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