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
|
c Extern "C" declaration has the form:
c
c void meam_force_(int *, int *, int *, double *, int *, int *, int *, double *,
c int *, int *, int *, int *, double *, double *,
c double *, double *, double *, double *, double *, double *,
c double *, double *, double *, double *, double *, double *,
c double *, double *, double *, double *, double *, double *, int *);
c
c Call from pair_meam.cpp has the form:
c
c meam_force_(&i,&nmax,&eflag_either,&eflag_global,&eflag_atom,&vflag_atom,
c &eng_vdwl,eatom,&ntype,type,fmap,&x[0][0],
c &numneigh[i],firstneigh[i],&numneigh_full[i],firstneigh_full[i],
c &scrfcn[offset],&dscrfcn[offset],&fcpair[offset],
c dgamma1,dgamma2,dgamma3,rho0,rho1,rho2,rho3,frhop,
c &arho1[0][0],&arho2[0][0],arho2b,&arho3[0][0],&arho3b[0][0],
c &t_ave[0][0],&tsq_ave[0][0],&f[0][0],&vatom[0][0],&errorflag);
c
subroutine meam_force(i, nmax,
$ eflag_either, eflag_global, eflag_atom, vflag_atom,
$ eng_vdwl, eatom, ntype, type, fmap, x,
$ numneigh, firstneigh, numneigh_full, firstneigh_full,
$ scrfcn, dscrfcn, fcpair,
$ dGamma1, dGamma2, dGamma3, rho0, rho1, rho2, rho3, fp,
$ Arho1, Arho2, Arho2b, Arho3, Arho3b, t_ave, tsq_ave, f,
$ vatom, errorflag)
use meam_data
implicit none
integer eflag_either, eflag_global, eflag_atom, vflag_atom
integer nmax, ntype, type, fmap
real*8 eng_vdwl, eatom, x
integer numneigh, firstneigh, numneigh_full, firstneigh_full
real*8 scrfcn, dscrfcn, fcpair
real*8 dGamma1, dGamma2, dGamma3
real*8 rho0, rho1, rho2, rho3, fp
real*8 Arho1, Arho2, Arho2b
real*8 Arho3, Arho3b
real*8 t_ave, tsq_ave, f, vatom
integer errorflag
dimension eatom(nmax)
dimension type(nmax), fmap(ntype)
dimension x(3,nmax)
dimension firstneigh(numneigh), firstneigh_full(numneigh_full)
dimension scrfcn(numneigh), dscrfcn(numneigh), fcpair(numneigh)
dimension dGamma1(nmax), dGamma2(nmax), dGamma3(nmax)
dimension rho0(nmax), rho1(nmax), rho2(nmax), rho3(nmax), fp(nmax)
dimension Arho1(3,nmax), Arho2(6,nmax), Arho2b(nmax)
dimension Arho3(10,nmax), Arho3b(3,nmax)
dimension t_ave(3,nmax), tsq_ave(3,nmax), f(3,nmax), vatom(6,nmax)
integer i,j,jn,k,kn,kk,m,n,p,q
integer nv2,nv3,elti,eltj,eltk,ind
real*8 xitmp,yitmp,zitmp,delij(3),delref(3),rij2,rij,rij3
real*8 delik(3),deljk(3),v(6),fi(3),fj(3)
real*8 Eu,astar,astarp,third,sixth
real*8 pp,phiforce,dUdrij,dUdsij,dUdrijm(3),force,forcem
real*8 B,r,recip,phi,phip,rhop,a
real*8 sij,fcij,dfcij,ds(3)
real*8 a0,a1,a1i,a1j,a2,a2i,a2j
real*8 a3i,a3j,a3i1,a3i2,a3j1,a3j2
real*8 G,dG,Gbar,dGbar,gam,shpi(3),shpj(3),Z,denom
real*8 ai,aj,ro0i,ro0j,invrei,invrej
real*8 b0,rhoa0j,drhoa0j,rhoa0i,drhoa0i
real*8 b1,rhoa1j,drhoa1j,rhoa1i,drhoa1i
real*8 b2,rhoa2j,drhoa2j,rhoa2i,drhoa2i
real*8 a3,a3a,b3,rhoa3j,drhoa3j,rhoa3i,drhoa3i
real*8 drho0dr1,drho0dr2,drho0ds1,drho0ds2
real*8 drho1dr1,drho1dr2,drho1ds1,drho1ds2
real*8 drho1drm1(3),drho1drm2(3)
real*8 drho2dr1,drho2dr2,drho2ds1,drho2ds2
real*8 drho2drm1(3),drho2drm2(3)
real*8 drho3dr1,drho3dr2,drho3ds1,drho3ds2
real*8 drho3drm1(3),drho3drm2(3)
real*8 dt1dr1,dt1dr2,dt1ds1,dt1ds2
real*8 dt2dr1,dt2dr2,dt2ds1,dt2ds2
real*8 dt3dr1,dt3dr2,dt3ds1,dt3ds2
real*8 drhodr1,drhodr2,drhods1,drhods2,drhodrm1(3),drhodrm2(3)
real*8 arg,arg1,arg2
real*8 arg1i1,arg1j1,arg1i2,arg1j2,arg2i2,arg2j2
real*8 arg1i3,arg1j3,arg2i3,arg2j3,arg3i3,arg3j3
real*8 dsij1,dsij2,force1,force2
real*8 t1i,t2i,t3i,t1j,t2j,t3j
errorflag = 0
third = 1.0/3.0
sixth = 1.0/6.0
c Compute forces atom i
elti = fmap(type(i))
if (elti.gt.0) then
xitmp = x(1,i)
yitmp = x(2,i)
zitmp = x(3,i)
c Treat each pair
do jn = 1,numneigh
j = firstneigh(jn)
eltj = fmap(type(j))
if (scrfcn(jn).ne.0.d0.and.eltj.gt.0) then
sij = scrfcn(jn)*fcpair(jn)
delij(1) = x(1,j) - xitmp
delij(2) = x(2,j) - yitmp
delij(3) = x(3,j) - zitmp
rij2 = delij(1)*delij(1) + delij(2)*delij(2)
$ + delij(3)*delij(3)
if (rij2.lt.cutforcesq) then
rij = sqrt(rij2)
r = rij
c Compute phi and phip
ind = eltind(elti,eltj)
pp = rij*rdrar + 1.0D0
kk = pp
kk = min(kk,nrar-1)
pp = pp - kk
pp = min(pp,1.0D0)
phi = ((phirar3(kk,ind)*pp + phirar2(kk,ind))*pp
$ + phirar1(kk,ind))*pp + phirar(kk,ind)
phip = (phirar6(kk,ind)*pp + phirar5(kk,ind))*pp
$ + phirar4(kk,ind)
recip = 1.0d0/r
if (eflag_either.ne.0) then
if (eflag_global.ne.0) eng_vdwl = eng_vdwl + phi*sij
if (eflag_atom.ne.0) then
eatom(i) = eatom(i) + 0.5*phi*sij
eatom(j) = eatom(j) + 0.5*phi*sij
endif
endif
c write(1,*) "force_meamf: phi: ",phi
c write(1,*) "force_meamf: phip: ",phip
c Compute pair densities and derivatives
invrei = 1.d0/re_meam(elti,elti)
ai = rij*invrei - 1.d0
ro0i = rho0_meam(elti)
rhoa0i = ro0i*fm_exp(-beta0_meam(elti)*ai)
drhoa0i = -beta0_meam(elti)*invrei*rhoa0i
rhoa1i = ro0i*fm_exp(-beta1_meam(elti)*ai)
drhoa1i = -beta1_meam(elti)*invrei*rhoa1i
rhoa2i = ro0i*fm_exp(-beta2_meam(elti)*ai)
drhoa2i = -beta2_meam(elti)*invrei*rhoa2i
rhoa3i = ro0i*fm_exp(-beta3_meam(elti)*ai)
drhoa3i = -beta3_meam(elti)*invrei*rhoa3i
if (elti.ne.eltj) then
invrej = 1.d0/re_meam(eltj,eltj)
aj = rij*invrej - 1.d0
ro0j = rho0_meam(eltj)
rhoa0j = ro0j*fm_exp(-beta0_meam(eltj)*aj)
drhoa0j = -beta0_meam(eltj)*invrej*rhoa0j
rhoa1j = ro0j*fm_exp(-beta1_meam(eltj)*aj)
drhoa1j = -beta1_meam(eltj)*invrej*rhoa1j
rhoa2j = ro0j*fm_exp(-beta2_meam(eltj)*aj)
drhoa2j = -beta2_meam(eltj)*invrej*rhoa2j
rhoa3j = ro0j*fm_exp(-beta3_meam(eltj)*aj)
drhoa3j = -beta3_meam(eltj)*invrej*rhoa3j
else
rhoa0j = rhoa0i
drhoa0j = drhoa0i
rhoa1j = rhoa1i
drhoa1j = drhoa1i
rhoa2j = rhoa2i
drhoa2j = drhoa2i
rhoa3j = rhoa3i
drhoa3j = drhoa3i
endif
if (ialloy.eq.1) then
rhoa1j = rhoa1j * t1_meam(eltj)
rhoa2j = rhoa2j * t2_meam(eltj)
rhoa3j = rhoa3j * t3_meam(eltj)
rhoa1i = rhoa1i * t1_meam(elti)
rhoa2i = rhoa2i * t2_meam(elti)
rhoa3i = rhoa3i * t3_meam(elti)
drhoa1j = drhoa1j * t1_meam(eltj)
drhoa2j = drhoa2j * t2_meam(eltj)
drhoa3j = drhoa3j * t3_meam(eltj)
drhoa1i = drhoa1i * t1_meam(elti)
drhoa2i = drhoa2i * t2_meam(elti)
drhoa3i = drhoa3i * t3_meam(elti)
endif
nv2 = 1
nv3 = 1
arg1i1 = 0.d0
arg1j1 = 0.d0
arg1i2 = 0.d0
arg1j2 = 0.d0
arg1i3 = 0.d0
arg1j3 = 0.d0
arg3i3 = 0.d0
arg3j3 = 0.d0
do n = 1,3
do p = n,3
do q = p,3
arg = delij(n)*delij(p)*delij(q)*v3D(nv3)
arg1i3 = arg1i3 + Arho3(nv3,i)*arg
arg1j3 = arg1j3 - Arho3(nv3,j)*arg
nv3 = nv3+1
enddo
arg = delij(n)*delij(p)*v2D(nv2)
arg1i2 = arg1i2 + Arho2(nv2,i)*arg
arg1j2 = arg1j2 + Arho2(nv2,j)*arg
nv2 = nv2+1
enddo
arg1i1 = arg1i1 + Arho1(n,i)*delij(n)
arg1j1 = arg1j1 - Arho1(n,j)*delij(n)
arg3i3 = arg3i3 + Arho3b(n,i)*delij(n)
arg3j3 = arg3j3 - Arho3b(n,j)*delij(n)
enddo
c rho0 terms
drho0dr1 = drhoa0j * sij
drho0dr2 = drhoa0i * sij
c rho1 terms
a1 = 2*sij/rij
drho1dr1 = a1*(drhoa1j-rhoa1j/rij)*arg1i1
drho1dr2 = a1*(drhoa1i-rhoa1i/rij)*arg1j1
a1 = 2.d0*sij/rij
do m = 1,3
drho1drm1(m) = a1*rhoa1j*Arho1(m,i)
drho1drm2(m) = -a1*rhoa1i*Arho1(m,j)
enddo
c rho2 terms
a2 = 2*sij/rij2
drho2dr1 = a2*(drhoa2j - 2*rhoa2j/rij)*arg1i2
$ - 2.d0/3.d0*Arho2b(i)*drhoa2j*sij
drho2dr2 = a2*(drhoa2i - 2*rhoa2i/rij)*arg1j2
$ - 2.d0/3.d0*Arho2b(j)*drhoa2i*sij
a2 = 4*sij/rij2
do m = 1,3
drho2drm1(m) = 0.d0
drho2drm2(m) = 0.d0
do n = 1,3
drho2drm1(m) = drho2drm1(m)
$ + Arho2(vind2D(m,n),i)*delij(n)
drho2drm2(m) = drho2drm2(m)
$ - Arho2(vind2D(m,n),j)*delij(n)
enddo
drho2drm1(m) = a2*rhoa2j*drho2drm1(m)
drho2drm2(m) = -a2*rhoa2i*drho2drm2(m)
enddo
c rho3 terms
rij3 = rij*rij2
a3 = 2*sij/rij3
a3a = 6.d0/5.d0*sij/rij
drho3dr1 = a3*(drhoa3j - 3*rhoa3j/rij)*arg1i3
$ - a3a*(drhoa3j - rhoa3j/rij)*arg3i3
drho3dr2 = a3*(drhoa3i - 3*rhoa3i/rij)*arg1j3
$ - a3a*(drhoa3i - rhoa3i/rij)*arg3j3
a3 = 6*sij/rij3
a3a = 6*sij/(5*rij)
do m = 1,3
drho3drm1(m) = 0.d0
drho3drm2(m) = 0.d0
nv2 = 1
do n = 1,3
do p = n,3
arg = delij(n)*delij(p)*v2D(nv2)
drho3drm1(m) = drho3drm1(m)
$ + Arho3(vind3D(m,n,p),i)*arg
drho3drm2(m) = drho3drm2(m)
$ + Arho3(vind3D(m,n,p),j)*arg
nv2 = nv2 + 1
enddo
enddo
drho3drm1(m) = (a3*drho3drm1(m) - a3a*Arho3b(m,i))
$ *rhoa3j
drho3drm2(m) = (-a3*drho3drm2(m) + a3a*Arho3b(m,j))
$ *rhoa3i
enddo
c Compute derivatives of weighting functions t wrt rij
t1i = t_ave(1,i)
t2i = t_ave(2,i)
t3i = t_ave(3,i)
t1j = t_ave(1,j)
t2j = t_ave(2,j)
t3j = t_ave(3,j)
if (ialloy.eq.1) then
a1i = 0.d0
a1j = 0.d0
a2i = 0.d0
a2j = 0.d0
a3i = 0.d0
a3j = 0.d0
if ( tsq_ave(1,i) .ne. 0.d0 ) then
a1i = drhoa0j*sij/tsq_ave(1,i)
endif
if ( tsq_ave(1,j) .ne. 0.d0 ) then
a1j = drhoa0i*sij/tsq_ave(1,j)
endif
if ( tsq_ave(2,i) .ne. 0.d0 ) then
a2i = drhoa0j*sij/tsq_ave(2,i)
endif
if ( tsq_ave(2,j) .ne. 0.d0 ) then
a2j = drhoa0i*sij/tsq_ave(2,j)
endif
if ( tsq_ave(3,i) .ne. 0.d0 ) then
a3i = drhoa0j*sij/tsq_ave(3,i)
endif
if ( tsq_ave(3,j) .ne. 0.d0 ) then
a3j = drhoa0i*sij/tsq_ave(3,j)
endif
dt1dr1 = a1i*(t1_meam(eltj)-t1i*t1_meam(eltj)**2)
dt1dr2 = a1j*(t1_meam(elti)-t1j*t1_meam(elti)**2)
dt2dr1 = a2i*(t2_meam(eltj)-t2i*t2_meam(eltj)**2)
dt2dr2 = a2j*(t2_meam(elti)-t2j*t2_meam(elti)**2)
dt3dr1 = a3i*(t3_meam(eltj)-t3i*t3_meam(eltj)**2)
dt3dr2 = a3j*(t3_meam(elti)-t3j*t3_meam(elti)**2)
else if (ialloy.eq.2) then
dt1dr1 = 0.d0
dt1dr2 = 0.d0
dt2dr1 = 0.d0
dt2dr2 = 0.d0
dt3dr1 = 0.d0
dt3dr2 = 0.d0
else
ai = 0.d0
if( rho0(i) .ne. 0.d0 ) then
ai = drhoa0j*sij/rho0(i)
end if
aj = 0.d0
if( rho0(j) .ne. 0.d0 ) then
aj = drhoa0i*sij/rho0(j)
end if
dt1dr1 = ai*(t1_meam(eltj)-t1i)
dt1dr2 = aj*(t1_meam(elti)-t1j)
dt2dr1 = ai*(t2_meam(eltj)-t2i)
dt2dr2 = aj*(t2_meam(elti)-t2j)
dt3dr1 = ai*(t3_meam(eltj)-t3i)
dt3dr2 = aj*(t3_meam(elti)-t3j)
endif
c Compute derivatives of total density wrt rij, sij and rij(3)
call get_shpfcn(shpi,lattce_meam(elti,elti))
call get_shpfcn(shpj,lattce_meam(eltj,eltj))
drhodr1 = dGamma1(i)*drho0dr1
$ + dGamma2(i)*
$ (dt1dr1*rho1(i)+t1i*drho1dr1
$ + dt2dr1*rho2(i)+t2i*drho2dr1
$ + dt3dr1*rho3(i)+t3i*drho3dr1)
$ - dGamma3(i)*
$ (shpi(1)*dt1dr1+shpi(2)*dt2dr1+shpi(3)*dt3dr1)
drhodr2 = dGamma1(j)*drho0dr2
$ + dGamma2(j)*
$ (dt1dr2*rho1(j)+t1j*drho1dr2
$ + dt2dr2*rho2(j)+t2j*drho2dr2
$ + dt3dr2*rho3(j)+t3j*drho3dr2)
$ - dGamma3(j)*
$ (shpj(1)*dt1dr2+shpj(2)*dt2dr2+shpj(3)*dt3dr2)
do m = 1,3
drhodrm1(m) = 0.d0
drhodrm2(m) = 0.d0
drhodrm1(m) = dGamma2(i)*
$ (t1i*drho1drm1(m)
$ + t2i*drho2drm1(m)
$ + t3i*drho3drm1(m))
drhodrm2(m) = dGamma2(j)*
$ (t1j*drho1drm2(m)
$ + t2j*drho2drm2(m)
$ + t3j*drho3drm2(m))
enddo
c Compute derivatives wrt sij, but only if necessary
if (dscrfcn(jn).ne.0.d0) then
drho0ds1 = rhoa0j
drho0ds2 = rhoa0i
a1 = 2.d0/rij
drho1ds1 = a1*rhoa1j*arg1i1
drho1ds2 = a1*rhoa1i*arg1j1
a2 = 2.d0/rij2
drho2ds1 = a2*rhoa2j*arg1i2
$ - 2.d0/3.d0*Arho2b(i)*rhoa2j
drho2ds2 = a2*rhoa2i*arg1j2
$ - 2.d0/3.d0*Arho2b(j)*rhoa2i
a3 = 2.d0/rij3
a3a = 6.d0/(5.d0*rij)
drho3ds1 = a3*rhoa3j*arg1i3 - a3a*rhoa3j*arg3i3
drho3ds2 = a3*rhoa3i*arg1j3 - a3a*rhoa3i*arg3j3
if (ialloy.eq.1) then
a1i = 0.d0
a1j = 0.d0
a2i = 0.d0
a2j = 0.d0
a3i = 0.d0
a3j = 0.d0
if ( tsq_ave(1,i) .ne. 0.d0 ) then
a1i = rhoa0j/tsq_ave(1,i)
endif
if ( tsq_ave(1,j) .ne. 0.d0 ) then
a1j = rhoa0i/tsq_ave(1,j)
endif
if ( tsq_ave(2,i) .ne. 0.d0 ) then
a2i = rhoa0j/tsq_ave(2,i)
endif
if ( tsq_ave(2,j) .ne. 0.d0 ) then
a2j = rhoa0i/tsq_ave(2,j)
endif
if ( tsq_ave(3,i) .ne. 0.d0 ) then
a3i = rhoa0j/tsq_ave(3,i)
endif
if ( tsq_ave(3,j) .ne. 0.d0 ) then
a3j = rhoa0i/tsq_ave(3,j)
endif
dt1ds1 = a1i*(t1_meam(eltj)-t1i*t1_meam(eltj)**2)
dt1ds2 = a1j*(t1_meam(elti)-t1j*t1_meam(elti)**2)
dt2ds1 = a2i*(t2_meam(eltj)-t2i*t2_meam(eltj)**2)
dt2ds2 = a2j*(t2_meam(elti)-t2j*t2_meam(elti)**2)
dt3ds1 = a3i*(t3_meam(eltj)-t3i*t3_meam(eltj)**2)
dt3ds2 = a3j*(t3_meam(elti)-t3j*t3_meam(elti)**2)
else if (ialloy.eq.2) then
dt1ds1 = 0.d0
dt1ds2 = 0.d0
dt2ds1 = 0.d0
dt2ds2 = 0.d0
dt3ds1 = 0.d0
dt3ds2 = 0.d0
else
ai = 0.d0
if( rho0(i) .ne. 0.d0 ) then
ai = rhoa0j/rho0(i)
end if
aj = 0.d0
if( rho0(j) .ne. 0.d0 ) then
aj = rhoa0i/rho0(j)
end if
dt1ds1 = ai*(t1_meam(eltj)-t1i)
dt1ds2 = aj*(t1_meam(elti)-t1j)
dt2ds1 = ai*(t2_meam(eltj)-t2i)
dt2ds2 = aj*(t2_meam(elti)-t2j)
dt3ds1 = ai*(t3_meam(eltj)-t3i)
dt3ds2 = aj*(t3_meam(elti)-t3j)
endif
drhods1 = dGamma1(i)*drho0ds1
$ + dGamma2(i)*
$ (dt1ds1*rho1(i)+t1i*drho1ds1
$ + dt2ds1*rho2(i)+t2i*drho2ds1
$ + dt3ds1*rho3(i)+t3i*drho3ds1)
$ - dGamma3(i)*
$ (shpi(1)*dt1ds1+shpi(2)*dt2ds1+shpi(3)*dt3ds1)
drhods2 = dGamma1(j)*drho0ds2
$ + dGamma2(j)*
$ (dt1ds2*rho1(j)+t1j*drho1ds2
$ + dt2ds2*rho2(j)+t2j*drho2ds2
$ + dt3ds2*rho3(j)+t3j*drho3ds2)
$ - dGamma3(j)*
$ (shpj(1)*dt1ds2+shpj(2)*dt2ds2+shpj(3)*dt3ds2)
endif
c Compute derivatives of energy wrt rij, sij and rij(3)
dUdrij = phip*sij
$ + fp(i)*drhodr1 + fp(j)*drhodr2
dUdsij = 0.d0
if (dscrfcn(jn).ne.0.d0) then
dUdsij = phi
$ + fp(i)*drhods1 + fp(j)*drhods2
endif
do m = 1,3
dUdrijm(m) = fp(i)*drhodrm1(m) + fp(j)*drhodrm2(m)
enddo
c Add the part of the force due to dUdrij and dUdsij
force = dUdrij*recip + dUdsij*dscrfcn(jn)
do m = 1,3
forcem = delij(m)*force + dUdrijm(m)
f(m,i) = f(m,i) + forcem
f(m,j) = f(m,j) - forcem
enddo
c Tabulate per-atom virial as symmetrized stress tensor
if (vflag_atom.ne.0) then
fi(1) = delij(1)*force + dUdrijm(1)
fi(2) = delij(2)*force + dUdrijm(2)
fi(3) = delij(3)*force + dUdrijm(3)
v(1) = -0.5 * (delij(1) * fi(1))
v(2) = -0.5 * (delij(2) * fi(2))
v(3) = -0.5 * (delij(3) * fi(3))
v(4) = -0.25 * (delij(1)*fi(2) + delij(2)*fi(1))
v(5) = -0.25 * (delij(1)*fi(3) + delij(3)*fi(1))
v(6) = -0.25 * (delij(2)*fi(3) + delij(3)*fi(2))
vatom(1,i) = vatom(1,i) + v(1)
vatom(2,i) = vatom(2,i) + v(2)
vatom(3,i) = vatom(3,i) + v(3)
vatom(4,i) = vatom(4,i) + v(4)
vatom(5,i) = vatom(5,i) + v(5)
vatom(6,i) = vatom(6,i) + v(6)
vatom(1,j) = vatom(1,j) + v(1)
vatom(2,j) = vatom(2,j) + v(2)
vatom(3,j) = vatom(3,j) + v(3)
vatom(4,j) = vatom(4,j) + v(4)
vatom(5,j) = vatom(5,j) + v(5)
vatom(6,j) = vatom(6,j) + v(6)
endif
c Now compute forces on other atoms k due to change in sij
if (sij.eq.0.d0.or.sij.eq.1.d0) goto 100
do kn = 1,numneigh_full
k = firstneigh_full(kn)
eltk = fmap(type(k))
if (k.ne.j.and.eltk.gt.0) then
call dsij(i,j,k,jn,nmax,numneigh,rij2,dsij1,dsij2,
$ ntype,type,fmap,x,scrfcn,fcpair)
if (dsij1.ne.0.d0.or.dsij2.ne.0.d0) then
force1 = dUdsij*dsij1
force2 = dUdsij*dsij2
do m = 1,3
delik(m) = x(m,k) - x(m,i)
deljk(m) = x(m,k) - x(m,j)
enddo
do m = 1,3
f(m,i) = f(m,i) + force1*delik(m)
f(m,j) = f(m,j) + force2*deljk(m)
f(m,k) = f(m,k) - force1*delik(m)
$ - force2*deljk(m)
enddo
c Tabulate per-atom virial as symmetrized stress tensor
if (vflag_atom.ne.0) then
fi(1) = force1*delik(1)
fi(2) = force1*delik(2)
fi(3) = force1*delik(3)
fj(1) = force2*deljk(1)
fj(2) = force2*deljk(2)
fj(3) = force2*deljk(3)
v(1) = -third * (delik(1)*fi(1) + deljk(1)*fj(1))
v(2) = -third * (delik(2)*fi(2) + deljk(2)*fj(2))
v(3) = -third * (delik(3)*fi(3) + deljk(3)*fj(3))
v(4) = -sixth * (delik(1)*fi(2) + deljk(1)*fj(2) +
$ delik(2)*fi(1) + deljk(2)*fj(1))
v(5) = -sixth * (delik(1)*fi(3) + deljk(1)*fj(3) +
$ delik(3)*fi(1) + deljk(3)*fj(1))
v(6) = -sixth * (delik(2)*fi(3) + deljk(2)*fj(3) +
$ delik(3)*fi(2) + deljk(3)*fj(2))
vatom(1,i) = vatom(1,i) + v(1)
vatom(2,i) = vatom(2,i) + v(2)
vatom(3,i) = vatom(3,i) + v(3)
vatom(4,i) = vatom(4,i) + v(4)
vatom(5,i) = vatom(5,i) + v(5)
vatom(6,i) = vatom(6,i) + v(6)
vatom(1,j) = vatom(1,j) + v(1)
vatom(2,j) = vatom(2,j) + v(2)
vatom(3,j) = vatom(3,j) + v(3)
vatom(4,j) = vatom(4,j) + v(4)
vatom(5,j) = vatom(5,j) + v(5)
vatom(6,j) = vatom(6,j) + v(6)
vatom(1,k) = vatom(1,k) + v(1)
vatom(2,k) = vatom(2,k) + v(2)
vatom(3,k) = vatom(3,k) + v(3)
vatom(4,k) = vatom(4,k) + v(4)
vatom(5,k) = vatom(5,k) + v(5)
vatom(6,k) = vatom(6,k) + v(6)
endif
endif
endif
c end of k loop
enddo
endif
100 continue
endif
c end of j loop
enddo
c else if elti=0, this is not a meam atom
endif
return
end
|
