-
Notifications
You must be signed in to change notification settings - Fork 0
/
tstVGENmlr.f
599 lines (591 loc) · 27.2 KB
/
tstVGENmlr.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
real*8 rr,vv,dVdR,d2VdR2,RH,RMIN,RMAX
integer I
READ(5,*) RH,RMIN,RMAX
call VGENmlr(-1.d0,VDIST,dVdR,d2VdR2)
RR= RMIN - RH
DO I=1,10000
RR= RR+RH
call VGENmlr(RR,VV,dVdR,d2VdR2)
write(6,601) RR,VV,dVdR,d2VdR2
IF(RR.GE.RMAX) GOTO 99
ENDDO
99 STOP
601 FORMAT(f8.3,1PD17.8,3d17.8)
END
c***********************************************************************
SUBROUTINE VGENmlr(RDIST,VDIST,dVdR,d2VdR2)
c***********************************************************************
c** This subroutine will generate and return function values and radial
c derivatives of Morse/Long-Range potentials as required for
c semiclassical calculation (with quantum corrections) of virial
c coefficients and their (analytical) derivatives w.r.t. the potential
c parameters for use in direct potential fits
c+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
c+++ COPYRIGHT 2015 by R.J. Le Roy, Dept. of Chemistry,
c Univ. of Waterloo, Waterloo, Ontario, Canada +
c This software may not be sold or any other commercial use made +
c of it without the express written permission of the authors. +
c+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
c ----- Version of 29 March 2015 --------
c+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
c** On entry:
c RDIST: at the 1 input distances RDIST, calculate potl & derivs
c * return potential function at those points as VDIST, and the
c first and second radial derivartives as dVdR & d2VdR2
c * If RDIST.le.0 read in MLR potential parameters and print description
c of model
c-----------------------------------------------------------------------
c** On exit via common blocks:
c dVtot is array or p. derivatives w.r.t. the 2+NCMM+Nbeta+1 param
c DBDB & DBDRe are p.derives of beta(r) w.r.t. \beta_i & Re, respectively
c
c** Temp:
c BTEMP is used to represent the sum used for dV/dRe.
c is used in GPEF for De calculations.
c betaINF is used to represent the beta(\infty) value.
c YP is used to represent (R^p-Re^p)/(R^p+Re^p) or R-Re.
c XTEMP is used to represent (uLR/uLR_e)* exp{-betaINF*RTEMP}
c AZERO is used for the trial exponential calculations.
c AONE is used for the trial exponential calculations.
c ATWO is used for the trial exponential calculations.
c AZTEMP is used in the MMO trial exponential calculations.
c is used in the GPEF = (a+b)/k
c AOTEMP is used in the GPEF = [a(k+1)-b(k-1)]/k
c ATTEMP is used in the GPEF = [a^2(k+1)-b^2(k-1)]/k
c ARTEMP is used in the GPEF = [a^3(k+1)-b^3(k-1)]/k
c FSW is used to represent the MLJ switching function.
c======================================================================
REAL*8 RDIST,VDIST,dVdR,d2VdR2,DSCM,REQ,Rref,rhoAB,ULR,ULRE,
1 betaINF,PVSR,VAL,DVAL,D2VAL,DVALdRe,AREF,REP,AREFp,AREFq,
2 BETADIST,RVAL,RINV,RDp,RDq,YPE,YP,YQ,YPM,DYPDRE,DYQDRE,DYPEDRE,
3 DBDRe,DBDR,dULRdR,d2ULRdr,DYPDR,DYPEDR,DYQDR,D2YPDR,D2YPEDR,
4 D2YQDR,DYPpDRe,DYPEpDRe,DYPEdRe,DYQpDRe,YPP,YPPP,XTEMP,DXTEMP,
5 D2XTEMP,dULRdR,d2ULRdR,dLULRdR,dDULRdr,dLULRedRe,T0,T1,dBpdRe,
6 d2BdR,dYBdRe,dYBpdRe,d2ULRdR,d2DULRdR,DVDD,
6 CMM(20),CmEFF(20),DM(30),DMP(20),DMPP(20),BETA(0:20),
7 dULRdCm(20),dLULRdCm(20),dLULRedCm(20),dULRdRCm(20),bTT(-2:2),
8 cDS(-4:4),bDS(-4:4)
INTEGER Nbeta,PPAR,QPAR,NCMM,MCMM,IVSR,LVSR,IDSTT,IPVSTART,I,J,m,
1 IPV,MMLR(20)
c** Common block to return derivatives w.r.t. potential parameters
REAL*8 dVdPk(30),DVtot(30),DBDB(0:30),dXdP(30),dXpdP(30),dVpdP(30)
COMMON /VDER/dVtot,DBDB,DBDRe
c-----------------------------------------------------------------------
DATA bTT/2.10d0,2.44d0,2.78d0,3.13d0,3.47d0/
DATA bDS/2.50d0,2.90d0,3.30d0,3.69d0,3.95d0,0.d0,4.53d0,0.d0,
1 4.99d0/
DATA cDS/0.468d0,0.446d0,0.423d0,0.405d0,0.390d0,0.d0,0.360d0,
1 0.d0,0.340d0/
SAVE
IF(RDIST.LE.0.d0) THEN
c** if(RDIST.LE.0) READ MLR parameters & write description of potential
c=======================================================================
c** Define MLR potential [as per J.Phys.Chem. A117, 13373(2013).
c=======================================================================
READ(5,*) Nbeta, PPAR, QPAR
READ(5,*) DSCM, REQ, Rref
c** For MLR, DELR, HFD, Tang-Toennies or Tiemann-polynomial potentials .....
READ(5,*) NCMM, rhoAB, IVSR, IDSTT
DO I=1,NCMM
READ(5,*) MMLR(I), CMM(I)
ENDDO
c-----------------------------------------------------------------------
DO I=0,Nbeta
READ(5,*) BETA(I)
ENDDO
c-----------------------------------------------------------------------
c** for first need to define ULRE an print potential description
ULRe= 0.d0
c!! Initialize CmEFF on VERY first call from MAIN prog.
DO m= 1, NCMM
CmEFF(m)= CMM(m)
ENDDO
MCMM= NCMM
c=======================================================================
cc ! As appropriate - make (& write) 'Dattani' Cm{adj} correctons here
IF((MMLR(1).EQ.6).AND.(NCMM.GE.4)) THEN
c... First, consider C6/C12adj(C14adj) for MMLR(m)={6,8,10,(11),12,14} case
IF(MMLR(4).EQ.12) THEN ! explicitly MMLR(4)=12
CmEFF(4)= CMM(4) + 0.25D0*CMM(1)**2/DSCM
WRITE(6,710) MMLR(4),MMLR(4),CmEFF(4)
IF(NCMM.GE.5) THEN ! assuming MMLR(5)=14
CmEFF(5)= CMM(5) + 0.5d0*CMM(1)*CMM(2)/DSCM
WRITE(6,710) MMLR(5),MMLR(5),CmEFF(5)
ENDIF
ELSE !! Assuming explicitly MMLR(2)=11 & MMLR(5)=12
CmEFF(5)= CMM(5) + 0.25D0*CMM(1)**2/DSCM
WRITE(6,710) MMLR(5),MMLR(5),CmEFF(5)
IF(NCMM.GE.6) THEN ! implicitly MMLR(6)=14
CmEFF(6)= CMM(6)+0.5D0*CMM(1)*CMM(2)/DSCM
WRITE(6,710) MMLR(6),MMLR(6),CmEFF(6)
ENDIF
ENDIF
ENDIF
IF((MMLR(1).EQ.5).AND.(NCMM.GE.4)) THEN
c... Then, consider C5/C10adj + C12adj for MMLR(m)={5,6,8,10,12,14} cases
CmEFF(4)= CMM(4) + 0.25D0*CMM(1)**2/DSCM
WRITE(6,710) MMLR(4),MMLR(4),CmEFF(4)
IF(NCMM.GE.5) THEN ! introduce C12^{adj}
CmEFF(5)= CMM(5) + 0.25D0*CMM(2)**2/DSCM
WRITE(6,710) MMLR(5),MMLR(5),CmEFF(5)
IF(NCMM.GE.6) THEN ! introduce C14^{adj}
CmEFF(6)= CMM(6) + 0.5D0*CMM(2)*CMM(3)/DSCM
WRITE(6,710) MMLR(6),MMLR(6),CmEFF(6)
ENDIF
ENDIF
ENDIF
IF((MMLR(1).EQ.4).AND.(NCMM.GE.3)) THEN
c... Then, consider C4/C8adj + C12adj for MMLR(m)={4,6,7,8,10,12,14} cases
c... first, allowing for a C7: C8 is m=4, C10 is m=5 ... etc.
IF((MMLR(3).EQ.7).AND.(NCMM.GE.4)) THEN
CmEFF(4)= CMM(4) + 0.25D0*CMM(1)**2/DSCM
WRITE(6,712) MMLR(4),MMLR(4),CmEFF(4)
IF(NCMM.GE.5) THEN ! implicitly MMLR(5)=10
CmEFF(5)= CMM(5) + 0.5D0*CMM(1)*CMM(2)/DSCM
WRITE(6,710)MMLR(5),MMLR(5), CmEFF(5)
IF(NCMM.GE.6) THEN ! implicitly MMLR(6)=12
CmEFF(6)= CMM(6) + 0.5D0*CMM(1)*CmEFF(4)/DSCM
1 + 0.25D0*CMM(3)**2/DSCM
WRITE(6,710) MMLR(6),MMLR(6),CmEFF(6)
IF(NCMM.GE.7) THEN ! implicitly MMLR(7)=14
CmEFF(7)= CMM(7) + 0.25d0*CMM(3)**2/DSCM
2 + 0.5D0*CMM(2)*CMM(4)/DSCM + 0.5D0*CMM(1)*CMM(5)/DSCM
WRITE(6,710) MMLR(7),MMLR(7),CmEFF(7)
ENDIF
ENDIF
ENDIF
ELSE
c... Now, consider C4/C8adj + C12adj for MMLR(m)={4,6,8,10,12,14} cases
CmEFF(3)= CMM(3) + 0.25D0*CMM(1)**2/DSCM
WRITE(6,712) MMLR(3),MMLR(3),CmEFF(3)
IF(NCMM.GE.4) THEN ! implicitly MMLR(4)=10
CmEFF(4)= CMM(4) + 0.5D0*CMM(1)*CMM(2)/DSCM
WRITE(6,710) MMLR(4),MMLR(4),CmEFF(4)
IF(NCMM.GE.5) THEN ! implicitly MMLR(5)=12
CmEFF(5)= CMM(5) + 0.5D0*CMM(1)*CMM(3)/DSCM
1 + 0.25D0*CMM(2)**2/DSCM
WRITE(6,710) MMLR(5),MMLR(5),CmEFF(5)
IF(NCMM.GE.6) THEN ! implicitly MMLR(6)=14
CmEFF(6)= CMM(6)+0.5D0*CMM(2)*CMM(3)/DSCM
1 + 0.5D0*CMM(1)*CMM(4)/DSCM
WRITE(6,710) MMLR(6),MMLR(6),CmEFF(6)
ENDIF
ENDIF
ENDIF
ENDIF
ENDIF
IF((MMLR(1).EQ.3).AND.(NCMM.GE.2)) THEN
c... Then, consider C3/C6adj & C9adj for MMLR(m)={3,6,8,(9),10,12,14} cases
CmEFF(2)= CMM(2) + 0.25D0*CMM(1)**2/DSCM
WRITE(6,712) MMLR(2),MMLR(2),CmEFF(2)
IF(NCMM.GE.3) THEN ! introduce C9adj & MMLR=9
MCMM= NCMM+1 ! placing m=9 as last power
MMLR(MCMM)= 9
CmEFF(MCMM)= 0.5d0*CMM(1)*CmEFF(2)/DSCM
WRITE(6,714) MMLR(MCMM),CmEFF(MCMM)
IF(NCMM.GE.5) THEN ! implicitly MMLR(5)=12
CmEFF(5)= CMM(5) + 0.5D0*CMM(1)*CmEFF(MCMM)/DSCM
1 + 0.25D0*CmEFF(2)**2/DSCM
WRITE(6,710) MMLR(5),MMLR(5),CmEFF(5)
IF(NCMM.GE.6) THEN ! implicitly MMLR(6)=14
CmEFF(6)= CMM(6)+0.5D0*CmEFF(2)*CMM(3)/DSCM
WRITE(6,710) MMLR(6),MMLR(6),CmEFF(6)
ENDIF
ENDIF
ENDIF
ENDIF
c** End of CmEFF= Cm + CmADJ setup ===================================
c** Now - initialize for Damping at r= REQ
CALL dampF(REQ,rhoAB,MCMM,MMLR,IVSR,IDSTT,DM,DMP,DMPP)
DO m= 1,MCMM
dLULRedCm(m)= 1.d0/REQ**MMLR(m)
IF(rhoAB.GT.0.d0) dLULRedCm(m)= Dm(m)*dLULRedCm(m)
T0= CmEFF(m)*dLULRedCm(m)
ULRe= ULRe + T0
T1= T1 + MMLR(m)*T0
ENDDO
dLULRedRe= -T1/(ULRe*REQ)
DO m= 1,MCMM
dLULRedCm(m)= dLULRedCm(m)/ULRe
IF(rhoAB.GT.0) dLULRedRe= dLULRedRe +
1 dLULRedCm(m)*Dmp(m)/Dm(m)
ENDDO
betaINF= DLOG(2.d0*DSCM/ULRe)
c*** print for MLR form
WRITE(6,602) PPAR,QPAR,DSCM,REQ
c... for Huang form: \beta(yp)= Binf*yp + [1-yp]*{power series in yq}
WRITE(6,607) PPAR,PPAR,QPAR,Nbeta,Nbeta+1,(BETA(J),J= 0,Nbeta)
IF(Rref.GT.0) THEN
WRITE(6,613) Rref
ELSE
WRITE(6,615) REQ
Rref= REQ
ENDIF
IF(rhoAB.GT.0.d0) THEN !! describe type of Damping Fx
PVSR= 0.5d0*IVSR
IF(IDSTT.GT.0) THEN !! first option: Douketis-Scoles
WRITE(6,664) rhoAB,PVSR,bDS(IVSR),cDS(IVSR),PVSR
ELSE !! second option: Tang-Toennies
LVSR= IVSR/2
WRITE(6,666) rhoAB,LVSR,bTT(LVSR)
ENDIF
ELSE !! ELSE ... for no damping ...
WRITE(6,668)
ENDIF
WRITE(6,617) betaINF,MMLR(1),CmEFF(1),MMLR(1)
IF(NCMM.GT.1) THEN
DO I= 2,NCMM
IF(MMLR(I).LE.9) WRITE(6,619) MMLR(I),CMM(I)
1 ,MMLR(I)
IF(MMLR(I).GT.9) WRITE(6,621) MMLR(I),CMM(I)
1 ,MMLR(I)
ENDDO
ENDIF
c====================================================================
602 FORMAT(/' MLR(p=',I1,', q=',I1,') Potential with: De='
1 ,F10.4,'[cm-1] Re=',F12.8,'[A]')
607 FORMAT(' with exponent coefficient beta(r)= beta{INF}*y',I1,
1 ' + [1-y',i1,']*Sum{beta_i*y',i1,'^i}'/6x,'exponent coefft. powe
2r series order',I3/6x,'and',i3,' coefficients:',1PD16.8,2D16.8:/
3 (10x,4D16.8:))
613 FORMAT(9x,'with radial variables y_p and/or y_q defined w.r.t.',
1 ' Rref=',F10.7)
615 FORMAT(6x,'radial variables y_p and/or y_q defined w.r.t.',
1 ' Rref= Re=' F10.7)
617 FORMAT(' betaINF=',f16.12,' & uLR defined by C',i1,' =',
1 1PD13.6,'[cm-1 Ang','^',0P,I1,']')
619 FORMAT(50x,'C',I1,' =',1PD13.6,'[cm-1 Ang','^',0P,I1,']')
621 FORMAT(50x,'C',I2,'=',1PD13.6,'[cm-1 Ang','^',0P,I2,']')
664 FORMAT(4x,'uLR inverse-power terms incorporate DS-type damping wit
1h rhoAB=',f10.7/8x,'defined to give very short-range Dm(r)*Cm/r
2^m behaviour r^{',SS,f4.1,'}'/8x,'Dm(r)= [1 - exp(-',f5.2,
3 '(rhoAB*r)/m -',f6.3,'(rhoAB*r)^2/sqrt{m})]^{m',SP,F4.1,'}')
666 FORMAT(4x,'uLR inverse-power terms incorporate TT-type damping wit
1h rhoAB=',f10.7/8x,'defined to give very short-range Dm(r)*Cm/r
2^m behaviour r^{',I2,'}'/8x,'Dm(r)= [1 - exp(-bTT*r)*SUM{(bTT*r
3)^k/k!}] where bTT=',f6.3,'*rhoAB')
668 FORMAT(4x,'uLR inverse-power terms incorporate NO damping function
1s')
710 Format(" 'Dattani adjustment' for MLR C",I2,' yields internal
1 C', I2,'{adj}=',1PD14.7)
712 Format(" 'Dattani adjustment' for MLR C",I1, ' yields internal
1 C', I1,'{adj}=',1PD15.8)
714 Format(" 'Dattani adjustment' for MLR(m1=3) yields internal C",
1 I1,'{adj}=',1PD15.8)
c** End of initialization & printout
REP= REQ**PPAR
IF(Rref.LE.0) AREF= REQ
IF(Rref.GT.0) AREF= Rref
AREFp= AREF**PPAR
AREFq= AREF**QPAR
ENDIF
c=======================================================================
VDIST= 0.0d0
BETADIST= 0.d0
c** Initialize parameter counter for this state ...
IPVSTART= 0
RVAL= RDIST
RINV= 1.d0/RVAL
RDp= RVAL**PPAR
RDq= RVAL**QPAR
YPE= (RDp-REP)/(RDp+REP)
YP= (RDp-AREFp)/(RDp+AREFp)
YQ= (RDq-AREFq)/(RDq+AREFq)
YPM= 1.d0 - YP
DYPDRE= -0.5d0*PPAR*(1.d0 - YP**2)/REQ
DYQDRE= -0.5d0*QPAR*(1.d0 - YQ**2)/REQ
DYPEDRE= -0.5d0*PPAR*(1.d0 - YPE**2)/REQ
DYPDR= -DYPDRE*REQ*RINV
DYPEDR= 0.5d0*PPAR*RINV*(1.d0 - YPE**2)
DYQDR= -DYQDRE*REQ*RINV
D2YPDR= -DYPDR*RINV*(1.d0 + PPAR*YP)
D2YPEDR= -DYPEDR*RINV*(1.d0 + PPAR*YPE)
D2YQDR= -DYQDR*RINV*(1.d0 + QPAR*YQ)
DYPpDRE= -PPAR*YP*RINV*DYPDRE
DYPEpDRE= -PPAR*YPE*RINV*DYPEDRE
DYQpDRE= -QPAR*YQ*RINV*DYQDRE
D2VAL= 0.d0
YPP= 1.d0
DVAL= 0.d0
DBDB(0)= 1.0d0
VAL= BETA(0) + YQ*BETA(1)
DVAL= BETA(1)
Nbeta= Nbeta
c-------------------------------------------------------------------
DO J= 2,Nbeta
c... now calculate power series part of the Morse-like exponent,along
c with its radial derivatives
D2VAL= D2VAL + BETA(J)* DBLE(J)*DBLE(J - 1) *YPP
YPP= YPP*YQ
DVAL= DVAL + BETA(J)* DBLE(J)* YPP
YPPP= YPP* YQ
VAL= VAL + BETA(J)*YPPP
DBDB(J)= YPM*YPPP
ENDDO
YPP= YPPP
c~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
c*** DBDB & DBDRe= dBeta/dRe used in uncertainty calculation in fununc.f
DBDRe= -YP*dLULRedRe
dVALdRe= DBDRe + (betaINF - VAL)*DYPDRE + (1.d0 - YP)*DVAL*DYQDRE
IF(Rref.LE.0.d0) DBDRe= dVALdRe
c-----------------------------------------------------------------------
c... now the power series and its radial derivatives are used in the
c construction of the derivatives with respect to the parameters
dBpdRe= DYPpDRE*(betaINF - VAL) - DYPDR*dLULRedRe
1 + (-DYPDR*DYQDRE + (1.d0 - YP)*DYQpDRE - DYPDRE*DYQDR)*DVAL
2 + (1.d0 - YP)*DYQDR*DYQDRE*D2VAL
D2VAL= (betaINF - VAL)*D2YPDR - 2.d0*DYPDR*DYQDR*DVAL
1 + (1.d0- YP)*(D2YQDR*DVAL + DYQDR**2*D2VAL)
DVAL= (betaINF - VAL)*DYPDR + (1.d0- YP)*DYQDR*DVAL
VAL= YP*betaINF + (1.d0- YP)*VAL
dBdR= dYPEdR*VAL + YPE*DVAL
d2BdR= d2YPEdR*VAL + 2.d0*dYPEdR*DVAL + YPE*D2VAL
dYBdRe= DYPEDRE*VAL + YPE*dVALdRe
dYBpdRe= VAL*DYPEpDRE + DYPEDRE*DVAL + DYPEDR*dVALdRe+ YPE*dBpdRe
c~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
XTEMP= DEXP(-VAL*YPE)
c** Now begin by generating uLR(r)
ULR= 0.d0
c-------------------------------------------------------------------
dULRdR= 0.d0
d2ULRdR= 0.d0
dULRdRCm= 0.d0
c~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
IF(rhoAB.GT.0.d0) THEN
CALL dampF(RVAL,rhoAB,NCMM,MMLR,IVSR,IDSTT,Dm,Dmp,Dmpp)
ENDIF
DO m= 1,NCMM
IF(rhoAB.LE.0.d0) THEN
c-----------------------------------------------------------------------
dULRdCm(m)= 1.d0*RINV**MMLR(m)
dULRdRCm(m)= -dULRdCm(m)*RINV*DBLE(MMLR(m))
dDULRdR= 0.d0
d2DULRdR= 0.d0
ELSE
dULRdCm(m)= Dm(m)*RINV**MMLR(m)
dULRdRCm(m)= -dULRdCm(m)*RINV *DBLE(MMLR(m))
2 + Dmp(m)*RINV**MMLR(m)
dDULRdR= Dmp(m)*RINV**MMLR(m)
d2DULRdR= Dmpp(m)*RINV**MMLR(m)
ENDIF
ULR= ULR + CmEFF(m)*dULRdCm(m)
dULRdR= dULRdR + CmEFF(m)*(dDULRdR
1 - dULRdCm(m)*RINV*DBLE(MMLR(m)))
d2ULRdR= d2ULRdR + CmEFF(m)*(d2DULRdR
1 - 2.d0*dDULRdR*RINV*DBLE(MMLR(m)) + dULRdCm(m)*RINV**2
2 *DBLE(MMLR(m))*DBLE((MMLR(m) + 1)))
ENDDO
dLULRdR= dULRdR/ULR
DO m= 1,NCMM
dLULRdCm(m)= dULRdCm(m)/ULR
ENDDO
c~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
XTEMP= XTEMP*ULR/ULRe
c... note ... reference energy for each state is asymptote ...
DVDD= XTEMP*(XTEMP - 2.D0)
VDIST= DSCM*DVDD
BETADIST= VAL
YPP= 2.d0*DSCM*(1.0d0-XTEMP)*XTEMP
IPV= IPVSTART+2
c... derivatives w.r.t R
DXTEMP= XTEMP*(dLULRdR - dBdR)
D2XTEMP= XTEMP*(dBdR**2 - d2BdR + (d2ULRdR - 2*dBdR*dULRdR)/ULR)
dVdR= 2.d0*DSCM*DXTEMP*(XTEMP - 1.d0)
d2VdR2= 2.d0*DSCM*(DXTEMP**2 + D2XTEMP*(XTEMP - 1.d0))
c... derivative w.r.t. De
IPV= IPVSTART+1
dXdP(IPV)= -XTEMP*YPE*YP
dXpdP(IPV)= -(XTEMP*(YPE*DYPDR + DYPEDR*YP)+ YPE*YP*DXTEMP)
DVDD= DVDD + YPP*YP*YPE/DSCM
YPP= YPP*YPE*(1.d0 - YP)
dVpdP(IPV)= 2.d0*(dXdP(IPV)*DXTEMP + (XTEMP - 1.d0)*dXpdP(IPV))
1 + 2.d0*(XTEMP - 1.d0)*DXTEMP
DVtot(IPV)= DVDD
c... derivative w.r.t. Re
IPV= IPV+1
dXdP(IPV)= -XTEMP*(dYBdRe + dLULRedRe)
dXpdP(IPV)= -DXTEMP*(dYBdRe + dLULRedRe) - XTEMP*dYBpdRe
dVpdP(IPV)= 2.d0*DSCM*(dXdP(IPV)*DXTEMP
1 + (XTEMP - 1.d0)*dXpdP(IPV))
DVtot(IPV)= YPP*(dYBdRe + dLULRedRe)
c ... derivative w.r.t. Cm's
DO m= 1, NCMM
IPV= IPV+1
dXdP(IPV)= XTEMP*(dLULRdCm(m) + (YPE*YP - 1.d0)*dLULRedCm(m))
dXpdP(IPV)= DEXP(-VAL*YPE)/ULRe*(dULRdRCm(m)- dBdR*dULRdCm(m))
1 + (DXTEMP*(YPE*YP - 1.d0) + XTEMP*(dYPEdR*YP
2 + YPE*dYPdR))*dLULRedCm(m)
dVpdP(IPV)= 2.d0*DSCM*(dXdP(IPV)*DXTEMP
1 + (XTEMP - 1.d0)*dXpdP(IPV))
ENDDO
c... finally ... derivatives w.r.t. exponent expansion coefficients
DO J= 0,Nbeta
IPV= IPV+1
dXdP(IPV)= XTEMP*YPE*(1.d0 - YP)*YQ**J
dXpdP(IPV)= (XTEMP*((1.d0 - YP)*DYPEDR - DYPDR*YQ)
1 + YPE*(1.d0 - YP)*DXTEMP)*YQ**J + XTEMP*J*(YPE
2 *(1.d0 - YP))*YQ**(J - 1)
dVpdP(IPV)= 2.d0*DSCM*(dXdP(IPV)*DXTEMP
1 + (XTEMP - 1.d0)*dXpdP(IPV))
DVtot(IPV)= YPP
YPP= YPP*YQ
ENDDO
ccccc Print for testing
cc rewind(10)
cc write(10,610) (RD(i),vpot(i,istate),BETAFX(i,istate),
cc 1 i= 1, NDATPT,50)
cc610 FORMAT(/(f10.4,f15.5,f12.6))
ccccc End of Print for testing
c======================================================================
c**************************** BLOCK END ******************************72
999 RETURN
END
c23456789 123456789 123456789 123456789 123456789 123456789 123456789 12
c***********************************************************************
SUBROUTINE dampF(r,rhoAB,NCMM,MMLR,IVSR,IDSTT,DM,DMP,DMPP)
c** Subroutine to generate values 'Dm' and its first `Dmp' and second
c 'Dmpp' derivatives w.r.t. r of the chosen form of the damping
c function, for m= 1 to MMAX.
c---------------------- RJL Version of 05 August 2014 ------------------
c-----------------------------------------------------------------------
c Upon Input
c* r - the radial distance in Angsroms (!)
c* RHOab 'universal' scaling coefficient used for systems other than H_2
c RHOab= 2*(RHOa*RHOb)/(RHOa+RHOb) where RHOa = (I_p^A/I_p^H)^0.66
c where I_p^A is the ionization potential of atom A
c and I_p^H is the ionization potential of atomic hydrogen
c* NCMM the number of inverse-power terms to be considered
c* MMLR are the powers of the NCMM inverse-power terms
c* IVSR defines damping s.th. Dm(r)/r^m --> r^{IVSR/2} as r --> 0
c* IDSTT specifies damping function type: > 0 use Douketis et al. form
c if IDSTT .LE. 0 use Tang-Toennies form
c-----------------------------------------------------------------------
c Upon Output
c DM(m) - The value of the damping function for the long range term
c C_MMLR(m)/r^MMLR(m) {m= 1, NCMM}
c DMP(m): first derivative of the damping function DM(m) w.r.t. r
c DMPP(m): second derivative of the damping function DM(m) w.r.t. r
c-----------------------------------------------------------------------
INTEGER NCMM,NCMMax,MMLR(NCMM),IVSR,IDSTT,IVSRF,FIRST, Lsr,m,
1 MM,MMAX,MMTEMP
REAL*8 r,rhoAB,bTT(-2:2),cDS(-4:4),bDS(-4:4),aTT,br,XP,YP,
1 TK, DM(NCMM),DMP(NCMM),DMPP(NCMM),SM(-3:25),
2 bpm(20,-4:0), cpm(20,-4:0),ZK
c------------------------------------------------------------------------
c The following values for the numerical factors used in both TT and DS
c were normalized to the Hydrogen data presented
c by Kreek and Meath in J.Chem.Phys. 50, 2289 (1969).
c The ratio has been chosen such that b= FACTOR*(I_p^X / I_p^H)^{2/3}
c for the homoatomic diatomic species X_2, where I_p^A is the ionization
c------------------------------------------------------------------------
DATA bTT/2.10d0,2.44d0,2.78d0,3.13d0,3.47d0/
DATA bDS/2.50d0,2.90d0,3.30d0,3.69d0,3.95d0,0.d0,4.53d0,0.d0,
1 4.99d0/
DATA cDS/0.468d0,0.446d0,0.423d0,0.405d0,0.390d0,0.d0,0.360d0,
1 0.d0,0.340d0/
DATA FIRST/ 1/
SAVE FIRST, bpm, cpm
c------------------------------------------------------------------------
MMTEMP = MMLR(1) ! temporary substn.: corrected@end
IF(MMLR(1).LE.0) MMLR(1) = 1 ! enforce stability for A-F cases
IF(RHOab.LE.0) THEN
DO m=1,NCMMax
DM(m)=1.d0
DMP(m)= 0.d0
DMPP(m)= 0.d0
ENDDO
WRITE(6,602) RHOab
RETURN
ENDIF
IF(IDSTT.LE.0) THEN
c===========================================
c** For Tang-Toennies type damping functions
c===========================================
Lsr= IVSR/2
IF((IVSR.LT.-4).OR.(IVSR.GT.4).OR.((2*LSR).NE.IVSR)) THEN
WRITE(6,600) 'TT',IVSR
STOP
ENDIF
MMAX= MMLR(NCMM) + Lsr - 1
aTT= RHOab*bTT(Lsr)
br= aTT*r
XP= DEXP(-br)
SM(-3)= 0.d0
SM(-2)= 0.d0
SM(-1)= 0.d0
SM(0)= 1.d0
TK= 1.d0
IF(br.GT.0.5d0) THEN
DO m= 1,MMAX
TK= TK*br/DFLOAT(m)
SM(m)= SM(m-1)+ TK
ENDDO
DO m= 1, NCMM
MM= MMLR(m) - 1 + Lsr
DM(m)= 1.d0 - XP*SM(MM)
DMP(m)= aTT*XP*(SM(MM) - SM(MM-1))
DMPP(m)= -aTT*aTT*XP*(SM(MM)
1 - 2.d0*SM(MM-1) + SM(MM-2))
ENDDO
c-----------------------------------------------------------------------
c The above section handles the calculation of the value of the damping
c function for most values of r. However, at very small r that algorithm
c becomes unstable due to numerical noise. To avoid this, if the
c argument is very small it is re-evaluated as a finite sum ...
c-----------------------------------------------------------------------
ELSE
MMAX= MMAX+5
DO m= 1, MMAX
c... NOTE that here SM(m) is the m'th term (b*r)^m/m! [not a sum]
SM(m)= SM(m-1)*br/DFLOAT(m)
ENDDO
DO m= 1, NCMM
MM= MMLR(m) + Lsr
DM(m)= XP*(SM(MM)+ SM(MM+1)+ SM(MM+2)+ SM(MM+3)
1 + SM(MM+4))
DMP(m)= aTT*XP*SM(m-1)
DMPP(m)= aTT*aTT*XP*(SM(m-2)-SM(m-1))
ENDDO
ENDIF
ENDIF
c
IF(IDSTT.GT.0) THEN
c=======================================================================
c** For Douketis-Scoles-Marchetti-Zen-Thakkar type damping function ...
c=======================================================================
IF((IVSR.LT.-4).OR.(IVSR.GT.4).OR.(IVSR.EQ.1).OR.(IVSR.EQ.3))
1 THEN
WRITE(6,600) 'DS',IVSR
STOP
ENDIF
IF(FIRST.EQ.1) THEN
DO m= 1, 20
DO IVSRF= -4,0
bpm(m,IVSRF)= bDS(IVSRF)/DFLOAT(m)
cpm(m,IVSRF)= cDS(IVSRF)/DSQRT(DFLOAT(m))
ENDDO
ENDDO
FIRST= 0
ENDIF
br= rhoAB*r
DO m= 1, NCMM
MM= MMLR(m)
XP= DEXP(-(bpm(MM,IVSR) + cpm(MM,IVSR)*br)*br)
YP= 1.d0 - XP
ZK= MM + 0.5d0*IVSR
DM(m)= YP**ZK
TK= (bpm(MM,IVSR) + 2.d0*cpm(MM,IVSR)*br)*rhoAB
DMP(m) = ZK*XP*TK*DM(m)/YP
c ... calculate second derivative [for DELR case] {check this!}
DMPP(m)= (ZK-1.d0)*DMP(m)*(XP*TK)/YP
1 - DMP(m)*TK + DMP(m)*2.d0*cpm(MM,IVSR)*rhoAB**2/TK
ENDDO
ENDIF
MMLR(1) = MMTEMP
RETURN
600 FORMAT(/,' *** ERROR *** For ',A2,'-damping functions not yet de
1fined for IVSR=',i3)
602 FORMAT( /,' ***ERROR *** should not call dampF when rhoAB=',
1 F7.4)
END
c23456789 123456789 123456789 123456789 123456789 123456789 123456789 12