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
992
993
994
995
996
997
998
999
1000
1001
1002
1003
1004
1005
1006
1007
1008
1009
1010
1011
1012
1013
1014
1015
1016
1017
1018
1019
1020
1021
1022
1023
1024
1025
|
SUBROUTINE SYMPOP(H,I,ISKIP,DELDIP)
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
INCLUDE 'SIZES'
DIMENSION H(*), DELDIP(3,*)
COMMON /SYMOPS/ R(14,120), NSYM, IPO(NUMATM,120), NENT
COMMON /SYMOPC/ ISYMT(6)
CHARACTER*10 ISYMT
COMMON /ATOMS/ COORD, NATOMS, NVAR
DO 10 J = 1, NSYM
IF (IPO(I,J).LT.I) THEN
CALL SYMH(H, DELDIP, I, J)
ISKIP=3
C atom ipo(i,j) is suitable for transition dipole calc'n
C
K=I*3-2
C
C INSERT DELDIP ROTATION HERE
C
GOTO 20
ENDIF
10 CONTINUE
ISKIP=0
20 CONTINUE
RETURN
END
SUBROUTINE SYMR
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
INCLUDE 'SIZES'
COMMON /SYMOPS/ R(14,120), NSYM, IPO(NUMATM,120), NENT
COMMON /SYMOPC/ ISYMT(6)
CHARACTER*10 ISYMT
*****************************************************************
*
* ON INPUT NONE
*
* ON OUTPUT R = SYMMETRY OPERATIONS
* IPO = PERMUTATION OPERATOR FOR SYMMETRY OPERATIONS
* NSYM = NUMBER OF SYMMETRY OPERATIONS
* NENT = NUMBER OF SYMMETRY OPERATIONS ENTERED
*
*****************************************************************
C
C A SUBROUTINE THAT WILL READ IN THE PRIMATIVE SYMMETRY OPERATIONS
C AND DETERMINE IF THEY ARE VALID FOR THIS MOLECULE. THIS
C INFORMATION IS THEN EXPANDED TO THE COMPLETE SET AND USED FOR
C SYMMATRIZING THE HESSIAN.
C
C THE CORRECT FORMAT FOR DESCRIBING A SYMMETRY FUNCTION IS:
C LABEL IFNCN AXIS
C
C WHERE:
C LABEL - MUST BE INCLUDED AND IS THE LABEL THAT WILL
C BE USED TO IDENTIFY THAT FUNCTION
C IFNCN - THE NUMBER OF THE SYMMETRY FUNCTION TO BE USED:
C 0 - INVERSION OPERATOR
C 1 - REFLECTION PLANE PERPENDICULAR TO THE AXIS
C 2-X - A C(N) AXIS
C -3-X - A S(N) AXIS
C AXIS - THE AXIS FOR THE OPERATION. MAY BE SPECIFIED AS:
C X, Y, Z COORDINATES -> MUST USE 3 VALUES. AT LEAST ONE
C MUST BE NON-INTEGER OR TWO MUST BE IDENTICAL
C AN ATOM LIST -> THE COORDINATES OF THE ATOMS LISTED WILL
C BE SUMMED TO GENERATE THE AXIS.
C A -B -> THE VECTOR FROM ATOM B TO ATOM A WILL BE USED AS
C THE AXIS.
C
C A MAXIMUM OF 6 SYMMETRY OPERATIONS CAN BE INPUTTED. THESE SHOULD BE THE
C UNIQUE GENERATING FUNCTIONS FROM WHICH ALL THE OPERATIONS OF THE GROUP
C CAN BE CONSTRUCTED. E.G. ONLY C5 NEEDS TO BE SPECIFIED SINCE C5(2)
C THROUGH C5(4) CAN BE GENERATED FROM THIS SINGLE FUNCTION.
C
C A MAXIMUM OF 8 UNIQUE ATOMS CAN BE USED TO SPECIFY AN AXIS.
C
C THE E FUNCTION IS BY DEFAULT THE FIRST SYMMETRY FUNCTION. THIS FUNCTION
C NEVER NEEDS TO BE EXPLICTLY INCLUDED IN YOUR LIST. IT CANNOT BE
C ENTERED.
C
C IF YOU ENTER A GIVEN SYMMETRY FUNCTION MORE THAN ONCE, ONLY THE FIRST
C OCCURANCE WILL BE USED. ALL DUPLICATES WILL BE DELETED.
C
DIMENSION TEMP(9), TEMP2(9), ISTART(7)
INTEGER ITEMP(9)
COMMON /MOLKST/ NUMAT,NAT(NUMATM),NFIRST(NUMATM),NMIDLE(NUMATM),
1 NLAST(NUMATM), NORBS, NELECS,NALPHA,NBETA,
2 NCLOSE,NOPEN,NDUMY,FRACT
COMMON /COORD / COORD(3,NUMATM)
COMMON /KEYWRD/ KEYWRD
CHARACTER KEYWRD*241
CHARACTER*80 LINE
LOGICAL LEADSP, PROB, ALLINT
C THE NEXT PARAMETERS ARE THE MAX NUMBER OF SYMM FUNCTIONS, THE
C MAX NUMBER OF SYMM FUNCTIONS TO READ IN, AND THE
C TOLERENCE USED TO DETERMINE IF TWO FUNCTIONS ARE IDENTICAL
PARAMETER (MAXFUN=120)
PARAMETER (MAXENT=6)
PARAMETER (TOL =1D-3)
C
C
C Variables used: (n represents the number of atomic centers)
C TEMP(9), TEMP2(9): Temporary matricies used to hold small parts
C larger matricies for specific matrix operations.
C
C For the next two items, the last index represents the symmetry
C operation number.
C R(9,*): The 9 elements of each record are a packed 3 by 3
C array of a given symmetry operations.
C IPO(n,*): A vector that contains the symmetry mapping of atomic ce
C
PROB = .FALSE.
C Get the symmetry functions: (NOTE: THE FIRST IS ALWAY E)
R(1,1) = 1.D0
R(2,1) = 0.D0
R(3,1) = 0.D0
R(4,1) = 0.D0
R(5,1) = 1.D0
R(6,1) = 0.D0
R(7,1) = 0.D0
R(8,1) = 0.D0
R(9,1) = 1.D0
C
X = 0.D0
Y = 0.D0
Z = 0.D0
DO 10 I=1,NUMAT
X = X + COORD(1,I)
Y = Y + COORD(2,I)
Z = Z + COORD(3,I)
IPO(I,1) = I
10 CONTINUE
XA = X/FLOAT(NUMAT)
YA = Y/FLOAT(NUMAT)
ZA = Z/FLOAT(NUMAT)
DO 20 I=1,NUMAT
COORD(1,I) = -XA + COORD(1,I)
COORD(2,I) = -YA + COORD(2,I)
COORD(3,I) = -ZA + COORD(3,I)
20 CONTINUE
WRITE(6,'(/'' SYMMETRY OPERATIONS USED FOR SYMMETRIZING'',
1'' THE HESSIAN'')')
WRITE(6,'(/,'' OPERATOR TYPE AXIS DEFINITION '')')
C
NENT = 1
NSYM = 0
ISYMT(1)='E'
30 NSYM = NSYM + 1
READ(5,'(A)',END=120,ERR=120)LINE
LEADSP=.TRUE.
NVALUE=0
ALLINT=.TRUE.
DO 40 I=1,80
IF (LEADSP.AND.LINE(I:I).NE.' ') THEN
NVALUE=NVALUE+1
ISTART(NVALUE)=I
ENDIF
LEADSP=(LINE(I:I).EQ.' ')
40 CONTINUE
IF (NVALUE.EQ.0) GOTO 120
IF (NVALUE.EQ.1) THEN
WRITE(6,200)
200 FORMAT(' NOT A VALID LINE. ONLY HAS ONE ENTRY')
PROB = .TRUE.
GOTO 120
ENDIF
ISYMT(1+NENT)=LINE(ISTART(1):ISTART(2)-1)
DO 50 I=2,NVALUE
TEMP(I-1)=READA(LINE,ISTART(I))
ITEMP(I-1)=NINT(TEMP(I-1))
IF((ABS(ITEMP(I-1)-TEMP(I-1)).GT.TOL).AND.(I.NE.2))
+ ALLINT=.FALSE.
50 CONTINUE
IF (ALLINT) THEN
WRITE(6,210)ISYMT(1+NENT),(ITEMP(I),I=1,NVALUE-1)
210 FORMAT(X,A10,I7,8I7)
ELSE
WRITE(6,220)ISYMT(1+NENT),ITEMP(1),(TEMP(I),I=2,NVALUE-1)
220 FORMAT(X,A10,I7,8F7.3)
ENDIF
SIGMA = 1
IF (ITEMP(1) .LE. -3) SIGMA = -1
TEMP(1) = ABS( TEMP(1))
ITEMP(1)= ABS(ITEMP(1))
IF (ABS(ITEMP(1)-TEMP(1)) .GE. TOL) THEN
WRITE(6,230)
230 FORMAT(' THE SYMMETRY FUNCTION MUST BE INTEGER')
PROB = .TRUE.
GOTO 120
ENDIF
IF (ITEMP(1) .EQ. 0) THEN
C WITH INVERSION, THE AXIS IS UNIMPORTANT
R(1,1+NENT) = -1.D0
R(2,1+NENT) = 0.D0
R(3,1+NENT) = 0.D0
R(4,1+NENT) = 0.D0
R(5,1+NENT) = -1.D0
R(6,1+NENT) = 0.D0
R(7,1+NENT) = 0.D0
R(8,1+NENT) = 0.D0
R(9,1+NENT) = -1.D0
GOTO 70
ENDIF
C WITH ANYTHING ELSE, THE AXIS MUST BE DETERMINED. IF NO AXIS IS DEFINED
C FLAG IT AS A PROBLEM
IF (NVALUE .EQ. 2) THEN
PROB = .TRUE.
WRITE(6,240) NSYM
240 FORMAT(' NO AXIS INFORMATION WAS ENTERED FOR FUNCTION',I2)
GOTO 120
ENDIF
IF ((NVALUE .EQ. 5).AND.((TEMP(2).EQ.TEMP(3))
+ .OR.(TEMP(2).EQ.TEMP(4)).OR.
+ (TEMP(3).EQ.TEMP(4)).OR.(.NOT. ALLINT).OR.
+ (ABS(ITEMP(2)).LT. 1).OR.(ABS(ITEMP(2)).GT.NUMAT) .OR.
+ (ABS(ITEMP(3)).LT. 1).OR.(ABS(ITEMP(3)).GT.NUMAT) .OR.
+ (ABS(ITEMP(4)).LT. 1).OR.(ABS(ITEMP(4)).GT.NUMAT))) THEN
C IT APPEARS TO BE XYZ INPUT
X = TEMP(2)
Y = TEMP(3)
Z = TEMP(4)
ELSE
C APPEARS TO BE ATOM NUMBER INPUT
IF (.NOT. ALLINT) THEN
PROB = .TRUE.
WRITE(6,250)
250 FORMAT(' YOU MUST HAVE ALL INTEGER INPUT WHEN NOT',
+ ' USING XYZ INPUT')
GOTO 120
ENDIF
X = 0.D0
Y = 0.D0
Z = 0.D0
DO 60 I = 2, NVALUE-1
IF ((ABS(ITEMP(I)).LT.1).OR.(ABS(ITEMP(I)).GT.NUMAT)) THEN
WRITE(6,260)ITEMP(I)
260 FORMAT(' ATOM NUMBER',I3,' IS OUT OF RANGE')
PROB=.TRUE.
ENDIF
X = X + ITEMP(I)/ABS(ITEMP(I))*COORD(1,ABS(ITEMP(I)))
Y = Y + ITEMP(I)/ABS(ITEMP(I))*COORD(2,ABS(ITEMP(I)))
Z = Z + ITEMP(I)/ABS(ITEMP(I))*COORD(3,ABS(ITEMP(I)))
60 CONTINUE
ENDIF
C
C TIME TO DECIPHER THE SYMMETRY FUNCTION
C
IF (ITEMP(1) .GT. 10) THEN
WRITE(6,270)
270 FORMAT(' A C-10 AXIS IS THE HIGHEST THAT CAN BE SPECIFIED')
PROB = .TRUE.
GOTO 120
ENDIF
ROT=4.D0*ASIN(1.D0)/ITEMP(1)
IF(ITEMP(1).EQ. 1) SIGMA = -1
C
C First, construct the matrix defining the rotation axis
XY=X**2+Y**2
RA=SQRT(XY+Z**2)
IF (RA.LT. TOL) THEN
PROB = .TRUE.
WRITE(6,280)
280 FORMAT(' YOUR VECTOR AXIS MUST HAVE A NON-ZERO LENGTH ')
GOTO 120
ENDIF
XY=SQRT(XY)
IF (XY.GT.1.D-10) THEN
CA=Y/XY
CB=Z/RA
SA=X/XY
SB=XY/RA
ELSEIF (Z.GT. 0.D0) THEN
CA=1.D0
CB=1.D0
SA=0.D0
SB=0.D0
ELSE
CA=-1.D0
CB=-1.D0
SA=0.D0
SB=0.D0
ENDIF
C GENERATE THE MATRIX ELEMENTS BY DOING THE EULER TRANSFORM
TEMP( 1)=CA
TEMP( 2)=-SA
TEMP( 3)=0.D0
TEMP( 4)=SA*CB
TEMP( 5)=CA*CB
TEMP( 6)=-SB
TEMP( 7)=SA*SB
TEMP( 8)=CA*SB
TEMP( 9)=CB
C
C
CA = DCOS(ROT)
SA = DSIN(ROT)
C
C The construct the actual R matrix to be used
C
C
TEMP2(1) = CA
TEMP2(2) = SA
TEMP2(3) = 0.D0
TEMP2(4) = -SA
TEMP2(5) = CA
TEMP2(6) = 0.D0
TEMP2(7) = 0.D0
TEMP2(8) = 0.D0
TEMP2(9) = SIGMA
CALL MAT33(TEMP, TEMP2, R(1,1+NENT))
C
C Now, verify that this is a unique and valid function
70 CONTINUE
C
RES = 10.D0
DO 90 I = 2, NENT
RESO = 0.D0
DO 80 J = 1, 9
80 RESO= ABS( R(J,I) - R(J,1+NENT)) + RESO
RES = MIN(RES, RESO)
90 CONTINUE
IF (RES .LT. TOL) THEN
C THIS IS NOT VALID FUNCTION
WRITE(6,290)
290 FORMAT(' THIS FUNCTION IS IDENTICAL TO AN EARLIER ONE')
GOTO 120
ENDIF
C NOW, TO CALCULATE THE IPO OF THIS FUNCTION
NENT = 1+NENT
N = NENT
C Now, to initialize IPO(n) and
C Perform R on each atomic center and determine where it maps to.
DO 110 I = 1, NUMAT
X=COORD(1,I)*R(1,N) + COORD(2,I)*R(2,N) + COORD(3,I)*R(3,N)
Y=COORD(1,I)*R(4,N) + COORD(2,I)*R(5,N) + COORD(3,I)*R(6,N)
Z=COORD(1,I)*R(7,N) + COORD(2,I)*R(8,N) + COORD(3,I)*R(9,N)
IPO(I,N) = 0
DO 100 J = 1, NUMAT
DIST=ABS(X-COORD(1,J))+ABS(Y-COORD(2,J))+ABS(Z-COORD(3,J))
IF (DIST .LT. 5.D-2) THEN
IF (IPO(I,N) .EQ. 0) THEN
IPO(I,N) = J
ELSE
WRITE(6,300)
PROB = .TRUE.
GOTO 120
300 FORMAT(' ONE ATOM MAPS ONTO TWO DIFFERENT ATOMIC C',
1'ENTERS')
ENDIF
ENDIF
100 CONTINUE
IF (IPO(I,N) .EQ. 0) THEN
WRITE(6,310)
310 FORMAT(' ONE ATOM MAPS ONTO NO OTHER ATOM ')
PROB = .TRUE.
GOTO 120
ENDIF
110 CONTINUE
C
C IF THIS POINT IS REACHED, THE FUNCTION IS VALID
C CHECK IF THE R MATRIX SHOULD BE PRINTED
C
IF (INDEX(KEYWRD,' RMAT') .NE. 0) THEN
WRITE(6,320)(R(I,N),I=1,3)
WRITE(6,330)N,(R(I,N),I=4,6)
WRITE(6,340)(R(I,N),I=7,9)
320 FORMAT(/,10X,'| ',3F10.6,' |')
330 FORMAT(I5,' = | ',3F10.6,' |')
340 FORMAT(10X,'| ',3F10.6,' |',/)
ENDIF
C
120 IF((NVALUE.NE.0).AND.(NSYM.LT.MAXENT)) GOTO 30
C
C If a problem exists. Stop the program.
C
IF (PROB) THEN
CLOSE (6)
STOP 'PROBLEM IN SYMR'
ENDIF
C
C NOW, ALL USER FUNCTIONS ARE IN WITH NO ERRORS (JUST ELIMINATION OF DUPS)
C
IF(NVALUE.NE.0) READ(5,'(A)',END=130)LINE
130 CONTINUE
NSYM = NENT
C
C NEXT, EXPAND THE EXISTING OPERATORS TO THE FULL SET
C
CALL SYMP
C
RETURN
END
SUBROUTINE SYMH(H, DIP, I, N)
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
INCLUDE 'SIZES'
DIMENSION H(*), DIP(3,*)
COMMON /SYMOPS/ R(14,120), NSYM, IPO(NUMATM,120), NENT
COMMON /SYMOPC/ ISYMT(6)
CHARACTER*10 ISYMT
*****************************************************************
*
C INPUT: H() A packed lower triangular hessian
C DIP(,) A MATRIX OF DIPOLE TENSORS TO BE SYMM
C R(,) A matrix of symmetry operations
C IPO(,) A matrix of atomic mapping according to R
C I The atom (row and column) to add to H()
C N The symmetry operation to use to generate I
C
C OUTPUT: H() A packed lower triangular Hessian with information
C about atom I added
C DIP(,) A MATRIX OF DIPOLE TENSORS THAT HAVE BEEN SYMM
C
*****************************************************************
C
C
C This subroutine will add all necessary information to the Hessian con
C atom I. Since the Hessian is a packed lower half triangle, the exi
C information for atom pair (K,L) where K,L < I is fully known, (K >
C L < I) or (vice versa) is half known, K,L > I is completely unknown
C Therefore, start in unknown region and make it half known. Double
C known values, and move in the diagonal element at full strength.
C
C
DIMENSION TEMP(9), TEMP2(9)
COMMON /FOKMAT/ HA(MPACK*2)
COMMON /MOLKST/ NUMAT,NAT(NUMATM),NFIRST(NUMATM),NMIDLE(NUMATM),
1 NLAST(NUMATM), NORBS, NELECS,NALPHA,NBETA,
2 NCLOSE,NOPEN,NDUMY,FRACT
COMMON /COORD / COORD(3,NUMATM)
C
C
C
C Variables used: (n represents the number of atomic centers)
C H(3n,3n): Input/output matrix. It is a packed lower half triangu
C matrix. Commonly, the Hessian.
C TEMP(9), TEMP2(9): Temporary matricies used to hold small parts
C larger matricies for specific matrix operations.
C
C For the next two items, the last indicy represents the symmetry
C operation number.
C R(14,*): The first 9 elements of each record are a packed 3 by 3
C array of a given symmetry operations. Elements 10 - 14 are t
C users input describing the symmetry operation.
C IPO(n,*): A vector that contains the symmetry mapping of atomic c
C
C
K = IPO(I,N)
C
C Now, to climb up the matrix
DO 10 J = NUMAT, I+1, -1
L = IPO(J,N)
C
C Now, to actually perform R H R
C
C Do this multiplication in a 3 by 3 block at a time. Store H(i,j) in
C H( IPO(I,N), IPO(J,N))
C
IF (K .GT. L) THEN
IEL33 = (3*K*(3*K-1))/2 + 3*L
TEMP(9) = 0.5D0 * H(IEL33)
TEMP(8) = 0.5D0 * H(IEL33-1)
TEMP(7) = 0.5D0 * H(IEL33-2)
TEMP(6) = 0.5D0 * H(IEL33-K*3+1)
TEMP(5) = 0.5D0 * H(IEL33-K*3)
TEMP(4) = 0.5D0 * H(IEL33-K*3-1)
TEMP(3) = 0.5D0 * H(IEL33-6*K+3)
TEMP(2) = 0.5D0 * H(IEL33-6*K+2)
TEMP(1) = 0.5D0 * H(IEL33-6*K+1)
ELSE
IEL33 = (3*L*(3*L-1))/2 + 3*K
FACT = 1.0D0
IF (L .LT. I) FACT = 0.5D0
TEMP(9) = FACT * H(IEL33)
TEMP(6) = FACT * H(IEL33-1)
TEMP(3) = FACT * H(IEL33-2)
TEMP(8) = FACT * H(IEL33-L*3+1)
TEMP(5) = FACT * H(IEL33-L*3)
TEMP(2) = FACT * H(IEL33-L*3-1)
TEMP(7) = FACT * H(IEL33-6*L+3)
TEMP(4) = FACT * H(IEL33-6*L+2)
TEMP(1) = FACT * H(IEL33-6*L+1)
ENDIF
C
CALL MAT33(R(1,N), TEMP, TEMP2)
C
IEL33 = J*3*(J*3-1)/2 + I*3
H(IEL33) = TEMP2(9)
H(IEL33-3*J+1) = TEMP2(8)
H(IEL33-6*J+3) = TEMP2(7)
H(IEL33-1) = TEMP2(6)
H(IEL33-3*J) = TEMP2(5)
H(IEL33-6*J+2) = TEMP2(4)
H(IEL33-2) = TEMP2(3)
H(IEL33-3*J-1) = TEMP2(2)
H(IEL33-6*J+1) = TEMP2(1)
10 CONTINUE
C
C Now, to do the diagonal term
C
IEL33 = (3*K*(3*K+1))/2
TEMP(9) = 0.5D0 * H(IEL33)
TEMP(8) = 0.5D0 * H(IEL33-1)
TEMP(7) = 0.5D0 * H(IEL33-2)
TEMP(6) = TEMP(8)
TEMP(5) = 0.5D0 * H(IEL33-K*3)
TEMP(4) = 0.5D0 * H(IEL33-K*3-1)
TEMP(3) = TEMP(7)
TEMP(2) = TEMP(4)
TEMP(1) = 0.5D0 * H(IEL33-6*K+1)
C
CALL MAT33(R(1,N), TEMP, TEMP2)
C
IEL33 = I*3*(I*3+1)/2
H(IEL33) = TEMP2(9)
H(IEL33-1) = TEMP2(8)
H(IEL33-2) = TEMP2(7)
H(IEL33-I*3) = TEMP2(5)
H(IEL33-I*3-1) = TEMP2(4)
H(IEL33-6*I+1) = TEMP2(1)
C
C NOW, TO ROTATE THE DIPOLE TENSOR TERM
C
TEMP(9) = DIP(3,K*3 )
TEMP(8) = DIP(2,K*3 )
TEMP(7) = DIP(1,K*3 )
TEMP(6) = DIP(3,K*3-1)
TEMP(5) = DIP(2,K*3-1)
TEMP(4) = DIP(1,K*3-1)
TEMP(3) = DIP(3,K*3-2)
TEMP(2) = DIP(2,K*3-2)
TEMP(1) = DIP(1,K*3-2)
C
CALL MAT33(R(1,N), TEMP, TEMP2)
C
DIP(3,I*3 ) = TEMP2(9)
DIP(2,I*3 ) = TEMP2(8)
DIP(1,I*3 ) = TEMP2(7)
DIP(3,I*3-1) = TEMP2(6)
DIP(2,I*3-1) = TEMP2(5)
DIP(1,I*3-1) = TEMP2(4)
DIP(3,I*3-2) = TEMP2(3)
DIP(2,I*3-2) = TEMP2(2)
DIP(1,I*3-2) = TEMP2(1)
C
C
C Now, to double all existing values going across
ISTART = (I-1)*3*((I-1)*3+1)/2+1
DO 20 J = ISTART, IEL33
H(J) = H(J) + H(J)
20 CONTINUE
C Everything is now done for this symmetry element.
C
RETURN
END
SUBROUTINE SYMA(E, V)
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
INCLUDE 'SIZES'
DIMENSION E(NUMAT*3), V(NUMAT*NUMAT*9)
COMMON /SYMOPS/ R(14,120), NSYM, IPO(NUMATM,120), NENT
COMMON /SYMOPC/ ISYMT(6)
CHARACTER*10 ISYMT
*********************************************************************
*
* ON INPUT E = FREQUENCIES IN CM(-1)
* V = EIGENVECTORS OF NORMAL MODES, NORMALIZED
* R = SYMMETRY OPERATIONS
* IPO = MAP OF ATOMS BEING MOVED
* NSYM = NUMBER OF SYMMETRY OPERATION
*
*********************************************************************
C
C THIS SUBROUTINE DETERMINES THE SYMMETRY FUNCTION VALUE OF EACH
C VIBRATIONAL MODE. IT DOES IT BY DOING <EV R EV>
C
COMMON /COORD / COORD(3,NUMATM)
COMMON /KEYWRD/ KEYWRD
DIMENSION T1(MAXPAR), T2(MAXPAR,7)
COMMON /MOLKST/ NUMAT,NAT(NUMATM),NFIRST(NUMATM),NMIDLE(NUMATM),
1 NLAST(NUMATM), NORBS, NELECS,NALPHA,NBETA,
2 NCLOSE,NOPEN,NDUMY,FRACT
CHARACTER KEYWRD*241
C
TOL=1.D-3
C
NVAR=NUMAT*3
C
C T1(NVAR) AND T2(NVAR,NSYM) ARE THE ONLY ADDITIONAL ARRAYS NEEDED. TH
C ARE TEMPORARY ARRAYS.
DO 30 K = 0, NVAR-1
DO 20 N = 1, NENT
DO 10 I = 1, NUMAT
C
J=IPO(I,N)
T1(I*3-2)=V(J*3-2+K*NVAR)*R(1,N)+
1 V(J*3-1+K*NVAR)*R(4,N)+
2 V(J*3 +K*NVAR)*R(7,N)
T1(I*3-1)=V(J*3-2+K*NVAR)*R(2,N)+
1 V(J*3-1+K*NVAR)*R(5,N)+
2 V(J*3 +K*NVAR)*R(8,N)
T1(I*3 )=V(J*3-2+K*NVAR)*R(3,N)+
1 V(J*3-1+K*NVAR)*R(6,N)+
2 V(J*3 +K*NVAR)*R(9,N)
10 CONTINUE
T2(K+1,N) = 0.0D0
DO 20 I = 1, NVAR
T2(K+1,N) = T2(K+1,N) + T1(I)*V(I+K*NVAR)
20 CONTINUE
30 CONTINUE
WRITE(6,100)
WRITE(6,'('' '',7A9)')(ISYMT(I),I=1,NENT)
100 FORMAT(' FREQ.',/,' NO. FREQ. CHARACTER TABLE ')
I=1
J=I+1
IF (INDEX(KEYWRD,' NODEGEN') .NE. 0) TOL = -1.D0
EREF = E(1)
110 IF(ABS((E(J)-EREF)) .LE. TOL) THEN
DO 120 K = 1, NENT
120 T2(I,K) = T2(I,K) + T2(J,K)
E(I) = (E(I) + E(J))
J = J+1
ELSE
E(I)=E(I)/FLOAT(J-I)
WRITE(6,130)I,E(I),(T2(I,K),K=1,NENT)
I=J
J=J+1
EREF=E(I)
ENDIF
IF (J .LE. NVAR) GOTO 110
E(I)=E(I)/FLOAT(J-I)
WRITE(6,130)I,E(I),(T2(I,K),K=1,NENT)
130 FORMAT(I4,F9.3,3X,7F9.4)
END
SUBROUTINE SYMT(H, DELDIP)
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
INCLUDE 'SIZES'
DIMENSION H(*), DELDIP(3,*)
COMMON /SYMOPS/ R(14,120), NSYM, IPO(NUMATM,120), NENT
COMMON /SYMOPC/ ISYMT(6)
CHARACTER*10 ISYMT
*****************************************************************
*
* ON INPUT H = HESSIAN MATRIX, PACKED LOWER HALF TRIANGLE
* R = SYMMETRY OPERATIONS
* IPO = MAP OF ATOMS MOVED
* NSYM = NUMBER OF SYMMETRY OPERATIONS
*
* ON OUTPUT H = SYMMETRIZED HESSIAN MATRIX
*
*****************************************************************
C A subroutine that will symmatrize the Hamiltonian, or other matrix
C by successive application of group operations. The method used
C is R H R added to HA then divided by the total number of symmetry
C operations used. This in effects averages all the values in a
C symmetry correct fashion.
C
DIMENSION TEMP(9), TEMP2(9), DELTMP(3,MAXPAR)
COMMON /FOKMAT/ HA(MPACK*2)
COMMON /MOLKST/ NUMAT,NAT(NUMATM),NFIRST(NUMATM),NMIDLE(NUMATM),
1 NLAST(NUMATM), NORBS, NELECS,NALPHA,NBETA,
2 NCLOSE,NOPEN,NDUMY,FRACT
COMMON /COORD / COORD(3,NUMATM)
C
C
C Variables used: (n represents the number of atomic centers)
C H(3n,3n): Input/output matrix. It is a packed lower half triangu
C matrix. Commonly, the Hessian.
C HA(3n,3n): An internal matrix used to sum the symatrized Hessian
C NSYM: Input, the value of this symmetry operation.
C TEMP(9), TEMP2(9): Temporary matricies used to hold small parts
C larger matricies for specific matrix operations.
C
C For the next two items, the last indicy represents the symmetry
C operation number.
C IPO(n,*): A vector that contains the symmetry mapping of atomic c
C
C Skip this subroutine if NSYMM <= 0. This implies that only E is pre
IF (NSYM .LT. 2) RETURN
C
DO 10 I=1,(3*NUMAT*(NUMAT*3+1))/2
10 HA(I)=0.D0
C
DO 15 I = 1, NUMAT*3
DELTMP(1,I) = 0.D0
DELTMP(2,I) = 0.D0
15 DELTMP(3,I) = 0.D0
C
DO 40 N = 1, NSYM
C
C Now, to actually perform R H R
DO 30 I = 1, NUMAT
DO 20 J = 1, I-1
C
C Do this multiplication in a 3 by 3 block at a time. Store H(i,j) in
C HA( IPO(I,N), IPO(J,N)) or HS( IPO(I,N), IPO(J,N))
C
K = IPO(I,N)
L = IPO(J,N)
IF (K .GT. L) THEN
IEL33 = (3*K*(3*K-1))/2 + 3*L
TEMP(9) = H(IEL33)
TEMP(8) = H(IEL33-1)
TEMP(7) = H(IEL33-2)
TEMP(6) = H(IEL33-K*3+1)
TEMP(5) = H(IEL33-K*3)
TEMP(4) = H(IEL33-K*3-1)
TEMP(3) = H(IEL33-6*K+3)
TEMP(2) = H(IEL33-6*K+2)
TEMP(1) = H(IEL33-6*K+1)
ELSE
IEL33 = (3*L*(3*L-1))/2 + 3*K
TEMP(9) = H(IEL33)
TEMP(6) = H(IEL33-1)
TEMP(3) = H(IEL33-2)
TEMP(8) = H(IEL33-L*3+1)
TEMP(5) = H(IEL33-L*3)
TEMP(2) = H(IEL33-L*3-1)
TEMP(7) = H(IEL33-6*L+3)
TEMP(4) = H(IEL33-6*L+2)
TEMP(1) = H(IEL33-6*L+1)
ENDIF
C
CALL MAT33(R(1,N), TEMP, TEMP2)
C
IEL33 = I*3*(I*3-1)/2 + J*3
HA(IEL33) = TEMP2(9) + HA(IEL33)
HA(IEL33-1) = TEMP2(8) + HA(IEL33-1)
HA(IEL33-2) = TEMP2(7) + HA(IEL33-2)
HA(IEL33-I*3+1) = TEMP2(6) + HA(IEL33-I*3+1)
HA(IEL33-I*3) = TEMP2(5) + HA(IEL33-I*3)
HA(IEL33-I*3-1) = TEMP2(4) + HA(IEL33-I*3-1)
HA(IEL33-6*I+3) = TEMP2(3) + HA(IEL33-6*I+3)
HA(IEL33-6*I+2) = TEMP2(2) + HA(IEL33-6*I+2)
HA(IEL33-6*I+1) = TEMP2(1) + HA(IEL33-6*I+1)
20 CONTINUE
K = IPO(I,N)
IEL33 = (3*K*(3*K+1))/2
TEMP(9) = H(IEL33)
TEMP(8) = H(IEL33-1)
TEMP(7) = H(IEL33-2)
TEMP(6) = TEMP(8)
TEMP(5) = H(IEL33-K*3)
TEMP(4) = H(IEL33-K*3-1)
TEMP(3) = TEMP(7)
TEMP(2) = TEMP(4)
TEMP(1) = H(IEL33-6*K+1)
C
CALL MAT33(R(1,N), TEMP, TEMP2)
C
IEL33 = I*3*(I*3+1)/2
HA(IEL33) = TEMP2(9) + HA(IEL33)
HA(IEL33-1) = TEMP2(8) + HA(IEL33-1)
HA(IEL33-2) = TEMP2(7) + HA(IEL33-2)
HA(IEL33-I*3) = TEMP2(5) + HA(IEL33-I*3)
HA(IEL33-I*3-1) = TEMP2(4) + HA(IEL33-I*3-1)
HA(IEL33-6*I+1) = TEMP2(1) + HA(IEL33-6*I+1)
C
C APPLY SYMMETRY TO DIPOLE TERM AS WELL
C
TEMP(9) = DELDIP(3,K*3 )
TEMP(8) = DELDIP(2,K*3 )
TEMP(7) = DELDIP(1,K*3 )
TEMP(6) = DELDIP(3,K*3-1)
TEMP(5) = DELDIP(2,K*3-1)
TEMP(4) = DELDIP(1,K*3-1)
TEMP(3) = DELDIP(3,K*3-2)
TEMP(2) = DELDIP(2,K*3-2)
TEMP(1) = DELDIP(1,K*3-2)
C
CALL MAT33(R(1,N), TEMP, TEMP2)
C
DELTMP(3,I*3 ) = TEMP2(9) + DELTMP(3,I*3 )
DELTMP(2,I*3 ) = TEMP2(8) + DELTMP(2,I*3 )
DELTMP(1,I*3 ) = TEMP2(7) + DELTMP(1,I*3 )
DELTMP(3,I*3-1) = TEMP2(6) + DELTMP(3,I*3-1)
DELTMP(2,I*3-1) = TEMP2(5) + DELTMP(2,I*3-1)
DELTMP(1,I*3-1) = TEMP2(4) + DELTMP(1,I*3-1)
DELTMP(3,I*3-2) = TEMP2(3) + DELTMP(3,I*3-2)
DELTMP(2,I*3-2) = TEMP2(2) + DELTMP(2,I*3-2)
DELTMP(1,I*3-2) = TEMP2(1) + DELTMP(1,I*3-2)
C
30 CONTINUE
40 CONTINUE
C
DO 50 I = 1, (NUMAT*3*(NUMAT*3+1))/2
50 H(I) = HA(I)/NSYM
C
DO 60 I = 1, 3*NUMAT
DELDIP(1,I) = DELTMP(1,I)/NSYM
DELDIP(2,I) = DELTMP(2,I)/NSYM
60 DELDIP(3,I) = DELTMP(3,I)/NSYM
C
RETURN
END
SUBROUTINE MAT33(A, B, C)
C A subroutine that will multiply two 3 by 3 matricies in the following
C fashion: C = A(transpose) B A
C
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
DIMENSION A(9), B(9), C(9), T(9)
C
C
T(1) = B(1)*A(1) + B(2)*A(4) + B(3)*A(7)
T(2) = B(1)*A(2) + B(2)*A(5) + B(3)*A(8)
T(3) = B(1)*A(3) + B(2)*A(6) + B(3)*A(9)
T(4) = B(4)*A(1) + B(5)*A(4) + B(6)*A(7)
T(5) = B(4)*A(2) + B(5)*A(5) + B(6)*A(8)
T(6) = B(4)*A(3) + B(5)*A(6) + B(6)*A(9)
T(7) = B(7)*A(1) + B(8)*A(4) + B(9)*A(7)
T(8) = B(7)*A(2) + B(8)*A(5) + B(9)*A(8)
T(9) = B(7)*A(3) + B(8)*A(6) + B(9)*A(9)
C
C(1) = A(1)*T(1) + A(4)*T(4) + A(7)*T(7)
C(2) = A(1)*T(2) + A(4)*T(5) + A(7)*T(8)
C(3) = A(1)*T(3) + A(4)*T(6) + A(7)*T(9)
C(4) = A(2)*T(1) + A(5)*T(4) + A(8)*T(7)
C(5) = A(2)*T(2) + A(5)*T(5) + A(8)*T(8)
C(6) = A(2)*T(3) + A(5)*T(6) + A(8)*T(9)
C(7) = A(3)*T(1) + A(6)*T(4) + A(9)*T(7)
C(8) = A(3)*T(2) + A(6)*T(5) + A(9)*T(8)
C(9) = A(3)*T(3) + A(6)*T(6) + A(9)*T(9)
C
RETURN
END
SUBROUTINE SYMP
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
INCLUDE 'SIZES'
COMMON /SYMOPS/ R(14,120), NSYM, IPO(NUMATM,120), NENT
COMMON /SYMOPC/ ISYMT(6)
CHARACTER*10 ISYMT
CHARACTER*5 OPER
*****************************************************************
*
* ON INPUT R = SYMMETRY OPERATIONS (7 MAX)
* IPO = PERM OPR FOR ABOVE OPERATIONS
* NSYM = CURRENT NUMBER OF SYMMETRY OPERATIONS
* NENT = NUMBER OF USER SUPPLIED OPERATIONS
*
* ON OUTPUT R = SYMMETRY OPERATIONS (120 MAX)
* IPO = PERMUTATION OPERATOR FOR SYMMETRY OPERATIONS
* NSYM = NUMBER OF SYMMETRY OPERATIONS
*
*****************************************************************
C
C A SUBROUTINE THAT WILL EXPAND THE SYMMETRY OPERATIONS READ IN INTO
C THE COMPLETE SET. NOTE: VERY FEW OPERATIONS ARE REQUIRED TO
C GENERATE EVEN VERY LARGE GROUPS OF OPERATIONS.
C
C
COMMON /MOLKST/ NUMAT,NAT(NUMATM),NFIRST(NUMATM),NMIDLE(NUMATM),
1 NLAST(NUMATM), NORBS, NELECS,NALPHA,NBETA,
2 NCLOSE,NOPEN,NDUMY,FRACT
COMMON /COORD / COORD(3,NUMATM)
COMMON /KEYWRD/ KEYWRD
CHARACTER KEYWRD*241
C THE NEXT PARAMETERS ARE THE MAX NUMBER OF SYMM FUNCTIONS, THE
C MAX NUMBER OF SYMM FUNCTIONS TO READ IN, AND THE
C TOLERENCE USED TO DETERMINE IF TWO FUNCTIONS ARE IDENTICAL
PARAMETER (MAXFUN=120)
PARAMETER (TOL =1D-2)
C
C
C Variables used: (n represents the number of atomic centers)
C
C For the next two items, the last index represents the symmetry
C operation number.
C R(9,*): The 9 elements of each record are a packed 3 by 3
C array of a given symmetry operations.
C IPO(n,*): A vector that contains the symmetry mapping of atomic ce
C
C NSYM IS ALWAYS THE UPPER BOUND OF THE VALID FUNCTIONS. QUIT IF IT
C REACHES 120.
C I IS THE SLOW INDEX OF FUNCTIONS TO MULTIPLY
C J IS THE FAST INDEX OF FUNCTIONS TO MULTIPLY
C ALWAYS DO R(I)*R(J) AND TAKE I,J FROM 2 TO NSYM
C
I = 2
J = 1
C
C IF MORE INFORMATION IS WANTED, PRINT HEADDER.
C
IF (INDEX(KEYWRD,' RMAT') .NE. 0)WRITE(6,100)
100 FORMAT(/,' ENTERING THE SYMMETRY GENERATING ROUTINE ',
+/,' NUMBER SYMM. OPER. * ',
+ ' NUMBER SYMM. OPER. = ',
+ ' NUMBER SYMM. OPER.')
C DETERMINE IF IT IS TIME TO STOP
C
10 J = J+1
IF (J .GT. NSYM) THEN
J = 2
I = I+1
IF (I .GT. NSYM) GOTO 50
ENDIF
IF(NSYM .EQ. MAXFUN) GOTO 50
C
C NOW TO START THE MULTIPLICATION
C
R(1,NSYM+1)=R(1,I)*R(1,J)+R(2,I)*R(4,J)+R(3,I)*R(7,J)
R(2,NSYM+1)=R(1,I)*R(2,J)+R(2,I)*R(5,J)+R(3,I)*R(8,J)
R(3,NSYM+1)=R(1,I)*R(3,J)+R(2,I)*R(6,J)+R(3,I)*R(9,J)
R(4,NSYM+1)=R(4,I)*R(1,J)+R(5,I)*R(4,J)+R(6,I)*R(7,J)
R(5,NSYM+1)=R(4,I)*R(2,J)+R(5,I)*R(5,J)+R(6,I)*R(8,J)
R(6,NSYM+1)=R(4,I)*R(3,J)+R(5,I)*R(6,J)+R(6,I)*R(9,J)
R(7,NSYM+1)=R(7,I)*R(1,J)+R(8,I)*R(4,J)+R(9,I)*R(7,J)
R(8,NSYM+1)=R(7,I)*R(2,J)+R(8,I)*R(5,J)+R(9,I)*R(8,J)
R(9,NSYM+1)=R(7,I)*R(3,J)+R(8,I)*R(6,J)+R(9,I)*R(9,J)
C
C IS IT UNIQUE?
C
DO 30 N = 1, NSYM
RES = 0.D0
DO 20 M = 1, 9
20 RES = RES + ABS(R(M,N) - R(M,NSYM+1))
IF (RES .LT. TOL) GOTO 10
30 CONTINUE
C
C YES, IT IS UNIQUE. NOW, GENERATE THE NEW IPO(,NSYM)
C
NSYM = NSYM + 1
DO 40 N = 1, NUMAT
40 IPO(N,NSYM) = IPO(IPO(N,J),I)
C
C ALL DONE ADDING THE NEW FUNCTION. GO TRY TO FIND A NEW ONE.
C BUT FIRST, SEE IF WE NEED TO PRINT THIS.
C
IF (INDEX(KEYWRD,' RMAT') .NE. 0)
+ WRITE(6,110)I,OPER(R(1,I)),J,OPER(R(1,J)),NSYM,OPER(R(1,NSYM))
110 FORMAT(8X,I3,6X,A5,4X,'*',8X,I3,6X,A5,4X,'=',8X,I3,6X,A5)
IF (INDEX(KEYWRD,' RMAT') .NE. 0) THEN
WRITE(6,120)(R(K,I),K=1,3),(R(K,J),K=1,3),(R(K,NSYM),K=1,3)
WRITE(6,130)(R(K,I),K=4,6),(R(K,J),K=4,6),(R(K,NSYM),K=4,6)
WRITE(6,140)(R(K,I),K=7,9),(R(K,J),K=7,9),(R(K,NSYM),K=7,9)
120 FORMAT(' |',3F7.3,' | |',3F7.3,' | |',3F7.3,' |')
130 FORMAT(' |',3F7.3,' | * |',3F7.3,' | = |',3F7.3,' |')
140 FORMAT(' |',3F7.3,' | |',3F7.3,' | |',3F7.3,' |',/)
ENDIF
C
GOTO 10
C
C
50 CONTINUE
C
C NOW, TO DO FINAL WRAPUP
C
WRITE(6,150)NSYM
150 FORMAT(/,' THERE ARE ',I3,' UNIQUE SYMMETRY FUNCTIONS.',/)
C
C PRINT THE IPO MATRIX IF ASKED FOR.
C
IF(INDEX(KEYWRD,' IPO') .NE. 0) THEN
WRITE(6,160)
160 FORMAT(/,20X,'THE PERMUTATION MATRIX')
I = 1
J = MIN(12,NSYM)
60 WRITE(6,170)(K,K=I,J)
170 FORMAT(/,/,5X,'OPER. NO. ',12I5)
WRITE(6,175)(OPER(R(1,K)),K=I,J)
175 FORMAT(5X,'SYMM. OPER. ',12A5)
WRITE(6,180)
180 FORMAT(5X,'ATOM NO.')
DO 70 K = 1, NUMAT
70 WRITE(6,190)K,(IPO(K,L),L=I,J)
190 FORMAT(I10,5X,12I5)
IF (J .LT. NSYM) THEN
I = J+1
J = MIN(J+12,NSYM)
GOTO 60
ENDIF
ENDIF
RETURN
END
CHARACTER*5 FUNCTION OPER(R)
C
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
CHARACTER OPR*5, NUM*10
DIMENSION R(9)
C
C
OPR = ' '
NUM = '0123456789'
TRACE = R(1) + R(5) + R(9)
DET = R(1)*R(5)*R(9) + R(2)*R(6)*R(7) + R(3)*R(4)*R(8)
+ - R(1)*R(6)*R(8) - R(2)*R(4)*R(9) - R(3)*R(5)*R(7)
TRACE = (TRACE - DET)/2.D0
IF (DET .GT. 0.D0) THEN
OPR(1:1) = 'C'
IF (TRACE .GT. 0.97D0) THEN
OPR(1:1) = 'E'
GOTO 20
ENDIF
ELSE
OPR(1:1) = 'S'
IF (TRACE .GT. 0.97D0) THEN
OPR(1:5) = 'Sigma'
GOTO 20
ENDIF
IF (TRACE .LT. -0.97D0) THEN
OPR(1:5) = ' Inv '
GOTO 20
ENDIF
ENDIF
IF (TRACE .LT. -0.97D0) THEN
OPR(2:2) = NUM(3:3)
GOTO 20
ENDIF
ANG = ACOS(TRACE)
AFULL = ACOS(-1.0D0)*2.D0
DO 10 I = 3, 18
ANS = I*ANG/AFULL
IF (ABS(ANS - NINT(ANS)) .LE. 2.5D-3) THEN
IF(I .GE.10) THEN
OPR(2:2) = NUM(2:2)
OPR(3:3) = NUM(I-9:I-9)
ELSE
OPR(2:2) = NUM(I+1:I+1)
ENDIF
IF (NINT(ANS) .NE. 1) THEN
OPR(4:5) = '* '
OPR(5:5) = NUM(NINT(ANS)+1:NINT(ANS)+1)
ENDIF
GOTO 20
ENDIF
10 CONTINUE
OPR(2:5) = 'Unkn'
C
20 OPER = OPR
RETURN
END
|
