potentials/albe.c

   1 /*
   2  * albe.c - albe 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 "albe.h"
  21
  22 /* create mixed terms from parameters and set them */
  23 int albe_mult_complete_params(t_albe_mult_params *p) {
  24
  25         printf("[moldyn] albe 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->S2mixed=p->Smixed*p->Smixed;
  29
  30         printf("[moldyn] albe mult parameter info:\n");
  31         printf("  S (A)  | %f | %f | %f\n",p->S[0],p->S[1],p->Smixed);
  32         printf("  R (A)  | %f | %f | %f\n",p->R[0],p->R[1],p->Rmixed);
  33         printf("  A (eV) | %f | %f | %f\n",p->A[0]/EV,p->A[1]/EV,p->Amixed/EV);
  34         printf("  B (eV) | %f | %f | %f\n",p->B[0]/EV,p->B[1]/EV,p->Bmixed/EV);
  35         printf("  lambda | %f | %f | %f\n",p->lambda[0],p->lambda[1],
  36                                           p->lambda_m);
  37         printf("  mu     | %f | %f | %f\n",p->mu[0],p->mu[1],p->mu_m);
  38         printf("  gamma  | %f | %f\n",p->gamma[0],p->gamma[1]);
  39         printf("  c      | %f | %f\n",p->c[0],p->c[1]);
  40         printf("  d      | %f | %f\n",p->d[0],p->d[1]);
  41         printf("  h      | %f | %f\n",p->h[0],p->h[1]);
  42
  43         return 0;
  44 }
  45
  46 /* albe 3 body potential function (first ij loop) */
  47 int albe_mult_3bp_j1(t_moldyn *moldyn,t_atom *ai,t_atom *aj,u8 bc) {
  48
  49         t_albe_mult_params *params;
  50         t_albe_exchange *exchange;
  51         unsigned char brand;
  52         double S2;
  53         t_3dvec dist_ij;
  54         double d_ij2,d_ij;
  55
  56         params=moldyn->pot_params;
  57         exchange=&(params->exchange);
  58
  59         /* reset zeta sum */
  60         exchange->zeta_ij=0.0;
  61
  62         /*
  63          * set ij depending values
  64          */
  65
  66         brand=ai->brand;
  67         if(brand==aj->brand) {
  68                 S2=params->S2[brand];
  69         }
  70         else {
  71                 S2=params->S2mixed;
  72         }
  73
  74         /* dist_ij, d_ij2 */
  75         v3_sub(&dist_ij,&(aj->r),&(ai->r));
  76         if(bc) check_per_bound(moldyn,&dist_ij);
  77         d_ij2=v3_absolute_square(&dist_ij);
  78
  79         /* if d_ij2 > S2 => no force & potential energy contribution */
  80         if(d_ij2>S2) {
  81                 moldyn->run3bp=0;
  82                 return 0;
  83         }
  84
  85         /* d_ij */
  86         d_ij=sqrt(d_ij2);
  87
  88         /* store values */
  89         exchange->dist_ij=dist_ij;
  90         exchange->d_ij2=d_ij2;
  91         exchange->d_ij=d_ij;
  92
  93         /* reset k counter for first k loop */
  94         exchange->kcount=0;
  95
  96         return 0;
  97 }
  98
  99 /* albe 3 body potential function (first k loop) */
 100 int albe_mult_3bp_k1(t_moldyn *moldyn,
 101                      t_atom *ai,t_atom *aj,t_atom *ak,u8 bc) {
 102
 103         t_albe_mult_params *params;
 104         t_albe_exchange *exchange;
 105         unsigned char brand;
 106         double R,S,S2;
 107         t_3dvec dist_ij,dist_ik;
 108         double d_ik2,d_ik,d_ij;
 109         double cos_theta,h_cos,d2_h_cos2,frac,g,dg,s_r,arg;
 110         double f_c_ik,df_c_ik;
 111         int kcount;
 112
 113         params=moldyn->pot_params;
 114         exchange=&(params->exchange);
 115         kcount=exchange->kcount;
 116
 117         if(kcount>ALBE_MAXN) {
 118                 printf("FATAL: neighbours = %d\n",kcount);
 119                 printf("  -> %d %d %d\n",ai->tag,aj->tag,ak->tag);
 120         }
 121
 122         /* ik constants */
 123         brand=ai->brand;
 124         if(brand==ak->brand) {
 125                 R=params->R[brand];
 126                 S=params->S[brand];
 127                 S2=params->S2[brand];
 128                 /* albe needs i,k depending c,d,h and gamma values */
 129                 exchange->gamma_i=&(params->gamma[brand]);
 130                 exchange->c_i=&(params->c[brand]);
 131                 exchange->d_i=&(params->d[brand]);
 132                 exchange->h_i=&(params->h[brand]);
 133         }
 134         else {
 135                 R=params->Rmixed;
 136                 S=params->Smixed;
 137                 S2=params->S2mixed;
 138                 /* albe needs i,k depending c,d,h and gamma values */
 139                 exchange->gamma_i=&(params->gamma_m);
 140                 exchange->c_i=&(params->c_mixed);
 141                 exchange->d_i=&(params->d_mixed);
 142                 exchange->h_i=&(params->h_mixed);
 143         }
 144         exchange->ci2=*(exchange->c_i)**(exchange->c_i);
 145         exchange->di2=*(exchange->d_i)**(exchange->d_i);
 146         exchange->ci2di2=exchange->ci2/exchange->di2;
 147
 148         /* dist_ik, d_ik2 */
 149         v3_sub(&dist_ik,&(ak->r),&(ai->r));
 150         if(bc) check_per_bound(moldyn,&dist_ik);
 151         d_ik2=v3_absolute_square(&dist_ik);
 152
 153         /* store data for second k loop */
 154         exchange->dist_ik[kcount]=dist_ik;
 155         exchange->d_ik2[kcount]=d_ik2;
 156
 157         /* return if not within cutoff */
 158         if(d_ik2>S2) {
 159                 exchange->kcount++;
 160                 return 0;
 161         }
 162
 163         /* d_ik */
 164         d_ik=sqrt(d_ik2);
 165
 166         /* dist_ij, d_ij */
 167         dist_ij=exchange->dist_ij;
 168         d_ij=exchange->d_ij;
 169
 170         /* cos theta */
 171         cos_theta=v3_scalar_product(&dist_ij,&dist_ik)/(d_ij*d_ik);
 172
 173         /* g_ijk */
 174         h_cos=*(exchange->h_i)+cos_theta; // + in albe formalism
 175         d2_h_cos2=exchange->di2+(h_cos*h_cos);
 176         frac=exchange->ci2/d2_h_cos2;
 177         g=*(exchange->gamma_i)*(1.0+exchange->ci2di2-frac);
 178         dg=2.0*frac**(exchange->gamma_i)*h_cos/d2_h_cos2; // + in albe f..
 179
 180         /* zeta sum += f_c_ik * g_ijk */
 181         if(d_ik<=R) {
 182                 exchange->zeta_ij+=g;
 183                 f_c_ik=1.0;
 184                 df_c_ik=0.0;
 185         }
 186         else {
 187                 s_r=S-R;
 188                 arg=M_PI*(d_ik-R)/s_r;
 189                 f_c_ik=0.5+0.5*cos(arg);
 190                 df_c_ik=0.5*sin(arg)*(M_PI/(s_r*d_ik));
 191                 exchange->zeta_ij+=f_c_ik*g;
 192         }
 193
 194         /* store even more data for second k loop */
 195         exchange->g[kcount]=g;
 196         exchange->dg[kcount]=dg;
 197         exchange->d_ik[kcount]=d_ik;
 198         exchange->cos_theta[kcount]=cos_theta;
 199         exchange->f_c_ik[kcount]=f_c_ik;
 200         exchange->df_c_ik[kcount]=df_c_ik;
 201
 202         /* increase k counter */
 203         exchange->kcount++;
 204
 205         return 0;
 206 }
 207
 208 int albe_mult_3bp_j2(t_moldyn *moldyn,t_atom *ai,t_atom *aj,u8 bc) {
 209
 210         t_albe_mult_params *params;
 211         t_albe_exchange *exchange;
 212         t_3dvec force;
 213         double f_a,df_a,b,db,f_c,df_c;
 214         double f_r,df_r;
 215         double scale;
 216         double mu,B;
 217         double lambda,A;
 218         double d_ij,r0;
 219         unsigned char brand;
 220         double S,R,s_r,arg;
 221         double energy;
 222
 223         params=moldyn->pot_params;
 224         exchange=&(params->exchange);
 225
 226         brand=aj->brand;
 227         if(brand==ai->brand) {
 228                 S=params->S[brand];
 229                 R=params->R[brand];
 230                 B=params->B[brand];
 231                 A=params->A[brand];
 232                 r0=params->r0[brand];
 233                 mu=params->mu[brand];
 234                 lambda=params->lambda[brand];
 235         }
 236         else {
 237                 S=params->Smixed;
 238                 R=params->Rmixed;
 239                 B=params->Bmixed;
 240                 A=params->Amixed;
 241                 r0=params->r0_mixed;
 242                 mu=params->mu_m;
 243                 lambda=params->lambda_m;
 244         }
 245
 246         d_ij=exchange->d_ij;
 247
 248         /* f_c, df_c */
 249         if(d_ij<R) {
 250                 f_c=1.0;
 251                 df_c=0.0;
 252         }
 253         else {
 254                 s_r=S-R;
 255                 arg=M_PI*(d_ij-R)/s_r;
 256                 f_c=0.5+0.5*cos(arg);
 257                 df_c=0.5*sin(arg)*(M_PI/(s_r*d_ij));
 258         }
 259
 260         /* f_a, df_a */
 261         f_a=-B*exp(-mu*(d_ij-r0));
 262         df_a=mu*f_a/d_ij;
 263
 264         /* f_r, df_r */
 265         f_r=A*exp(-lambda*(d_ij-r0));
 266         df_r=lambda*f_r/d_ij;
 267
 268         /* b, db */
 269         if(exchange->zeta_ij==0.0) {
 270                 b=1.0;
 271                 db=0.0;
 272         }
 273         else {
 274                 b=1.0/sqrt(1.0+exchange->zeta_ij);
 275                 db=-0.5*b/(1.0+exchange->zeta_ij);
 276         }
 277
 278         /* force contribution for atom i */
 279         scale=-0.5*(f_c*(df_r-b*df_a)+df_c*(f_r-b*f_a)); // - in albe formalism
 280         v3_scale(&force,&(exchange->dist_ij),scale);
 281         v3_add(&(ai->f),&(ai->f),&force);
 282
 283         /* force contribution for atom j */
 284         v3_scale(&force,&force,-1.0); // dri rij = - drj rij
 285         v3_add(&(aj->f),&(aj->f),&force);
 286
 287         /* virial */
 288         virial_calc(aj,&force,&(exchange->dist_ij));
 289
 290 #ifdef DEBUG
 291 if(moldyn->time>DSTART&&moldyn->time<DEND) {
 292         if((ai==&(moldyn->atom[DATOM]))|(aj==&(moldyn->atom[DATOM]))) {
 293                 printf("force 3bp (j2): [%d %d sum]\n",ai->tag,aj->tag);
 294                 printf("  adding %f %f %f\n",force.x,force.y,force.z);
 295                 if(ai==&(moldyn->atom[0]))
 296                         printf("  total i: %f %f %f\n",ai->f.x,ai->f.y,ai->f.z);
 297                 if(aj==&(moldyn->atom[0]))
 298                         printf("  total j: %f %f %f\n",aj->f.x,aj->f.y,aj->f.z);
 299                 printf("  energy: %f = %f %f %f %f\n",0.5*f_c*(b*f_a+f_r),
 300                                                     f_c,b,f_a,f_r);
 301                 printf("          %f %f %f\n",exchange->zeta_ij,.0,.0);
 302         }
 303 }
 304 #endif
 305
 306         /* dzeta prefactor = - f_c f_a db, (* -0.5 due to force calc) */
 307         exchange->pre_dzeta=0.5*f_a*f_c*db;
 308
 309         /* energy contribution */
 310         energy=0.5*f_c*(f_r-b*f_a); // - in albe formalism
 311         moldyn->energy+=energy;
 312         ai->e+=energy;
 313
 314         /* reset k counter for second k loop */
 315         exchange->kcount=0;
 316
 317         return 0;
 318 }
 319
 320 /* albe 3 body potential function (second k loop) */
 321 int albe_mult_3bp_k2(t_moldyn *moldyn,
 322                      t_atom *ai,t_atom *aj,t_atom *ak,u8 bc) {
 323
 324         t_albe_mult_params *params;
 325         t_albe_exchange *exchange;
 326         int kcount;
 327         t_3dvec dist_ik,dist_ij;
 328         double d_ik2,d_ik,d_ij2,d_ij;
 329         unsigned char brand;
 330         double S2;
 331         double g,dg,cos_theta;
 332         double pre_dzeta;
 333         double f_c_ik,df_c_ik;
 334         double dijdik_inv,fcdg,dfcg;
 335         t_3dvec dcosdrj,dcosdrk;
 336         t_3dvec force,tmp;
 337
 338         params=moldyn->pot_params;
 339         exchange=&(params->exchange);
 340         kcount=exchange->kcount;
 341
 342         if(kcount>ALBE_MAXN)
 343                 printf("FATAL: neighbours!\n");
 344
 345         /* d_ik2 */
 346         d_ik2=exchange->d_ik2[kcount];
 347
 348         brand=ak->brand;
 349         if(brand==ai->brand)
 350                 S2=params->S2[brand];
 351         else
 352                 S2=params->S2mixed;
 353
 354         /* return if d_ik > S */
 355         if(d_ik2>S2) {
 356                 exchange->kcount++;
 357                 return 0;
 358         }
 359
 360         /* prefactor dzeta */
 361         pre_dzeta=exchange->pre_dzeta;
 362
 363         /* dist_ik, d_ik */
 364         dist_ik=exchange->dist_ik[kcount];
 365         d_ik=exchange->d_ik[kcount];
 366
 367         /* f_c_ik, df_c_ik */
 368         f_c_ik=exchange->f_c_ik[kcount];
 369         df_c_ik=exchange->df_c_ik[kcount];
 370
 371         /* dist_ij, d_ij2, d_ij */
 372         dist_ij=exchange->dist_ij;
 373         d_ij2=exchange->d_ij2;
 374         d_ij=exchange->d_ij;
 375
 376         /* g, dg, cos_theta */
 377         g=exchange->g[kcount];
 378         dg=exchange->dg[kcount];
 379         cos_theta=exchange->cos_theta[kcount];
 380
 381         /* cos_theta derivatives wrt j,k */
 382         dijdik_inv=1.0/(d_ij*d_ik);
 383         v3_scale(&dcosdrj,&dist_ik,dijdik_inv);         // j
 384         v3_scale(&tmp,&dist_ij,-cos_theta/d_ij2);
 385         v3_add(&dcosdrj,&dcosdrj,&tmp);
 386         v3_scale(&dcosdrk,&dist_ij,dijdik_inv);         // k
 387         v3_scale(&tmp,&dist_ik,-cos_theta/d_ik2);
 388         v3_add(&dcosdrk,&dcosdrk,&tmp);
 389
 390         /* f_c_ik * dg, df_c_ik * g */
 391         fcdg=f_c_ik*dg;
 392         dfcg=df_c_ik*g;
 393
 394         /* derivative wrt j */
 395         v3_scale(&force,&dcosdrj,fcdg*pre_dzeta);
 396
 397         /* force contribution */
 398         v3_add(&(aj->f),&(aj->f),&force);
 399
 400 #ifdef DEBUG
 401 if(moldyn->time>DSTART&&moldyn->time<DEND) {
 402         if(aj==&(moldyn->atom[DATOM])) {
 403                 printf("force 3bp (k2): [%d %d %d]\n",ai->tag,aj->tag,ak->tag);
 404                 printf("  adding %f %f %f\n",force.x,force.y,force.z);
 405                 printf("  total j: %f %f %f\n",aj->f.x,aj->f.y,aj->f.z);
 406                 printf("  angle: %f\n",acos(cos_theta)*360.0/(2*M_PI));
 407                 printf("    d ij ik = %f %f\n",d_ij,d_ik);
 408         }
 409 }
 410 #endif
 411
 412         /* force contribution to atom i */
 413         v3_scale(&force,&force,-1.0);
 414         v3_add(&(ai->f),&(ai->f),&force);
 415
 416         /* virial */
 417         virial_calc(ai,&force,&dist_ij);
 418
 419         /* derivative wrt k */
 420         v3_scale(&force,&dist_ik,-1.0*dfcg); // dri rik = - drk rik
 421         v3_scale(&tmp,&dcosdrk,fcdg);
 422         v3_add(&force,&force,&tmp);
 423         v3_scale(&force,&force,pre_dzeta);
 424
 425         /* force contribution */
 426         v3_add(&(ak->f),&(ak->f),&force);
 427
 428 #ifdef DEBUG
 429 if(moldyn->time>DSTART&&moldyn->time<DEND) {
 430         if(ak==&(moldyn->atom[DATOM])) {
 431                 printf("force 3bp (k2): [%d %d %d]\n",ai->tag,aj->tag,ak->tag);
 432                 printf("  adding %f %f %f\n",force.x,force.y,force.z);
 433                 printf("  total k: %f %f %f\n",ak->f.x,ak->f.y,ak->f.z);
 434                 printf("  angle: %f\n",acos(cos_theta)*360.0/(2*M_PI));
 435                 printf("    d ij ik = %f %f\n",d_ij,d_ik);
 436         }
 437 }
 438 #endif
 439
 440         /* force contribution to atom i */
 441         v3_scale(&force,&force,-1.0);
 442         v3_add(&(ai->f),&(ai->f),&force);
 443
 444         /* virial */
 445         virial_calc(ai,&force,&dist_ik);
 446
 447         /* increase k counter */
 448         exchange->kcount++;
 449
 450         return 0;
 451
 452 }