-
Notifications
You must be signed in to change notification settings - Fork 14
/
Copy pathmd-multitimestep.f
527 lines (400 loc) · 18.3 KB
/
md-multitimestep.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
********************************************************************************
** FICHE F.21. MULTIPLE TIMESTEP MOLECULAR DYNAMICS **
** This FORTRAN code is intended to illustrate points made in the text. **
** To our knowledge it works correctly. However it is the responsibility of **
** the user to test it, if it is to be used in a research application. **
********************************************************************************
SUBROUTINE FORMTS ( STEP, DT, RCUT, RPRIM, BOX, NTS, V, W )
COMMON / BLOCK1 / RX, RY, RZ, RX1, RY1, RZ1,
: RX2, RY2, RZ2, RX3, RY3, RZ3,
: FX, FY, FZ
COMMON / BLOCK2 / POINT, LIST
COMMON / BLOCK3 / FXS, FYS, FZS, FX1, FY1, FZ1,
: FX2, FY2, FZ2, FX3, FY3, FZ3,
: VS, V1, V2, V3, WS, W1, W2, W3, START
C *******************************************************************
C ** CALCULATES THE FORCE ON AN ATOM USING THE MTS METHOD **
C ** **
C ** PRINCIPAL VARIABLES **
C ** **
C ** REAL STEP NUMBER OF CURRENT TIME STEP **
C ** REAL RCUT CUTOFF DISTANCE FOR THE FORCE **
C ** REAL RPRIM RADIUS OF THE PRIMARY LIST **
C ** REAL BOX BOX LENGTH IN SIGMA **
C ** REAL V POTENTIAL ENERGY **
C ** REAL W VIRIAL **
C ** REAL RX(N),RY(N),RZ(N) ATOM POSITIONS **
C ** REAL RX1(N),RY1(N),RZ1(N) VELOCITIES **
C ** REAL FX(N),FY(N),FZ(N) FORCE ON AN ATOM **
C ** REAL FXP(N),FYP(N),FZP(N) FORCE FROM PRIMARY ATOMS **
C ** REAL FXS(N),FYS(N),FZS(N) FORCE FROM SECONDARY ATOMS **
C ** REAL FX1(N),FY1(N),FZ1(N) 1ST DERIVATIVE SECONDARY FORCE **
C ** REAL FX2(N),FY2(N),FZ2(N) 2ND DERIVATIVE SECONDARY FORCE **
C ** REAL FY3(N),FZ3(N),FZ3(N) 3RD DERIVATIVE SECONDARY FORCE **
C ** REAL VP, WP PRIMARY ENERGY AND VIRIAL **
C ** REAL VS, WS SECONDARY ENERGY AND VIRIAL **
C ** REAL V1, V2, V3 DERIVATIVES OF SECONDARY ENERGY **
C ** REAL W1, W2, W3 DERIVATIVES OF SECONDARY VIRIAL **
C ** INTEGER START STEP ZERO FOR EXTRAPOLATION **
C ** INTEGER POINT(N) INDEX TO THE NEIGHBOUR LIST **
C ** INTEGER LIST(MAXNAB) LIST OF PRIMARY NEIGHBOURS **
C ** INTEGER NTS STEPS BETWEEN RECALCULATION OF **
C ** THE SECONDARY FORCE **
C ** LOGICAL MTS TRUE FOR AN EXTRAPOLATED STEP **
C ** **
C ** USAGE: **
C ** **
C ** FORMTS IS CALLED IN TWO MODES. IF MTS IS FALSE, THE PRIMARY **
C ** FORCES ARE CALCULATED EXPLICITLY. THE SECONDARY FORCES AND **
C ** THEIR THREE DERIVATIVES ARE CALCULATED AND STORED. A LIST OF **
C ** PRIMARY NEIGHBOURS IS COMPILED. WHILE MTS IS TRUE FOR THE **
C ** NEXT NTS-1 STEPS, THE PRIMARY FORCES ARE CALCULATED **
C ** EXPLICITLY AND THE SECONDARY FORCES ESTIMATED FROM A TAYLOR **
C ** SERIES APPROXIMATION. THE SECONDARY FORCES, THEIR DERIVATIVES **
C ** AND AN EXTRAPOLATION STEP MARKER ARE STORED IN COMMON BLOCK3 **
C ** FOR USE DURING THE EXTRAPOLATION STEPS. **
C ** IN THIS EXAMPLE WE TAKE THE SHIFTED-FORCE LENNARD-JONES **
C ** PAIR POTENTIAL. IN PRACTICE THE MTS METHOD IS MOST EFFECTIVE **
C ** FOR MORE COMPLICATED MOLECULAR SYSTEMS. **
C ** **
C ** UNITS: **
C ** **
C ** THIS ROUTINE USES LENNARD-JONES UNITS. THE BOX IS A CUBE **
C ** CENTRED AT THE ORIGIN. **
C *******************************************************************
INTEGER N, MAXNAB
PARAMETER ( N = 108, MAXNAB = 25 * N )
REAL RX(N), RY(N), RZ(N), RX1(N), RY1(N), RZ1(N)
REAL RX2(N), RY2(N), RZ2(N), RX3(N), RY3(N), RZ3(N)
REAL FX(N), FY(N), FZ(N), RCUT, BOX, V, W, RPRIM
REAL FXS(N), FYS(N), FZS(N), FX1(N), FY1(N), FZ1(N)
REAL FX2(N), FY2(N), FZ2(N), FX3(N), FY3(N), FZ3(N)
REAL VS, V1, V2, V3
REAL WS, W1, W2, W3
INTEGER POINT(N), LIST(MAXNAB), NTS, STEP, START
REAL DT
REAL RXI, RYI, RZI, RX1I, RY1I, RZ1I, RIJ
REAL RX2I, RY2I, RZ2I, RX3I, RY3I, RZ3I
REAL FXP(N), FYP(N), FZP(N), VP, WP
REAL FXPI, FYPI, FZPI, FXSI, FYSI, FZSI
REAL FX1I, FY1I, FZ1I, FX2I, FY2I, FZ2I
REAL FX3I, FY3I, FZ3I
REAL RIJSQ, WIJ, VIJ, FIJ
REAL SR, SR2, SR3, SR5, SR6, SR7, SR8, SR10, SR12, SR14
REAL BOXINV, RCUTSQ, RPRMSQ, SF1, SF2, SRCUT
REAL RXIJ, RYIJ, RZIJ, RX1IJ, RY1IJ, RZ1IJ
REAL RX2IJ, RY2IJ, RZ2IJ, RX3IJ, RY3IJ, RZ3IJ
REAL R0R1, R1R1, R0R2, R0R3, R1R2
REAL FXIJ, FYIJ, FZIJ, FX1IJ, FY1IJ, FZ1IJ
REAL FX2IJ, FY2IJ, FZ2IJ, FX3IJ, FY3IJ, FZ3IJ
REAL BB, BC, BD, X, Y, Z, A, B, C, D
REAL ESTEP, ET1, ET2, ET3
INTEGER I, J, NLIST, JBEG, JEND, JNAB
LOGICAL MTS
C *******************************************************************
RPRMSQ = RPRIM * RPRIM
RCUTSQ = RCUT * RCUT
BOXINV = 1.0 / BOX
C ** SHIFTED FORCE CONSTANTS **
SRCUT = 1.0 / RCUT
SF1 = 48.0 * SRCUT ** 13 - 24.0 * SRCUT ** 7
SF2 = 28.0 * SRCUT ** 6 - 52.0 * SRCUT ** 12
C ** IDENTIFY FIRST STEP IN SEQUENCE **
IF ( MOD ( ( STEP - 1 ), NTS ) .EQ. 0 ) THEN
MTS = .FALSE.
START = STEP
ELSE
MTS = .TRUE.
ENDIF
IF ( .NOT. MTS ) THEN
C ** AN INITIAL STEP IN A GROUP OF NTS STEPS **
C ** COMPLETE CALCULATION OF FORCES REQUIRED **
NLIST = 0
DO 100 I = 1, N
C ** ZERO PRIMARY FORCES **
FXP(I) = 0.0
FYP(I) = 0.0
FZP(I) = 0.0
C ** ZERO SECONDARY FORCES **
FXS(I) = 0.0
FYS(I) = 0.0
FZS(I) = 0.0
C ** ZERO DERIVATIVES OF SECONDARY FORCES **
FX1(I) = 0.0
FY1(I) = 0.0
FZ1(I) = 0.0
FX2(I) = 0.0
FY2(I) = 0.0
FZ2(I) = 0.0
FX3(I) = 0.0
FY3(I) = 0.0
FZ3(I) = 0.0
100 CONTINUE
C ** ZERO PRIMARY AND SECONDARY ENERGY AND VIRIAL **
VP = 0.0
WP = 0.0
VS = 0.0
WS = 0.0
C ** ZERO SECONDARY ENERGY AND VIRIAL DERIVATIVES **
V1 = 0.0
V2 = 0.0
V3 = 0.0
W1 = 0.0
W2 = 0.0
W3 = 0.0
C ** BEGINNING OF DOUBLE LOOP OVER ATOMS **
DO 102 I = 1, N - 1
C ** PLACE ARRAY ELEMENTS IN LOCAL VARIABLES **
RXI = RX(I)
RYI = RY(I)
RZI = RZ(I)
RX1I = RX1(I)
RY1I = RY1(I)
RZ1I = RZ1(I)
RX2I = RX2(I)
RY2I = RY2(I)
RZ2I = RZ2(I)
RX3I = RX3(I)
RY3I = RY3(I)
RZ3I = RZ3(I)
FXPI = FXP(I)
FYPI = FYP(I)
FZPI = FZP(I)
FXSI = FXS(I)
FYSI = FYS(I)
FZSI = FZS(I)
FX1I = FX1(I)
FY1I = FY1(I)
FZ1I = FZ1(I)
FX2I = FX2(I)
FY2I = FY2(I)
FZ2I = FZ2(I)
FX3I = FX3(I)
FY3I = FY3(I)
FZ3I = FZ3(I)
POINT (I) = NLIST + 1
DO 101 J = I + 1, N
RXIJ = RXI - RX(J)
RYIJ = RYI - RY(J)
RZIJ = RZI - RZ(J)
RXIJ = RXIJ - ANINT ( RXIJ * BOXINV ) * BOX
RYIJ = RYIJ - ANINT ( RYIJ * BOXINV ) * BOX
RZIJ = RZIJ - ANINT ( RZIJ * BOXINV ) * BOX
RIJSQ = RXIJ * RXIJ + RYIJ * RYIJ + RZIJ * RZIJ
IF ( RIJSQ .LT. RCUTSQ ) THEN
C ** PAIR INSIDE CUTOFF **
RIJ = SQRT ( RIJSQ )
SR = 1.0 / RIJ
SR2 = SR * SR
SR6 = SR2 * SR2 * SR2
VIJ = 4.0 * SR6 * ( SR6 - 1.0 ) + SF1 * RIJ + SF2
WIJ = 48.0 * SR6 * ( SR6 - 0.5 ) - SF1 * RIJ
FIJ = SR2 * WIJ
FXIJ = RXIJ * FIJ
FYIJ = RYIJ * FIJ
FZIJ = RZIJ * FIJ
IF ( RIJSQ .LT. RPRMSQ ) THEN
C ** J IS A PRIMARY NEIGHBOUR OF I **
NLIST = NLIST + 1
LIST(NLIST) = J
FXPI = FXPI + FXIJ
FYPI = FYPI + FYIJ
FZPI = FZPI + FZIJ
FXP(J) = FXP(J) - FXIJ
FYP(J) = FYP(J) - FYIJ
FZP(J) = FZP(J) - FZIJ
VP = VP + VIJ
WP = WP + WIJ
ELSE
C ** J IS A SECONDARY NEIGHBOUR OF I **
FXSI = FXSI + FXIJ
FYSI = FYSI + FYIJ
FZSI = FZSI + FZIJ
FXS(J) = FXS(J) - FXIJ
FYS(J) = FYS(J) - FYIJ
FZS(J) = FZS(J) - FZIJ
VS = VS + VIJ
WS = WS + WIJ
C ** CALCULATE THE FIRST THREE DERIVATIVES **
SR3 = SR2 * SR
SR5 = SR3 * SR2
SR7 = SR5 * SR2
SR8 = SR6 * SR2
SR10 = SR5 * SR5
SR12 = SR10 * SR2
SR14 = SR12 * SR2
A = FIJ
B = 192.0 * SR10 * ( 1.0 - 3.5 * SR6 )
: + SR3 * SF1
C = 1920.0 * SR12 * ( 5.6 * SR6 - 1.0 )
: - 3.0 * SR5 * SF1
D = 23040.0 * SR14 * ( 1.0 - 8.4 * SR6 )
: + 15.0 * SR7 * SF1
C ** DERIVATIVES OF PAIR SEPARATIONS **
RX1IJ = RX1I - RX1(J)
RY1IJ = RY1I - RY1(J)
RZ1IJ = RZ1I - RZ1(J)
RX2IJ = RX2I - RX2(J)
RY2IJ = RY2I - RY2(J)
RZ2IJ = RZ2I - RZ2(J)
RX3IJ = RX3I - RX3(J)
RY3IJ = RY3I - RY3(J)
RZ3IJ = RZ3I - RZ3(J)
C ** APPROPRIATE DOT PRODUCTS **
R0R1 = RXIJ*RX1IJ + RYIJ*RY1IJ + RZIJ*RZ1IJ
R0R2 = RXIJ*RX2IJ + RYIJ*RY2IJ + RZIJ*RZ2IJ
R0R3 = RXIJ*RX3IJ + RYIJ*RY3IJ + RZIJ*RZ3IJ
R1R1 = RX1IJ*RX1IJ + RY1IJ*RY1IJ + RZ1IJ*RZ1IJ
R1R2 = RX1IJ*RX2IJ + RY1IJ*RY2IJ + RZ1IJ*RZ2IJ
C ** FIRST DERIVATIVES OF SECONDARY FORCES **
BB = B * R0R1
FX1IJ = A * RX1IJ + BB * RXIJ
FY1IJ = A * RY1IJ + BB * RYIJ
FZ1IJ = A * RZ1IJ + BB * RZIJ
FX1I = FX1I + FX1IJ
FY1I = FY1I + FY1IJ
FZ1I = FZ1I + FZ1IJ
FX1(J) = FX1(J) - FX1IJ
FY1(J) = FY1(J) - FY1IJ
FZ1(J) = FZ1(J) - FZ1IJ
C ** SECOND DERIVATIVES OF SECONDARY FORCES **
BC = B * ( R0R2 + R1R1 ) + C * R0R1 * R0R1
FX2IJ = BC * RXIJ + 2.0 * BB * RX1IJ + A * RX2IJ
FY2IJ = BC * RYIJ + 2.0 * BB * RY1IJ + A * RY2IJ
FZ2IJ = BC * RZIJ + 2.0 * BB * RZ1IJ + A * RZ2IJ
FX2I = FX2I + FX2IJ
FY2I = FY2I + FY2IJ
FZ2I = FZ2I + FZ2IJ
FX2(J) = FX2(J) - FX2IJ
FY2(J) = FY2(J) - FY2IJ
FZ2(J) = FZ2(J) - FZ2IJ
C ** THIRD DERIVATIVES OF SECONDARY FORCES **
BD = B*(R0R3 + 3.0*R1R2) + 3.0*C*(R0R1*R0R2 +
: R0R1*R1R1) + D*R0R1*R0R1*R0R1
FX3IJ =BD*RXIJ+3.0*BC*RX1IJ+3.0*BB*RX2IJ+A*RX3IJ
FY3IJ =BD*RYIJ+3.0*BC*RY1IJ+3.0*BB*RY2IJ+A*RY3IJ
FZ3IJ =BD*RZIJ+3.0*BC*RZ1IJ+3.0*BB*RZ2IJ+A*RZ3IJ
FX3I = FX3I + FX3IJ
FY3I = FY3I + FY3IJ
FZ3I = FZ3I + FZ3IJ
FX3(J) = FX3(J) - FX3IJ
FY3(J) = FY3(J) - FY3IJ
FZ3(J) = FZ3(J) - FZ3IJ
C ** ENERGY DERIVATIVES **
V1 = V1 - A * R0R1
V2 = V2 - B*R0R1*R0R1 - A*(R0R2+R1R1)
V3 = V3 - C*R0R1*R0R1*R0R1 - 3.0*B*R0R1*(R0R2+
: R1R1) - A*(R0R3+3.0*R1R2)
C ** VIRIAL DERIVATIVES **
X = 144.0*SR8 *( 1.0 - 4.0*SR6) - SR *SF1
Y = 1152.0*SR10*( 7.0*SR6 - 1.0) + SR3*SF1
Z = 11520.0*SR12*( 1.0 - 11.2*SR6) - SR5*SF1*3.0
W1 = W1 + X * R0R1
W2 = W2 + Y*R0R1*R0R1 + X*(R0R2+R1R1)
W3 = W3 + Z*R0R1*R0R1*R0R1 + 3.0*Y*R0R1*(R0R2+
: R1R1) + X*(R0R3+3.0*R1R2)
ENDIF
ENDIF
101 CONTINUE
C ** COLLECT ACCUMULATORS FOR FORCES AND DERIVATIVES **
FXP(I) = FXPI
FYP(I) = FYPI
FZP(I) = FZPI
FXS(I) = FXSI
FYS(I) = FYSI
FZS(I) = FZSI
FX1(I) = FX1I
FY1(I) = FY1I
FZ1(I) = FZ1I
FX2(I) = FX2I
FY2(I) = FY2I
FZ2(I) = FZ2I
FX3(I) = FX3I
FY3(I) = FY3I
FZ3(I) = FZ3I
102 CONTINUE
C ** END OF DOUBLE LOOP OVER ATOMS **
POINT(N) = NLIST + 1
C ** ADD PRIMARY AND SECONDARY FORCES **
DO 103 I = 1, N
FX(I) = FXP(I) + FXS(I)
FY(I) = FYP(I) + FYS(I)
FZ(I) = FZP(I) + FZS(I)
103 CONTINUE
V = VP + VS
W = WP + WS
ELSE
C ** A MULTIPLE TIMESTEP EXTRAPOLATION STEP **
C ** SECONDARY FORCES FROM TAYLOR SERIES **
C ** ZERO PRIMARY FORCES **
DO 104 I = 1, N
FXP(I) = 0.0
FYP(I) = 0.0
FZP(I) = 0.0
104 CONTINUE
VP = 0.0
WP = 0.0
C ** BEGINNING OF DOUBLE LOOP OVER PRIMARY ATOMS USING LIST **
DO 106 I = 1, N - 1
JBEG = POINT(I)
JEND = POINT(I+1) - 1
IF ( JBEG .LE. JEND ) THEN
RXI = RX(I)
RYI = RY(I)
RZI = RZ(I)
FXPI = FXP(I)
FYPI = FYP(I)
FZPI = FZP(I)
DO 105 JNAB = JBEG, JEND
J = LIST(JNAB)
RXIJ = RXI - RX(J)
RYIJ = RYI - RY(J)
RZIJ = RZI - RZ(J)
RXIJ = RXIJ - ANINT ( RXIJ * BOXINV ) * BOX
RYIJ = RYIJ - ANINT ( RYIJ * BOXINV ) * BOX
RZIJ = RZIJ - ANINT ( RZIJ * BOXINV ) * BOX
RIJSQ = RXIJ * RXIJ + RYIJ * RYIJ + RZIJ * RZIJ
IF ( RIJSQ .LT. RCUTSQ ) THEN
RIJ = SQRT ( RIJSQ )
SR = 1.0 / RIJ
SR2 = SR * SR
SR6 = SR2 * SR2 * SR2
VIJ = 4.0 * SR6 * ( SR6 - 1.0 ) + SF1*RIJ + SF2
WIJ = 48.0 * SR6 * ( SR6 - 0.5 ) - SF1 * RIJ
FIJ = WIJ * SR2
FXIJ = FIJ * RXIJ
FYIJ = FIJ * RYIJ
FZIJ = FIJ * RZIJ
FXPI = FXPI + FXIJ
FYPI = FYPI + FYIJ
FZPI = FZPI + FZIJ
FXP(J) = FXP(J) - FXIJ
FYP(J) = FYP(J) - FYIJ
FZP(J) = FZP(J) - FZIJ
VP = VP + VIJ
WP = WP + WIJ
ENDIF
105 CONTINUE
FXP(I) = FXPI
FYP(I) = FYPI
FZP(I) = FZPI
ENDIF
106 CONTINUE
C ** END OF DOUBLE LOOP OVER PRIMARY ATOMS USING LIST **
C ** ESTIMATE SECONDARY FORCES **
ESTEP = REAL ( STEP - START )
ET1 = ESTEP * DT
ET2 = 0.5 * ET1 * ET1
ET3 = ( 1.0 / 3.0 ) * ET1 * ET2
C ** TAYLOR SERIES EXPANSION **
DO 107 I = 1, N
FX(I) = FXP(I)+FXS(I)+ET1*FX1(I)+ET2*FX2(I)+ET3*FX3(I)
FY(I) = FYP(I)+FYS(I)+ET1*FY1(I)+ET2*FY2(I)+ET3*FY3(I)
FZ(I) = FZP(I)+FZS(I)+ET1*FZ1(I)+ET2*FZ2(I)+ET3*FZ3(I)
107 CONTINUE
V = VP + VS + ET1 * V1 + ET2 * V2 + ET3 * V3
W = WP + WS + ET1 * W1 + ET2 * W2 + ET3 * W3
ENDIF
W = W / 3.0
RETURN
END