moldyn.c

   1 /*
   2  * moldyn.c - molecular dynamics library main file
   3  *
   4  * author: Frank Zirkelbach <frank.zirkelbach@physik.uni-augsburg.de>
   5  *
   6  */
   7
   8 #define _GNU_SOURCE
   9 #include <stdio.h>
  10 #include <stdlib.h>
  11 #include <string.h>
  12 #include <sys/types.h>
  13 #include <sys/stat.h>
  14 #include <fcntl.h>
  15 #include <unistd.h>
  16 #include <math.h>
  17
  18 #include "moldyn.h"
  19
  20 #include "math/math.h"
  21 #include "init/init.h"
  22 #include "random/random.h"
  23 #include "visual/visual.h"
  24 #include "list/list.h"
  25
  26 int moldyn_usage(char **argv) {
  27
  28         printf("\n%s usage:\n\n",argv[0]);
  29         printf("--- general options ---\n");
  30         printf("-E <steps> <file> (log total energy)\n");
  31         printf("-M <steps> <file> (log total momentum)\n");
  32         printf("-D <steps> <file> (dump total information)\n");
  33         printf("-S <steps> <filebase> (single save file)\n");
  34         printf("-V <steps> <filebase> (rasmol file)\n");
  35         printf("--- physics options ---\n");
  36         printf("-T <temperature> [K] (%f)\n",MOLDYN_TEMP);
  37         printf("-t <timestep tau> [s] (%.15f)\n",MOLDYN_TAU);
  38         printf("-C <cutoff radius> [m] (%.15f)\n",MOLDYN_CUTOFF);
  39         printf("-R <runs> (%d)\n",MOLDYN_RUNS);
  40         printf(" -- integration algo --\n");
  41         printf("  -I <number> (%d)\n",MOLDYN_INTEGRATE_DEFAULT);
  42         printf("     0: velocity verlet\n");
  43         printf(" -- potential --\n");
  44         printf("  -P <number> <param1 param2 ...>\n");
  45         printf("     0: harmonic oscillator\n");
  46         printf("        param1: spring constant\n");
  47         printf("        param2: equilibrium distance\n");
  48         printf("     1: lennard jones\n");
  49         printf("        param1: epsilon\n");
  50         printf("        param2: sigma\n");
  51         printf("\n");
  52
  53         return 0;
  54 }
  55
  56 int moldyn_parse_argv(t_moldyn *moldyn,int argc,char **argv) {
  57
  58         int i;
  59
  60         memset(moldyn,0,sizeof(t_moldyn));
  61
  62         /* default values */
  63         moldyn->t=MOLDYN_TEMP;
  64         moldyn->tau=MOLDYN_TAU;
  65         moldyn->time_steps=MOLDYN_RUNS;
  66         moldyn->integrate=velocity_verlet;
  67
  68         /* parse argv */
  69         for(i=1;i<argc;i++) {
  70                 if(argv[i][0]=='-') {
  71                         switch(argv[i][1]){
  72                                 case 'E':
  73                                         moldyn->ewrite=atoi(argv[++i]);
  74                                         strncpy(moldyn->efb,argv[++i],64);
  75                                         break;
  76                                 case 'M':
  77                                         moldyn->mwrite=atoi(argv[++i]);
  78                                         strncpy(moldyn->mfb,argv[++i],64);
  79                                         break;
  80                                 case 'S':
  81                                         moldyn->swrite=atoi(argv[++i]);
  82                                         strncpy(moldyn->sfb,argv[++i],64);
  83                                         break;
  84                                 case 'V':
  85                                         moldyn->vwrite=atoi(argv[++i]);
  86                                         strncpy(moldyn->vfb,argv[++i],64);
  87                                         break;
  88                                 case 'T':
  89                                         moldyn->t=atof(argv[++i]);
  90                                         break;
  91                                 case 't':
  92                                         moldyn->tau=atof(argv[++i]);
  93                                         break;
  94                                 case 'C':
  95                                         moldyn->cutoff=atof(argv[++i]);
  96                                         break;
  97                                 case 'R':
  98                                         moldyn->time_steps=atoi(argv[++i]);
  99                                         break;
 100                                 case 'I':
 101         /* integration algorithm */
 102         switch(atoi(argv[++i])) {
 103                 case MOLDYN_INTEGRATE_VERLET:
 104                         moldyn->integrate=velocity_verlet;
 105                         break;
 106                 default:
 107                         printf("unknown integration algo %s\n",argv[i]);
 108                         moldyn_usage(argv);
 109                         return -1;
 110         }
 111
 112                                 case 'P':
 113         /* potential + params */
 114         switch(atoi(argv[++i])) {
 115                 case MOLDYN_POTENTIAL_HO:
 116                         hop.spring_constant=atof(argv[++i]);
 117                         hop.equilibrium_distance=atof(argv[++i]);
 118                         moldyn->pot_params=malloc(sizeof(t_ho_params));
 119                         memcpy(moldyn->pot_params,&hop,sizeof(t_ho_params));
 120                         moldyn->potential_force_function=harmonic_oscillator;
 121                         break;
 122                 case MOLDYN_POTENTIAL_LJ:
 123                         e=atof(argv[++i]);
 124                         s=atof(argv[++i]);
 125                         ljp.epsilon4=4*e;
 126                         ljp.sigma6=s*s*s*s*s*s;
 127                         ljp.sigma12=ljp.sigma6*ljp.sigma6;
 128                         moldyn->pot_params=malloc(sizeof(t_lj_params));
 129                         memcpy(moldyn->pot_params,&ljp,sizeof(t_lj_params));
 130                         moldyn->potential_force_function=lennard_jones;
 131                         break;
 132                 default:
 133                         printf("unknown potential %s\n",argv[i]);
 134                         moldyn_usage(argv);
 135                         return -1;
 136         }
 137
 138                                 default:
 139                                         printf("unknown option %s\n",argv[i]);
 140                                         moldyn_usage(argv);
 141                                         return -1;
 142                         }
 143                 } else {
 144                         moldyn_usage(argv);
 145                         return -1;
 146                 }
 147         }
 148
 149         return 0;
 150 }
 151
 152 int moldyn_log_init(t_moldyn *moldyn) {
 153
 154         moldyn->lvstat=0;
 155         t_visual *vis;
 156
 157         vis=&(moldyn->vis);
 158
 159         if(moldyn->ewrite) {
 160                 moldyn->efd=open(moldyn->efb,O_WRONLY|O_CREAT|O_TRUNC);
 161                 if(moldyn->efd<0) {
 162                         perror("[moldyn] efd open");
 163                         return moldyn->efd;
 164                 }
 165                 dprintf(moldyn->efd,"# moldyn total energy logfile\n");
 166                 moldyn->lvstat|=MOLDYN_LVSTAT_TOTAL_E;
 167         }
 168
 169         if(moldyn->mwrite) {
 170                 moldyn->mfd=open(moldyn->mfb,O_WRONLY|O_CREAT|O_TRUNC);
 171                 if(moldyn->mfd<0) {
 172                         perror("[moldyn] mfd open");
 173                         return moldyn->mfd;
 174                 }
 175                 dprintf(moldyn->mfd,"# moldyn total momentum logfile\n");
 176                 moldyn->lvstat|=MOLDYN_LVSTAT_TOTAL_M;
 177         }
 178
 179         if(moldyn->swrite)
 180                 moldyn->lvstat|=MOLDYN_LVSTAT_SAVE;
 181
 182         if((moldyn->vwrite)&&(vis)) {
 183                 moldyn->visual=vis;
 184                 visual_init(vis,moldyn->vfb);
 185                 moldyn->lvstat|=MOLDYN_LVSTAT_VISUAL;
 186         }
 187
 188         moldyn->lvstat|=MOLDYN_LVSTAT_INITIALIZED;
 189
 190         return 0;
 191 }
 192
 193 int moldyn_log_shutdown(t_moldyn *moldyn) {
 194
 195         if(moldyn->efd) close(moldyn->efd);
 196         if(moldyn->mfd) close(moldyn->efd);
 197         if(moldyn->dfd) close(moldyn->efd);
 198         if(moldyn->visual) visual_tini(moldyn->visual);
 199
 200         return 0;
 201 }
 202
 203 int moldyn_init(t_moldyn *moldyn,int argc,char **argv) {
 204
 205         int ret;
 206
 207         ret=moldyn_parse_argv(moldyn,argc,argv);
 208         if(ret<0) return ret;
 209
 210         ret=moldyn_log_init(moldyn);
 211         if(ret<0) return ret;
 212
 213         rand_init(&(moldyn->random),NULL,1);
 214         moldyn->random.status|=RAND_STAT_VERBOSE;
 215
 216         moldyn->status=0;
 217
 218         return 0;
 219 }
 220
 221 int moldyn_shutdown(t_moldyn *moldyn) {
 222
 223         moldyn_log_shutdown(moldyn);
 224         rand_close(&(moldyn->random));
 225         free(moldyn->atom);
 226
 227         return 0;
 228 }
 229
 230 int create_lattice(u8 type,int element,double mass,double lc,
 231                    int a,int b,int c,t_atom **atom) {
 232
 233         int count;
 234         int ret;
 235         t_3dvec origin;
 236
 237         count=a*b*c;
 238
 239         if(type==FCC) count*=4;
 240         if(type==DIAMOND) count*=8;
 241
 242         *atom=malloc(count*sizeof(t_atom));
 243         if(*atom==NULL) {
 244                 perror("malloc (atoms)");
 245                 return -1;
 246         }
 247
 248         v3_zero(&origin);
 249
 250         switch(type) {
 251                 case FCC:
 252                         ret=fcc_init(a,b,c,lc,*atom,&origin);
 253                         break;
 254                 case DIAMOND:
 255                         ret=diamond_init(a,b,c,lc,*atom,&origin);
 256                         break;
 257                 default:
 258                         printf("unknown lattice type (%02x)\n",type);
 259                         return -1;
 260         }
 261
 262         /* debug */
 263         if(ret!=count) {
 264                 printf("ok, there is something wrong ...\n");
 265                 printf("calculated -> %d atoms\n",count);
 266                 printf("created -> %d atoms\n",ret);
 267                 return -1;
 268         }
 269
 270         while(count) {
 271                 (*atom)[count-1].element=element;
 272                 (*atom)[count-1].mass=mass;
 273                 count-=1;
 274         }
 275
 276         return ret;
 277 }
 278
 279 int destroy_lattice(t_atom *atom) {
 280
 281         if(atom) free(atom);
 282
 283         return 0;
 284 }
 285
 286 int thermal_init(t_moldyn *moldyn) {
 287
 288         /*
 289          * - gaussian distribution of velocities
 290          * - zero total momentum
 291          * - velocity scaling (E = 3/2 N k T), E: kinetic energy
 292          */
 293
 294         int i;
 295         double v,sigma;
 296         t_3dvec p_total,delta;
 297         t_atom *atom;
 298         t_random *random;
 299
 300         atom=moldyn->atom;
 301         random=&(moldyn->random);
 302
 303         /* gaussian distribution of velocities */
 304         v3_zero(&p_total);
 305         for(i=0;i<moldyn->count;i++) {
 306                 sigma=sqrt(2.0*K_BOLTZMANN*moldyn->t/atom[i].mass);
 307                 /* x direction */
 308                 v=sigma*rand_get_gauss(random);
 309                 atom[i].v.x=v;
 310                 p_total.x+=atom[i].mass*v;
 311                 /* y direction */
 312                 v=sigma*rand_get_gauss(random);
 313                 atom[i].v.y=v;
 314                 p_total.y+=atom[i].mass*v;
 315                 /* z direction */
 316                 v=sigma*rand_get_gauss(random);
 317                 atom[i].v.z=v;
 318                 p_total.z+=atom[i].mass*v;
 319         }
 320
 321         /* zero total momentum */
 322         v3_scale(&p_total,&p_total,1.0/moldyn->count);
 323         for(i=0;i<moldyn->count;i++) {
 324                 v3_scale(&delta,&p_total,1.0/atom[i].mass);
 325                 v3_sub(&(atom[i].v),&(atom[i].v),&delta);
 326         }
 327
 328         /* velocity scaling */
 329         scale_velocity(moldyn);
 330
 331         return 0;
 332 }
 333
 334 int scale_velocity(t_moldyn *moldyn) {
 335
 336         int i;
 337         double e,c;
 338         t_atom *atom;
 339
 340         atom=moldyn->atom;
 341
 342         /*
 343          * - velocity scaling (E = 3/2 N k T), E: kinetic energy
 344          */
 345         e=0.0;
 346         for(i=0;i<moldyn->count;i++)
 347                 e+=0.5*atom[i].mass*v3_absolute_square(&(atom[i].v));
 348         c=sqrt((2.0*e)/(3.0*moldyn->count*K_BOLTZMANN*moldyn->t));
 349         for(i=0;i<moldyn->count;i++)
 350                 v3_scale(&(atom[i].v),&(atom[i].v),(1.0/c));
 351
 352         return 0;
 353 }
 354
 355 double get_e_kin(t_atom *atom,int count) {
 356
 357         int i;
 358         double e;
 359
 360         e=0.0;
 361
 362         for(i=0;i<count;i++) {
 363                 e+=0.5*atom[i].mass*v3_absolute_square(&(atom[i].v));
 364         }
 365
 366         return e;
 367 }
 368
 369 double get_e_pot(t_moldyn *moldyn) {
 370
 371         return moldyn->energy;
 372 }
 373
 374 double get_total_energy(t_moldyn *moldyn) {
 375
 376         double e;
 377
 378         e=get_e_kin(moldyn->atom,moldyn->count);
 379         e+=get_e_pot(moldyn);
 380
 381         return e;
 382 }
 383
 384 t_3dvec get_total_p(t_atom *atom, int count) {
 385
 386         t_3dvec p,p_total;
 387         int i;
 388
 389         v3_zero(&p_total);
 390         for(i=0;i<count;i++) {
 391                 v3_scale(&p,&(atom[i].v),atom[i].mass);
 392                 v3_add(&p_total,&p_total,&p);
 393         }
 394
 395         return p_total;
 396 }
 397
 398 double estimate_time_step(t_moldyn *moldyn,double nn_dist,double t) {
 399
 400         double tau;
 401
 402         tau=0.05*nn_dist/(sqrt(3.0*K_BOLTZMANN*t/moldyn->atom[0].mass));
 403         tau*=1.0E-9;
 404         if(tau<moldyn->tau)
 405                 printf("[moldyn] warning: time step  (%f > %.15f)\n",
 406                        moldyn->tau,tau);
 407
 408         return tau;
 409 }
 410
 411 /*
 412  * numerical tricks
 413  */
 414
 415 /* linked list / cell method */
 416
 417 int link_cell_init(t_moldyn *moldyn) {
 418
 419         t_linkcell *lc;
 420         int i;
 421
 422         lc=&(moldyn->lc);
 423
 424         /* list log fd */
 425         lc->listfd=open("/dev/null",O_WRONLY);
 426
 427         /* partitioning the md cell */
 428         lc->nx=moldyn->dim.x/moldyn->cutoff;
 429         lc->x=moldyn->dim.x/lc->nx;
 430         lc->ny=moldyn->dim.y/moldyn->cutoff;
 431         lc->y=moldyn->dim.y/lc->ny;
 432         lc->nz=moldyn->dim.z/moldyn->cutoff;
 433         lc->z=moldyn->dim.z/lc->nz;
 434
 435         lc->cells=lc->nx*lc->ny*lc->nz;
 436         lc->subcell=malloc(lc->cells*sizeof(t_list));
 437
 438         printf("initializing linked cells (%d)\n",lc->cells);
 439
 440         for(i=0;i<lc->cells;i++)
 441                 //list_init(&(lc->subcell[i]),1);
 442                 list_init(&(lc->subcell[i]));
 443
 444         link_cell_update(moldyn);
 445
 446         return 0;
 447 }
 448
 449 int link_cell_update(t_moldyn *moldyn) {
 450
 451         int count,i,j,k;
 452         int nx,ny,nz;
 453         t_atom *atom;
 454         t_linkcell *lc;
 455
 456         atom=moldyn->atom;
 457         lc=&(moldyn->lc);
 458
 459         nx=lc->nx;
 460         ny=lc->ny;
 461         nz=lc->nz;
 462
 463         for(i=0;i<lc->cells;i++)
 464                 list_destroy(&(moldyn->lc.subcell[i]));
 465
 466         for(count=0;count<moedyn->count;count++) {
 467                 i=(atom[count].r.x+(moldyn->dim.x/2))/lc->x;
 468                 j=(atom[count].r.y+(moldyn->dim.y/2))/lc->y;
 469                 k=(atom[count].r.z+(moldyn->dim.z/2))/lc->z;
 470                 list_add_immediate_ptr(&(moldyn->lc.subcell[i+j*nx+k*nx*ny]),
 471                                        &(atom[count]));
 472         }
 473
 474         return 0;
 475 }
 476
 477 int link_cell_neighbour_index(t_moldyn *moldyn,int i,int j,int k,t_list *cell) {
 478
 479         t_linkcell *lc;
 480         int a;
 481         int count1,count2;
 482         int ci,cj,ck;
 483         int nx,ny,nz;
 484         int x,y,z;
 485         u8 bx,by,bz;
 486
 487         lc=&(moldyn->lc);
 488         nx=lc->nx;
 489         ny=lc->ny;
 490         nz=lc->nz;
 491         count1=1;
 492         count2=27;
 493         a=nx*ny;
 494
 495
 496         cell[0]=lc->subcell[i+j*nx+k*a];
 497         for(ci=-1;ci<=1;ci++) {
 498                 bx=0;
 499                 x=i+ci;
 500                 if((x<0)||(x>=nx)) {
 501                         x=(x+nx)%nx;
 502                         bx=1;
 503                 }
 504                 for(cj=-1;cj<=1;cj++) {
 505                         by=0;
 506                         y=j+cj;
 507                         if((y<0)||(y>=ny)) {
 508                                 y=(y+ny)%ny;
 509                                 by=1;
 510                         }
 511                         for(ck=-1;ck<=1;ck++) {
 512                                 bz=0;
 513                                 z=k+ck;
 514                                 if((z<0)||(z>=nz)) {
 515                                         z=(z+nz)%nz;
 516                                         bz=1;
 517                                 }
 518                                 if(!(ci|cj|ck)) continue;
 519                                 if(bx|by|bz) {
 520                                         cell[--count2]=lc->subcell[x+y*nx+z*a];
 521                                 }
 522                                 else {
 523                                         cell[count1++]=lc->subcell[x+y*nx+z*a];
 524                                 }
 525                         }
 526                 }
 527         }
 528
 529         lc->dnlc=count2;
 530         lc->countn=27;
 531
 532         return count2;
 533 }
 534
 535 int link_cell_shutdown(t_moldyn *moldyn) {
 536
 537         int i;
 538         t_linkcell *lc;
 539
 540         lc=&(moldyn->lc);
 541
 542         for(i=0;i<lc->nx*lc->ny*lc->nz;i++)
 543                 list_shutdown(&(moldyn->lc.subcell[i]));
 544
 545         if(lc->listfd) close(lc->listfd);
 546
 547         return 0;
 548 }
 549
 550 /*
 551  *
 552  * 'integration of newtons equation' - algorithms
 553  *
 554  */
 555
 556 /* start the integration */
 557
 558 int moldyn_integrate(t_moldyn *moldyn) {
 559
 560         int i,sched;
 561         unsigned int e,m,s,d,v;
 562         t_3dvec p;
 563
 564         int fd;
 565         char fb[128];
 566
 567         /* initialize linked cell method */
 568         link_cell_init(moldyn);
 569
 570         /* logging & visualization */
 571         e=moldyn->ewrite;
 572         m=moldyn->mwrite;
 573         s=moldyn->swrite;
 574         d=moldyn->dwrite;
 575         v=moldyn->vwrite;
 576
 577         if(!(moldyn->lvstat&MOLDYN_LVSTAT_INITIALIZED)) {
 578                 printf("[moldyn] warning, lv system not initialized\n");
 579                 return -1;
 580         }
 581
 582         /* sqaure of some variables */
 583         moldyn->tau_square=moldyn->tau*moldyn->tau;
 584         moldyn->cutoff_square=moldyn->cutoff*moldyn->cutoff;
 585
 586         /* calculate initial forces */
 587         moldyn->potential_force_function(moldyn);
 588
 589         for(sched=0;sched<moldyn->schedule.content_count;sched++) {
 590                 moldyn->tau=;
 591                 moldyn->tau_square=;
 592
 593         // hier weiter ...
 594
 595         for(i=0;i<moldyn->time_steps;i++) {
 596
 597                 /* integration step */
 598                 moldyn->integrate(moldyn);
 599
 600                 /* check for log & visualization */
 601                 if(e) {
 602                         if(!(i%e))
 603                                 dprintf(moldyn->efd,
 604                                         "%.15f %.45f\n",i*moldyn->tau,
 605                                         get_total_energy(moldyn));
 606                 }
 607                 if(m) {
 608                         if(!(i%m)) {
 609                                 p=get_total_p(moldyn->atom,moldyn->count);
 610                                 dprintf(moldyn->mfd,
 611                                         "%.15f %.45f\n",i*moldyn->tau,
 612                                         v3_norm(&p));
 613                         }
 614                 }
 615                 if(s) {
 616                         if(!(i%s)) {
 617                                 snprintf(fb,128,"%s-%f-%.15f.save",moldyn->sfb,
 618                                          moldyn->t,i*moldyn->tau);
 619                                 fd=open(fb,O_WRONLY|O_TRUNC|O_CREAT);
 620                                 if(fd<0) perror("[moldyn] save fd open");
 621                                 else {
 622                                         write(fd,moldyn,sizeof(t_moldyn));
 623                                         write(fd,moldyn->atom,
 624                                               moldyn->count*sizeof(t_atom));
 625                                 }
 626                                 close(fd);
 627                         }
 628                 }
 629                 if(v) {
 630                         if(!(i%v)) {
 631                                 visual_atoms(moldyn->visual,i*moldyn->tau,
 632                                              moldyn->atom,moldyn->count);
 633                                 printf("\rsteps: %d",i);
 634                                 fflush(stdout);
 635                         }
 636                 }
 637         }
 638
 639         return 0;
 640 }
 641
 642 /* velocity verlet */
 643
 644 int velocity_verlet(t_moldyn *moldyn) {
 645
 646         int i,count;
 647         double tau,tau_square;
 648         t_3dvec delta;
 649         t_atom *atom;
 650
 651         atom=moldyn->atom;
 652         count=moldyn->count;
 653         tau=moldyn->tau;
 654         tau_square=moldyn->tau_square;
 655
 656         for(i=0;i<count;i++) {
 657                 /* new positions */
 658                 v3_scale(&delta,&(atom[i].v),tau);
 659                 v3_add(&(atom[i].r),&(atom[i].r),&delta);
 660                 v3_scale(&delta,&(atom[i].f),0.5*tau_square/atom[i].mass);
 661                 v3_add(&(atom[i].r),&(atom[i].r),&delta);
 662                 v3_per_bound(&(atom[i].r),&(moldyn->dim));
 663
 664                 /* velocities */
 665                 v3_scale(&delta,&(atom[i].f),0.5*tau/atom[i].mass);
 666                 v3_add(&(atom[i].v),&(atom[i].v),&delta);
 667         }
 668
 669         /* neighbour list update */
 670 printf("list update ...\n");
 671         link_cell_update(moldyn);
 672 printf("done\n");
 673
 674         /* forces depending on chosen potential */
 675 printf("calc potential/force ...\n");
 676         potential_force_calc(moldyn);
 677         //moldyn->potential_force_function(moldyn);
 678 printf("done\n");
 679
 680         for(i=0;i<count;i++) {
 681                 /* again velocities */
 682                 v3_scale(&delta,&(atom[i].f),0.5*tau/atom[i].mass);
 683                 v3_add(&(atom[i].v),&(atom[i].v),&delta);
 684         }
 685
 686         return 0;
 687 }
 688
 689
 690 /*
 691  *
 692  * potentials & corresponding forces
 693  *
 694  */
 695
 696 /* generic potential and force calculation */
 697
 698 int potential_force_calc(t_moldyn *moldyn) {
 699
 700         int i,count;
 701         t_atom *atom;
 702         t_linkcell *lc;
 703         t_list neighbour[27];
 704         t_list *this;
 705         double u;
 706         u8 bc,bc3;
 707         int countn,dnlc;
 708
 709         count=moldyn->count;
 710         atom=moldyn->atom;
 711         lc=&(moldyn->lc);
 712
 713         /* reset energy */
 714         moldyn->energy=0.0;
 715
 716         for(i=0;i<count;i++) {
 717
 718                 /* reset force */
 719                 v3_zero(&(atom[i].f));
 720
 721                 /* single particle potential/force */
 722                 if(atom[i].attr&ATOM_ATTR_1BP)
 723                         moldyn->pf_func1b(moldyn,&(atom[i]));
 724
 725                 /* 2 body pair potential/force */
 726                 if(atom[i].attr&(ATOM_ATTR_2BP|ATOM_ATTR_3BP)) {
 727
 728                         link_cell_neighbour_index(moldyn,
 729                                 (atom[i].r.x+moldyn->dim.x/2)/lc->x,
 730                                 (atom[i].r.y+moldyn->dim.y/2)/lc->y,
 731                                 (atom[i].r.z+moldyn->dim.z/2)/lc->z,
 732                                 neighbour);
 733
 734                         countn=lc->countn;
 735                         dnlc=lc->dnlc;
 736
 737                         for(j=0;j<countn;j++) {
 738
 739                                 this=&(neighbour[j]);
 740                                 list_reset(this);
 741
 742                                 if(this->start==NULL)
 743                                         continue;
 744
 745                                 bc=(j<dnlc)?0:1;
 746
 747                                 do {
 748                                         btom=this->current->data;
 749
 750                                         if(btom==&(atom[i]))
 751                                                 continue;
 752
 753                                         if((btom->attr&ATOM_ATTR_2BP)&
 754                                            (atom[i].attr&ATOM_ATTR_2BP))
 755                                                 moldyn->pf_func2b(moldyn,
 756                                                                   &(atom[i]),
 757                                                                   btom,
 758                                                                   bc);
 759
 760                                         /* 3 body potential/force */
 761
 762                                         if(!(atom[i].attr&ATOM_ATTR_3BP)||
 763                                            !(btom->attr&ATOM_ATTR_3BP))
 764                                                 continue;
 765
 766                                         link_cell_neighbour_index(moldyn,
 767                                            (btom->r.x+moldyn->dim.x/2)/lc->x,
 768                                            (btom->r.y+moldyn->dim.y/2)/lc->y,
 769                                            (btom->r.z+moldyn->dim.z/2)/lc->z,
 770                                            neighbourk);
 771
 772                                         for(k=0;k<lc->countn;k++) {
 773
 774                                                 thisk=&(neighbourk[k]);
 775                                                 list_reset(thisk);
 776
 777                                                 if(thisk->start==NULL)
 778                                                         continue;
 779
 780                                                 bck=(k<lc->dnlc)?0:1;
 781
 782                                                 do {
 783
 784                         ktom=thisk->current->data;
 785
 786                         if(!(ktom->attr&ATOM_ATTR_3BP))
 787                                 continue;
 788
 789                         if(ktom==btom)
 790                                 continue;
 791
 792                         if(ktom==&(atom[i]))
 793                                 continue;
 794
 795                         moldyn->pf_func3b(moldyn,&(atom[i]),btom,ktom,bck);
 796
 797                                                 } while(list_next(thisk)!=\
 798                                                         L_NO_NEXT_ELEMENT);
 799
 800                                 } while(list_next(this)!=L_NO_NEXT_ELEMENT);
 801                         }
 802                 }
 803         }
 804
 805         return 0;
 806 }
 807
 808 /*
 809  * periodic boundayr checking
 810  */
 811
 812 int check_per_bound(t_moldyn *moldyn,t_3dvec *a) {
 813
 814         double x,y,z;
 815
 816         x=0.5*dim->x;
 817         y=0.5*dim->y;
 818         z=0.5*dim->z;
 819
 820         if(moldyn->MOLDYN_ATTR_PBX)
 821                 if(a->x>=x) a->x-=dim->x;
 822                 else if(-a->x>x) a->x+=dim->x;
 823         if(moldyn->MOLDYN_ATTR_PBY)
 824                 if(a->y>=y) a->y-=dim->y;
 825                 else if(-a->y>y) a->y+=dim->y;
 826         if(moldyn->MOLDYN_ATTR_PBZ)
 827                 if(a->z>=z) a->z-=dim->z;
 828                 else if(-a->z>z) a->z+=dim->z;
 829
 830         return 0;
 831 }
 832
 833
 834 /*
 835  * example potentials
 836  */
 837
 838 /* harmonic oscillator potential and force */
 839
 840 int harmonic_oscillator(t_moldyn *moldyn,t_atom *ai,t_atom *aj,u8 bc)) {
 841
 842         t_ho_params *params;
 843         t_3dvec force,distance;
 844         double d;
 845         double sc,equi_dist;
 846
 847         params=moldyn->pot2b_params;
 848         sc=params->spring_constant;
 849         equi_dist=params->equilibrium_distance;
 850
 851         v3_sub(&distance,&(ai->r),&(aj->r);
 852
 853         v3_per_bound(&distance,&(moldyn->dim));
 854         if(bc) check_per_bound(moldyn,&distance);
 855         d=v3_norm(&distance);
 856         if(d<=moldyn->cutoff) {
 857                 /* energy is 1/2 (d-d0)^2, but we will add this twice ... */
 858                 moldyn->energy+=(0.25*sc*(d-equi_dist)*(d-equi_dist));
 859                 v3_scale(&force,&distance,-sc*(1.0-(equi_dist/d)));
 860                 v3_add(&(ai->f),&(ai->f),&force);
 861         }
 862
 863         return 0;
 864 }
 865
 866 /* lennard jones potential & force for one sort of atoms */
 867
 868 int lennard_jones(t_moldyn *moldyn,t_atom *ai,t_atom *aj,u8 bc) {
 869
 870         t_lj_params *params;
 871         t_3dvec force,distance;
 872         double d,h1,h2,u;
 873         double eps,sig6,sig12;
 874
 875         params=moldyn->pot_params;
 876         eps=params->epsilon4;
 877         sig6=params->sigma6;
 878         sig12=params->sigma12;
 879
 880         v3_sub(&distance,&(ai->r),&(aj->r));
 881         if(bc) check_per_bound(moldyn,&distance);
 882         d=v3_absolute_square(&distance);        /* 1/r^2 */
 883         if(d<=moldyn->cutoff_square) {
 884                 d=1.0/d;                        /* 1/r^2 */
 885                 h2=d*d;                         /* 1/r^4 */
 886                 h2*=d;                          /* 1/r^6 */
 887                 h1=h2*h2;                       /* 1/r^12 */
 888                 /* energy is eps*..., but we will add this twice ... */
 889                 moldyn->energy+=0.5*eps*(sig12*h1-sig6*h2);
 890                 h2*=d;                          /* 1/r^8 */
 891                 h1*=d;                          /* 1/r^14 */
 892                 h2*=6*sig6;
 893                 h1*=12*sig12;
 894                 d=+h1-h2;
 895                 d*=eps;
 896                 v3_scale(&force,&distance,d);
 897                 v3_add(&(ai->f),&(aj->f),&force);
 898         }
 899
 900         return 0;
 901 }
 902
 903 /*
 904  * tersoff potential & force for 2 sorts of atoms
 905  */
 906
 907 /* tersoff 1 body part */
 908 int tersoff_mult_1bp(t_moldyn *moldyn,t_atom *ai) {
 909
 910         int num;
 911         t_tersoff_mult_params *params;
 912         t_tersoff_exchange *exchange;
 913
 914         num=ai->bnum;
 915         params=moldyn->pot1b_params;
 916         exchange=&(params->exchange);
 917
 918         /*
 919          * simple: point constant parameters only depending on atom i to
 920          *         their right values
 921          */
 922
 923         exchange->beta=&(params->beta[num]);
 924         exchange->n=&(params->n[num]);
 925         exchange->c=&(params->c[num]);
 926         exchange->d=&(params->d[num]);
 927         exchange->h=&(params->h[num]);
 928
 929         exchange->betan=pow(*(exchange->beta),*(exchange->n));
 930         exchange->c2=params->c[num]*params->c[num];
 931         exchange->d2=params->d[num]*params->d[num];
 932         exchange->c2d2=exchange->c2/exchange->d2;
 933
 934         return 0;
 935 }
 936
 937 /* tersoff 2 body part */
 938 int tersoff_mult_2bp(t_moldyn *moldyn,t_atom *ai,t_atom *aj,u8 bc) {
 939
 940         t_tersoff_mult_params *params;
 941         t_tersoff_exchange *exchange;
 942         t_3dvec dist_ij;
 943         double d_ij;
 944         double A,B,R,S,lambda;
 945         int num;
 946
 947         params=moldyn->pot_params;
 948         num=ai->bnum;
 949         exchange=&(params->exchange);
 950
 951         exchange->run3bp=0;
 952
 953         /*
 954          * we need: f_c, df_c, f_r, df_r
 955          *
 956          * therefore we need: R, S, A, lambda
 957          */
 958
 959         v3_sub(&dist_ij,&(ai->r),&(aj->r));
 960
 961         if(bc) check_per_bound(moldyn,&dist_ij);
 962
 963         /* save for use in 3bp */ /* REALLY ?!?!?! */
 964         exchange->dist_ij=dist_ij;
 965
 966         /* constants */
 967         if(num==aj->bnum) {
 968                 S=params->S[num];
 969                 R=params->R[num];
 970                 A=params->A[num];
 971                 lambda=params->lambda[num];
 972                 /* more constants depending of atoms i and j, needed in 3bp */
 973                 params->exchange.B=&(params->B[num]);
 974                 params->exchange.mu=params->mu[num];
 975                 params->exchange.chi=1.0;
 976         }
 977         else {
 978                 S=params->Smixed;
 979                 R=params->Rmixed;
 980                 A=params->Amixed;
 981                 lambda=params->lambda_m;
 982                 /* more constants depending of atoms i and j, needed in 3bp */
 983                 params->exchange.B=&(params->Bmixed);
 984                 params->exchange.mu=&(params->mu_m);
 985                 params->exchange.chi=params->chi;
 986         }
 987
 988         d_ij=v3_norm(&dist_ij);
 989
 990         /* save for use in 3bp */
 991         exchange->d_ij=d_ij;
 992
 993         if(d_ij>S)
 994                 return 0;
 995
 996         f_r=A*exp(-lamda*d_ij);
 997         df_r=-lambda*f_r/d_ij;
 998
 999         /* f_a, df_a calc + save for 3bp use */
1000         exchange->f_a=-B*exp(-mu*d_ij);
1001         exchange->df_a=-mu*exchange->f_a/d_ij;
1002
1003         if(d_ij<R) {
1004                 /* f_c = 1, df_c = 0 */
1005                 f_c=1.0;
1006                 df_c=0.0;
1007                 v3_scale(&force,&dist_ij,df_r);
1008         }
1009         else {
1010                 s_r=S-R;
1011                 arg=PI*(d_ij-R)/s_r;
1012                 f_c=0.5+0.5*cos(arg);
1013                 df_c=-0.5*sin(arg)*(PI/(s_r*d_ij));
1014                 scale=df_c*f_r+df_r*f_c;
1015                 v3_scale(&force,&dist_ij,scale);
1016         }
1017
1018         /* add forces */
1019         v3_add(&(ai->f),&(ai->f),&force);
1020         /* energy is 0.5 f_r f_c, but we will sum it up twice ... */
1021         moldyn->energy+=(0.25*f_r*f_c);
1022
1023         /* save for use in 3bp */
1024         exchange->f_c=f_c;
1025         exchange->df_c=df_c;
1026
1027         /* enable the run of 3bp function */
1028         exchange->run3bp=1;
1029
1030         return 0;
1031 }
1032
1033 /* tersoff 3 body part */
1034
1035 int tersoff_mult_3bp(t_moldyn *moldyn,t_atom *ai,t_atom *aj,t_atom *ak,u8 bc) {
1036
1037         t_tersoff_mult_params *params;
1038         t_tersoff_exchange *exchange;
1039         t_3dvec dist_ij,dist_ik,dist_jk;
1040         t_3dvec temp,force;
1041         double R,S,s_r;
1042         double d_ij,d_ik,d_jk;
1043         double f_c,df_c,b_ij,f_a,df_a;
1044         double n,c,d,h,neta,betan,betan_1;
1045         double theta,cos_theta,sin_theta;
1046         int num;
1047
1048         params=moldyn->pot_params;
1049         num=ai->bnum;
1050         exchange=params->exchange;
1051
1052         if(!(exchange->run3bp))
1053                 return 0;
1054
1055         /*
1056          * we need: f_c, d_fc, b_ij, db_ij, f_a, df_a
1057          *
1058          * we got f_c, df_c, f_a, df_a from 2bp calculation
1059          */
1060
1061         d_ij=exchange->d_ij;
1062         d_ij2=exchange->d_ij2;
1063
1064         f_a=params->exchange.f_a;
1065         df_a=params->exchange.df_a;
1066
1067         /* d_ij is <= S, as we didn't return so far! */
1068
1069         /*
1070          * calc of b_ij (scalar) and db_ij (vector)
1071          *
1072          * - for b_ij: chi, beta, f_c_ik, w(=1), c, d, h, n, cos_theta
1073          *
1074          * - for db_ij: d_theta, sin_theta, cos_theta, f_c_ik, df_c_ik,
1075          *              w_ik,
1076          *
1077          */
1078
1079
1080         v3_sub(&dist_ik,&(aj->i),&(ak->r));
1081         if(bc) check_per_bound(moldyn,&dist_ik);
1082         d_ik=v3_norm(&dist_ik);
1083
1084         /* constants for f_c_ik calc */
1085         if(num==ak->bnum) {
1086                 R=params->R[num];
1087                 S=params->S[num];
1088         }
1089         else {
1090                 R=params->Rmixed;
1091                 S=params->Smixed;
1092         }
1093
1094         /* calc of f_c_ik */
1095         if(d_ik>S)
1096                 return 0;
1097
1098         if(d_ik<R) {
1099                 /* f_c_ik = 1, df_c_ik = 0 */
1100                 f_c_ik=1.0;
1101                 df_c_ik=0.0;
1102         }
1103         else {
1104                 s_r=S-R;
1105                 arg=PI*(d_ik-R)/s_r;
1106                 f_c_ik=0.5+0.5*cos(arg);
1107                 df_c_ik=-0.5*sin(arg)*(PI/(s_r*d_ik));
1108         }
1109
1110         v3_sub(&dist_jk,&(aj->r),&(ak->r));
1111         if(bc) check_per_bound(moldyn,&dist_jk);
1112         d_jk=v3_norm(&dist_jk);
1113
1114         beta=*(exchange->beta);
1115         betan=exchange->betan;
1116         n=*(exchange->n);
1117         c=*(exchange->c);
1118         d=*(exchange->d);
1119         h=*(exchange->h);
1120         c2=exchange->c2;
1121         d2=exchange->d2;
1122         c2d2=exchange->c2d2;
1123
1124         numer=d_ij2+d_ik*d_ik-d_jk*d_jk;
1125         denom=2*d_ij*d_ik;
1126         cos_theta=numer/denom;
1127         sin_theta=sqrt(1.0-(cos_theta*cos_theta));
1128         theta=arccos(cos_theta);
1129         d_theta=(-1.0/sqrt(1.0-cos_theta*cos_theta))/(denom*denom);
1130         d_theta1=2*denom-numer*2*d_ik/d_ij;
1131         d_theta2=2*denom-numer*2*d_ij/d_ik;
1132         d_theta1*=d_theta;
1133         d_theta2*=d_theta;
1134
1135         h_cos=(h-cos_theta);
1136         h_cos2=h_cos*h_cos;
1137         d2_h_cos2=d2-h_cos2;
1138
1139         /* some usefull expressions */
1140         frac1=c2/(d2-h_cos2);
1141         bracket1=1+c2d2-frac1;
1142         bracket2=f_c_ik*bracket1;
1143         bracket2_n_1=pow(bracket2,n-1.0);
1144         bracket2_n=bracket2_n_1*bracket2;
1145         bracket3=1+betan*bracket2_n;
1146         bracket3_pow_1=pow(bracket3,(-1.0/(2.0*n))-1.0);
1147         bracket3_pow=bracket3_pow_1*bracket3;
1148
1149         /* now go on with calc of b_ij and derivation of b_ij */
1150         b_ij=chi*bracket3_pow;
1151
1152         /* derivation of theta */
1153         v3_scale(&force,&dist_ij,d1_theta);
1154         v3_scale(&temp,&dist_ik,d_theta2);
1155         v3_add(&force,&force,&temp);
1156
1157         /* part 1 of derivation of b_ij */
1158         v3_scale(&force,sin_theta*2*h_cos*f_c_ik*frac1);
1159
1160         /* part 2 of derivation of b_ij */
1161         v3_scale(&temp,&dist_ik,df_c_ik*bracket1);
1162
1163         /* sum up and scale ... */
1164         v3_add(&temp,&temp,&force);
1165         scale=bracket2_n_1*n*betan*(1+betan*bracket3_pow_1)*chi*(1.0/(2.0*n));
1166         v3_scale(&temp,&temp,scale);
1167
1168         /* now construct an energy and a force out of that */
1169         v3_scale(&temp,&temp,f_a);
1170         v3_scale(&force,&dist_ij,df_a*b_ij);
1171         v3_add(&temp,&temp,&force);
1172         v3_scale(&temp,&temp,f_c);
1173         v3_scale(&force,&dist_ij,df_c*b_ij*f_a);
1174         v3_add(&force,&force,&temp);
1175
1176         /* add forces */
1177         v3_add(&(ai->f),&(ai->f),&force);
1178         /* energy is 0.5 f_r f_c, but we will sum it up twice ... */
1179         moldyn->energy+=(0.25*f_a*b_ij*f_c);
1180
1181         return 0;
1182 }
1183