal_t
29 : : use m_pawang, only : pawang_type
30 : : use m_pawtab, only : pawtab_type
31 : : use m_pawcprj, only : pawcprj_type, pawcprj_alloc, pawcprj_free, pawcprj_copy
32 : : use m_bz_mesh, only : kmesh_t
33 : :
34 : : implicit none
35 : :
36 : : private
37 : :
38 : : !public procedures.
39 : : public :: paw_symcprj ! Symetrize the projections cprj=<n,k|p_i> (p_i=NL PAW projector) - in-place version
40 : : public :: paw_symcprj_op ! Symetrize the projections cprj=<n,k|p_i> (p_i=NL PAW projector) - out-of-place version
41 : :
42 : : CONTAINS !========================================================================================
43 : : !!***
44 : :
45 : : !----------------------------------------------------------------------
46 : :
47 : : !!****f* m_paw_sym/paw_symcprj
48 : : !! NAME
49 : : !! paw_symcprj
50 : : !!
51 : : !! FUNCTION
52 : : !! Symetrize the projections cprj=<n,k|p_i> (p_i=NL PAW projector) - in-place version
53 : : !!
54 : : !! INPUTS
55 : : !! ik_ibz=The index of the k-point in the full BZ where the matrix elements have to be symmetrized.
56 : : !! nspinor=Number of spinorial components
57 : : !! nband_k=Number of bands stored in cprjnk_kibz for this k-point.
58 : : !! Cryst<crystal_t>=data type gathering information on unit cell and symmetries.
59 : : !! %ntypat=number of type of atoms
60 : : !! %natom=number of atoms in the unit cell
61 : : !! %typat(natom)=type of each atom
62 : : !! %indsym(4,nsym,natom)=indirect indexing array:
63 : : !! for each isym,iatom, fourth element is label of atom into which iatom is sent by the INVERSE of the
64 : : !! symmetry operation symrel(isym); first three elements are the primitive translations that must be subtracted
65 : : !! after the transformation to get back to the original unit cell.
66 : : !! Kmesh<kmesh_t>: datatype gathering information on the k-point sampling.
67 : : !! %nbz=number of k-points in the full Brillouin zone
68 : : !! %nibz=number of k-points in the irreducible wedge
69 : : !! %tab(nkbz)=table giving for each k-point in the BZ (array kbz), the corresponding irred. point in the IBZ.
70 : : !! i.e k_BZ = (IS) kIBZ where S is one of the symrec operations and I is the inversion or the identity
71 : : !! %tabi(nkbz)=for each k-point in the BZ defines whether inversion has to be considered in the
72 : : !! relation k_BZ=(IS) k_IBZ (1 => only S; -1 => -S)
73 : : !! %tabo(nkbz)= the symmetry operation S that takes k_IBZ to each k_BZ
74 : : !! Pawtab(Cryst%ntypat) <type(pawtab_type)>=paw tabulated starting data.
75 : : !! Pawang <type(pawang_type)>=paw angular mesh and related data
76 : : !! %lmax=Max angular momentum included in the PAW datasets used. mentioned at the second line of the psp file
77 : : !! %zarot(2*lmax+1,2*lmax+1,lmax+1,nsym)=coefficients of the transformation of real spherical
78 : : !! harmonics under the symmetry operations.
79 : : !!
80 : : !! NOTES
81 : : !! Derivatives are not symmetrized.
82 : : !!
83 : : !! OUTPUT
84 : : !!
85 : : !! SOURCE
86 : :
87 : 127533 : subroutine paw_symcprj(ik_bz,nspinor,nband_k,Cryst,Kmesh,Pawtab,Pawang,Cprj_bz)
88 : :
89 : : !Arguments ------------------------------------
90 : : !scalars
91 : : integer,intent(in) :: nspinor,nband_k,ik_bz
92 : : type(crystal_t),intent(in) :: Cryst
93 : : type(kmesh_t),intent(in) :: Kmesh
94 : : type(Pawang_type),intent(in) :: Pawang
95 : : !arrays
96 : : type(Pawtab_type),target,intent(in) :: Pawtab(Cryst%ntypat)
97 : : type(pawcprj_type),intent(inout) :: Cprj_bz(Cryst%natom,nspinor*nband_k)
98 : :
99 : : !Local variables-------------------------------
100 : : !scalars
101 : : integer :: iatom,iat_sym,iband,ibsp_bz
102 : : integer :: ibsp_ibz,ik_ibz,indexj,ispinor,isym,itim
103 : : integer :: itypat,jl,jl0,jlmn,jln,jln0,jlpm,jm,jn,lmax,mm,ncpgr
104 : : real(dp) :: arg,wtk
105 : : logical :: isirred
106 : : !arrays
107 : 255066 : integer :: r0(3),nlmn_atom(Cryst%natom)
108 : 127533 : integer,ABI_CONTIGUOUS pointer :: indlmn(:,:)
109 : 23045 : real(dp) :: dum(2,nspinor),kbz(3),kirr(3),phase(2),swp(2),tmp(2,nspinor)
110 : 127533 : real(dp),allocatable :: DS_mmpl(:,:,:)
111 [ + + + + : 1828302 : type(pawcprj_type) :: Cprjnk_kibz(Cryst%natom,nspinor*nband_k)
+ + + + +
- + - + +
+ - + - ]
112 : :
113 : : ! *********************************************************************
114 : :
115 : 127533 : ncpgr = Cprj_bz(1,1)%ncpgr
116 [ - + ]: 127533 : ABI_CHECK(ncpgr==0,"Derivatives of cprj are not coded")
117 : :
118 : : !Get the index of the IBZ image associated to the BZ k-point ik_bz and related simmetry.
119 : 127533 : call Kmesh%get_BZ_item(ik_bz,kbz,ik_ibz,isym,itim,isirred=isirred)
120 : :
121 [ + + ]: 281931 : if (isirred) RETURN ! It is a point in the IBZ, Symmetrization is not needed.
122 : : !
123 : : !The corresponding point kirr in the IBZ.
124 : 104488 : call kmesh%get_IBZ_item(ik_ibz,kirr,wtk)
125 : :
126 : : !Local copy.
127 [ + + ]: 316656 : do iatom=1,Cryst%natom
128 : 316656 : nlmn_atom(iatom)=Pawtab(Cryst%typat(iatom))%lmn_size
129 : : end do
130 : :
131 : 104488 : call pawcprj_alloc(Cprjnk_kibz,ncpgr,nlmn_atom)
132 : 104488 : call pawcprj_copy(Cprj_bz,Cprjnk_kibz)
133 : : !
134 : : !=== DS_mmpl is the rotation matrix for real spherical harmonics associated to symrec(:,:,isym) ===
135 : : !* Note the convention used by Blanco in Eq. 27 : DS_mmp multiply spherical harmonics as row vectors
136 : 104488 : lmax=Pawang%l_max-1 ! l_max is Max l+1
137 [ + - - + : 626928 : ABI_MALLOC(DS_mmpl,(2*lmax+1,2*lmax+1,lmax+1))
+ - - + +
- + - - +
+ - + - +
- - + -
+ ]
138 [ + - + - : 2956216 : DS_mmpl=Pawang%zarot(:,:,:,isym)
+ - - + -
- + + + +
+ + ]
139 : : !
140 : : !===========================================
141 : : !==== Loop over atoms to be symmetrized ====
142 : : !===========================================
143 [ + + ]: 316656 : do iatom=1,Cryst%natom
144 : 212168 : itypat=Cryst%typat(iatom)
145 : 212168 : iat_sym=Cryst%indsym(4,isym,iatom)
146 : 212168 : indlmn => Pawtab(itypat)%indlmn
147 [ + + ]: 848672 : r0=Cryst%indsym(1:3,isym,iatom) ! R^{-1} (xred(:,iatom)-tnons) = xred(:,iat_sym) + r0.
148 [ + + ]: 848672 : arg=two_pi*dot_product(kirr,r0)
149 : 212168 : phase(1)=COS(arg)
150 : 212168 : phase(2)=SIN(arg)
151 : : !
152 : : ! Loop over the (jl,jm,jn) components to be symmetrized.
153 : 212168 : jl0=-1; jln0=-1; indexj=1
154 [ + + ]: 2018950 : do jlmn=1,Pawtab(itypat)%lmn_size
155 : 1702294 : jl =indlmn(1,jlmn)
156 : 1702294 : jm =indlmn(2,jlmn)
157 : 1702294 : jn =indlmn(3,jlmn)
158 : 1702294 : jln =indlmn(5,jlmn)
159 : 1702294 : jlpm=1+jl+jm
160 [ + + ]: 1702294 : if (jln/=jln0) indexj=indexj+2*jl0+1
161 : : !
162 : : ! === For each band, calculate contribution due to rotated real spherical harmonics ===
163 : : ! FIXME check this expression; according to Blanco I should have D(S^-1} but it seems D(S) is correct
164 : : ! Recheck spinorial case, presently is wrong
165 : 1702294 : ibsp_ibz=0
166 : 1702294 : ibsp_bz=0
167 [ + + ]: 3404588 : do iband=1,nband_k
168 : :
169 [ + + + + ]: 6809176 : tmp(:,:)=zero
170 [ + + ]: 3404588 : do ispinor=1,nspinor
171 : 1702294 : ibsp_ibz=ibsp_ibz+1
172 [ + + ]: 7676478 : do mm=1,2*jl+1
173 : 4271890 : tmp(1,ispinor)=tmp(1,ispinor)+DS_mmpl(mm,jlpm,jl+1)*Cprjnk_kibz(iat_sym,ibsp_ibz)%cp(1,indexj+mm)
174 : 5974184 : tmp(2,ispinor)=tmp(2,ispinor)+DS_mmpl(mm,jlpm,jl+1)*Cprjnk_kibz(iat_sym,ibsp_ibz)%cp(2,indexj+mm)
175 : : end do
176 : : end do !ispinor
177 : : !
178 : : ! * Apply the phase to account if the symmetric atom belongs to a different unit cell.
179 [ + + ]: 3404588 : do ispinor=1,nspinor
180 : 1702294 : dum(1,ispinor)=tmp(1,ispinor)*phase(1)-tmp(2,ispinor)*phase(2)
181 : 3404588 : dum(2,ispinor)=tmp(1,ispinor)*phase(2)+tmp(2,ispinor)*phase(1)
182 : : end do
183 : : !
184 : : ! * If required, apply time-reversal symmetry to retrieve the correct point in the BZ.
185 [ - + ]: 1702294 : if (itim==2) then
186 [ # # ]: 0 : if (nspinor==1) then
187 : 0 : dum(2,1)=-dum(2,1)
188 [ # # ]: 0 : else if (nspinor==2) then ! TODO rotate wavefunction in spinor space.
189 [ # # ]: 0 : swp(:)=dum(:,1)
190 : 0 : dum(1,1)= dum(1,2)
191 : 0 : dum(2,1)=-dum(2,2)
192 : 0 : dum(1,2)=-swp(1)
193 : 0 : dum(2,2)= swp(2)
194 : : end if
195 : : end if
196 : : !
197 : : ! ==== Save values ====
198 [ + + ]: 5106882 : do ispinor=1,nspinor
199 : 1702294 : ibsp_bz=ibsp_bz+1
200 : 1702294 : Cprj_bz(iatom,ibsp_bz)%cp(1,jlmn)=dum(1,ispinor)
201 : 3404588 : Cprj_bz(iatom,ibsp_bz)%cp(2,jlmn)=dum(2,ispinor)
202 : : end do
203 : : end do !iband
204 : :
205 : 1914462 : jl0=jl; jln0=jln
206 : : end do !jlmn
207 : : end do !iatom
208 : :
209 : 104488 : call pawcprj_free(Cprjnk_kibz)
210 [ - + ]: 104488 : ABI_FREE(DS_mmpl)
211 : :
212 : 127533 : end subroutine paw_symcprj
213 : : !!***
214 : :
215 : : !----------------------------------------------------------------------
216 : :
217 : : !!****f* m_paw_sym/paw_symcprj_op
218 : : !! NAME
219 : : !! paw_symcprj_op
220 : : !!
221 : : !! FUNCTION
222 : : !! Symetrize the projections cprj=<n,k|p_i> (p_i=NL PAW projector) - in-place version
223 : : !!
224 : : !! INPUTS
225 : : !! ik_ibz=The index of the k-point in the full BZ where the matrix elements have to be symmetrized.
226 : : !! nspinor=Number of spinorial components
227 : : !! nband_k=Number of bands stored in cprjnk_kibz for this k-point.
228 : : !! Cryst<crystal_t>=data type gathering information on unit cell and symmetries.
229 : : !! %ntypat=number of type of atoms
230 : : !! %natom=number of atoms in the unit cell
231 : : !! %typat(natom)=type of each atom
232 : : !! %indsym(4,nsym,natom)=indirect indexing array:
233 : : !! for each isym,iatom, fourth element is label of atom into which iatom is sent by the INVERSE of the
234 : : !! symmetry operation symrel(isym); first three elements are the primitive translations that must be subtracted
235 : : !! after the transformation to get back to the original unit cell.
236 : : !! Kmesh<kmesh_t>: datatype gathering information on the k-point sampling.
237 : : !! %nbz=number of k-points in the full Brillouin zone
238 : : !! %nibz=number of k-points in the irreducible wedge
239 : : !! %tab(nkbz)=table giving for each k-point in the BZ (array kbz), the corresponding irred. point in the IBZ.
240 : : !! i.e k_BZ = (IS) kIBZ where S is one of the symrec operations and I is the inversion or the identity
241 : : !! %tabi(nkbz)=for each k-point in the BZ defines whether inversion has to be considered in the
242 : : !! relation k_BZ=(IS) k_IBZ (1 => only S; -1 => -S)
243 : : !! %tabo(nkbz)= the symmetry operation S that takes k_IBZ to each k_BZ
244 : : !! Pawtab(Cryst%ntypat) <type(pawtab_type)>=paw tabulated starting data.
245 : : !! Pawang <type(pawang_type)>=paw angular mesh and related data
246 : : !! %lmax=Max angular momentum included in the PAW datasets used. mentioned at the second line of the psp file
247 : : !! %zarot(2*lmax+1,2*lmax+1,lmax+1,nsym)=coefficients of the transformation of real spherical
248 : : !! harmonics under the symmetry operations.
249 : : !! in_Cprj(Cryst%natom,nspinor*nband_k)<pawcprj_type>=Input cprj
250 : : !!
251 : : !! OUTPUT
252 : : !! out_Cprj(Cryst%natom,nspinor*nband_k)<pawcprj_type>=Symmetrized cprj matrix elements.
253 : : !!
254 : : !! NOTES
255 : : !! Derivatives are not symmetrized.
256 : : !!
257 : : !! SOURCE
258 : :
259 : 216184 : subroutine paw_symcprj_op(ik_bz,nspinor,nband_k,Cryst,Kmesh,Pawtab,Pawang,in_Cprj,out_Cprj)
260 : :
261 : : !Arguments ------------------------------------
262 : : !scalars
263 : : integer,intent(in) :: nspinor,nband_k,ik_bz
264 : : type(crystal_t),intent(in) :: Cryst
265 : : type(kmesh_t),intent(in) :: Kmesh
266 : : type(Pawang_type),intent(in) :: Pawang
267 : : !arrays
268 : : type(Pawtab_type),target,intent(in) :: Pawtab(Cryst%ntypat)
269 : : type(pawcprj_type),intent(in) :: in_Cprj(Cryst%natom,nspinor*nband_k)
270 : : type(pawcprj_type),intent(inout) :: out_Cprj(Cryst%natom,nspinor*nband_k) !vz_i
271 : :
272 : : !Local variables-------------------------------
273 : : !scalars
274 : : integer :: iatom,iat_sym,iband,ibsp_bz
275 : : integer :: ibsp_ibz,ik_ibz,indexj,ispinor,isym,itim
276 : : integer :: itypat,jl,jl0,jlmn,jln,jln0,jlpm,jm,jn,lmax,mm,ncpgr
277 : : real(dp) :: arg,wtk
278 : : logical :: isirred
279 : : !arrays
280 : : integer :: r0(3) !,nlmn_atom(Cryst%natom)
281 : 216184 : integer,ABI_CONTIGUOUS pointer :: indlmn(:,:)
282 : 12572 : real(dp) :: dum(2,nspinor),kbz(3),kirr(3),phase(2),swp(2),tmp(2,nspinor)
283 : 216184 : real(dp),allocatable :: DS_mmpl(:,:,:)
284 : :
285 : : ! *********************************************************************
286 : :
287 : 216184 : ncpgr = in_Cprj(1,1)%ncpgr
288 : 0 : ABI_CHECK(ncpgr==0,"Derivatives of cprj are not coded")
289 : :
290 : : !Get the index of the IBZ image associated to the BZ k-point ik_bz and related simmetry.
291 : 216184 : call Kmesh%get_BZ_item(ik_bz,kbz,ik_ibz,isym,itim,isirred=isirred)
292 : :
293 [ + + ]: 216184 : if (isirred) then ! It is a point in the IBZ, Symmetrization is not needed.
294 : 12572 : call pawcprj_copy(in_Cprj,out_Cprj)
295 : : RETURN
296 : : end if
297 : : !
298 : : !The corresponding point kirr in the IBZ.
299 : 203612 : call Kmesh%get_IBZ_item(ik_ibz,kirr,wtk)
300 : : !
301 : : !=== DS_mmpl is the rotation matrix for real spherical harmonics associated to symrec(:,:,isym) ===
302 : : !* Note the convention used by Blanco in Eq. 27 : DS_mmp multiply spherical harmonics as row vectors
303 : 203612 : lmax=Pawang%l_max-1 ! l_max is Max l+1
304 [ + - - + : 1221672 : ABI_MALLOC(DS_mmpl,(2*lmax+1,2*lmax+1,lmax+1))
+ - - + +
- + - - +
+ - + - +
- - + -
+ ]
305 [ + - + - : 5701136 : DS_mmpl=Pawang%zarot(:,:,:,isym)
+ - - + -
- + + + +
+ + ]
306 : :
307 : : !Local copy.
308 : : !do iatom=1,Cryst%natom
309 : : !nlmn_atom(iatom)=Pawtab(Cryst%typat(iatom))%lmn_size
310 : : !end do
311 : : !call pawcprj_alloc(out_Cprj,ncpgr,nlmn_atom)
312 : : !
313 : : !===========================================
314 : : !==== Loop over atoms to be symmetrized ====
315 : : !===========================================
316 [ + + ]: 610836 : do iatom=1,Cryst%natom
317 : 407224 : itypat=Cryst%typat(iatom)
318 : 407224 : iat_sym=Cryst%indsym(4,isym,iatom)
319 : 407224 : indlmn => Pawtab(itypat)%indlmn
320 [ + + ]: 1628896 : r0=Cryst%indsym(1:3,isym,iatom) ! R^{-1} (xred(:,iatom)-tnons) = xred(:,iat_sym) + r0.
321 [ + + ]: 1628896 : arg=two_pi*dot_product(kirr,r0)
322 : 407224 : phase(1)=COS(arg)
323 : 407224 : phase(2)=SIN(arg)
324 : : !
325 : : ! Loop over the (jl,jm,jn) components to be symmetrized.
326 : 407224 : jl0=-1; jln0=-1; indexj=1
327 [ + + ]: 3863168 : do jlmn=1,Pawtab(itypat)%lmn_size
328 : 3252332 : jl =indlmn(1,jlmn)
329 : 3252332 : jm =indlmn(2,jlmn)
330 : 3252332 : jn =indlmn(3,jlmn)
331 : 3252332 : jln =indlmn(5,jlmn)
332 : 3252332 : jlpm=1+jl+jm
333 [ + + ]: 3252332 : if (jln/=jln0) indexj=indexj+2*jl0+1
334 : : !
335 : : ! === For each band, calculate contribution due to rotated real spherical harmonics ===
336 : : ! FIXME check this expression; according to Blanco I should have D(S^-1} but it seems D(S) is correct
337 : : ! Recheck spinorial case, presently is wrong
338 : 3252332 : ibsp_ibz=0
339 : 3252332 : ibsp_bz=0
340 [ + + ]: 6504664 : do iband=1,nband_k
341 : :
342 [ + + + + ]: 13009328 : tmp(:,:)=zero
343 [ + + ]: 6504664 : do ispinor=1,nspinor
344 : 3252332 : ibsp_ibz=ibsp_ibz+1
345 [ + + ]: 14632764 : do mm=1,2*jl+1
346 : 8128100 : tmp(1,ispinor)=tmp(1,ispinor)+DS_mmpl(mm,jlpm,jl+1)*in_Cprj(iat_sym,ibsp_ibz)%cp(1,indexj+mm)
347 : 11380432 : tmp(2,ispinor)=tmp(2,ispinor)+DS_mmpl(mm,jlpm,jl+1)*in_Cprj(iat_sym,ibsp_ibz)%cp(2,indexj+mm)
348 : : end do
349 : : end do !ispinor
350 : : !
351 : : ! * Apply the phase to account if the symmetric atom belongs to a different unit cell.
352 [ + + ]: 6504664 : do ispinor=1,nspinor
353 : 3252332 : dum(1,ispinor)=tmp(1,ispinor)*phase(1)-tmp(2,ispinor)*phase(2)
354 : 6504664 : dum(2,ispinor)=tmp(1,ispinor)*phase(2)+tmp(2,ispinor)*phase(1)
355 : : end do
356 : : !
357 : : ! * If required, apply time-reversal symmetry to retrieve the correct point in the BZ.
358 [ - + ]: 3252332 : if (itim==2) then
359 [ # # ]: 0 : if (nspinor==1) then
360 : 0 : dum(2,1)=-dum(2,1)
361 [ # # ]: 0 : else if (nspinor==2) then ! TODO rotate wavefunction in spinor space.
362 [ # # ]: 0 : swp(:)=dum(:,1)
363 : 0 : dum(1,1)= dum(1,2)
364 : 0 : dum(2,1)=-dum(2,2)
365 : 0 : dum(1,2)=-swp(1)
366 : 0 : dum(2,2)= swp(2)
367 : : end if
368 : : end if
369 : : !
370 : : ! ==== Save values ====
371 [ + + ]: 9756996 : do ispinor=1,nspinor
372 : 3252332 : ibsp_bz=ibsp_bz+1
373 : 3252332 : out_Cprj(iatom,ibsp_bz)%cp(1,jlmn)=dum(1,ispinor)
374 : 6504664 : out_Cprj(iatom,ibsp_bz)%cp(2,jlmn)=dum(2,ispinor)
375 : : end do
376 : : end do !iband
377 : :
378 : 3659556 : jl0=jl; jln0=jln
379 : : end do !jlmn
380 : : end do !iatom
381 : :
382 [ - + ]: 203612 : ABI_FREE(DS_mmpl)
383 : :
384 [ - + ]: 216184 : end subroutine paw_symcprj_op
385 : : !!***
386 : :
387 : : !----------------------------------------------------------------------
388 : :
389 : : END MODULE m_paw_sym
390 : : !!***
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