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 link_cell_shutdown(moldyn);
45 moldyn_log_shutdown(moldyn);
46 rand_close(&(moldyn->random));
52 int set_int_alg(t_moldyn *moldyn,u8 algo) {
55 case MOLDYN_INTEGRATE_VERLET:
56 moldyn->integrate=velocity_verlet;
59 printf("unknown integration algorithm: %02x\n",algo);
66 int set_cutoff(t_moldyn *moldyn,double cutoff) {
68 moldyn->cutoff=cutoff;
73 int set_temperature(t_moldyn *moldyn,double t) {
80 int set_dim(t_moldyn *moldyn,double x,double y,double z,u8 visualize) {
95 int set_pbc(t_moldyn *moldyn,u8 x,u8 y,u8 z) {
98 moldyn->status|=MOLDYN_STAT_PBX;
101 moldyn->status|=MOLDYN_STAT_PBY;
104 moldyn->status|=MOLDYN_STAT_PBZ;
109 int set_potential1b(t_moldyn *moldyn,pf_func1b func,void *params) {
112 moldyn->pot1b_params=params;
117 int set_potential2b(t_moldyn *moldyn,pf_func2b func,void *params) {
120 moldyn->pot2b_params=params;
125 int set_potential3b(t_moldyn *moldyn,pf_func3b func,void *params) {
128 moldyn->pot3b_params=params;
133 int moldyn_set_log(t_moldyn *moldyn,u8 type,char *fb,int timer) {
136 case LOG_TOTAL_ENERGY:
137 moldyn->ewrite=timer;
138 moldyn->efd=open(fb,O_WRONLY|O_CREAT|O_TRUNC);
140 perror("[moldyn] efd open");
143 dprintf(moldyn->efd,"# total energy log file\n");
145 case LOG_TOTAL_MOMENTUM:
146 moldyn->mwrite=timer;
147 moldyn->mfd=open(fb,O_WRONLY|O_CREAT|O_TRUNC);
149 perror("[moldyn] mfd open");
152 dprintf(moldyn->efd,"# total momentum log file\n");
155 moldyn->swrite=timer;
156 strncpy(moldyn->sfb,fb,63);
159 moldyn->mwrite=timer;
160 strncpy(moldyn->vfb,fb,63);
161 visual_init(&(moldyn->vis),fb);
164 printf("unknown log mechanism: %02x\n",type);
171 int moldyn_log_shutdown(t_moldyn *moldyn) {
173 if(moldyn->efd) close(moldyn->efd);
174 if(moldyn->mfd) close(moldyn->mfd);
175 if(moldyn->visual) visual_tini(moldyn->visual);
180 int create_lattice(t_moldyn *moldyn,u8 type,double lc,int element,double mass,
181 u8 attr,u8 bnum,int a,int b,int c) {
191 if(type==FCC) count*=4;
193 if(type==DIAMOND) count*=8;
195 atom=malloc(count*sizeof(t_atom));
197 perror("malloc (atoms)");
205 ret=fcc_init(a,b,c,lc,atom,&origin);
208 ret=diamond_init(a,b,c,lc,atom,&origin);
211 printf("unknown lattice type (%02x)\n",type);
217 printf("ok, there is something wrong ...\n");
218 printf("calculated -> %d atoms\n",count);
219 printf("created -> %d atoms\n",ret);
226 atom[count-1].element=element;
227 atom[count-1].mass=mass;
228 atom[count-1].attr=attr;
229 atom[count-1].bnum=bnum;
236 int add_atom(t_moldyn *moldyn,int element,double mass,u8 bnum,u8 attr,
237 t_3dvec r,t_3dvec v) {
244 count=++(moldyn->count);
246 ptr=realloc(atom,count*sizeof(t_atom));
248 perror("[moldyn] realloc (add atom)");
255 atom->element=element;
262 int destroy_atoms(t_moldyn *moldyn) {
264 if(moldyn->atom) free(moldyn->atom);
269 int thermal_init(t_moldyn *moldyn) {
272 * - gaussian distribution of velocities
273 * - zero total momentum
274 * - velocity scaling (E = 3/2 N k T), E: kinetic energy
279 t_3dvec p_total,delta;
284 random=&(moldyn->random);
286 /* gaussian distribution of velocities */
288 for(i=0;i<moldyn->count;i++) {
289 sigma=sqrt(2.0*K_BOLTZMANN*moldyn->t/atom[i].mass);
291 v=sigma*rand_get_gauss(random);
293 p_total.x+=atom[i].mass*v;
295 v=sigma*rand_get_gauss(random);
297 p_total.y+=atom[i].mass*v;
299 v=sigma*rand_get_gauss(random);
301 p_total.z+=atom[i].mass*v;
304 /* zero total momentum */
305 v3_scale(&p_total,&p_total,1.0/moldyn->count);
306 for(i=0;i<moldyn->count;i++) {
307 v3_scale(&delta,&p_total,1.0/atom[i].mass);
308 v3_sub(&(atom[i].v),&(atom[i].v),&delta);
311 /* velocity scaling */
312 scale_velocity(moldyn);
317 int scale_velocity(t_moldyn *moldyn) {
326 * - velocity scaling (E = 3/2 N k T), E: kinetic energy
329 for(i=0;i<moldyn->count;i++)
330 e+=0.5*atom[i].mass*v3_absolute_square(&(atom[i].v));
331 c=sqrt((2.0*e)/(3.0*moldyn->count*K_BOLTZMANN*moldyn->t));
332 for(i=0;i<moldyn->count;i++)
333 v3_scale(&(atom[i].v),&(atom[i].v),(1.0/c));
338 double get_e_kin(t_moldyn *moldyn) {
346 for(i=0;i<moldyn->count;i++)
347 moldyn->ekin+=0.5*atom[i].mass*v3_absolute_square(&(atom[i].v));
352 double get_e_pot(t_moldyn *moldyn) {
354 return moldyn->energy;
357 double update_e_kin(t_moldyn *moldyn) {
359 return(get_e_kin(moldyn));
362 double get_total_energy(t_moldyn *moldyn) {
364 return(moldyn->ekin+moldyn->energy);
367 t_3dvec get_total_p(t_moldyn *moldyn) {
376 for(i=0;i<moldyn->count;i++) {
377 v3_scale(&p,&(atom[i].v),atom[i].mass);
378 v3_add(&p_total,&p_total,&p);
384 double estimate_time_step(t_moldyn *moldyn,double nn_dist,double t) {
388 tau=0.05*nn_dist/(sqrt(3.0*K_BOLTZMANN*t/moldyn->atom[0].mass));
391 printf("[moldyn] warning: time step (%f > %.15f)\n",
401 /* linked list / cell method */
403 int link_cell_init(t_moldyn *moldyn) {
410 /* partitioning the md cell */
411 lc->nx=moldyn->dim.x/moldyn->cutoff;
412 lc->x=moldyn->dim.x/lc->nx;
413 lc->ny=moldyn->dim.y/moldyn->cutoff;
414 lc->y=moldyn->dim.y/lc->ny;
415 lc->nz=moldyn->dim.z/moldyn->cutoff;
416 lc->z=moldyn->dim.z/lc->nz;
418 lc->cells=lc->nx*lc->ny*lc->nz;
419 lc->subcell=malloc(lc->cells*sizeof(t_list));
421 printf("initializing linked cells (%d)\n",lc->cells);
423 for(i=0;i<lc->cells;i++)
424 list_init(&(lc->subcell[i]),1);
426 link_cell_update(moldyn);
431 int link_cell_update(t_moldyn *moldyn) {
445 for(i=0;i<lc->cells;i++)
446 list_destroy(&(moldyn->lc.subcell[i]));
448 for(count=0;count<moldyn->count;count++) {
449 i=(atom[count].r.x+(moldyn->dim.x/2))/lc->x;
450 j=(atom[count].r.y+(moldyn->dim.y/2))/lc->y;
451 k=(atom[count].r.z+(moldyn->dim.z/2))/lc->z;
452 list_add_immediate_ptr(&(moldyn->lc.subcell[i+j*nx+k*nx*ny]),
459 int link_cell_neighbour_index(t_moldyn *moldyn,int i,int j,int k,t_list *cell) {
478 cell[0]=lc->subcell[i+j*nx+k*a];
479 for(ci=-1;ci<=1;ci++) {
486 for(cj=-1;cj<=1;cj++) {
493 for(ck=-1;ck<=1;ck++) {
500 if(!(ci|cj|ck)) continue;
502 cell[--count2]=lc->subcell[x+y*nx+z*a];
505 cell[count1++]=lc->subcell[x+y*nx+z*a];
517 int link_cell_shutdown(t_moldyn *moldyn) {
524 for(i=0;i<lc->nx*lc->ny*lc->nz;i++)
525 list_shutdown(&(moldyn->lc.subcell[i]));
530 int moldyn_add_schedule(t_moldyn *moldyn,int runs,double tau) {
534 t_moldyn_schedule *schedule;
536 schedule=&(moldyn->schedule);
537 count=++(schedule->content_count);
539 ptr=realloc(moldyn->schedule.runs,count*sizeof(int));
541 perror("[moldyn] realloc (runs)");
544 moldyn->schedule.runs[count-1]=runs;
546 ptr=realloc(schedule->tau,count*sizeof(double));
548 perror("[moldyn] realloc (tau)");
551 moldyn->schedule.tau[count-1]=tau;
556 int moldyn_set_schedule_hook(t_moldyn *moldyn,void *hook,void *hook_params) {
558 moldyn->schedule.hook=hook;
559 moldyn->schedule.hook_params=hook_params;
566 * 'integration of newtons equation' - algorithms
570 /* start the integration */
572 int moldyn_integrate(t_moldyn *moldyn) {
575 unsigned int e,m,s,v;
577 t_moldyn_schedule *schedule;
582 schedule=&(moldyn->schedule);
584 /* initialize linked cell method */
585 link_cell_init(moldyn);
587 /* logging & visualization */
593 /* sqaure of some variables */
594 moldyn->tau_square=moldyn->tau*moldyn->tau;
595 moldyn->cutoff_square=moldyn->cutoff*moldyn->cutoff;
597 /* calculate initial forces */
598 potential_force_calc(moldyn);
600 /* zero absolute time */
603 for(sched=0;sched<moldyn->schedule.content_count;sched++) {
605 /* setting amount of runs and finite time step size */
606 moldyn->tau=schedule->tau[sched];
607 moldyn->tau_square=moldyn->tau*moldyn->tau;
608 moldyn->time_steps=schedule->runs[sched];
610 /* integration according to schedule */
612 for(i=0;i<moldyn->time_steps;i++) {
614 /* integration step */
615 moldyn->integrate(moldyn);
617 /* increase absolute time */
618 moldyn->time+=moldyn->tau;
620 /* check for log & visualization */
624 "%.15f %.45f %.45f %.45f\n",
625 moldyn->time,update_e_kin(moldyn),
627 get_total_energy(moldyn));
631 p=get_total_p(moldyn);
633 "%.15f %.45f\n",moldyn->time,
639 snprintf(fb,128,"%s-%f-%.15f.save",moldyn->sfb,
640 moldyn->t,i*moldyn->tau);
641 fd=open(fb,O_WRONLY|O_TRUNC|O_CREAT);
642 if(fd<0) perror("[moldyn] save fd open");
644 write(fd,moldyn,sizeof(t_moldyn));
645 write(fd,moldyn->atom,
646 moldyn->count*sizeof(t_atom));
653 visual_atoms(moldyn->visual,i*moldyn->tau,
654 moldyn->atom,moldyn->count);
655 printf("\rsteps: %d",i);
661 /* check for hooks */
663 schedule->hook(moldyn,schedule->hook_params);
670 /* velocity verlet */
672 int velocity_verlet(t_moldyn *moldyn) {
675 double tau,tau_square;
682 tau_square=moldyn->tau_square;
684 for(i=0;i<count;i++) {
686 v3_scale(&delta,&(atom[i].v),tau);
687 v3_add(&(atom[i].r),&(atom[i].r),&delta);
688 v3_scale(&delta,&(atom[i].f),0.5*tau_square/atom[i].mass);
689 v3_add(&(atom[i].r),&(atom[i].r),&delta);
690 v3_per_bound(&(atom[i].r),&(moldyn->dim));
693 v3_scale(&delta,&(atom[i].f),0.5*tau/atom[i].mass);
694 v3_add(&(atom[i].v),&(atom[i].v),&delta);
697 /* neighbour list update */
698 printf("list update ...\n");
699 link_cell_update(moldyn);
702 /* forces depending on chosen potential */
703 printf("calc potential/force ...\n");
704 potential_force_calc(moldyn);
705 //moldyn->potential_force_function(moldyn);
708 for(i=0;i<count;i++) {
709 /* again velocities */
710 v3_scale(&delta,&(atom[i].f),0.5*tau/atom[i].mass);
711 v3_add(&(atom[i].v),&(atom[i].v),&delta);
720 * potentials & corresponding forces
724 /* generic potential and force calculation */
726 int potential_force_calc(t_moldyn *moldyn) {
729 t_atom *atom,*btom,*ktom;
731 t_list neighbour[27];
732 t_list *this,*thisk,*neighbourk;
743 for(i=0;i<count;i++) {
746 v3_zero(&(atom[i].f));
748 /* single particle potential/force */
749 if(atom[i].attr&ATOM_ATTR_1BP)
750 moldyn->func1b(moldyn,&(atom[i]));
752 /* 2 body pair potential/force */
753 if(atom[i].attr&(ATOM_ATTR_2BP|ATOM_ATTR_3BP)) {
755 link_cell_neighbour_index(moldyn,
756 (atom[i].r.x+moldyn->dim.x/2)/lc->x,
757 (atom[i].r.y+moldyn->dim.y/2)/lc->y,
758 (atom[i].r.z+moldyn->dim.z/2)/lc->z,
764 for(j=0;j<countn;j++) {
766 this=&(neighbour[j]);
769 if(this->start==NULL)
775 btom=this->current->data;
780 if((btom->attr&ATOM_ATTR_2BP)&
781 (atom[i].attr&ATOM_ATTR_2BP))
782 moldyn->func2b(moldyn,
787 /* 3 body potential/force */
789 if(!(atom[i].attr&ATOM_ATTR_3BP)||
790 !(btom->attr&ATOM_ATTR_3BP))
793 link_cell_neighbour_index(moldyn,
794 (btom->r.x+moldyn->dim.x/2)/lc->x,
795 (btom->r.y+moldyn->dim.y/2)/lc->y,
796 (btom->r.z+moldyn->dim.z/2)/lc->z,
799 for(k=0;k<lc->countn;k++) {
801 thisk=&(neighbourk[k]);
804 if(thisk->start==NULL)
807 bck=(k<lc->dnlc)?0:1;
811 ktom=thisk->current->data;
813 if(!(ktom->attr&ATOM_ATTR_3BP))
822 moldyn->func3b(moldyn,&(atom[i]),btom,ktom,bck);
824 } while(list_next(thisk)!=\
829 } while(list_next(this)!=L_NO_NEXT_ELEMENT);
838 * periodic boundayr checking
841 int check_per_bound(t_moldyn *moldyn,t_3dvec *a) {
852 if(moldyn->status&MOLDYN_STAT_PBX) {
853 if(a->x>=x) a->x-=dim->x;
854 else if(-a->x>x) a->x+=dim->x;
856 if(moldyn->status&MOLDYN_STAT_PBY) {
857 if(a->y>=y) a->y-=dim->y;
858 else if(-a->y>y) a->y+=dim->y;
860 if(moldyn->status&MOLDYN_STAT_PBZ) {
861 if(a->z>=z) a->z-=dim->z;
862 else if(-a->z>z) a->z+=dim->z;
873 /* harmonic oscillator potential and force */
875 int harmonic_oscillator(t_moldyn *moldyn,t_atom *ai,t_atom *aj,u8 bc) {
878 t_3dvec force,distance;
882 params=moldyn->pot2b_params;
883 sc=params->spring_constant;
884 equi_dist=params->equilibrium_distance;
886 v3_sub(&distance,&(ai->r),&(aj->r));
888 v3_per_bound(&distance,&(moldyn->dim));
889 if(bc) check_per_bound(moldyn,&distance);
890 d=v3_norm(&distance);
891 if(d<=moldyn->cutoff) {
892 /* energy is 1/2 (d-d0)^2, but we will add this twice ... */
893 moldyn->energy+=(0.25*sc*(d-equi_dist)*(d-equi_dist));
894 v3_scale(&force,&distance,-sc*(1.0-(equi_dist/d)));
895 v3_add(&(ai->f),&(ai->f),&force);
901 /* lennard jones potential & force for one sort of atoms */
903 int lennard_jones(t_moldyn *moldyn,t_atom *ai,t_atom *aj,u8 bc) {
906 t_3dvec force,distance;
908 double eps,sig6,sig12;
910 params=moldyn->pot2b_params;
911 eps=params->epsilon4;
913 sig12=params->sigma12;
915 v3_sub(&distance,&(ai->r),&(aj->r));
916 if(bc) check_per_bound(moldyn,&distance);
917 d=v3_absolute_square(&distance); /* 1/r^2 */
918 if(d<=moldyn->cutoff_square) {
922 h1=h2*h2; /* 1/r^12 */
923 /* energy is eps*..., but we will add this twice ... */
924 moldyn->energy+=0.5*eps*(sig12*h1-sig6*h2);
931 v3_scale(&force,&distance,d);
932 v3_add(&(ai->f),&(aj->f),&force);
939 * tersoff potential & force for 2 sorts of atoms
942 /* tersoff 1 body part */
943 int tersoff_mult_1bp(t_moldyn *moldyn,t_atom *ai) {
946 t_tersoff_mult_params *params;
947 t_tersoff_exchange *exchange;
950 params=moldyn->pot1b_params;
951 exchange=&(params->exchange);
954 * simple: point constant parameters only depending on atom i to
958 exchange->beta=&(params->beta[num]);
959 exchange->n=&(params->n[num]);
960 exchange->c=&(params->c[num]);
961 exchange->d=&(params->d[num]);
962 exchange->h=&(params->h[num]);
964 exchange->betan=pow(*(exchange->beta),*(exchange->n));
965 exchange->c2=params->c[num]*params->c[num];
966 exchange->d2=params->d[num]*params->d[num];
967 exchange->c2d2=exchange->c2/exchange->d2;
972 /* tersoff 2 body part */
973 int tersoff_mult_2bp(t_moldyn *moldyn,t_atom *ai,t_atom *aj,u8 bc) {
975 t_tersoff_mult_params *params;
976 t_tersoff_exchange *exchange;
977 t_3dvec dist_ij,force;
979 double A,B,R,S,lambda,mu;
987 params=moldyn->pot2b_params;
989 exchange=&(params->exchange);
994 * we need: f_c, df_c, f_r, df_r
996 * therefore we need: R, S, A, lambda
999 v3_sub(&dist_ij,&(ai->r),&(aj->r));
1001 if(bc) check_per_bound(moldyn,&dist_ij);
1003 /* save for use in 3bp */ /* REALLY ?!?!?! */
1004 exchange->dist_ij=dist_ij;
1011 lambda=params->lambda[num];
1012 /* more constants depending of atoms i and j, needed in 3bp */
1013 params->exchange.B=&(params->B[num]);
1014 params->exchange.mu=&(params->mu[num]);
1016 params->exchange.chi=1.0;
1022 lambda=params->lambda_m;
1023 /* more constants depending of atoms i and j, needed in 3bp */
1024 params->exchange.B=&(params->Bmixed);
1025 params->exchange.mu=&(params->mu_m);
1027 params->exchange.chi=params->chi;
1030 d_ij=v3_norm(&dist_ij);
1032 /* save for use in 3bp */
1033 exchange->d_ij=d_ij;
1038 f_r=A*exp(-lambda*d_ij);
1039 df_r=-lambda*f_r/d_ij;
1041 /* f_a, df_a calc + save for 3bp use */
1042 exchange->f_a=-B*exp(-mu*d_ij);
1043 exchange->df_a=-mu*exchange->f_a/d_ij;
1046 /* f_c = 1, df_c = 0 */
1049 v3_scale(&force,&dist_ij,df_r);
1053 arg=M_PI*(d_ij-R)/s_r;
1054 f_c=0.5+0.5*cos(arg);
1055 df_c=-0.5*sin(arg)*(M_PI/(s_r*d_ij));
1056 scale=df_c*f_r+df_r*f_c;
1057 v3_scale(&force,&dist_ij,scale);
1061 v3_add(&(ai->f),&(ai->f),&force);
1062 /* energy is 0.5 f_r f_c, but we will sum it up twice ... */
1063 moldyn->energy+=(0.25*f_r*f_c);
1065 /* save for use in 3bp */
1067 exchange->df_c=df_c;
1069 /* enable the run of 3bp function */
1075 /* tersoff 3 body part */
1077 int tersoff_mult_3bp(t_moldyn *moldyn,t_atom *ai,t_atom *aj,t_atom *ak,u8 bc) {
1079 t_tersoff_mult_params *params;
1080 t_tersoff_exchange *exchange;
1081 t_3dvec dist_ij,dist_ik,dist_jk;
1084 double d_ij,d_ij2,d_ik,d_jk;
1085 double f_c,df_c,b_ij,f_a,df_a;
1086 double f_c_ik,df_c_ik,arg;
1089 double n,c,d,h,beta,betan;
1092 double theta,cos_theta,sin_theta;
1093 double d_theta,d_theta1,d_theta2;
1094 double h_cos,h_cos2,d2_h_cos2;
1095 double frac1,bracket1,bracket2,bracket2_n_1,bracket2_n;
1096 double bracket3,bracket3_pow_1,bracket3_pow;
1099 params=moldyn->pot3b_params;
1101 exchange=&(params->exchange);
1103 if(!(exchange->run3bp))
1107 * we need: f_c, d_fc, b_ij, db_ij, f_a, df_a
1109 * we got f_c, df_c, f_a, df_a from 2bp calculation
1112 d_ij=exchange->d_ij;
1113 d_ij2=exchange->d_ij2;
1115 f_a=params->exchange.f_a;
1116 df_a=params->exchange.df_a;
1118 /* d_ij is <= S, as we didn't return so far! */
1121 * calc of b_ij (scalar) and db_ij (vector)
1123 * - for b_ij: chi, beta, f_c_ik, w(=1), c, d, h, n, cos_theta
1125 * - for db_ij: d_theta, sin_theta, cos_theta, f_c_ik, df_c_ik,
1131 v3_sub(&dist_ik,&(ai->r),&(ak->r));
1132 if(bc) check_per_bound(moldyn,&dist_ik);
1133 d_ik=v3_norm(&dist_ik);
1135 /* constants for f_c_ik calc */
1145 /* calc of f_c_ik */
1150 /* f_c_ik = 1, df_c_ik = 0 */
1156 arg=M_PI*(d_ik-R)/s_r;
1157 f_c_ik=0.5+0.5*cos(arg);
1158 df_c_ik=-0.5*sin(arg)*(M_PI/(s_r*d_ik));
1161 v3_sub(&dist_jk,&(aj->r),&(ak->r));
1162 if(bc) check_per_bound(moldyn,&dist_jk);
1163 d_jk=v3_norm(&dist_jk);
1165 beta=*(exchange->beta);
1166 betan=exchange->betan;
1173 c2d2=exchange->c2d2;
1175 numer=d_ij2+d_ik*d_ik-d_jk*d_jk;
1177 cos_theta=numer/denom;
1178 sin_theta=sqrt(1.0-(cos_theta*cos_theta));
1179 theta=acos(cos_theta);
1180 d_theta=(-1.0/sqrt(1.0-cos_theta*cos_theta))/(denom*denom);
1181 d_theta1=2*denom-numer*2*d_ik/d_ij;
1182 d_theta2=2*denom-numer*2*d_ij/d_ik;
1186 h_cos=(h-cos_theta);
1188 d2_h_cos2=d2-h_cos2;
1190 /* some usefull expressions */
1191 frac1=c2/(d2-h_cos2);
1192 bracket1=1+c2d2-frac1;
1193 bracket2=f_c_ik*bracket1;
1194 bracket2_n_1=pow(bracket2,n-1.0);
1195 bracket2_n=bracket2_n_1*bracket2;
1196 bracket3=1+betan*bracket2_n;
1197 bracket3_pow_1=pow(bracket3,(-1.0/(2.0*n))-1.0);
1198 bracket3_pow=bracket3_pow_1*bracket3;
1200 /* now go on with calc of b_ij and derivation of b_ij */
1201 b_ij=chi*bracket3_pow;
1203 /* derivation of theta */
1204 v3_scale(&force,&dist_ij,d_theta1);
1205 v3_scale(&temp,&dist_ik,d_theta2);
1206 v3_add(&force,&force,&temp);
1208 /* part 1 of derivation of b_ij */
1209 v3_scale(&force,&force,sin_theta*2*h_cos*f_c_ik*frac1);
1211 /* part 2 of derivation of b_ij */
1212 v3_scale(&temp,&dist_ik,df_c_ik*bracket1);
1214 /* sum up and scale ... */
1215 v3_add(&temp,&temp,&force);
1216 scale=bracket2_n_1*n*betan*(1+betan*bracket3_pow_1)*chi*(1.0/(2.0*n));
1217 v3_scale(&temp,&temp,scale);
1219 /* now construct an energy and a force out of that */
1220 v3_scale(&temp,&temp,f_a);
1221 v3_scale(&force,&dist_ij,df_a*b_ij);
1222 v3_add(&temp,&temp,&force);
1223 v3_scale(&temp,&temp,f_c);
1224 v3_scale(&force,&dist_ij,df_c*b_ij*f_a);
1225 v3_add(&force,&force,&temp);
1228 v3_add(&(ai->f),&(ai->f),&force);
1229 /* energy is 0.5 f_r f_c, but we will sum it up twice ... */
1230 moldyn->energy+=(0.25*f_a*b_ij*f_c);