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
|
SUBROUTINE INTERP(N,NP,NQ,MODE,E,FP,CP,VEC,FOCK,P,H,VECL)
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
INCLUDE 'SIZES'
DIMENSION FP(MPACK), CP(N,N)
DIMENSION VEC(N,N), FOCK(N,N),
1 P(N,N), H(N*N), VECL(N*N)
**********************************************************************
*
* INTERP: AN INTERPOLATION PROCEDURE FOR FORCING SCF CONVERGANCE
* ORIGINAL THEORY AND FORTRAN WRITTEN BY R.N. CAMP AND
* H.F. KING, J. CHEM. PHYS. 75, 268 (1981)
**********************************************************************
*
* ON INPUT N = NUMBER OF ORBITALS
* NP = NUMBER OF FILLED LEVELS
* NQ = NUMBER OF EMPTY LEVELS
* MODE = 1, DO NOT RESET.
* E = ENERGY
* FP = FOCK MATRIX, AS LOWER HALF TRIANGLE, PACKED
* CP = EIGENVECTORS OF FOCK MATRIX OF ITERATION -1
* AS PACKED ARRAY OF N*N COEFFICIENTS
*
* ON OUTPUT CP = BEST GUESSED SET OF EIGENVECTORS
* MODE = 2 OR 3 - USED BY CALLING PROGRAM
**********************************************************************
DIMENSION THETA(MAXORB)
COMMON /KEYWRD/ KEYWRD
COMMON /NUMCAL/ NUMCAL
COMMON/FIT/NPNTS,IDUM2,XLOW,XHIGH,XMIN,EMIN,DEMIN,X(12),F(12),
1 DF(12)
LOGICAL DEBUG
CHARACTER*241 KEYWRD
SAVE ZERO, FF, RADMAX, ICALCN, DEBUG
DATA ICALCN/0/
DATA ZERO,FF,RADMAX/0.0D0,0.9D0,1.5708D0/
IF(ICALCN.NE.NUMCAL)THEN
DEBUG=(INDEX(KEYWRD,'INTERP').NE.0)
ICALCN=NUMCAL
ENDIF
C
C RADMAX=MAXIMUM ROTATION ANGLE (RADIANS). 1.5708 = 90 DEGREES.
C FF=FACTOR FOR CONVERGENCE TEST FOR 1D SEARCH.
C
MINPQ=MIN0(NP,NQ)
NP1=NP+1
NP2=MAX0(1,NP/2)
IF(MODE.EQ.2) GO TO 110
C
C (MODE=1 OR 3 ENTRY)
C TRANSFORM FOCK MATRIX TO CURRENT MO BASIS.
C ONLY THE OFF DIAGONAL OCC-VIRT BLOCK IS COMPUTED.
C STORE IN FOCK ARRAY
C
II=0
DO 50 I=1,N
I1=I+1
DO 40 J=1,NQ
DUM=ZERO
DO 20 K=1,I
20 DUM=DUM+FP(II+K)*CP(K,J+NP)
IF(I.EQ.N) GO TO 40
IK=II+I+I
DO 30 K=I1,N
DUM=DUM+FP(IK)*CP(K,J+NP)
30 IK=IK+K
40 P(I,J)=DUM
50 II=II+I
DO 80 I=1,NP
DO 70 J=1,NQ
DUM=ZERO
DO 60 K=1,N
60 DUM=DUM+CP(K,I)*P(K,J)
FOCK(I,J)=DUM
70 CONTINUE
80 CONTINUE
IF(MODE.EQ.3) GO TO 100
C
C CURRENT POINT BECOMES OLD POINT (MODE=1 ENTRY)
C
DO 90 I=1,N
DO 90 J=1,N
90 VEC(I,J)=CP(I,J)
EOLD=E
XOLD=1.0D0
MODE=2
RETURN
C
C (MODE=3 ENTRY)
C FOCK CORRESPONDS TO CURRENT POINT IN CORRESPONDING REPRESENTATION.
C VEC DOES NOT HOLD CURRENT VECTORS. VEC SET IN LAST MODE=2 ENTRY.
C
100 NPNTS=NPNTS+1
IF(DEBUG)WRITE(6,'('' INTERPOLATED ENERGY:'',F13.6)')E*23.061D0
IPOINT=NPNTS
GO TO 500
C
C (MODE=2 ENTRY) CALCULATE THETA, AND U, V, W MATRICES.
C U ROTATES CURRENT INTO OLD MO.
C V ROTATES CURRENT INTO CORRESPONDING CURRENT MO.
C W ROTATES OLD INTO CORRESPONDING OLD MO.
C
110 J1=1
DO 140 I=1,N
IF(I.EQ.NP1) J1=NP1
DO 130 J=J1,N
P(I,J)=ZERO
DO 120 K=1,N
120 P(I,J)=P(I,J)+CP(K,I)*VEC(K,J)
130 CONTINUE
140 CONTINUE
C
C U = CP(DAGGER)*VEC IS NOW IN P ARRAY.
C VEC IS NOW AVAILABLE FOR TEMPORARY STORAGE.
C
IJ=0
DO 170 I=1,NP
DO 160 J=1,I
IJ=IJ+1
H(IJ)=0.D0
DO 150 K=NP1,N
150 H(IJ)=H(IJ)+P(I,K)*P(J,K)
160 CONTINUE
170 CONTINUE
CALL HQRII(H,NP,NP,THETA,VECL)
DO 180 I=NP,1,-1
IL=I*NP-NP
DO 180 J=NP,1,-1
180 VEC(J,I)=VECL(J+IL)
DO 200 I=1,NP2
DUM=THETA(NP1-I)
THETA(NP1-I)=THETA(I)
THETA(I)=DUM
DO 190 J=1,NP
DUM=VEC(J,NP1-I)
VEC(J,NP1-I)=VEC(J,I)
190 VEC(J,I)=DUM
200 CONTINUE
DO 210 I=1,MINPQ
THETA(I)=MAX(THETA(I),ZERO)
THETA(I)=MIN(THETA(I),1.D0)
210 THETA(I)=ASIN(SQRT(THETA(I)))
C
C THETA MATRIX HAS NOW BEEN CALCULATED, ALSO UNITARY VP MATRIX
C HAS BEEN CALCULATED AND STORED IN FIRST NP COLUMNS OF VEC MATRIX.
C NOW COMPUTE WQ
C
DO 240 I=1,NQ
DO 230 J=1,MINPQ
VEC(I,NP+J)=ZERO
DO 220 K=1,NP
220 VEC(I,NP+J)=VEC(I,NP+J)+P(K,NP+I)*VEC(K,J)
230 CONTINUE
240 CONTINUE
CALL SCHMIT(VEC(1,NP1),NQ,N)
C
C UNITARY WQ MATRIX NOW IN LAST NQ COLUMNS OF VEC MATRIX.
C TRANSPOSE NP BY NP BLOCK OF U STORED IN P
C
DO 260 I=1,NP
DO 250 J=1,I
DUM=P(I,J)
P(I,J)=P(J,I)
250 P(J,I)=DUM
260 CONTINUE
C
C CALCULATE WP MATRIX AND HOLD IN FIRST NP COLUMNS OF P
C
DO 300 I=1,NP
DO 270 K=1,NP
270 H(K)=P(I,K)
DO 290 J=1,NP
P(I,J)=ZERO
DO 280 K=1,NP
280 P(I,J)=P(I,J)+H(K)*VEC(K,J)
290 CONTINUE
300 CONTINUE
CALL SCHMIB(P,NP,N)
C
C CALCULATE VQ MATRIX AND HOLD IN LAST NQ COLUMNS OF P MATRIX.
C
DO 340 I=1,NQ
DO 310 K=1,NQ
310 H(K)=P(NP+I,NP+K)
DO 330 J=NP1,N
P(I,J)=ZERO
DO 320 K=1,NQ
320 P(I,J)=P(I,J)+H(K)*VEC(K,J)
330 CONTINUE
340 CONTINUE
CALL SCHMIB(P(1,NP1),NQ,N)
C
C CALCULATE (DE/DX) AT OLD POINT
C
DEDX=ZERO
DO 370 I=1,NP
DO 360 J=1,NQ
DUM=ZERO
DO 350 K=1,MINPQ
350 DUM=DUM+THETA(K)*P(I,K)*VEC(J,NP+K)
360 DEDX=DEDX+DUM*FOCK(I,J)
370 CONTINUE
C
C STORE OLD POINT INFORMATION FOR SPLINE FIT
C
DEOLD=-4.0D0*DEDX
X(2)=XOLD
F(2)=EOLD
DF(2)=DEOLD
C
C MOVE VP OUT OF VEC ARRAY INTO FIRST NP COLUMNS OF P MATRIX.
C
DO 380 I=1,NP
DO 380 J=1,NP
380 P(I,J)=VEC(I,J)
K1=0
K2=NP
DO 410 J=1,N
IF(J.EQ.NP1) K1=NP
IF(J.EQ.NP1) K2=NQ
DO 400 I=1,N
DUM=ZERO
DO 390 K=1,K2
390 DUM=DUM+CP(I,K1+K)*P(K,J)
400 VEC(I,J)=DUM
410 CONTINUE
C
C CORRESPONDING CURRENT MO VECTORS NOW HELD IN VEC.
C COMPUTE VEC(DAGGER)*FP*VEC
C STORE OFF-DIAGONAL BLOCK IN FOCK ARRAY.
C
420 II=0
DO 460 I=1,N
I1=I+1
DO 450 J=1,NQ
DUM=ZERO
DO 430 K=1,I
430 DUM=DUM+FP(II+K)*VEC(K,J+NP)
IF(I.EQ.N) GO TO 450
IK=II+I+I
DO 440 K=I1,N
DUM=DUM+FP(IK)*VEC(K,J+NP)
440 IK=IK+K
450 P(I,J)=DUM
460 II=II+I
DO 490 I=1,NP
DO 480 J=1,NQ
DUM=ZERO
DO 470 K=1,N
470 DUM=DUM+VEC(K,I)*P(K,J)
FOCK(I,J)=DUM
480 CONTINUE
490 CONTINUE
C
C SET LIMITS ON RANGE OF 1-D SEARCH
C
NPNTS=2
IPOINT=1
XNOW=ZERO
XHIGH=RADMAX/THETA(1)
XLOW=-0.5D0*XHIGH
C
C CALCULATE (DE/DX) AT CURRENT POINT AND
C STORE INFORMATION FOR SPLINE FIT
C ***** JUMP POINT FOR MODE=3 ENTRY *****
C
500 DEDX=ZERO
DO 510 K=1,MINPQ
510 DEDX=DEDX+THETA(K)*FOCK(K,K)
DENOW=-4.0D0*DEDX
ENOW=E
IF(IPOINT.LE.12) GO TO 530
520 FORMAT(//,'EXCESSIVE DATA PNTS FOR SPLINE.',/
1,'IPOINT =',I3,'MAXIMUM IS 12.')
C
C PERFORM 1-D SEARCH AND DETERMINE EXIT MODE.
C
530 X(IPOINT)=XNOW
F(IPOINT)=ENOW
DF(IPOINT)=DENOW
CALL SPLINE
IF((EOLD-ENOW).GT.FF*(EOLD-EMIN).OR.IPOINT.GT.10) GO TO 560
C
C (MODE=3 EXIT) RECOMPUTE CP VECTORS AT PREDICTED MINIMUM.
C
XNOW=XMIN
DO 550 K=1,MINPQ
CK=COS(XNOW*THETA(K))
SK=SIN(XNOW*THETA(K))
IF(DEBUG)WRITE(6,'('' ROTATION ANGLE:'',F12.4)')SK*57.29578D0
DO 540 I=1,N
CP(I,K) =CK*VEC(I,K)-SK*VEC(I,NP+K)
540 CP(I,NP+K)=SK*VEC(I,K)+CK*VEC(I,NP+K)
550 CONTINUE
MODE=3
RETURN
C
C (MODE=2 EXIT) CURRENT VECTORS GIVE SATISFACTORY ENERGY IMPROVEMENT
C CURRENT POINT BECOMES OLD POINT FOR THE NEXT 1-D SEARCH.
C
560 IF(MODE.EQ.2) GO TO 580
DO 570 I=1,N
DO 570 J=1,N
570 VEC(I,J)=CP(I,J)
MODE=2
580 ROLD=XOLD*THETA(1)*57.29578D0
RNOW=XNOW*THETA(1)*57.29578D0
RMIN=XMIN*THETA(1)*57.29578D0
IF(DEBUG)WRITE(6,600) XOLD,EOLD*23.061D0,DEOLD,ROLD
1, XNOW,ENOW*23.061D0,DENOW,RNOW
2, XMIN,EMIN*23.061D0,DEMIN,RMIN
EOLD=ENOW
IF(NPNTS.LE.200) RETURN
WRITE(6,610)
DO 590 K=1,NPNTS
590 WRITE(6,620) K,X(K),F(K),DF(K)
WRITE(6,630)
RETURN
600 FORMAT(
1/14X,3H X ,10X,6H F(X) ,9X,7H DF/DX ,21H ROTATION (DEGREES),
2/10H OLD ,F10.5,3F15.10,
3/10H CURRENT ,F10.5,3F15.10,
4/10H PREDICTED,F10.5,3F15.10/)
610 FORMAT(3H K,10H X(K) ,15H F(K) ,10H DF(K))
620 FORMAT(I3,F10.5,2F15.10)
630 FORMAT(10X)
END
SUBROUTINE SPLINE
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
INCLUDE 'SIZES'
LOGICAL SKIP1,SKIP2
C
C FIT F(X) BY A CUBIC SPLINE GIVEN VALUES OF THE FUNCTION
C AND ITS FIRST DERIVATIVE AT N PNTS.
C SUBROUTINE RETURNS VALUES OF XMIN,FMIN, AND DFMIN
C AND MAY REORDER THE DATA.
C CALLING PROGRAM SUPPLIES ALL OTHER VALUES IN THE
C COMMON BLOCK.
C XLOW AND XHIGH SET LIMITS ON THE INTERVAL WITHIN WHICH
C TO SEARCH. SUBROUTINE MAY FURTHER REDUCE THIS INTERVAL.
C
COMMON/FIT/N,IDUM2,XLOW,XHIGH,XMIN,FMIN,DFMIN,X(12),F(12),DF(12)
SAVE CLOSE, BIG, HUGE, USTEP, DSTEP
DATA CLOSE, BIG, HUGE, USTEP, DSTEP/1.0E-8,500.0,1.0E+10,1.0,2.0/
C
C SUBROUTINE ASSUMES THAT THE FIRST N-1 DATA PNTS HAVE BEEN
C PREVIOUSLY ORDERED, X(I).LT.X(I+1) FOR I=1,2,...,N-2
C NOW MOVE NTH POINT TO ITS PROPER PLACE.
C
XMIN=X(N)
FMIN=F(N)
DFMIN=DF(N)
N1=N-1
K=N1
10 IF(X(K).LT.XMIN) GO TO 20
X(K+1)=X(K)
F(K+1)=F(K)
DF(K+1)=DF(K)
K=K-1
IF(K.GT.0) GO TO 10
20 X(K+1)=XMIN
F(K+1)=FMIN
DF(K+1)=DFMIN
C
C DEFINE THE INTERVAL WITHIN WHICH WE TRUST THE SPLINE FIT.
C USTEP = UP HILL STEP SIZE FACTOR
C DSTEP = DOWN HILL STEP SIZE FACTOR
C
IF(DF(1).GT.0.0) STEP=DSTEP
IF(DF(1).LE.0.0) STEP=USTEP
XSTART=X(1)-STEP*(X(2)-X(1))
XSTART=MAX(XSTART,XLOW)
IF(DF(N).GT.0.0) STEP=USTEP
IF(DF(N).LE.0.0) STEP=DSTEP
XSTOP=X(N)+STEP*(X(N)-X(N1))
XSTOP=MIN(XSTOP,XHIGH)
C
C SEARCH FOR MINIMUM
C
DO 110 K=1,N1
SKIP1=K.NE.1
SKIP2=K.NE.N1
IF(F(K).GE.FMIN) GO TO 30
XMIN=X(K)
FMIN=F(K)
DFMIN=DF(K)
30 DX=X(K+1)-X(K)
C
C SKIP INTERVAL IF PNTS ARE TOO CLOSE TOGETHER
C
IF(DX.LE.CLOSE) GO TO 110
X1=0.0D0
IF(K.EQ.1) X1=XSTART-X(1)
X2=DX
IF(K.EQ.N1) X2=XSTOP-X(N1)
C
C (A,B,C)=COEF OF (CUBIC,QUADRATIC,LINEAR) TERMS
C
DUM=(F(K+1)-F(K))/DX
A=(DF(K)+DF(K+1)-DUM-DUM)/(DX*DX)
B=(DUM+DUM+DUM-DF(K)-DF(K)-DF(K+1))/DX
C=DF(K)
C
C XK = X-X(K) AT THE MINIMUM WITHIN THE KTH SUBINTERVAL
C TEST FOR PATHOLOGICAL CASES.
C
BB=B*B
AC3=(A+A+A)*C
IF(BB.LT.AC3) GO TO 90
IF( B.GT.0.0) GO TO 40
IF(ABS(B).GT.HUGE*ABS(A)) GO TO 90
GO TO 50
40 IF(BB.GT.BIG*ABS(AC3)) GO TO 60
C
C WELL BEHAVED CUBIC
C
50 XK=(-B+SQRT(BB-AC3))/(A+A+A)
GO TO 70
C
C CUBIC IS DOMINATED BY QUADRATIC TERM
C
60 R=AC3/BB
XK=-(((0.039063D0*R+0.0625D0)*R+0.125D0)*R+0.5D0)*C/B
70 IF(XK.LT.X1.OR.XK.GT.X2) GO TO 90
80 FM=((A*XK+B)*XK+C)*XK+F(K)
IF(FM.GT.FMIN) GO TO 90
XMIN=XK+X(K)
FMIN=FM
DFMIN=((A+A+A)*XK+B+B)*XK+C
C
C EXTRAPOLATE TO END OF INTERVAL IF K=1 AND/OR K=N1
C
90 IF(SKIP1) GO TO 100
SKIP1=.TRUE.
XK=X1
GO TO 80
100 IF(SKIP2) GO TO 110
SKIP2=.TRUE.
XK=X2
GO TO 80
110 CONTINUE
RETURN
END
SUBROUTINE SCHMIT(U,N,NDIM)
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
INCLUDE 'SIZES'
DIMENSION U(NDIM,NDIM)
SAVE ZERO, SMALL, ONE
DATA ZERO,SMALL,ONE/0.0,0.01,1.0/
II=0
DO 110 K=1,N
K1=K-1
C
C NORMALIZE KTH COLUMN VECTOR
C
DOT = ZERO
DO 10 I=1,N
10 DOT=DOT+U(I,K)*U(I,K)
IF(DOT.EQ.ZERO) GO TO 100
SCALE=ONE/SQRT(DOT)
DO 20 I=1,N
20 U(I,K)=SCALE*U(I,K)
30 IF(K1.EQ.0) GO TO 110
NPASS=0
C
C PROJECT OUT K-1 PREVIOUS ORTHONORMAL VECTORS FROM KTH VECTOR
C
40 NPASS=NPASS+1
DO 70 J=1,K1
DOT=ZERO
DO 50 I=1,N
50 DOT=DOT+U(I,J)*U(I,K)
DO 60 I=1,N
60 U(I,K)=U(I,K)-DOT*U(I,J)
70 CONTINUE
C
C SECOND NORMALIZATION (AFTER PROJECTION)
C IF KTH VECTOR IS SMALL BUT NOT ZERO THEN NORMALIZE
C AND PROJECT AGAIN TO CONTROL ROUND-OFF ERRORS.
C
DOT=ZERO
DO 80 I=1,N
80 DOT=DOT+U(I,K)*U(I,K)
IF(DOT.EQ.ZERO) GO TO 100
IF(DOT.LT.SMALL.AND.NPASS.GT.2) GO TO 100
SCALE=ONE/SQRT(DOT)
DO 90 I=1,N
90 U(I,K)=SCALE*U(I,K)
IF(DOT.LT.SMALL) GO TO 40
GO TO 110
C
C REPLACE LINEARLY DEPENDENT KTH VECTOR BY A UNIT VECTOR.
C
100 II=II+1
C IF(II.GT.N) STOP
U(II,K)=ONE
GO TO 30
110 CONTINUE
RETURN
END
SUBROUTINE SCHMIB(U,N,NDIM)
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
INCLUDE 'SIZES'
C
C SAME AS SCHMIDT BUT WORKS FROM RIGHT TO LEFT.
C
DIMENSION U(NDIM,NDIM)
SAVE ZERO, SMALL, ONE
DATA ZERO,SMALL,ONE/0.0,0.01,1.0/
N1=N+1
II=0
DO 110 K=1,N
K1=K-1
C
C NORMALIZE KTH COLUMN VECTOR
C
DOT = ZERO
DO 10 I=1,N
10 DOT=DOT+U(I,N1-K)*U(I,N1-K)
IF(DOT.EQ.ZERO) GO TO 100
SCALE=ONE/SQRT(DOT)
DO 20 I=1,N
20 U(I,N1-K)=SCALE*U(I,N1-K)
30 IF(K1.EQ.0) GO TO 110
NPASS=0
C
C PROJECT OUT K-1 PREVIOUS ORTHONORMAL VECTORS FROM KTH VECTOR
C
40 NPASS=NPASS+1
DO 70 J=1,K1
DOT=ZERO
DO 50 I=1,N
50 DOT=DOT+U(I,N1-J)*U(I,N1-K)
DO 60 I=1,N
60 U(I,N1-K)=U(I,N1-K)-DOT*U(I,N1-J)
70 CONTINUE
C
C SECOND NORMALIZATION (AFTER PROJECTION)
C IF KTH VECTOR IS SMALL BUT NOT ZERO THEN NORMALIZE
C AND PROJECT AGAIN TO CONTROL ROUND-OFF ERRORS.
C
DOT=ZERO
DO 80 I=1,N
80 DOT=DOT+U(I,N1-K)*U(I,N1-K)
IF(DOT.EQ.ZERO) GO TO 100
IF(DOT.LT.SMALL.AND.NPASS.GT.2) GO TO 100
SCALE=ONE/SQRT(DOT)
DO 90 I=1,N
90 U(I,N1-K)=SCALE*U(I,N1-K)
IF(DOT.LT.SMALL) GO TO 40
GO TO 110
C
C REPLACE LINEARLY DEPENDENT KTH VECTOR BY A UNIT VECTOR.
C
100 II=II+1
C IF(II.GT.N) STOP
U(II,N1-K)=ONE
GO TO 30
110 CONTINUE
RETURN
END
SUBROUTINE PULAY(F,P,N,FPPF,FOCK,EMAT,LFOCK,NFOCK,MSIZE,START,PL)
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
DIMENSION F(*), P(*), FPPF(*), FOCK(*)
LOGICAL START
************************************************************************
*
* PULAY USES DR. PETER PULAY'S METHOD FOR CONVERGENCE.
* A MATHEMATICAL DESCRIPTION CAN BE FOUND IN
* "P. PULAY, J. COMP. CHEM. 3, 556 (1982).
*
* ARGUMENTS:-
* ON INPUT F = FOCK MATRIX, PACKED, LOWER HALF TRIANGLE.
* P = DENSITY MATRIX, PACKED, LOWER HALF TRIANGLE.
* N = NUMBER OF ORBITALS.
* FPPF = WORKSTORE OF SIZE MSIZE, CONTENTS WILL BE
* OVERWRITTEN.
* FOCK = " " " "
* EMAT = WORKSTORE OF AT LEAST 15**2 ELEMENTS.
* START = LOGICAL, = TRUE TO START PULAY.
* PL = UNDEFINED ELEMENT.
* ON OUTPUT F = "BEST" FOCK MATRIX, = LINEAR COMBINATION
* OF KNOWN FOCK MATRICES.
* START = FALSE
* PL = MEASURE OF NON-SELF-CONSISTENCY
* = [F*P] = F*P - P*F.
*
************************************************************************
COMMON /KEYWRD/ KEYWRD
COMMON /NUMCAL/ NUMCAL
DIMENSION EMAT(20,20), EVEC(1000), COEFFS(20)
CHARACTER*241 KEYWRD
LOGICAL DEBUG
DATA ICALCN/0/
IF (ICALCN.NE.NUMCAL) THEN
ICALCN=NUMCAL
MAXLIM=6
DEBUG=(INDEX(KEYWRD,'DEBUGPULAY') .NE.0)
ENDIF
IF(START) THEN
LINEAR=(N*(N+1))/2
MFOCK=MSIZE/LINEAR
IF(MFOCK.GT.MAXLIM)MFOCK=MAXLIM
IF(DEBUG)
1 WRITE(6,'('' MAXIMUM SIZE:'',I5)')MFOCK
NFOCK=1
LFOCK=1
START=.FALSE.
ELSE
IF(NFOCK.LT.MFOCK) NFOCK=NFOCK+1
IF(LFOCK.NE.MFOCK)THEN
LFOCK=LFOCK+1
ELSE
LFOCK=1
ENDIF
ENDIF
LBASE=(LFOCK-1)*LINEAR
*
* FIRST, STORE FOCK MATRIX FOR FUTURE REFERENCE.
*
DO 10 I=1,LINEAR
10 FOCK((I-1)*MFOCK+LFOCK)=F(I)
*
* NOW FORM /FOCK*DENSITY-DENSITY*FOCK/, AND STORE THIS IN FPPF
*
CALL MAMULT(P,F,FPPF(LBASE+1),N,0.D0)
CALL MAMULT(F,P,FPPF(LBASE+1),N,-1.D0)
*
* FPPF NOW CONTAINS THE RESULT OF FP - PF.
*
NFOCK1=NFOCK+1
DO 20 I=1,NFOCK
EMAT(NFOCK1,I)=-1.D0
EMAT(I,NFOCK1)=-1.D0
EMAT(LFOCK,I)=DOT(FPPF((I-1)*LINEAR+1),FPPF(LBASE+1),LINEAR)
20 EMAT(I,LFOCK)=EMAT(LFOCK,I)
PL=EMAT(LFOCK,LFOCK)/LINEAR
EMAT(NFOCK1,NFOCK1)=0.D0
CONST=1.D0/EMAT(LFOCK,LFOCK)
DO 30 I=1,NFOCK
DO 30 J=1,NFOCK
30 EMAT(I,J)=EMAT(I,J)*CONST
IF(DEBUG) THEN
WRITE(6,'('' EMAT'')')
DO 40 I=1,NFOCK1
40 WRITE(6,'(6E13.6)')(EMAT(J,I),J=1,NFOCK1)
ENDIF
L=0
DO 50 I=1,NFOCK1
DO 50 J=1,NFOCK1
L=L+1
50 EVEC(L)=EMAT(I,J)
CONST=1.D0/CONST
DO 60 I=1,NFOCK
DO 60 J=1,NFOCK
60 EMAT(I,J)=EMAT(I,J)*CONST
*********************************************************************
* THE MATRIX EMAT SHOULD HAVE FORM
*
* |<E(1)*E(1)> <E(1)*E(2)> ... -1.0|
* |<E(2)*E(1)> <E(2)*E(2)> ... -1.0|
* |<E(3)*E(1)> <E(3)*E(2)> ... -1.0|
* |<E(4)*E(1)> <E(4)*E(2)> ... -1.0|
* | . . ... . |
* | -1.0 -1.0 ... 0. |
*
* WHERE <E(I)*E(J)> IS THE SCALAR PRODUCT OF [F*P] FOR ITERATION I
* TIMES [F*P] FOR ITERATION J.
*
*********************************************************************
CALL OSINV(EVEC,NFOCK1,D)
IF(ABS(D).LT.1.D-6)THEN
START=.TRUE.
RETURN
ENDIF
IF(NFOCK.LT.2) RETURN
IL=NFOCK*NFOCK1
DO 70 I=1,NFOCK
70 COEFFS(I)=-EVEC(I+IL)
IF(DEBUG) THEN
WRITE(6,'('' EVEC'')')
WRITE(6,'(6F12.6)')(COEFFS(I),I=1,NFOCK)
WRITE(6,'('' LAGRANGIAN MULTIPLIER (ERROR) =''
1 ,F13.6)')EVEC(NFOCK1*NFOCK1)
ENDIF
DO 90 I=1,LINEAR
SUM=0
L=0
II=(I-1)*MFOCK
DO 80 J=1,NFOCK
80 SUM=SUM+COEFFS(J)*FOCK(J+II)
90 F(I)=SUM
RETURN
END
SUBROUTINE OSINV (A,N,D)
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
INCLUDE 'SIZES'
DIMENSION A(*)
************************************************************************
*
* OSINV INVERTS A GENERAL SQUARE MATRIX OF ORDER UP TO MAXORB. SEE
* DIMENSION STATEMENTS BELOW.
*
* ON INPUT A = GENERAL SQUARE MATRIX STORED LINEARLY.
* N = DIMENSION OF MATRIX A.
* D = VARIABLE, NOT DEFINED ON INPUT.
*
* ON OUTPUT A = INVERSE OF ORIGINAL A.
* D = DETERMINANT OF ORIGINAL A, UNLESS A WAS SINGULAR,
* IN WHICH CASE D = 0.0
*
************************************************************************
DIMENSION L(MAXORB), M(MAXORB)
************************************************************************
*
* IF THE VALUE OF TOL GIVEN HERE IS UNSUITABLE, IT CAN BE CHANGED.
TOL=1.D-8
*
*
************************************************************************
D=1.0D0
NK=-N
DO 180 K=1,N
NK=NK+N
L(K)=K
M(K)=K
KK=NK+K
BIGA=A(KK)
DO 20 J=K,N
IZ=N*(J-1)
DO 20 I=K,N
IJ=IZ+I
C
C 10 FOLLOWS
C
IF (ABS(BIGA)-ABS(A(IJ))) 10,20,20
10 BIGA=A(IJ)
L(K)=I
M(K)=J
20 CONTINUE
J=L(K)
IF (J-K) 50,50,30
30 KI=K-N
DO 40 I=1,N
KI=KI+N
HOLO=-A(KI)
JI=KI-K+J
A(KI)=A(JI)
40 A(JI)=HOLO
50 I=M(K)
IF (I-K) 80,80,60
60 JP=N*(I-1)
DO 70 J=1,N
JK=NK+J
JI=JP+J
HOLO=-A(JK)
A(JK)=A(JI)
70 A(JI)=HOLO
80 IF (ABS(BIGA)-TOL) 90,100,100
90 D=0.0D0
RETURN
100 DO 120 I=1,N
IF (I-K) 110,120,110
110 IK=NK+I
A(IK)=A(IK)/(-BIGA)
120 CONTINUE
DO 150 I=1,N
IK=NK+I
IJ=I-N
DO 150 J=1,N
IJ=IJ+N
IF (I-K) 130,150,130
130 IF (J-K) 140,150,140
140 KJ=IJ-I+K
A(IJ)=A(IK)*A(KJ)+A(IJ)
150 CONTINUE
KJ=K-N
DO 170 J=1,N
KJ=KJ+N
IF (J-K) 160,170,160
160 A(KJ)=A(KJ)/BIGA
170 CONTINUE
D=MIN(D*BIGA,1.D10)
A(KK)=1.0D0/BIGA
180 CONTINUE
K=N
190 K=K-1
IF (K) 260,260,200
200 I=L(K)
IF (I-K) 230,230,210
210 JQ=N*(K-1)
JR=N*(I-1)
DO 220 J=1,N
JK=JQ+J
HOLO=A(JK)
JI=JR+J
A(JK)=-A(JI)
220 A(JI)=HOLO
230 J=M(K)
IF (J-K) 190,190,240
240 KI=K-N
DO 250 I=1,N
KI=KI+N
HOLO=A(KI)
JI=KI+J-K
A(KI)=-A(JI)
250 A(JI)=HOLO
GO TO 190
260 RETURN
C
END
|
