-
Notifications
You must be signed in to change notification settings - Fork 0
/
Copy pathbse_properties.F
991 lines (882 loc) · 48.9 KB
/
bse_properties.F
1
2
3
4
5
6
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
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
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
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
!--------------------------------------------------------------------------------------------------!
! CP2K: A general program to perform molecular dynamics simulations !
! Copyright 2000-2024 CP2K developers group <https://cp2k.org> !
! !
! SPDX-License-Identifier: GPL-2.0-or-later !
!--------------------------------------------------------------------------------------------------!
! **************************************************************************************************
!> \brief Routines for computing excitonic properties, e.g. exciton diameter, from the BSE
!> \par History
!> 10.2024 created [Maximilian Graml]
! **************************************************************************************************
MODULE bse_properties
USE bse_util, ONLY: fm_general_add_bse,&
print_bse_nto_cubes,&
reshuffle_eigvec,&
trace_exciton_descr
USE cp_files, ONLY: close_file,&
open_file
USE cp_fm_basic_linalg, ONLY: cp_fm_scale_and_add,&
cp_fm_trace
USE cp_fm_diag, ONLY: cp_fm_svd
USE cp_fm_struct, ONLY: cp_fm_struct_create,&
cp_fm_struct_release,&
cp_fm_struct_type
USE cp_fm_types, ONLY: cp_fm_create,&
cp_fm_get_submatrix,&
cp_fm_release,&
cp_fm_set_all,&
cp_fm_to_fm,&
cp_fm_to_fm_submat,&
cp_fm_to_fm_submat_general,&
cp_fm_type
USE cp_log_handling, ONLY: cp_get_default_logger,&
cp_logger_get_default_unit_nr,&
cp_logger_type
USE input_section_types, ONLY: section_vals_get_subs_vals,&
section_vals_type,&
section_vals_val_get
USE kinds, ONLY: dp
USE mp2_types, ONLY: mp2_type
USE parallel_gemm_api, ONLY: parallel_gemm
USE particle_methods, ONLY: write_qs_particle_coordinates
USE particle_types, ONLY: particle_type
USE physcon, ONLY: evolt
USE qs_environment_types, ONLY: get_qs_env,&
qs_environment_type
USE qs_kind_types, ONLY: qs_kind_type
USE qs_mo_types, ONLY: allocate_mo_set,&
deallocate_mo_set,&
init_mo_set,&
mo_set_type
#include "./base/base_uses.f90"
IMPLICIT NONE
PRIVATE
CHARACTER(len=*), PARAMETER, PRIVATE :: moduleN = 'bse_properties'
PUBLIC :: exciton_descr_type
PUBLIC :: get_exciton_descriptors, get_oscillator_strengths, compute_absorption_spectrum, &
calculate_NTOs
! TYPE definitions for exciton wavefunction descriptors
TYPE exciton_descr_type
REAL(KIND=dp), DIMENSION(3) :: r_e = 0.0_dp, &
r_h = 0.0_dp, &
r_e_sq = 0.0_dp, &
r_h_sq = 0.0_dp, &
r_e_h = 0.0_dp, &
r_e_shift = 0.0_dp, &
r_h_shift = 0.0_dp, &
cov_e_h = 0.0_dp
REAL(KIND=dp) :: sigma_e = 0.0_dp, &
sigma_h = 0.0_dp, &
cov_e_h_sum = 0.0_dp, &
corr_e_h = 0.0_dp, &
diff_r_abs = 0.0_dp, &
diff_r_sqr = 0.0_dp, &
norm_XpY = 0.0_dp
LOGICAL :: flag_TDA = .FALSE.
END TYPE exciton_descr_type
CONTAINS
! **************************************************************************************************
!> \brief Compute and return BSE dipoles d_r^n = sqrt(2) sum_ia < ψ_i | r | ψ_a > ( X_ia^n + Y_ia^n )
!> and oscillator strengths f^n = 2/3 * Ω^n sum_r∈(x,y,z) ( d_r^n )^2
!> Prelim Ref.: Eqs. (23), (24)
!> in J. Chem. Phys. 152, 044105 (2020); https://doi.org/10.1063/1.5123290
!> \param fm_eigvec_X ...
!> \param Exc_ens ...
!> \param fm_dipole_ai_trunc ...
!> \param trans_mom_bse BSE dipole vectors in real space per excitation level
!> \param oscill_str Oscillator strength per excitation level
!> \param polarizability_residues Residues of polarizability ("tensorial oscillator strength")
!> per excitation level
!> \param mp2_env ...
!> \param homo_red ...
!> \param virtual_red ...
!> \param unit_nr ...
!> \param fm_eigvec_Y ...
! **************************************************************************************************
SUBROUTINE get_oscillator_strengths(fm_eigvec_X, Exc_ens, fm_dipole_ai_trunc, &
trans_mom_bse, oscill_str, polarizability_residues, &
mp2_env, homo_red, virtual_red, unit_nr, &
fm_eigvec_Y)
TYPE(cp_fm_type), INTENT(IN) :: fm_eigvec_X
REAL(KIND=dp), ALLOCATABLE, DIMENSION(:), &
INTENT(IN) :: Exc_ens
TYPE(cp_fm_type), DIMENSION(3) :: fm_dipole_ai_trunc
REAL(KIND=dp), ALLOCATABLE, DIMENSION(:, :, :), &
INTENT(OUT) :: trans_mom_bse
REAL(KIND=dp), ALLOCATABLE, DIMENSION(:), &
INTENT(OUT) :: oscill_str
REAL(KIND=dp), ALLOCATABLE, DIMENSION(:, :, :), &
INTENT(OUT) :: polarizability_residues
TYPE(mp2_type), INTENT(IN) :: mp2_env
INTEGER, INTENT(IN) :: homo_red, virtual_red, unit_nr
TYPE(cp_fm_type), INTENT(IN), OPTIONAL :: fm_eigvec_Y
CHARACTER(LEN=*), PARAMETER :: routineN = 'get_oscillator_strengths'
INTEGER :: handle, idir, jdir, n
TYPE(cp_fm_struct_type), POINTER :: fm_struct_dipole_MO_trunc_reordered, &
fm_struct_trans_mom_bse
TYPE(cp_fm_type) :: fm_eigvec_XYsum
TYPE(cp_fm_type), DIMENSION(3) :: fm_dipole_MO_trunc_reordered, &
fm_dipole_per_dir, fm_trans_mom_bse
CALL timeset(routineN, handle)
CALL cp_fm_struct_create(fm_struct_dipole_MO_trunc_reordered, fm_eigvec_X%matrix_struct%para_env, &
fm_eigvec_X%matrix_struct%context, 1, homo_red*virtual_red)
CALL cp_fm_struct_create(fm_struct_trans_mom_bse, fm_eigvec_X%matrix_struct%para_env, &
fm_eigvec_X%matrix_struct%context, 1, homo_red*virtual_red)
! Include excitonic amplitudes in dipoles, i.e. obtain "BSE dipoles":
! \vec{D}_n = sqrt(2) * sum_{i,a} \vec{D}_ai (X_{ai}^{(n)} + Y_{ai}^{(n)})
! Reorder dipoles in order to execute the sum over i and a by parallel gemm
DO idir = 1, 3
CALL cp_fm_create(fm_dipole_MO_trunc_reordered(idir), matrix_struct=fm_struct_dipole_MO_trunc_reordered, &
name="dipoles_mo_reordered")
CALL cp_fm_set_all(fm_dipole_MO_trunc_reordered(idir), 0.0_dp)
CALL fm_general_add_bse(fm_dipole_MO_trunc_reordered(idir), fm_dipole_ai_trunc(idir), 1.0_dp, &
1, 1, &
1, virtual_red, &
unit_nr, (/2, 4, 3, 1/), mp2_env)
CALL cp_fm_release(fm_dipole_per_dir(idir))
END DO
DO idir = 1, 3
CALL cp_fm_create(fm_trans_mom_bse(idir), matrix_struct=fm_struct_trans_mom_bse, &
name="excitonic_dipoles")
CALL cp_fm_set_all(fm_trans_mom_bse(idir), 0.0_dp)
END DO
! If TDA is invoked, Y is not present as it is simply 0
CALL cp_fm_create(fm_eigvec_XYsum, matrix_struct=fm_eigvec_X%matrix_struct, name="excit_amplitude_sum")
CALL cp_fm_set_all(fm_eigvec_XYsum, 0.0_dp)
CALL cp_fm_to_fm(fm_eigvec_X, fm_eigvec_XYsum)
IF (PRESENT(fm_eigvec_Y)) THEN
CALL cp_fm_scale_and_add(1.0_dp, fm_eigvec_XYsum, 1.0_dp, fm_eigvec_Y)
END IF
DO idir = 1, 3
CALL parallel_gemm('N', 'N', 1, homo_red*virtual_red, homo_red*virtual_red, SQRT(2.0_dp), &
fm_dipole_MO_trunc_reordered(idir), fm_eigvec_XYsum, 0.0_dp, fm_trans_mom_bse(idir))
END DO
! Get oscillator strengths themselves
ALLOCATE (oscill_str(homo_red*virtual_red))
ALLOCATE (trans_mom_bse(3, 1, homo_red*virtual_red))
ALLOCATE (polarizability_residues(3, 3, homo_red*virtual_red))
trans_mom_bse(:, :, :) = 0.0_dp
! Sum over all directions
DO idir = 1, 3
CALL cp_fm_get_submatrix(fm_trans_mom_bse(idir), trans_mom_bse(idir, :, :))
END DO
DO n = 1, homo_red*virtual_red
DO idir = 1, 3
DO jdir = 1, 3
polarizability_residues(idir, jdir, n) = 2.0_dp*Exc_ens(n)*trans_mom_bse(idir, 1, n)*trans_mom_bse(jdir, 1, n)
END DO
END DO
oscill_str(n) = 2.0_dp/3.0_dp*Exc_ens(n)*SUM(ABS(trans_mom_bse(:, :, n))**2)
END DO
CALL cp_fm_struct_release(fm_struct_dipole_MO_trunc_reordered)
CALL cp_fm_struct_release(fm_struct_trans_mom_bse)
DO idir = 1, 3
CALL cp_fm_release(fm_dipole_MO_trunc_reordered(idir))
CALL cp_fm_release(fm_trans_mom_bse(idir))
CALL cp_fm_release(fm_dipole_ai_trunc(idir))
END DO
CALL cp_fm_release(fm_eigvec_XYsum)
CALL timestop(handle)
END SUBROUTINE get_oscillator_strengths
! **************************************************************************************************
!> \brief Computes and returns absorption spectrum for the frequency range and broadening
!> provided by the user.
!> Prelim Ref.: C. Ullrich, Time-Dependent Density-Functional Theory: Concepts and Applications
!> (Oxford University Press, Oxford, 2012), Eq. 7.51
!> \param oscill_str ...
!> \param polarizability_residues ...
!> \param Exc_ens ...
!> \param info_approximation ...
!> \param unit_nr ...
!> \param mp2_env ...
! **************************************************************************************************
SUBROUTINE compute_absorption_spectrum(oscill_str, polarizability_residues, Exc_ens, &
info_approximation, unit_nr, mp2_env)
REAL(KIND=dp), ALLOCATABLE, DIMENSION(:), &
INTENT(IN) :: oscill_str
REAL(KIND=dp), ALLOCATABLE, DIMENSION(:, :, :), &
INTENT(IN) :: polarizability_residues
REAL(KIND=dp), ALLOCATABLE, DIMENSION(:), &
INTENT(IN) :: Exc_ens
CHARACTER(LEN=10) :: info_approximation
INTEGER, INTENT(IN) :: unit_nr
TYPE(mp2_type), INTENT(INOUT) :: mp2_env
CHARACTER(LEN=*), PARAMETER :: routineN = 'compute_absorption_spectrum'
CHARACTER(LEN=10) :: eta_str, width_eta_format_str
CHARACTER(LEN=30) :: file_name_spectrum
INTEGER :: handle, i, idir, j, jdir, k, num_steps, &
unit_nr_file, width_eta
REAL(KIND=dp) :: eta, freq_end, freq_start, freq_step, &
omega
REAL(KIND=dp), ALLOCATABLE, DIMENSION(:, :) :: abs_spectrum
REAL(KIND=dp), DIMENSION(:), POINTER :: eta_list
TYPE(cp_logger_type), POINTER :: logger
CALL timeset(routineN, handle)
freq_step = mp2_env%bse%bse_spectrum_freq_step_size
freq_start = mp2_env%bse%bse_spectrum_freq_start
freq_end = mp2_env%bse%bse_spectrum_freq_end
eta_list => mp2_env%bse%bse_eta_spectrum_list
! Calculate number of steps to fit given frequency range
num_steps = NINT((freq_end - freq_start)/freq_step) + 1
DO k = 1, SIZE(eta_list)
eta = eta_list(k)
! Some magic to get a nice formatting of the eta value in filenames
width_eta = MAX(1, INT(LOG10(eta)) + 1) + 4
WRITE (width_eta_format_str, "(A2,I0,A3)") '(F', width_eta, '.3)'
WRITE (eta_str, width_eta_format_str) eta*evolt
! Filename itself
file_name_spectrum = 'BSE'//TRIM(ADJUSTL(info_approximation))//'eta='//TRIM(eta_str)//'.spectrum'
! First column is frequency in eV, second column is imaginary part of the trace of the polarizability
! The following 9 columns are the entries of the polarizability tensor
ALLOCATE (abs_spectrum(num_steps, 11))
abs_spectrum(:, :) = 0.0_dp
! Calculate the imaginary part of the mean dipole polarizability α_{avg}(ω)
! which is given by (cf. C. Ullrichs Book on TDDFT, Eq. 7.51)
! α_{avg}(ω) = \sum_{n=1}^{N_exc} \frac{f_n}{(ω+iη)² - (Ω^n)²}
! and then the imaginary part is (in the limit η -> 0)
! Im[α_{avg}(ω)] = \sum_{n=1}^{N_exc} f_n * η / ((ω - Ω^n)² + η²)
! where f_n are the oscillator strengths and E_exc the excitation energies
! For the full polarizability tensor, we have
! α_{µ µ'}(ω) = \sum_n [2 Ω^n d^n_µ d^n_µ'] / [(ω+iη)^2- (Ω^n)^2]
! = \sum_n "polarizability_residues" / [(ω+iη)^2- (Ω^n)^2]
DO i = 1, num_steps
omega = freq_start + (i - 1)*freq_step
abs_spectrum(i, 1) = omega
DO j = 1, SIZE(oscill_str)
abs_spectrum(i, 2) = abs_spectrum(i, 2) - oscill_str(j)* &
AIMAG(1/((omega + CMPLX(0.0, eta, kind=dp))**2 - Exc_ens(j)**2))
DO idir = 1, 3
DO jdir = 1, 3
! Factor 2 from formula for tensor is already in the polarizability_residues
! to follow the same convention as the oscillator strengths
abs_spectrum(i, 2 + (idir - 1)*3 + jdir) = abs_spectrum(i, 2 + (idir - 1)*3 + jdir) &
- polarizability_residues(idir, jdir, j)* &
AIMAG(1/((omega + CMPLX(0.0, eta, kind=dp))**2 - Exc_ens(j)**2))
END DO
END DO
END DO
END DO
! Print it to file
logger => cp_get_default_logger()
IF (logger%para_env%is_source()) THEN
unit_nr_file = cp_logger_get_default_unit_nr()
ELSE
unit_nr_file = -1
END IF
IF (unit_nr_file > 0) THEN
CALL open_file(file_name_spectrum, unit_number=unit_nr_file, &
file_status="UNKNOWN", file_action="WRITE")
WRITE (unit_nr_file, '(A,A6)') "# Imaginary part of polarizability α_{µ µ'}(ω) = \sum_n "// &
"[2 Ω^n d_µ^n d_µ'^n] / [(ω+iη)²- (Ω^n)²] from Bethe Salpeter equation for method ", &
TRIM(ADJUSTL(info_approximation))
WRITE (unit_nr_file, '(A20,1X,10(2X,A20,1X))') "# Frequency (eV)", "Im{α_{avg}(ω)}", "Im{α_xx(ω)}", &
"Im{α_xy(ω)}", "Im{α_xz(ω)}", "Im{α_yx(ω)}", "Im{α_yy(ω)}", "Im{α_yz(ω)}", "Im{α_zx(ω)}", &
"Im{α_zy(ω)}", "Im{α_zz(ω)}"
DO i = 1, num_steps
WRITE (unit_nr_file, '(11(F20.8,1X))') abs_spectrum(i, 1)*evolt, abs_spectrum(i, 2:11)
END DO
CALL close_file(unit_nr_file)
END IF
DEALLOCATE (abs_spectrum)
END DO
IF (unit_nr > 0) THEN
WRITE (unit_nr, '(T2,A4)') 'BSE|'
WRITE (unit_nr, '(T2,A4,T7,A50,A)') &
'BSE|', "Printed optical absorption spectrum to local file ", file_name_spectrum
WRITE (unit_nr, '(T2,A4,T7,A50)') &
'BSE|', "using the Eq. 7.51 from C. Ullrichs Book on TDDFT:"
WRITE (unit_nr, '(T2,A4)') 'BSE|'
WRITE (unit_nr, '(T2,A4,T10,A73)') &
'BSE|', "Im{α_{avg}(ω)} = Im{\sum_{n=1}^{N_exc} \frac{f_n}{(ω+iη)² - (Ω^n)²}}"
WRITE (unit_nr, '(T2,A4)') 'BSE|'
WRITE (unit_nr, '(T2,A4,T7,A)') &
'BSE|', "or for the full polarizability tensor:"
WRITE (unit_nr, '(T2,A4,T10,A)') &
'BSE|', "α_{µ µ'}(ω) = \sum_n [2 Ω^n d_µ^n d_µ'^n] / [(ω+iη)²- (Ω^n)²]"
WRITE (unit_nr, '(T2,A4)') 'BSE|'
WRITE (unit_nr, '(T2,A4,T7,A)') &
'BSE|', "with transition moments d_µ^n, oscillator strengths f_n,"
WRITE (unit_nr, '(T2,A4,T7,A)') &
'BSE|', "and excitation energies Ω^n."
WRITE (unit_nr, '(T2,A4)') 'BSE|'
END IF
CALL timestop(handle)
END SUBROUTINE
! **************************************************************************************************
!> \brief ...
!> \param fm_X ...
!> \param fm_Y ...
!> \param mo_coeff ...
!> \param homo ...
!> \param virtual ...
!> \param info_approximation ...
!> \param oscill_str ...
!> \param qs_env ...
!> \param unit_nr ...
!> \param mp2_env ...
! **************************************************************************************************
SUBROUTINE calculate_NTOs(fm_X, fm_Y, &
mo_coeff, homo, virtual, &
info_approximation, &
oscill_str, &
qs_env, unit_nr, mp2_env)
TYPE(cp_fm_type), INTENT(IN) :: fm_X
TYPE(cp_fm_type), INTENT(IN), OPTIONAL :: fm_Y
TYPE(cp_fm_type), DIMENSION(:), INTENT(IN) :: mo_coeff
INTEGER, INTENT(IN) :: homo, virtual
CHARACTER(LEN=10) :: info_approximation
REAL(KIND=dp), ALLOCATABLE, DIMENSION(:) :: oscill_str
TYPE(qs_environment_type), POINTER :: qs_env
INTEGER, INTENT(IN) :: unit_nr
TYPE(mp2_type), INTENT(INOUT) :: mp2_env
CHARACTER(LEN=*), PARAMETER :: routineN = 'calculate_NTOs'
CHARACTER(LEN=20), DIMENSION(2) :: nto_name
INTEGER :: handle, homo_irred, i, i_nto, info_svd, &
j, n_exc, n_nto, nao_full, nao_trunc
INTEGER, DIMENSION(:), POINTER :: stride
LOGICAL :: append_cube, cube_file
REAL(KIND=dp), ALLOCATABLE, DIMENSION(:) :: eigval_svd_squ
REAL(KIND=dp), DIMENSION(:), POINTER :: eigval_svd
TYPE(cp_fm_struct_type), POINTER :: fm_struct_m, fm_struct_mo_coeff, &
fm_struct_nto_holes, &
fm_struct_nto_particles, &
fm_struct_nto_set
TYPE(cp_fm_type) :: fm_eigvl, fm_eigvr_t, fm_m, fm_mo_coeff, fm_nto_coeff_holes, &
fm_nto_coeff_particles, fm_nto_set, fm_X_ia, fm_Y_ai
TYPE(mo_set_type), ALLOCATABLE, DIMENSION(:) :: nto_set
TYPE(section_vals_type), POINTER :: bse_section, input, nto_section
CALL timeset(routineN, handle)
CALL get_qs_env(qs_env=qs_env, &
input=input)
bse_section => section_vals_get_subs_vals(input, "DFT%XC%WF_CORRELATION%RI_RPA%GW%BSE")
nao_full = qs_env%mos(1)%nao
nao_trunc = homo + virtual
! This is not influenced by the BSE cutoff
homo_irred = qs_env%mos(1)%homo
! M will have a block structure and is quadratic in homo+virtual, i.e.
! occ virt
! | 0 X_i,a | occ = homo
! M = | Y_a,i 0 | virt = virtual
!
! X and Y are here not the eigenvectors X_ia,n - instead we fix n and reshape the combined ia index
! Notice the index structure of the lower block, i.e. X is transposed
CALL cp_fm_struct_create(fm_struct_m, &
fm_X%matrix_struct%para_env, fm_X%matrix_struct%context, &
nao_trunc, nao_trunc)
CALL cp_fm_struct_create(fm_struct_mo_coeff, &
fm_X%matrix_struct%para_env, fm_X%matrix_struct%context, &
nao_full, nao_trunc)
CALL cp_fm_struct_create(fm_struct_nto_holes, &
fm_X%matrix_struct%para_env, fm_X%matrix_struct%context, &
nao_full, nao_trunc)
CALL cp_fm_struct_create(fm_struct_nto_particles, &
fm_X%matrix_struct%para_env, fm_X%matrix_struct%context, &
nao_full, nao_trunc)
CALL cp_fm_create(fm_mo_coeff, matrix_struct=fm_struct_mo_coeff, &
name="mo_coeff")
! Here, we take care of possible cutoffs
! Simply truncating the matrix causes problems with the print function
! Therefore, we keep the dimension, but set the coefficients of truncated indices to 0
CALL cp_fm_to_fm_submat_general(mo_coeff(1), fm_mo_coeff, &
nao_full, nao_trunc, &
1, homo_irred - homo + 1, &
1, 1, &
mo_coeff(1)%matrix_struct%context)
! Print some information about the NTOs
IF (unit_nr > 0) THEN
WRITE (unit_nr, '(T2,A4,T7,A)') 'BSE|', &
'The Natural Transition Orbital (NTO) pairs φ_I(r_e) and χ_I(r_h) for a fixed'
WRITE (unit_nr, '(T2,A4,T7,A)') 'BSE|', &
'excitation index n are obtained by singular value decomposition of T'
WRITE (unit_nr, '(T2,A4)') 'BSE|'
WRITE (unit_nr, '(T2,A4,T15,A)') 'BSE|', &
' = (0 X)'
IF (PRESENT(fm_Y)) THEN
WRITE (unit_nr, '(T2,A4,T15,A)') 'BSE|', &
'T = (Y^T 0)'
ELSE
WRITE (unit_nr, '(T2,A4,T15,A)') 'BSE|', &
'T = (0 0)'
END IF
WRITE (unit_nr, '(T2,A4)') 'BSE|'
WRITE (unit_nr, '(T2,A4,T15,A)') 'BSE|', &
'T = U Λ V^T'
WRITE (unit_nr, '(T2,A4,T15,A)') 'BSE|', &
'φ_I(r_e) = \sum_p V_pI ψ_p(r_e)'
WRITE (unit_nr, '(T2,A4,T15,A)') 'BSE|', &
'χ_I(r_h) = \sum_p U_pI ψ_p(r_e)'
WRITE (unit_nr, '(T2,A4)') 'BSE|'
WRITE (unit_nr, '(T2,A4,T7,A)') 'BSE|', &
'where we have introduced'
WRITE (unit_nr, '(T2,A4)') 'BSE|'
WRITE (unit_nr, '(T2,A4,T7,A,T20,A)') &
'BSE|', "ψ_p:", "occupied and virtual molecular orbitals,"
WRITE (unit_nr, '(T2,A4,T7,A,T20,A)') &
'BSE|', "φ_I(r_e):", "NTO state for the electron,"
WRITE (unit_nr, '(T2,A4,T7,A,T20,A)') &
'BSE|', "χ_I(r_h):", "NTO state for the hole,"
WRITE (unit_nr, '(T2,A4,T7,A,T20,A)') &
'BSE|', "Λ:", "diagonal matrix of NTO weights λ_I,"
WRITE (unit_nr, '(T2,A4)') 'BSE|'
WRITE (unit_nr, '(T2,A4,T7,A)') 'BSE|', &
"The NTOs are calculated with the following settings:"
WRITE (unit_nr, '(T2,A4)') 'BSE|'
WRITE (unit_nr, '(T2,A4,T7,A,T71,I10)') 'BSE|', 'Number of excitations, for which NTOs are computed', &
mp2_env%bse%num_print_exc_ntos
IF (mp2_env%bse%eps_nto_osc_str > 0.0_dp) THEN
WRITE (unit_nr, '(T2,A4,T7,A,T71,F10.3)') 'BSE|', 'Threshold for oscillator strength f^n', &
mp2_env%bse%eps_nto_osc_str
ELSE
WRITE (unit_nr, '(T2,A4,T7,A,T71,A10)') 'BSE|', 'Threshold for oscillator strength f^n', &
ADJUSTL("---")
END IF
WRITE (unit_nr, '(T2,A4,T7,A,T72,F10.3)') 'BSE|', 'Threshold for NTO weights (λ_I)^2', &
mp2_env%bse%eps_nto_eigval
END IF
! Write the header of NTO info table
IF (unit_nr > 0) THEN
WRITE (unit_nr, '(T2,A4)') 'BSE|'
IF (.NOT. PRESENT(fm_Y)) THEN
WRITE (unit_nr, '(T2,A4,T7,A)') 'BSE|', &
'NTOs from solving the BSE within the TDA:'
ELSE
WRITE (unit_nr, '(T2,A4,T7,A)') 'BSE|', &
'NTOs from solving the BSE without the TDA:'
END IF
WRITE (unit_nr, '(T2,A4)') 'BSE|'
WRITE (unit_nr, '(T2,A4,T8,A12,T22,A8,T33,A14,T62,A)') 'BSE|', &
'Excitation n', "TDA/ABBA", "Index of NTO I", 'NTO weights (λ_I)^2'
END IF
DO j = 1, mp2_env%bse%num_print_exc_ntos
n_exc = mp2_env%bse%bse_nto_state_list_final(j)
! Takes care of unallocated oscill_str array in case of Triplet
IF (mp2_env%bse%eps_nto_osc_str > 0.0_dp) THEN
! Check actual values
IF (oscill_str(n_exc) < mp2_env%bse%eps_nto_osc_str) THEN
! Print skipped levels to table
IF (unit_nr > 0) THEN
WRITE (unit_nr, '(T2,A4)') 'BSE|'
WRITE (unit_nr, '(T2,A4,T8,I12,T24,A6,T42,A39)') 'BSE|', &
n_exc, info_approximation, "Skipped (Oscillator strength too small)"
END IF
CYCLE
END IF
END IF
CALL cp_fm_create(fm_m, matrix_struct=fm_struct_m, &
name="single_part_trans_dm")
CALL cp_fm_set_all(fm_m, 0.0_dp)
CALL cp_fm_create(fm_nto_coeff_holes, matrix_struct=fm_struct_nto_holes, &
name="nto_coeffs_holes")
CALL cp_fm_set_all(fm_nto_coeff_holes, 0.0_dp)
CALL cp_fm_create(fm_nto_coeff_particles, matrix_struct=fm_struct_nto_particles, &
name="nto_coeffs_particles")
CALL cp_fm_set_all(fm_nto_coeff_particles, 0.0_dp)
! Reshuffle from X_ia,n_exc to X_i,a
CALL reshuffle_eigvec(fm_X, fm_X_ia, homo, virtual, n_exc, &
.FALSE., unit_nr, mp2_env)
! Copy X to upper block in M, i.e. starting from column homo+1
CALL cp_fm_to_fm_submat(fm_X_ia, fm_m, &
homo, virtual, &
1, 1, &
1, homo + 1)
CALL cp_fm_release(fm_X_ia)
! Copy Y if present
IF (PRESENT(fm_Y)) THEN
! Reshuffle from Y_ia,n_exc to Y_a,i
CALL reshuffle_eigvec(fm_Y, fm_Y_ai, homo, virtual, n_exc, &
.TRUE., unit_nr, mp2_env)
! Copy Y^T to lower block in M, i.e. starting from row homo+1
CALL cp_fm_to_fm_submat(fm_Y_ai, fm_m, &
virtual, homo, &
1, 1, &
homo + 1, 1)
CALL cp_fm_release(fm_Y_ai)
END IF
! Now we compute the SVD of M_{occ+virt,occ+virt}, which yields
! M = U * Lambda * V^T
! Initialize matrices and arrays to store left/right eigenvectors and singular values
CALL cp_fm_create(matrix=fm_eigvl, &
matrix_struct=fm_m%matrix_struct, &
name="LEFT_SINGULAR_MATRIX")
CALL cp_fm_set_all(fm_eigvl, alpha=0.0_dp)
CALL cp_fm_create(matrix=fm_eigvr_t, &
matrix_struct=fm_m%matrix_struct, &
name="RIGHT_SINGULAR_MATRIX")
CALL cp_fm_set_all(fm_eigvr_t, alpha=0.0_dp)
ALLOCATE (eigval_svd(nao_trunc))
eigval_svd(:) = 0.0_dp
info_svd = 0
CALL cp_fm_svd(fm_m, fm_eigvl, fm_eigvr_t, eigval_svd, info_svd)
IF (info_svd /= 0) THEN
IF (unit_nr > 0) THEN
CALL cp_warn(__LOCATION__, &
"SVD for computation of NTOs not successful. "// &
"Skipping print of NTOs.")
IF (info_svd > 0) THEN
CALL cp_warn(__LOCATION__, &
"PDGESVD detected heterogeneity. "// &
"Decreasing number of MPI ranks might solve this issue.")
END IF
END IF
! Release matrices to avoid memory leaks
CALL cp_fm_release(fm_m)
CALL cp_fm_release(fm_nto_coeff_holes)
CALL cp_fm_release(fm_nto_coeff_particles)
ELSE
! Rescale singular values as done in Martin2003 (10.1063/1.1558471)
ALLOCATE (eigval_svd_squ(nao_trunc))
eigval_svd_squ(:) = eigval_svd(:)**2
! Sanity check for TDA: In case of TDA, the sum should be \sum_ia |X_ia|^2 = 1
IF (.NOT. PRESENT(fm_Y)) THEN
IF (ABS(SUM(eigval_svd_squ) - 1) >= 1e-5) THEN
CPWARN("Sum of NTO coefficients deviates from 1!")
END IF
END IF
! Create NTO coefficients for later print to grid via TDDFT routine
! Apply U = fm_eigvl to MO coeffs, which yields hole states
CALL parallel_gemm("N", "N", nao_full, nao_trunc, nao_trunc, 1.0_dp, fm_mo_coeff, fm_eigvl, 0.0_dp, &
fm_nto_coeff_holes)
! Apply V^T = fm_eigvr_t to MO coeffs, which yields particle states
CALL parallel_gemm("N", "T", nao_full, nao_trunc, nao_trunc, 1.0_dp, fm_mo_coeff, fm_eigvr_t, 0.0_dp, &
fm_nto_coeff_particles)
!Release intermediary work matrices
CALL cp_fm_release(fm_m)
CALL cp_fm_release(fm_eigvl)
CALL cp_fm_release(fm_eigvr_t)
! Transfer NTO coefficients to sets
nto_name(1) = 'Hole_coord'
nto_name(2) = 'Particle_coord'
ALLOCATE (nto_set(2))
! Extract number of significant NTOs
n_nto = 0
DO i_nto = 1, nao_trunc
IF (eigval_svd_squ(i_nto) > mp2_env%bse%eps_nto_eigval) THEN
n_nto = n_nto + 1
ELSE
! Since svd orders in descending order, we can exit the loop if smaller
EXIT
END IF
END DO
IF (unit_nr > 0) THEN
WRITE (unit_nr, '(T2,A4)') 'BSE|'
DO i_nto = 1, n_nto
WRITE (unit_nr, '(T2,A4,T8,I12,T24,A6,T41,I6,T71,F10.5)') 'BSE|', &
n_exc, info_approximation, i_nto, eigval_svd_squ(i_nto)
END DO
END IF
CALL cp_fm_struct_create(fm_struct_nto_set, template_fmstruct=fm_struct_nto_holes, &
ncol_global=n_nto)
CALL cp_fm_create(fm_nto_set, fm_struct_nto_set)
DO i = 1, 2
CALL allocate_mo_set(nto_set(i), nao_trunc, n_nto, 0, 0.0_dp, 2.0_dp, 0.0_dp)
CALL init_mo_set(nto_set(i), fm_ref=fm_nto_set, name=nto_name(i))
END DO
CALL cp_fm_release(fm_nto_set)
CALL cp_fm_struct_release(fm_struct_nto_set)
! Fill NTO sets
CALL cp_fm_to_fm(fm_nto_coeff_holes, nto_set(1)%mo_coeff, ncol=n_nto)
CALL cp_fm_to_fm(fm_nto_coeff_particles, nto_set(2)%mo_coeff, ncol=n_nto)
! Cube files
nto_section => section_vals_get_subs_vals(bse_section, "NTO_ANALYSIS")
CALL section_vals_val_get(nto_section, "CUBE_FILES", l_val=cube_file)
CALL section_vals_val_get(nto_section, "STRIDE", i_vals=stride)
CALL section_vals_val_get(nto_section, "APPEND", l_val=append_cube)
IF (cube_file) THEN
CALL print_bse_nto_cubes(qs_env, nto_set, n_exc, info_approximation, &
stride, append_cube, nto_section)
END IF
CALL cp_fm_release(fm_nto_coeff_holes)
CALL cp_fm_release(fm_nto_coeff_particles)
DEALLOCATE (eigval_svd)
DEALLOCATE (eigval_svd_squ)
DO i = 1, 2
CALL deallocate_mo_set(nto_set(i))
END DO
DEALLOCATE (nto_set)
END IF
END DO
CALL cp_fm_release(fm_mo_coeff)
CALL cp_fm_struct_release(fm_struct_m)
CALL cp_fm_struct_release(fm_struct_nto_holes)
CALL cp_fm_struct_release(fm_struct_nto_particles)
CALL cp_fm_struct_release(fm_struct_mo_coeff)
CALL timestop(handle)
END SUBROUTINE calculate_NTOs
! **************************************************************************************************
!> \brief ...
!> \param exc_descr ...
!> \param fm_eigvec_X ...
!> \param fm_dipole_ij_trunc ...
!> \param fm_dipole_ab_trunc ...
!> \param fm_dipole_ai_trunc ...
!> \param fm_quadpole_ij_trunc ...
!> \param fm_quadpole_ab_trunc ...
!> \param homo ...
!> \param virtual ...
!> \param unit_nr ...
!> \param mp2_env ...
!> \param qs_env ...
!> \param fm_eigvec_Y ...
! **************************************************************************************************
SUBROUTINE get_exciton_descriptors(exc_descr, fm_eigvec_X, &
fm_dipole_ij_trunc, fm_dipole_ab_trunc, fm_dipole_ai_trunc, &
fm_quadpole_ij_trunc, fm_quadpole_ab_trunc, &
homo, virtual, unit_nr, &
mp2_env, qs_env, &
fm_eigvec_Y)
TYPE(exciton_descr_type), ALLOCATABLE, &
DIMENSION(:) :: exc_descr
TYPE(cp_fm_type), INTENT(IN) :: fm_eigvec_X
TYPE(cp_fm_type), ALLOCATABLE, DIMENSION(:), &
INTENT(IN) :: fm_dipole_ij_trunc, fm_dipole_ab_trunc, &
fm_dipole_ai_trunc, &
fm_quadpole_ij_trunc, &
fm_quadpole_ab_trunc
INTEGER, INTENT(IN) :: homo, virtual, unit_nr
TYPE(mp2_type), INTENT(INOUT) :: mp2_env
TYPE(qs_environment_type), POINTER :: qs_env
TYPE(cp_fm_type), INTENT(IN), OPTIONAL :: fm_eigvec_Y
CHARACTER(LEN=*), PARAMETER :: routineN = 'get_exciton_descriptors'
INTEGER :: handle, i_dir, i_exc, n_exc
INTEGER, DIMENSION(3) :: mask_quadrupole
LOGICAL :: flag_TDA
REAL(KIND=dp) :: norm_X, norm_XpY, norm_Y
REAL(KIND=dp), DIMENSION(3) :: r_e_h_XX, r_e_h_XY, r_e_h_YX, r_e_h_YY, &
r_e_sq_X, r_e_sq_Y, r_e_X, r_e_Y, &
r_h_sq_X, r_h_sq_Y, r_h_X, r_h_Y
TYPE(cp_fm_struct_type), POINTER :: fm_struct_ab, fm_struct_ia
TYPE(cp_fm_type) :: fm_work_ba, fm_work_ia, fm_work_ia_2, &
fm_X_ia, fm_Y_ia
TYPE(particle_type), DIMENSION(:), POINTER :: particle_set
TYPE(qs_kind_type), DIMENSION(:), POINTER :: qs_kind_set
TYPE(section_vals_type), POINTER :: input, subsys_section
CALL timeset(routineN, handle)
n_exc = homo*virtual
IF (PRESENT(fm_eigvec_Y)) THEN
flag_TDA = .FALSE.
ELSE
flag_TDA = .TRUE.
END IF
! translates 1,2,3 to diagonal entries of quadrupoles xx, yy, zz
! Ordering in quadrupole moments is x, y, z, xx, xy, xz, yy, yz, zz
mask_quadrupole = (/4, 7, 9/)
ALLOCATE (exc_descr(mp2_env%bse%num_print_exc_descr))
CALL cp_fm_struct_create(fm_struct_ia, &
fm_eigvec_X%matrix_struct%para_env, fm_eigvec_X%matrix_struct%context, &
homo, virtual)
CALL cp_fm_struct_create(fm_struct_ab, &
fm_eigvec_X%matrix_struct%para_env, fm_eigvec_X%matrix_struct%context, &
virtual, virtual)
! print actual coords (might be centered and differing from input xyz) for debug runs
IF (mp2_env%bse%bse_debug_print) THEN
CALL get_qs_env(qs_env, particle_set=particle_set, &
qs_kind_set=qs_kind_set, input=input)
subsys_section => section_vals_get_subs_vals(input, "SUBSYS")
IF (unit_nr > 0) THEN
WRITE (unit_nr, '(T2,A10,T13,A)') 'BSE|DEBUG|', &
'Printing internal geometry for debug purposes'
END IF
CALL write_qs_particle_coordinates(particle_set, qs_kind_set, subsys_section, label="BSE")
END IF
DO i_exc = 1, mp2_env%bse%num_print_exc_descr
r_e_X(:) = 0.0_dp
r_e_Y(:) = 0.0_dp
r_h_X(:) = 0.0_dp
r_h_Y(:) = 0.0_dp
r_e_sq_X(:) = 0.0_dp
r_h_sq_X(:) = 0.0_dp
r_e_sq_Y(:) = 0.0_dp
r_h_sq_Y(:) = 0.0_dp
r_e_h_XX(:) = 0.0_dp
r_e_h_XY(:) = 0.0_dp
r_e_h_YX(:) = 0.0_dp
r_e_h_YY(:) = 0.0_dp
norm_X = 0.0_dp
norm_Y = 0.0_dp
norm_XpY = 0.0_dp
! Initialize values of exciton descriptors
exc_descr(i_exc)%r_e(:) = 0.0_dp
exc_descr(i_exc)%r_h(:) = 0.0_dp
exc_descr(i_exc)%r_e_sq(:) = 0.0_dp
exc_descr(i_exc)%r_h_sq(:) = 0.0_dp
exc_descr(i_exc)%r_e_h(:) = 0.0_dp
exc_descr(i_exc)%flag_TDA = flag_TDA
exc_descr(i_exc)%norm_XpY = 0.0_dp
CALL reshuffle_eigvec(fm_eigvec_X, fm_X_ia, homo, virtual, i_exc, &
.FALSE., unit_nr, mp2_env)
! Norm of X
CALL cp_fm_trace(fm_X_ia, fm_X_ia, norm_X)
norm_XpY = norm_X
IF (.NOT. flag_TDA) THEN
CALL reshuffle_eigvec(fm_eigvec_Y, fm_Y_ia, homo, virtual, i_exc, &
.FALSE., unit_nr, mp2_env)
! Norm of Y
CALL cp_fm_trace(fm_Y_ia, fm_Y_ia, norm_Y)
norm_XpY = norm_XpY + norm_Y
END IF
exc_descr(i_exc)%norm_XpY = norm_XpY
! <r_h>_X = Tr[ X^T µ_ij X + Y µ_ab Y^T ] = X_ai µ_ij X_ja + Y_ia µ_ab Y_bi
DO i_dir = 1, 3
! <r_h>_X = X_ai µ_ij X_ja + ...
CALL trace_exciton_descr(fm_X_ia, fm_dipole_ij_trunc(i_dir), fm_X_ia, r_h_X(i_dir))
r_h_X(i_dir) = r_h_X(i_dir)/norm_XpY
IF (.NOT. flag_TDA) THEN
! <r_h>_X = ... + Y_ia µ_ab Y_bi
CALL trace_exciton_descr(fm_Y_ia, fm_Y_ia, fm_dipole_ab_trunc(i_dir), r_h_Y(i_dir))
r_h_Y(i_dir) = r_h_Y(i_dir)/norm_XpY
END IF
END DO
exc_descr(i_exc)%r_h(:) = r_h_X(:) + r_h_Y(:)
! <r_e>_X = Tr[ X µ_ab X^T + Y^T µ_ij Y ] = X_ia µ_ab X_bi + Y_ai µ_ij Y_ja
DO i_dir = 1, 3
! <r_e>_X = work_ib X_bi + ... = X_ib^T work_ib + ...
CALL trace_exciton_descr(fm_X_ia, fm_X_ia, fm_dipole_ab_trunc(i_dir), r_e_X(i_dir))
r_e_X(i_dir) = r_e_X(i_dir)/norm_XpY
IF (.NOT. flag_TDA) THEN
! <r_e>_X = ... + Y_ai µ_ij Y_ja
CALL trace_exciton_descr(fm_Y_ia, fm_dipole_ij_trunc(i_dir), fm_Y_ia, r_e_Y(i_dir))
r_e_Y(i_dir) = r_e_Y(i_dir)/norm_XpY
END IF
END DO
exc_descr(i_exc)%r_e(:) = r_e_X(:) + r_e_Y(:)
! <r_h^2>_X = Tr[ X^T M_ij X + Y M_ab Y^T ] = X_ai M_ij X_ja + Y_ia M_ab Y_bi
DO i_dir = 1, 3
! <r_h^2>_X = X_ai M_ij X_ja + ...
CALL trace_exciton_descr(fm_X_ia, fm_quadpole_ij_trunc(mask_quadrupole(i_dir)), &
fm_X_ia, r_h_sq_X(i_dir))
r_h_sq_X(i_dir) = r_h_sq_X(i_dir)/norm_XpY
IF (.NOT. flag_TDA) THEN
! <r_h^2>_X = ... + Y_ia M_ab Y_bi
CALL trace_exciton_descr(fm_Y_ia, fm_Y_ia, &
fm_quadpole_ab_trunc(mask_quadrupole(i_dir)), r_h_sq_Y(i_dir))
r_h_sq_Y(i_dir) = r_h_sq_Y(i_dir)/norm_XpY
END IF
END DO
exc_descr(i_exc)%r_h_sq(:) = r_h_sq_X(:) + r_h_sq_Y(:)
! <r_e^2>_X = Tr[ X M_ab X^T + Y^T M_ij Y ] = X_ia M_ab X_bi + Y_ai M_ij Y_ja
DO i_dir = 1, 3
! <r_e^2>_X = work_ib X_bi + ... = X_ib^T work_ib + ...
CALL trace_exciton_descr(fm_X_ia, fm_X_ia, &
fm_quadpole_ab_trunc(mask_quadrupole(i_dir)), r_e_sq_X(i_dir))
r_e_sq_X(i_dir) = r_e_sq_X(i_dir)/norm_XpY
IF (.NOT. flag_TDA) THEN
! <r_e^2>_X = ... + Y_ai M_ij Y_ja
CALL trace_exciton_descr(fm_Y_ia, fm_quadpole_ij_trunc(mask_quadrupole(i_dir)), &
fm_Y_ia, r_e_sq_Y(i_dir))
r_e_sq_Y(i_dir) = r_e_sq_Y(i_dir)/norm_XpY
END IF
END DO
exc_descr(i_exc)%r_e_sq(:) = r_e_sq_X(:) + r_e_sq_Y(:)
! <r_h r_e>_X
! = Tr[ X^T µ_ij X µ_ab + Y^T µ_ij Y µ_ab + X µ_ai Y µ_ai + Y µ_ai X µ_ai]
! = X_bj µ_ji X_ia µ_ab + Y_bj µ_ji Y_ia µ_ab + X_ia µ_aj Y_jb µ_bi + Y_ia µ_aj X_jb µ_bi
CALL cp_fm_create(fm_work_ia, fm_struct_ia)
CALL cp_fm_create(fm_work_ia_2, fm_struct_ia)
CALL cp_fm_create(fm_work_ba, fm_struct_ab)
DO i_dir = 1, 3
! First term - X^T µ_ij X µ_ab
CALL cp_fm_set_all(fm_work_ia, 0.0_dp)
CALL cp_fm_set_all(fm_work_ia_2, 0.0_dp)
! work_ib = X_ia µ_ab
CALL parallel_gemm("N", "N", homo, virtual, virtual, 1.0_dp, &
fm_X_ia, fm_dipole_ab_trunc(i_dir), 0.0_dp, fm_work_ia)
! work_ja_2 = µ_ji work_ia
CALL parallel_gemm("N", "N", homo, virtual, homo, 1.0_dp, &
fm_dipole_ij_trunc(i_dir), fm_work_ia, 0.0_dp, fm_work_ia_2)
! <r_h r_e>_X = work_ia_2 X_bj + ... = X^T work_ia_2 + ...
CALL cp_fm_trace(fm_X_ia, fm_work_ia_2, r_e_h_XX(i_dir))
r_e_h_XX(i_dir) = r_e_h_XX(i_dir)/norm_XpY
IF (.NOT. flag_TDA) THEN
! Second term - Y^T µ_ij Y µ_ab
CALL cp_fm_set_all(fm_work_ia, 0.0_dp)
CALL cp_fm_set_all(fm_work_ia_2, 0.0_dp)
! work_ib = Y_ia µ_ab
CALL parallel_gemm("N", "N", homo, virtual, virtual, 1.0_dp, &
fm_Y_ia, fm_dipole_ab_trunc(i_dir), 0.0_dp, fm_work_ia)
! work_ja_2 = µ_ji work_ia
CALL parallel_gemm("N", "N", homo, virtual, homo, 1.0_dp, &
fm_dipole_ij_trunc(i_dir), fm_work_ia, 0.0_dp, fm_work_ia_2)
! <r_h r_e>_X = work_ia_2 Y_bj + ... = Y^T work_ia_2 + ...
CALL cp_fm_trace(fm_Y_ia, fm_work_ia_2, r_e_h_YY(i_dir))
r_e_h_YY(i_dir) = r_e_h_YY(i_dir)/norm_XpY
! Third term - X µ_ai Y µ_ai = X_ia µ_aj Y_jb µ_bi
! Reshuffle for usage of trace (where first argument is transposed)
! = µ_aj Y_jb µ_bi X_ia =
! \__________/
! fm_work_ai
! fm_work_ai = µ_aj Y_jb µ_bi
! fm_work_ia = µ_ib Y_bj µ_ja
! \_____/
! fm_work_ba
CALL cp_fm_set_all(fm_work_ba, 0.0_dp)
CALL cp_fm_set_all(fm_work_ia, 0.0_dp)
! fm_work_ba = Y_bj µ_ja
CALL parallel_gemm("T", "T", virtual, virtual, homo, 1.0_dp, &
fm_Y_ia, fm_dipole_ai_trunc(i_dir), 0.0_dp, fm_work_ba)
! fm_work_ia = µ_ib fm_work_ba
CALL parallel_gemm("T", "N", homo, virtual, virtual, 1.0_dp, &
fm_dipole_ai_trunc(i_dir), fm_work_ba, 0.0_dp, fm_work_ia)
! <r_h r_e>_X = ... + X_ia µ_aj Y_jb µ_bi
CALL cp_fm_trace(fm_work_ia, fm_X_ia, r_e_h_XY(i_dir))
r_e_h_XY(i_dir) = r_e_h_XY(i_dir)/norm_XpY
! Fourth term - Y µ_ai X µ_ai = Y_ia µ_aj X_jb µ_bi
! Reshuffle for usage of trace (where first argument is transposed)
! = µ_aj X_jb µ_bi Y_ia =
! \__________/
! fm_work_ai
! fm_work_ai = µ_aj X_jb µ_bi
! fm_work_ia = µ_ib X_bj µ_ja
! \_____/
! fm_work_ba
CALL cp_fm_set_all(fm_work_ba, 0.0_dp)
CALL cp_fm_set_all(fm_work_ia, 0.0_dp)
! fm_work_ba = Y_bj µ_ja
CALL parallel_gemm("T", "T", virtual, virtual, homo, 1.0_dp, &
fm_X_ia, fm_dipole_ai_trunc(i_dir), 0.0_dp, fm_work_ba)
! fm_work_ia = µ_ib fm_work_ba
CALL parallel_gemm("T", "N", homo, virtual, virtual, 1.0_dp, &
fm_dipole_ai_trunc(i_dir), fm_work_ba, 0.0_dp, fm_work_ia)
! <r_h r_e>_X = ... + X_ia µ_aj Y_jb µ_bi
CALL cp_fm_trace(fm_work_ia, fm_Y_ia, r_e_h_YX(i_dir))
r_e_h_YX(i_dir) = r_e_h_YX(i_dir)/norm_XpY
END IF
END DO
exc_descr(i_exc)%r_e_h(:) = r_e_h_XX(:) + r_e_h_XY(:) + r_e_h_YX(:) + r_e_h_YY(:)
CALL cp_fm_release(fm_work_ia)
CALL cp_fm_release(fm_work_ia_2)
CALL cp_fm_release(fm_work_ba)
! diff_r_abs = |<r_h>_X - <r_e>_X|
exc_descr(i_exc)%diff_r_abs = SQRT(SUM((exc_descr(i_exc)%r_h(:) - exc_descr(i_exc)%r_e(:))**2))
! σ_e = sqrt( <r_e^2>_X - <r_e>_X^2 )
exc_descr(i_exc)%sigma_e = SQRT(SUM(exc_descr(i_exc)%r_e_sq(:)) - SUM(exc_descr(i_exc)%r_e(:)**2))
! σ_h = sqrt( <r_h^2>_X - <r_h>_X^2 )
exc_descr(i_exc)%sigma_h = SQRT(SUM(exc_descr(i_exc)%r_h_sq(:)) - SUM(exc_descr(i_exc)%r_h(:)**2))
! COV(r_e, r_h) = < r_e r_h >_X - < r_e >_X < r_h >_X
exc_descr(i_exc)%cov_e_h_sum = 0.0_dp
exc_descr(i_exc)%cov_e_h(:) = 0.0_dp
DO i_dir = 1, 3
exc_descr(i_exc)%cov_e_h(i_dir) = exc_descr(i_exc)%r_e_h(i_dir) &
- exc_descr(i_exc)%r_e(i_dir)*exc_descr(i_exc)%r_h(i_dir)
exc_descr(i_exc)%cov_e_h_sum = exc_descr(i_exc)%cov_e_h_sum + &
exc_descr(i_exc)%r_e_h(i_dir) - exc_descr(i_exc)%r_e(i_dir)*exc_descr(i_exc)%r_h(i_dir)
END DO
! root-mean-square e-h separation
exc_descr(i_exc)%diff_r_sqr = SQRT(exc_descr(i_exc)%diff_r_abs**2 + &
exc_descr(i_exc)%sigma_e**2 + exc_descr(i_exc)%sigma_h**2 &
- 2*exc_descr(i_exc)%cov_e_h_sum)
! e-h-correlation coefficient R_eh = COV(r_e, r_h) / ( σ_e σ_h )
exc_descr(i_exc)%corr_e_h = exc_descr(i_exc)%cov_e_h_sum/(exc_descr(i_exc)%sigma_e*exc_descr(i_exc)%sigma_h)
! Expectation values of r_e and r_h
exc_descr(i_exc)%r_e_shift(:) = exc_descr(i_exc)%r_e(:)
exc_descr(i_exc)%r_h_shift(:) = exc_descr(i_exc)%r_h(:)
CALL cp_fm_release(fm_X_ia)
IF (.NOT. flag_TDA) THEN
CALL cp_fm_release(fm_Y_ia)
END IF
END DO
CALL cp_fm_struct_release(fm_struct_ia)
CALL cp_fm_struct_release(fm_struct_ab)
CALL timestop(handle)
END SUBROUTINE get_exciton_descriptors
END MODULE bse_properties