potentials/tersoff.c

   1 /*
   2  * tersoff.c - tersoff potential
   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 #include "../math/math.h"
  20 #include "tersoff.h"
  21
  22 /* create mixed terms from parameters and set them */
  23 int tersoff_mult_complete_params(t_tersoff_mult_params *p) {
  24
  25         printf("[moldyn] tersoff parameter completion\n");
  26         p->S2[0]=p->S[0]*p->S[0];
  27         p->S2[1]=p->S[1]*p->S[1];
  28         p->Smixed=sqrt(p->S[0]*p->S[1]);
  29         p->S2mixed=p->Smixed*p->Smixed;
  30         p->Rmixed=sqrt(p->R[0]*p->R[1]);
  31         p->Amixed=sqrt(p->A[0]*p->A[1]);
  32         p->Bmixed=sqrt(p->B[0]*p->B[1]);
  33         p->lambda_m=0.5*(p->lambda[0]+p->lambda[1]);
  34         p->mu_m=0.5*(p->mu[0]+p->mu[1]);
  35
  36         printf("[moldyn] tersoff mult parameter info:\n");
  37         printf("  S (A)  | %f | %f | %f\n",p->S[0],p->S[1],p->Smixed);
  38         printf("  R (A)  | %f | %f | %f\n",p->R[0],p->R[1],p->Rmixed);
  39         printf("  A (eV) | %f | %f | %f\n",p->A[0]/EV,p->A[1]/EV,p->Amixed/EV);
  40         printf("  B (eV) | %f | %f | %f\n",p->B[0]/EV,p->B[1]/EV,p->Bmixed/EV);
  41         printf("  lambda | %f | %f | %f\n",p->lambda[0],p->lambda[1],
  42                                           p->lambda_m);
  43         printf("  mu     | %f | %f | %f\n",p->mu[0],p->mu[1],p->mu_m);
  44         printf("  beta   | %.10f | %.10f\n",p->beta[0],p->beta[1]);
  45         printf("  n      | %f | %f\n",p->n[0],p->n[1]);
  46         printf("  c      | %f | %f\n",p->c[0],p->c[1]);
  47         printf("  d      | %f | %f\n",p->d[0],p->d[1]);
  48         printf("  h      | %f | %f\n",p->h[0],p->h[1]);
  49         printf("  chi    | %f \n",p->chi);
  50
  51         return 0;
  52 }
  53
  54 /* tersoff 1 body part */
  55 int tersoff_mult_1bp(t_moldyn *moldyn,t_atom *ai) {
  56
  57         int brand;
  58         t_tersoff_mult_params *params;
  59         t_tersoff_exchange *exchange;
  60
  61         brand=ai->brand;
  62         params=moldyn->pot_params;
  63         exchange=&(params->exchange);
  64
  65         /*
  66          * simple: point constant parameters only depending on atom i to
  67          *         their right values
  68          */
  69
  70         exchange->beta_i=&(params->beta[brand]);
  71         exchange->n_i=&(params->n[brand]);
  72         exchange->c_i=&(params->c[brand]);
  73         exchange->d_i=&(params->d[brand]);
  74         exchange->h_i=&(params->h[brand]);
  75
  76         exchange->betaini=pow(*(exchange->beta_i),*(exchange->n_i));
  77         exchange->ci2=params->c[brand]*params->c[brand];
  78         exchange->di2=params->d[brand]*params->d[brand];
  79         exchange->ci2di2=exchange->ci2/exchange->di2;
  80
  81         return 0;
  82 }
  83
  84 /* tersoff 2 body part */
  85 int tersoff_mult_2bp(t_moldyn *moldyn,t_atom *ai,t_atom *aj,u8 bc) {
  86
  87         t_tersoff_mult_params *params;
  88         t_3dvec dist_ij,force;
  89         double d_ij,d_ij2;
  90         double A,R,S,S2,lambda;
  91         double f_r,df_r;
  92         double f_c,df_c;
  93         int brand;
  94         double s_r;
  95         double arg;
  96
  97         printf("WARNING! - tersoff_mult_2bp is obsolete.\n");
  98         printf("WARNING! - repulsive part handled in 3bp/j2 routine.\n");
  99
 100         /* use newtons third law */
 101         if(ai<aj) return 0;
 102
 103         params=moldyn->pot_params;
 104         brand=aj->brand;
 105
 106         /* determine cutoff square */
 107         if(brand==ai->brand)
 108                 S2=params->S2[brand];
 109         else
 110                 S2=params->S2mixed;
 111
 112         /* dist_ij, d_ij2 */
 113         v3_sub(&dist_ij,&(aj->r),&(ai->r));
 114         if(bc) check_per_bound(moldyn,&dist_ij);
 115         d_ij2=v3_absolute_square(&dist_ij);
 116
 117         /* if d_ij2 > S2 => no force & potential energy contribution */
 118         if(d_ij2>S2) {
 119                 return 0;
 120         }
 121
 122         /* now we will need the distance */
 123         d_ij=sqrt(d_ij2);
 124
 125         /* more constants */
 126         if(brand==ai->brand) {
 127                 S=params->S[brand];
 128                 R=params->R[brand];
 129                 A=params->A[brand];
 130                 lambda=params->lambda[brand];
 131         }
 132         else {
 133                 S=params->Smixed;
 134                 R=params->Rmixed;
 135                 A=params->Amixed;
 136                 lambda=params->lambda_m;
 137         }
 138
 139         /* f_r_ij, df_r_ij */
 140         f_r=A*exp(-lambda*d_ij);
 141         df_r=lambda*f_r/d_ij;
 142
 143         /* f_c, df_c */
 144         if(d_ij<R) {
 145                 f_c=1.0;
 146                 df_c=0.0;
 147                 v3_scale(&force,&dist_ij,-df_r);
 148         }
 149         else {
 150                 s_r=S-R;
 151                 arg=M_PI*(d_ij-R)/s_r;
 152                 f_c=0.5+0.5*cos(arg);
 153                 df_c=0.5*sin(arg)*(M_PI/(s_r*d_ij));
 154                 v3_scale(&force,&dist_ij,-df_c*f_r-df_r*f_c);
 155         }
 156
 157         /* add forces */
 158         v3_add(&(ai->f),&(ai->f),&force);
 159         v3_sub(&(aj->f),&(aj->f),&force); // reason: dri rij = - drj rij
 160
 161 #ifdef DEBUG
 162         if((ai==&(moldyn->atom[0]))|(aj==&(moldyn->atom[0]))) {
 163                 printf("force 2bp: [%d %d]\n",ai->tag,aj->tag);
 164                 printf("adding %f %f %f\n",force.x,force.y,force.z);
 165                 if(ai==&(moldyn->atom[0]))
 166                         printf("total i: %f %f %f\n",ai->f.x,ai->f.y,ai->f.z);
 167                 if(aj==&(moldyn->atom[0]))
 168                         printf("total j: %f %f %f\n",aj->f.x,aj->f.y,aj->f.z);
 169         }
 170 #endif
 171
 172         /* virial */
 173         virial_calc(ai,&force,&dist_ij);
 174
 175         /* energy 2bp contribution */
 176         moldyn->energy+=f_r*f_c;
 177
 178         return 0;
 179 }
 180
 181 /* tersoff 3 body potential function (first ij loop) */
 182 int tersoff_mult_3bp_j1(t_moldyn *moldyn,t_atom *ai,t_atom *aj,u8 bc) {
 183
 184         t_tersoff_mult_params *params;
 185         t_tersoff_exchange *exchange;
 186         unsigned char brand;
 187         double S2;
 188         t_3dvec dist_ij;
 189         double d_ij2,d_ij;
 190
 191         params=moldyn->pot_params;
 192         exchange=&(params->exchange);
 193
 194         /* reset zeta sum */
 195         exchange->zeta_ij=0.0;
 196
 197         /*
 198          * set ij depending values
 199          */
 200
 201         brand=ai->brand;
 202
 203         if(brand==aj->brand)
 204                 S2=params->S2[brand];
 205         else
 206                 S2=params->S2mixed;
 207
 208         /* dist_ij, d_ij2 */
 209         v3_sub(&dist_ij,&(aj->r),&(ai->r));
 210         if(bc) check_per_bound(moldyn,&dist_ij);
 211         d_ij2=v3_absolute_square(&dist_ij);
 212
 213         /* if d_ij2 > S2 => no force & potential energy contribution */
 214         if(d_ij2>S2) {
 215                 moldyn->run3bp=0;
 216                 return 0;
 217         }
 218
 219         /* d_ij */
 220         d_ij=sqrt(d_ij2);
 221
 222         /* store values */
 223         exchange->dist_ij=dist_ij;
 224         exchange->d_ij2=d_ij2;
 225         exchange->d_ij=d_ij;
 226
 227         /* reset k counter for first k loop */
 228         exchange->kcount=0;
 229
 230         return 0;
 231 }
 232
 233 /* tersoff 3 body potential function (first k loop) */
 234 int tersoff_mult_3bp_k1(t_moldyn *moldyn,
 235                         t_atom *ai,t_atom *aj,t_atom *ak,u8 bc) {
 236
 237         t_tersoff_mult_params *params;
 238         t_tersoff_exchange *exchange;
 239         unsigned char brand;
 240         double R,S,S2;
 241         t_3dvec dist_ij,dist_ik;
 242         double d_ik2,d_ik,d_ij;
 243         double cos_theta,h_cos,d2_h_cos2,frac,g,dg,s_r,arg;
 244         double f_c_ik,df_c_ik;
 245         int kcount;
 246
 247         params=moldyn->pot_params;
 248         exchange=&(params->exchange);
 249         kcount=exchange->kcount;
 250
 251         if(kcount>TERSOFF_MAXN) {
 252                 printf("FATAL: neighbours = %d\n",kcount);
 253                 printf("  -> %d %d %d\n",ai->tag,aj->tag,ak->tag);
 254         }
 255
 256         /* ik constants */
 257         brand=ai->brand;
 258         if(brand==ak->brand) {
 259                 R=params->R[brand];
 260                 S=params->S[brand];
 261                 S2=params->S2[brand];
 262         }
 263         else {
 264                 R=params->Rmixed;
 265                 S=params->Smixed;
 266                 S2=params->S2mixed;
 267         }
 268
 269         /* dist_ik, d_ik2 */
 270         v3_sub(&dist_ik,&(ak->r),&(ai->r));
 271         if(bc) check_per_bound(moldyn,&dist_ik);
 272         d_ik2=v3_absolute_square(&dist_ik);
 273
 274         /* store data for second k loop */
 275         exchange->dist_ik[kcount]=dist_ik;
 276         exchange->d_ik2[kcount]=d_ik2;
 277
 278         /* return if not within cutoff */
 279         if(d_ik2>S2) {
 280                 exchange->kcount++;
 281                 return 0;
 282         }
 283
 284         /* d_ik */
 285         d_ik=sqrt(d_ik2);
 286
 287         /* dist_ij, d_ij */
 288         dist_ij=exchange->dist_ij;
 289         d_ij=exchange->d_ij;
 290
 291         /* cos theta */
 292         cos_theta=v3_scalar_product(&dist_ij,&dist_ik)/(d_ij*d_ik);
 293
 294         /* g_ijk */
 295         h_cos=*(exchange->h_i)-cos_theta;
 296         d2_h_cos2=exchange->di2+(h_cos*h_cos);
 297         frac=exchange->ci2/d2_h_cos2;
 298         g=1.0+exchange->ci2di2-frac;
 299         dg=-2.0*frac*h_cos/d2_h_cos2;
 300
 301         /* zeta sum += f_c_ik * g_ijk */
 302         if(d_ik<=R) {
 303                 exchange->zeta_ij+=g;
 304                 f_c_ik=1.0;
 305                 df_c_ik=0.0;
 306         }
 307         else {
 308                 s_r=S-R;
 309                 arg=M_PI*(d_ik-R)/s_r;
 310                 f_c_ik=0.5+0.5*cos(arg);
 311                 df_c_ik=0.5*sin(arg)*(M_PI/(s_r*d_ik));
 312                 exchange->zeta_ij+=f_c_ik*g;
 313         }
 314
 315 #ifdef DEBUG
 316         if((ai==&(moldyn->atom[0]))|
 317            (aj==&(moldyn->atom[864]))|
 318            (ak==&(moldyn->atom[1003]))) {
 319                 printf(" -> %f %f %f\n",exchange->ci2di2,frac,h_cos);
 320         }
 321 #endif
 322
 323         /* store even more data for second k loop */
 324         exchange->g[kcount]=g;
 325         exchange->dg[kcount]=dg;
 326         exchange->d_ik[kcount]=d_ik;
 327         exchange->cos_theta[kcount]=cos_theta;
 328         exchange->f_c_ik[kcount]=f_c_ik;
 329         exchange->df_c_ik[kcount]=df_c_ik;
 330
 331         /* increase k counter */
 332         exchange->kcount++;
 333
 334         return 0;
 335 }
 336
 337 int tersoff_mult_3bp_j2(t_moldyn *moldyn,t_atom *ai,t_atom *aj,u8 bc) {
 338
 339         t_tersoff_mult_params *params;
 340         t_tersoff_exchange *exchange;
 341         t_3dvec force;
 342         double f_a,df_a,b,db,f_c,df_c;
 343         double f_r,df_r;
 344         double scale;
 345         double mu,B,chi;
 346         double lambda,A;
 347         double d_ij;
 348         unsigned char brand;
 349         double ni,tmp;
 350         double S,R,s_r,arg;
 351
 352         params=moldyn->pot_params;
 353         exchange=&(params->exchange);
 354
 355         brand=aj->brand;
 356         if(brand==ai->brand) {
 357                 S=params->S[brand];
 358                 R=params->R[brand];
 359                 B=params->B[brand];
 360                 A=params->A[brand];
 361                 mu=params->mu[brand];
 362                 lambda=params->lambda[brand];
 363                 chi=1.0;
 364         }
 365         else {
 366                 S=params->Smixed;
 367                 R=params->Rmixed;
 368                 B=params->Bmixed;
 369                 A=params->Amixed;
 370                 mu=params->mu_m;
 371                 lambda=params->lambda_m;
 372                 chi=params->chi;
 373         }
 374
 375         d_ij=exchange->d_ij;
 376
 377         /* f_c, df_c */
 378         if(d_ij<R) {
 379                 f_c=1.0;
 380                 df_c=0.0;
 381         }
 382         else {
 383                 s_r=S-R;
 384                 arg=M_PI*(d_ij-R)/s_r;
 385                 f_c=0.5+0.5*cos(arg);
 386                 df_c=0.5*sin(arg)*(M_PI/(s_r*d_ij));
 387         }
 388
 389         /* f_a, df_a */
 390         f_a=-B*exp(-mu*d_ij);
 391         df_a=mu*f_a/d_ij;
 392
 393         /* f_r, df_r */
 394         f_r=A*exp(-lambda*d_ij);
 395         df_r=lambda*f_r/d_ij;
 396
 397         /* b, db */
 398         if(exchange->zeta_ij==0.0) {
 399                 b=chi;
 400                 db=0.0;
 401         }
 402         else {
 403                 ni=*(exchange->n_i);
 404                 tmp=exchange->betaini*pow(exchange->zeta_ij,ni-1.0);
 405                 b=(1.0+exchange->zeta_ij*tmp);
 406                 db=chi*pow(b,-1.0/(2.0*ni)-1.0);
 407                 b=db*b;
 408                 db*=-0.5*tmp;
 409         }
 410
 411         /* force contribution */
 412         scale=-0.5*(f_c*(df_r+b*df_a)+df_c*(f_r+b*df_a));
 413         v3_scale(&force,&(exchange->dist_ij),scale);
 414         v3_add(&(ai->f),&(ai->f),&force);
 415         v3_sub(&(aj->f),&(aj->f),&force); // dri rij = - drj rij
 416
 417 #ifdef DEBUG
 418         if((ai==&(moldyn->atom[0]))|(aj==&(moldyn->atom[0]))) {
 419                 printf("force 3bp (j2): [%d %d sum]\n",ai->tag,aj->tag);
 420                 printf("adding %f %f %f\n",force.x,force.y,force.z);
 421                 if(ai==&(moldyn->atom[0]))
 422                         printf("total i: %f %f %f\n",ai->f.x,ai->f.y,ai->f.z);
 423                 if(aj==&(moldyn->atom[0]))
 424                         printf("total j: %f %f %f\n",aj->f.x,aj->f.y,aj->f.z);
 425                 printf("energy: %f = %f %f %f %f\n",0.5*f_c*(b*f_a+f_r),
 426                                                     f_c,b,f_a,f_r);
 427                 printf("        %f %f %f\n",exchange->zeta_ij,.0,.0);
 428         }
 429 #endif
 430
 431         /* virial */
 432         if(aj<ai)
 433                 virial_calc(ai,&force,&(exchange->dist_ij));
 434
 435         /* dzeta prefactor = - 0.5 f_c f_a db */
 436         exchange->pre_dzeta=-0.5*f_a*f_c*db;
 437
 438         /* energy contribution */
 439         moldyn->energy+=0.5*f_c*(b*f_a+f_r);
 440
 441         /* reset k counter for second k loop */
 442         exchange->kcount=0;
 443
 444         return 0;
 445 }
 446
 447 /* tersoff 3 body potential function (second k loop) */
 448 int tersoff_mult_3bp_k2(t_moldyn *moldyn,
 449                         t_atom *ai,t_atom *aj,t_atom *ak,u8 bc) {
 450
 451         t_tersoff_mult_params *params;
 452         t_tersoff_exchange *exchange;
 453         int kcount;
 454         t_3dvec dist_ik,dist_ij;
 455         double d_ik2,d_ik,d_ij2,d_ij;
 456         unsigned char brand;
 457         double S2;
 458         double g,dg,cos_theta;
 459         double pre_dzeta;
 460         double f_c_ik,df_c_ik;
 461         double dijdik_inv,fcdg,dfcg;
 462         t_3dvec dcosdri,dcosdrj,dcosdrk;
 463         t_3dvec force,tmp;
 464
 465         params=moldyn->pot_params;
 466         exchange=&(params->exchange);
 467         kcount=exchange->kcount;
 468
 469         if(kcount>TERSOFF_MAXN)
 470                 printf("FATAL: neighbours!\n");
 471
 472         /* d_ik2 */
 473         d_ik2=exchange->d_ik2[kcount];
 474
 475         brand=ak->brand;
 476         if(brand==ai->brand)
 477                 S2=params->S2[brand];
 478         else
 479                 S2=params->S2mixed;
 480
 481         /* return if d_ik > S */
 482         if(d_ik2>S2) {
 483                 exchange->kcount++;
 484                 return 0;
 485         }
 486
 487         /* prefactor dzeta */
 488         pre_dzeta=exchange->pre_dzeta;
 489
 490         /* dist_ik, d_ik */
 491         dist_ik=exchange->dist_ik[kcount];
 492         d_ik=exchange->d_ik[kcount];
 493
 494         /* f_c_ik, df_c_ik */
 495         f_c_ik=exchange->f_c_ik[kcount];
 496         df_c_ik=exchange->df_c_ik[kcount];
 497
 498         /* dist_ij, d_ij2, d_ij */
 499         dist_ij=exchange->dist_ij;
 500         d_ij2=exchange->d_ij2;
 501         d_ij=exchange->d_ij;
 502
 503         /* g, dg, cos_theta */
 504         g=exchange->g[kcount];
 505         dg=exchange->dg[kcount];
 506         cos_theta=exchange->cos_theta[kcount];
 507
 508         /* cos_theta derivatives wrt i,j,k */
 509         dijdik_inv=1.0/(d_ij*d_ik);
 510         v3_scale(&dcosdrj,&dist_ik,dijdik_inv);
 511         v3_scale(&tmp,&dist_ij,-cos_theta/d_ij2);
 512         v3_add(&dcosdrj,&dcosdrj,&tmp);
 513         v3_scale(&dcosdrk,&dist_ij,dijdik_inv);
 514         v3_scale(&tmp,&dist_ik,-cos_theta/d_ik2);
 515         v3_add(&dcosdrk,&dcosdrk,&tmp);
 516         v3_add(&dcosdri,&dcosdrj,&dcosdrk);
 517         v3_scale(&dcosdri,&dcosdri,-1.0);
 518
 519         /* f_c_ik * dg, df_c_ik * g */
 520         fcdg=f_c_ik*dg;
 521         dfcg=df_c_ik*g;
 522
 523         /* derivative wrt i */
 524         v3_scale(&force,&dist_ik,dfcg);
 525         v3_scale(&tmp,&dcosdri,fcdg);
 526         v3_add(&force,&force,&tmp);
 527         v3_scale(&force,&force,pre_dzeta);
 528
 529         /* force contribution */
 530         v3_add(&(ai->f),&(ai->f),&force);
 531
 532 #ifdef DEBUG
 533         if(ai==&(moldyn->atom[0])) {
 534                 printf("force 3bp (k2): [%d %d %d]\n",ai->tag,aj->tag,ak->tag);
 535                 printf("adding %f %f %f\n",force.x,force.y,force.z);
 536                 printf("total i: %f %f %f\n",ai->f.x,ai->f.y,ai->f.z);
 537         }
 538 #endif
 539
 540         /* virial */
 541         //virial_calc(ai,&force,&dist_ij);
 542
 543         /* derivative wrt j */
 544         v3_scale(&force,&dcosdrj,fcdg*pre_dzeta);
 545
 546         /* force contribution */
 547         v3_add(&(aj->f),&(aj->f),&force);
 548
 549 #ifdef DEBUG
 550         if(aj==&(moldyn->atom[0])) {
 551                 printf("force 3bp (k2): [%d %d %d]\n",ai->tag,aj->tag,ak->tag);
 552                 printf("adding %f %f %f\n",force.x,force.y,force.z);
 553                 printf("total j: %f %f %f\n",aj->f.x,aj->f.y,aj->f.z);
 554         }
 555 #endif
 556
 557         /* virial */
 558         //v3_scale(&force,&force,-1.0);
 559         if(aj<ai)
 560                 virial_calc(ai,&force,&dist_ij);
 561
 562         /* derivative wrt k */
 563         v3_scale(&force,&dist_ik,-1.0*dfcg); // dri rik = - drk rik
 564         v3_scale(&tmp,&dcosdrk,fcdg);
 565         v3_add(&force,&force,&tmp);
 566         v3_scale(&force,&force,pre_dzeta);
 567
 568         /* force contribution */
 569         v3_add(&(ak->f),&(ak->f),&force);
 570
 571 #ifdef DEBUG
 572         if(ak==&(moldyn->atom[0])) {
 573                 printf("force 3bp (k2): [%d %d %d]\n",ai->tag,aj->tag,ak->tag);
 574                 printf("adding %f %f %f\n",force.x,force.y,force.z);
 575                 printf("total k: %f %f %f\n",ak->f.x,ak->f.y,ak->f.z);
 576         }
 577 #endif
 578
 579         /* virial */
 580         //v3_scale(&force,&force,-1.0);
 581         if(aj<ai)
 582                 virial_calc(ai,&force,&dist_ik);
 583
 584         /* increase k counter */
 585         exchange->kcount++;
 586
 587         return 0;
 588
 589 }