2 * moldyn.c - molecular dynamics library main file
4 * author: Frank Zirkelbach <frank.zirkelbach@physik.uni-augsburg.de>
12 #include <sys/types.h>
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"
27 int moldyn_init(t_moldyn *moldyn,int argc,char **argv) {
31 //ret=moldyn_parse_argv(moldyn,argc,argv);
32 //if(ret<0) return ret;
34 memset(moldyn,0,sizeof(t_moldyn));
36 rand_init(&(moldyn->random),NULL,1);
37 moldyn->random.status|=RAND_STAT_VERBOSE;
42 int moldyn_shutdown(t_moldyn *moldyn) {
44 printf("[moldyn] shutdown\n");
45 moldyn_log_shutdown(moldyn);
46 link_cell_shutdown(moldyn);
47 rand_close(&(moldyn->random));
53 int set_int_alg(t_moldyn *moldyn,u8 algo) {
56 case MOLDYN_INTEGRATE_VERLET:
57 moldyn->integrate=velocity_verlet;
60 printf("unknown integration algorithm: %02x\n",algo);
67 int set_cutoff(t_moldyn *moldyn,double cutoff) {
69 moldyn->cutoff=cutoff;
74 int set_temperature(t_moldyn *moldyn,double t) {
81 int set_dim(t_moldyn *moldyn,double x,double y,double z,u8 visualize) {
96 int set_nn_dist(t_moldyn *moldyn,double dist) {
103 int set_pbc(t_moldyn *moldyn,u8 x,u8 y,u8 z) {
106 moldyn->status|=MOLDYN_STAT_PBX;
109 moldyn->status|=MOLDYN_STAT_PBY;
112 moldyn->status|=MOLDYN_STAT_PBZ;
117 int set_potential1b(t_moldyn *moldyn,pf_func1b func,void *params) {
120 moldyn->pot1b_params=params;
125 int set_potential2b(t_moldyn *moldyn,pf_func2b func,void *params) {
128 moldyn->pot2b_params=params;
133 int set_potential3b(t_moldyn *moldyn,pf_func3b func,void *params) {
136 moldyn->pot3b_params=params;
141 int moldyn_set_log(t_moldyn *moldyn,u8 type,char *fb,int timer) {
144 case LOG_TOTAL_ENERGY:
145 moldyn->ewrite=timer;
146 moldyn->efd=open(fb,O_WRONLY|O_CREAT|O_TRUNC);
148 perror("[moldyn] efd open");
151 dprintf(moldyn->efd,"# total energy log file\n");
153 case LOG_TOTAL_MOMENTUM:
154 moldyn->mwrite=timer;
155 moldyn->mfd=open(fb,O_WRONLY|O_CREAT|O_TRUNC);
157 perror("[moldyn] mfd open");
160 dprintf(moldyn->efd,"# total momentum log file\n");
163 moldyn->swrite=timer;
164 strncpy(moldyn->sfb,fb,63);
167 moldyn->vwrite=timer;
168 strncpy(moldyn->vfb,fb,63);
169 visual_init(&(moldyn->vis),fb);
172 printf("unknown log mechanism: %02x\n",type);
179 int moldyn_log_shutdown(t_moldyn *moldyn) {
181 printf("[moldyn] log shutdown\n");
182 if(moldyn->efd) close(moldyn->efd);
183 if(moldyn->mfd) close(moldyn->mfd);
184 if(&(moldyn->vis)) visual_tini(&(moldyn->vis));
189 int create_lattice(t_moldyn *moldyn,u8 type,double lc,int element,double mass,
190 u8 attr,u8 bnum,int a,int b,int c) {
198 if(type==FCC) count*=4;
200 if(type==DIAMOND) count*=8;
202 moldyn->atom=malloc(count*sizeof(t_atom));
203 if(moldyn->atom==NULL) {
204 perror("malloc (atoms)");
212 ret=fcc_init(a,b,c,lc,moldyn->atom,&origin);
215 ret=diamond_init(a,b,c,lc,moldyn->atom,&origin);
218 printf("unknown lattice type (%02x)\n",type);
224 printf("ok, there is something wrong ...\n");
225 printf("calculated -> %d atoms\n",count);
226 printf("created -> %d atoms\n",ret);
231 printf("[moldyn] created lattice with %d atoms\n",count);
234 moldyn->atom[count-1].element=element;
235 moldyn->atom[count-1].mass=mass;
236 moldyn->atom[count-1].attr=attr;
237 moldyn->atom[count-1].bnum=bnum;
244 int add_atom(t_moldyn *moldyn,int element,double mass,u8 bnum,u8 attr,
245 t_3dvec *r,t_3dvec *v) {
252 count=++(moldyn->count);
254 ptr=realloc(atom,count*sizeof(t_atom));
256 perror("[moldyn] realloc (add atom)");
264 atom[count-1].element=element;
265 atom[count-1].mass=mass;
266 atom[count-1].bnum=bnum;
267 atom[count-1].attr=attr;
272 int destroy_atoms(t_moldyn *moldyn) {
274 if(moldyn->atom) free(moldyn->atom);
279 int thermal_init(t_moldyn *moldyn) {
282 * - gaussian distribution of velocities
283 * - zero total momentum
284 * - velocity scaling (E = 3/2 N k T), E: kinetic energy
289 t_3dvec p_total,delta;
294 random=&(moldyn->random);
296 /* gaussian distribution of velocities */
298 for(i=0;i<moldyn->count;i++) {
299 sigma=sqrt(2.0*K_BOLTZMANN*moldyn->t/atom[i].mass);
301 v=sigma*rand_get_gauss(random);
303 p_total.x+=atom[i].mass*v;
305 v=sigma*rand_get_gauss(random);
307 p_total.y+=atom[i].mass*v;
309 v=sigma*rand_get_gauss(random);
311 p_total.z+=atom[i].mass*v;
314 /* zero total momentum */
315 v3_scale(&p_total,&p_total,1.0/moldyn->count);
316 for(i=0;i<moldyn->count;i++) {
317 v3_scale(&delta,&p_total,1.0/atom[i].mass);
318 v3_sub(&(atom[i].v),&(atom[i].v),&delta);
321 /* velocity scaling */
322 scale_velocity(moldyn,VSCALE_INIT_EQUI);
327 int scale_velocity(t_moldyn *moldyn,u8 type) {
336 * - velocity scaling (E = 3/2 N k T), E: kinetic energy
340 for(i=0;i<moldyn->count;i++)
341 e+=0.5*atom[i].mass*v3_absolute_square(&(atom[i].v));
342 scale=(1.5*moldyn->count*K_BOLTZMANN*moldyn->t)/e;
343 if(type&VSCALE_INIT_EQUI) scale*=2.0; /* equipartition theorem */
345 for(i=0;i<moldyn->count;i++)
346 v3_scale(&(atom[i].v),&(atom[i].v),scale);
351 double get_e_kin(t_moldyn *moldyn) {
359 for(i=0;i<moldyn->count;i++)
360 moldyn->ekin+=0.5*atom[i].mass*v3_absolute_square(&(atom[i].v));
365 double get_e_pot(t_moldyn *moldyn) {
367 return moldyn->energy;
370 double update_e_kin(t_moldyn *moldyn) {
372 return(get_e_kin(moldyn));
375 double get_total_energy(t_moldyn *moldyn) {
377 return(moldyn->ekin+moldyn->energy);
380 t_3dvec get_total_p(t_moldyn *moldyn) {
389 for(i=0;i<moldyn->count;i++) {
390 v3_scale(&p,&(atom[i].v),atom[i].mass);
391 v3_add(&p_total,&p_total,&p);
397 double estimate_time_step(t_moldyn *moldyn,double nn_dist) {
401 /* nn_dist is the nearest neighbour distance */
404 printf("[moldyn] i do not estimate timesteps below %f K!\n",
405 MOLDYN_CRITICAL_EST_TEMP);
409 tau=(0.05*nn_dist*moldyn->atom[0].mass)/sqrt(3.0*K_BOLTZMANN*moldyn->t);
418 /* linked list / cell method */
420 int link_cell_init(t_moldyn *moldyn) {
426 fd=open("/dev/null",O_WRONLY);
430 /* partitioning the md cell */
431 lc->nx=moldyn->dim.x/moldyn->cutoff;
432 lc->x=moldyn->dim.x/lc->nx;
433 lc->ny=moldyn->dim.y/moldyn->cutoff;
434 lc->y=moldyn->dim.y/lc->ny;
435 lc->nz=moldyn->dim.z/moldyn->cutoff;
436 lc->z=moldyn->dim.z/lc->nz;
438 lc->cells=lc->nx*lc->ny*lc->nz;
439 lc->subcell=malloc(lc->cells*sizeof(t_list));
441 printf("[moldyn] initializing linked cells (%d)\n",lc->cells);
443 for(i=0;i<lc->cells;i++)
444 //list_init(&(lc->subcell[i]),1);
445 list_init(&(lc->subcell[i]),fd);
447 link_cell_update(moldyn);
452 int link_cell_update(t_moldyn *moldyn) {
466 for(i=0;i<lc->cells;i++)
467 list_destroy(&(moldyn->lc.subcell[i]));
469 for(count=0;count<moldyn->count;count++) {
470 i=(atom[count].r.x+(moldyn->dim.x/2))/lc->x;
471 j=(atom[count].r.y+(moldyn->dim.y/2))/lc->y;
472 k=(atom[count].r.z+(moldyn->dim.z/2))/lc->z;
473 list_add_immediate_ptr(&(moldyn->lc.subcell[i+j*nx+k*nx*ny]),
480 int link_cell_neighbour_index(t_moldyn *moldyn,int i,int j,int k,t_list *cell) {
499 cell[0]=lc->subcell[i+j*nx+k*a];
500 for(ci=-1;ci<=1;ci++) {
507 for(cj=-1;cj<=1;cj++) {
514 for(ck=-1;ck<=1;ck++) {
521 if(!(ci|cj|ck)) continue;
523 cell[--count2]=lc->subcell[x+y*nx+z*a];
526 cell[count1++]=lc->subcell[x+y*nx+z*a];
538 int link_cell_shutdown(t_moldyn *moldyn) {
545 for(i=0;i<lc->nx*lc->ny*lc->nz;i++)
546 list_shutdown(&(moldyn->lc.subcell[i]));
551 int moldyn_add_schedule(t_moldyn *moldyn,int runs,double tau) {
555 t_moldyn_schedule *schedule;
557 schedule=&(moldyn->schedule);
558 count=++(schedule->content_count);
560 ptr=realloc(moldyn->schedule.runs,count*sizeof(int));
562 perror("[moldyn] realloc (runs)");
565 moldyn->schedule.runs=ptr;
566 moldyn->schedule.runs[count-1]=runs;
568 ptr=realloc(schedule->tau,count*sizeof(double));
570 perror("[moldyn] realloc (tau)");
573 moldyn->schedule.tau=ptr;
574 moldyn->schedule.tau[count-1]=tau;
579 int moldyn_set_schedule_hook(t_moldyn *moldyn,void *hook,void *hook_params) {
581 moldyn->schedule.hook=hook;
582 moldyn->schedule.hook_params=hook_params;
589 * 'integration of newtons equation' - algorithms
593 /* start the integration */
595 int moldyn_integrate(t_moldyn *moldyn) {
598 unsigned int e,m,s,v;
600 t_moldyn_schedule *schedule;
606 schedule=&(moldyn->schedule);
609 /* initialize linked cell method */
610 link_cell_init(moldyn);
612 /* logging & visualization */
618 /* sqaure of some variables */
619 moldyn->tau_square=moldyn->tau*moldyn->tau;
620 moldyn->cutoff_square=moldyn->cutoff*moldyn->cutoff;
622 /* calculate initial forces */
623 potential_force_calc(moldyn);
625 /* do some checks before we actually start calculating bullshit */
626 if(moldyn->cutoff>0.5*moldyn->dim.x)
627 printf("[moldyn] warning: cutoff > 0.5 x dim.x\n");
628 if(moldyn->cutoff>0.5*moldyn->dim.y)
629 printf("[moldyn] warning: cutoff > 0.5 x dim.y\n");
630 if(moldyn->cutoff>0.5*moldyn->dim.z)
631 printf("[moldyn] warning: cutoff > 0.5 x dim.z\n");
632 ds=0.5*atom[0].f.x*moldyn->tau_square/atom[0].mass;
633 if(ds>0.05*moldyn->nnd)
634 printf("[moldyn] warning: forces too high / tau too small!\n");
636 /* zero absolute time */
639 for(sched=0;sched<moldyn->schedule.content_count;sched++) {
641 /* setting amount of runs and finite time step size */
642 moldyn->tau=schedule->tau[sched];
643 moldyn->tau_square=moldyn->tau*moldyn->tau;
644 moldyn->time_steps=schedule->runs[sched];
646 /* integration according to schedule */
648 for(i=0;i<moldyn->time_steps;i++) {
650 /* integration step */
651 moldyn->integrate(moldyn);
653 /* increase absolute time */
654 moldyn->time+=moldyn->tau;
656 /* check for log & visualization */
660 "%.15f %.45f %.45f %.45f\n",
661 moldyn->time,update_e_kin(moldyn),
663 get_total_energy(moldyn));
667 p=get_total_p(moldyn);
669 "%.15f %.45f\n",moldyn->time,
675 snprintf(fb,128,"%s-%f-%.15f.save",moldyn->sfb,
676 moldyn->t,i*moldyn->tau);
677 fd=open(fb,O_WRONLY|O_TRUNC|O_CREAT);
678 if(fd<0) perror("[moldyn] save fd open");
680 write(fd,moldyn,sizeof(t_moldyn));
681 write(fd,moldyn->atom,
682 moldyn->count*sizeof(t_atom));
689 visual_atoms(&(moldyn->vis),moldyn->time,
690 moldyn->atom,moldyn->count);
691 printf("\rsched: %d, steps: %d",sched,i);
698 /* check for hooks */
700 schedule->hook(moldyn,schedule->hook_params);
707 /* velocity verlet */
709 int velocity_verlet(t_moldyn *moldyn) {
712 double tau,tau_square;
719 tau_square=moldyn->tau_square;
721 for(i=0;i<count;i++) {
723 v3_scale(&delta,&(atom[i].v),tau);
724 v3_add(&(atom[i].r),&(atom[i].r),&delta);
725 v3_scale(&delta,&(atom[i].f),0.5*tau_square/atom[i].mass);
726 v3_add(&(atom[i].r),&(atom[i].r),&delta);
727 check_per_bound(moldyn,&(atom[i].r));
730 v3_scale(&delta,&(atom[i].f),0.5*tau/atom[i].mass);
731 v3_add(&(atom[i].v),&(atom[i].v),&delta);
734 /* neighbour list update */
735 link_cell_update(moldyn);
737 /* forces depending on chosen potential */
738 potential_force_calc(moldyn);
739 //moldyn->potential_force_function(moldyn);
741 for(i=0;i<count;i++) {
742 /* again velocities */
743 v3_scale(&delta,&(atom[i].f),0.5*tau/atom[i].mass);
744 v3_add(&(atom[i].v),&(atom[i].v),&delta);
753 * potentials & corresponding forces
757 /* generic potential and force calculation */
759 int potential_force_calc(t_moldyn *moldyn) {
762 t_atom *atom,*btom,*ktom;
764 t_list neighbour[27];
765 t_list *this,*thisk,*neighbourk;
776 for(i=0;i<count;i++) {
779 v3_zero(&(atom[i].f));
781 /* single particle potential/force */
782 if(atom[i].attr&ATOM_ATTR_1BP)
783 moldyn->func1b(moldyn,&(atom[i]));
785 /* 2 body pair potential/force */
786 if(atom[i].attr&(ATOM_ATTR_2BP|ATOM_ATTR_3BP)) {
788 link_cell_neighbour_index(moldyn,
789 (atom[i].r.x+moldyn->dim.x/2)/lc->x,
790 (atom[i].r.y+moldyn->dim.y/2)/lc->y,
791 (atom[i].r.z+moldyn->dim.z/2)/lc->z,
797 for(j=0;j<countn;j++) {
799 this=&(neighbour[j]);
802 if(this->start==NULL)
808 btom=this->current->data;
813 if((btom->attr&ATOM_ATTR_2BP)&
814 (atom[i].attr&ATOM_ATTR_2BP))
815 moldyn->func2b(moldyn,
820 /* 3 body potential/force */
822 if(!(atom[i].attr&ATOM_ATTR_3BP)||
823 !(btom->attr&ATOM_ATTR_3BP))
826 link_cell_neighbour_index(moldyn,
827 (btom->r.x+moldyn->dim.x/2)/lc->x,
828 (btom->r.y+moldyn->dim.y/2)/lc->y,
829 (btom->r.z+moldyn->dim.z/2)/lc->z,
832 for(k=0;k<lc->countn;k++) {
834 thisk=&(neighbourk[k]);
837 if(thisk->start==NULL)
840 bck=(k<lc->dnlc)?0:1;
844 ktom=thisk->current->data;
846 if(!(ktom->attr&ATOM_ATTR_3BP))
855 moldyn->func3b(moldyn,&(atom[i]),btom,ktom,bck);
857 } while(list_next(thisk)!=\
862 } while(list_next(this)!=L_NO_NEXT_ELEMENT);
871 * periodic boundayr checking
874 int check_per_bound(t_moldyn *moldyn,t_3dvec *a) {
885 if(moldyn->status&MOLDYN_STAT_PBX) {
886 if(a->x>=x) a->x-=dim->x;
887 else if(-a->x>x) a->x+=dim->x;
889 if(moldyn->status&MOLDYN_STAT_PBY) {
890 if(a->y>=y) a->y-=dim->y;
891 else if(-a->y>y) a->y+=dim->y;
893 if(moldyn->status&MOLDYN_STAT_PBZ) {
894 if(a->z>=z) a->z-=dim->z;
895 else if(-a->z>z) a->z+=dim->z;
906 /* harmonic oscillator potential and force */
908 int harmonic_oscillator(t_moldyn *moldyn,t_atom *ai,t_atom *aj,u8 bc) {
911 t_3dvec force,distance;
915 params=moldyn->pot2b_params;
916 sc=params->spring_constant;
917 equi_dist=params->equilibrium_distance;
919 v3_sub(&distance,&(ai->r),&(aj->r));
921 if(bc) check_per_bound(moldyn,&distance);
922 d=v3_norm(&distance);
923 if(d<=moldyn->cutoff) {
924 /* energy is 1/2 (d-d0)^2, but we will add this twice ... */
925 moldyn->energy+=(0.25*sc*(d-equi_dist)*(d-equi_dist));
926 v3_scale(&force,&distance,-sc*(1.0-(equi_dist/d)));
927 v3_add(&(ai->f),&(ai->f),&force);
933 /* lennard jones potential & force for one sort of atoms */
935 int lennard_jones(t_moldyn *moldyn,t_atom *ai,t_atom *aj,u8 bc) {
938 t_3dvec force,distance;
940 double eps,sig6,sig12;
942 params=moldyn->pot2b_params;
943 eps=params->epsilon4;
945 sig12=params->sigma12;
947 v3_sub(&distance,&(ai->r),&(aj->r));
948 if(bc) check_per_bound(moldyn,&distance);
949 d=v3_absolute_square(&distance); /* 1/r^2 */
950 if(d<=moldyn->cutoff_square) {
954 h1=h2*h2; /* 1/r^12 */
955 /* energy is eps*..., but we will add this twice ... */
956 moldyn->energy+=0.5*eps*(sig12*h1-sig6*h2);
963 v3_scale(&force,&distance,d);
964 v3_add(&(ai->f),&(ai->f),&force);
971 * tersoff potential & force for 2 sorts of atoms
974 /* tersoff 1 body part */
975 int tersoff_mult_1bp(t_moldyn *moldyn,t_atom *ai) {
978 t_tersoff_mult_params *params;
979 t_tersoff_exchange *exchange;
982 params=moldyn->pot1b_params;
983 exchange=&(params->exchange);
986 * simple: point constant parameters only depending on atom i to
990 exchange->beta=&(params->beta[num]);
991 exchange->n=&(params->n[num]);
992 exchange->c=&(params->c[num]);
993 exchange->d=&(params->d[num]);
994 exchange->h=&(params->h[num]);
996 exchange->betan=pow(*(exchange->beta),*(exchange->n));
997 exchange->c2=params->c[num]*params->c[num];
998 exchange->d2=params->d[num]*params->d[num];
999 exchange->c2d2=exchange->c2/exchange->d2;
1004 /* tersoff 2 body part */
1005 int tersoff_mult_2bp(t_moldyn *moldyn,t_atom *ai,t_atom *aj,u8 bc) {
1007 t_tersoff_mult_params *params;
1008 t_tersoff_exchange *exchange;
1009 t_3dvec dist_ij,force;
1011 double A,B,R,S,lambda,mu;
1019 params=moldyn->pot2b_params;
1021 exchange=&(params->exchange);
1026 * we need: f_c, df_c, f_r, df_r
1028 * therefore we need: R, S, A, lambda
1031 v3_sub(&dist_ij,&(ai->r),&(aj->r));
1033 if(bc) check_per_bound(moldyn,&dist_ij);
1035 /* save for use in 3bp */ /* REALLY ?!?!?! */
1036 exchange->dist_ij=dist_ij;
1043 lambda=params->lambda[num];
1044 /* more constants depending of atoms i and j, needed in 3bp */
1045 params->exchange.B=&(params->B[num]);
1046 params->exchange.mu=&(params->mu[num]);
1048 params->exchange.chi=1.0;
1054 lambda=params->lambda_m;
1055 /* more constants depending of atoms i and j, needed in 3bp */
1056 params->exchange.B=&(params->Bmixed);
1057 params->exchange.mu=&(params->mu_m);
1059 params->exchange.chi=params->chi;
1062 d_ij=v3_norm(&dist_ij);
1064 /* save for use in 3bp */
1065 exchange->d_ij=d_ij;
1070 f_r=A*exp(-lambda*d_ij);
1071 df_r=-lambda*f_r/d_ij;
1073 /* f_a, df_a calc + save for 3bp use */
1074 exchange->f_a=-B*exp(-mu*d_ij);
1075 exchange->df_a=-mu*exchange->f_a/d_ij;
1078 /* f_c = 1, df_c = 0 */
1081 v3_scale(&force,&dist_ij,df_r);
1085 arg=M_PI*(d_ij-R)/s_r;
1086 f_c=0.5+0.5*cos(arg);
1087 df_c=-0.5*sin(arg)*(M_PI/(s_r*d_ij));
1088 scale=df_c*f_r+df_r*f_c;
1089 v3_scale(&force,&dist_ij,scale);
1093 v3_add(&(ai->f),&(ai->f),&force);
1094 /* energy is 0.5 f_r f_c, but we will sum it up twice ... */
1095 moldyn->energy+=(0.25*f_r*f_c);
1097 /* save for use in 3bp */
1099 exchange->df_c=df_c;
1101 /* enable the run of 3bp function */
1107 /* tersoff 3 body part */
1109 int tersoff_mult_3bp(t_moldyn *moldyn,t_atom *ai,t_atom *aj,t_atom *ak,u8 bc) {
1111 t_tersoff_mult_params *params;
1112 t_tersoff_exchange *exchange;
1113 t_3dvec dist_ij,dist_ik,dist_jk;
1116 double d_ij,d_ij2,d_ik,d_jk;
1117 double f_c,df_c,b_ij,f_a,df_a;
1118 double f_c_ik,df_c_ik,arg;
1121 double n,c,d,h,beta,betan;
1124 double theta,cos_theta,sin_theta;
1125 double d_theta,d_theta1,d_theta2;
1126 double h_cos,h_cos2,d2_h_cos2;
1127 double frac1,bracket1,bracket2,bracket2_n_1,bracket2_n;
1128 double bracket3,bracket3_pow_1,bracket3_pow;
1131 params=moldyn->pot3b_params;
1133 exchange=&(params->exchange);
1135 if(!(exchange->run3bp))
1139 * we need: f_c, d_fc, b_ij, db_ij, f_a, df_a
1141 * we got f_c, df_c, f_a, df_a from 2bp calculation
1144 d_ij=exchange->d_ij;
1145 d_ij2=exchange->d_ij2;
1147 f_a=params->exchange.f_a;
1148 df_a=params->exchange.df_a;
1150 /* d_ij is <= S, as we didn't return so far! */
1153 * calc of b_ij (scalar) and db_ij (vector)
1155 * - for b_ij: chi, beta, f_c_ik, w(=1), c, d, h, n, cos_theta
1157 * - for db_ij: d_theta, sin_theta, cos_theta, f_c_ik, df_c_ik,
1163 v3_sub(&dist_ik,&(ai->r),&(ak->r));
1164 if(bc) check_per_bound(moldyn,&dist_ik);
1165 d_ik=v3_norm(&dist_ik);
1167 /* constants for f_c_ik calc */
1177 /* calc of f_c_ik */
1182 /* f_c_ik = 1, df_c_ik = 0 */
1188 arg=M_PI*(d_ik-R)/s_r;
1189 f_c_ik=0.5+0.5*cos(arg);
1190 df_c_ik=-0.5*sin(arg)*(M_PI/(s_r*d_ik));
1193 v3_sub(&dist_jk,&(aj->r),&(ak->r));
1194 if(bc) check_per_bound(moldyn,&dist_jk);
1195 d_jk=v3_norm(&dist_jk);
1197 beta=*(exchange->beta);
1198 betan=exchange->betan;
1205 c2d2=exchange->c2d2;
1207 numer=d_ij2+d_ik*d_ik-d_jk*d_jk;
1209 cos_theta=numer/denom;
1210 sin_theta=sqrt(1.0-(cos_theta*cos_theta));
1211 theta=acos(cos_theta);
1212 d_theta=(-1.0/sqrt(1.0-cos_theta*cos_theta))/(denom*denom);
1213 d_theta1=2*denom-numer*2*d_ik/d_ij;
1214 d_theta2=2*denom-numer*2*d_ij/d_ik;
1218 h_cos=(h-cos_theta);
1220 d2_h_cos2=d2-h_cos2;
1222 /* some usefull expressions */
1223 frac1=c2/(d2-h_cos2);
1224 bracket1=1+c2d2-frac1;
1225 bracket2=f_c_ik*bracket1;
1226 bracket2_n_1=pow(bracket2,n-1.0);
1227 bracket2_n=bracket2_n_1*bracket2;
1228 bracket3=1+betan*bracket2_n;
1229 bracket3_pow_1=pow(bracket3,(-1.0/(2.0*n))-1.0);
1230 bracket3_pow=bracket3_pow_1*bracket3;
1232 /* now go on with calc of b_ij and derivation of b_ij */
1233 b_ij=chi*bracket3_pow;
1235 /* derivation of theta */
1236 v3_scale(&force,&dist_ij,d_theta1);
1237 v3_scale(&temp,&dist_ik,d_theta2);
1238 v3_add(&force,&force,&temp);
1240 /* part 1 of derivation of b_ij */
1241 v3_scale(&force,&force,sin_theta*2*h_cos*f_c_ik*frac1);
1243 /* part 2 of derivation of b_ij */
1244 v3_scale(&temp,&dist_ik,df_c_ik*bracket1);
1246 /* sum up and scale ... */
1247 v3_add(&temp,&temp,&force);
1248 scale=bracket2_n_1*n*betan*(1+betan*bracket3_pow_1)*chi*(1.0/(2.0*n));
1249 v3_scale(&temp,&temp,scale);
1251 /* now construct an energy and a force out of that */
1252 v3_scale(&temp,&temp,f_a);
1253 v3_scale(&force,&dist_ij,df_a*b_ij);
1254 v3_add(&temp,&temp,&force);
1255 v3_scale(&temp,&temp,f_c);
1256 v3_scale(&force,&dist_ij,df_c*b_ij*f_a);
1257 v3_add(&force,&force,&temp);
1260 v3_add(&(ai->f),&(ai->f),&force);
1261 /* energy is 0.5 f_r f_c, but we will sum it up twice ... */
1262 moldyn->energy+=(0.25*f_a*b_ij*f_c);