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->vwrite=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)");
256 atom->element=element;
263 int destroy_atoms(t_moldyn *moldyn) {
265 if(moldyn->atom) free(moldyn->atom);
270 int thermal_init(t_moldyn *moldyn) {
273 * - gaussian distribution of velocities
274 * - zero total momentum
275 * - velocity scaling (E = 3/2 N k T), E: kinetic energy
280 t_3dvec p_total,delta;
285 random=&(moldyn->random);
287 /* gaussian distribution of velocities */
289 for(i=0;i<moldyn->count;i++) {
290 sigma=sqrt(2.0*K_BOLTZMANN*moldyn->t/atom[i].mass);
292 v=sigma*rand_get_gauss(random);
294 p_total.x+=atom[i].mass*v;
296 v=sigma*rand_get_gauss(random);
298 p_total.y+=atom[i].mass*v;
300 v=sigma*rand_get_gauss(random);
302 p_total.z+=atom[i].mass*v;
305 /* zero total momentum */
306 v3_scale(&p_total,&p_total,1.0/moldyn->count);
307 for(i=0;i<moldyn->count;i++) {
308 v3_scale(&delta,&p_total,1.0/atom[i].mass);
309 v3_sub(&(atom[i].v),&(atom[i].v),&delta);
312 /* velocity scaling */
313 scale_velocity(moldyn);
318 int scale_velocity(t_moldyn *moldyn) {
327 * - velocity scaling (E = 3/2 N k T), E: kinetic energy
330 for(i=0;i<moldyn->count;i++)
331 e+=0.5*atom[i].mass*v3_absolute_square(&(atom[i].v));
332 c=sqrt((2.0*e)/(3.0*moldyn->count*K_BOLTZMANN*moldyn->t));
333 for(i=0;i<moldyn->count;i++)
334 v3_scale(&(atom[i].v),&(atom[i].v),(1.0/c));
339 double get_e_kin(t_moldyn *moldyn) {
347 for(i=0;i<moldyn->count;i++)
348 moldyn->ekin+=0.5*atom[i].mass*v3_absolute_square(&(atom[i].v));
353 double get_e_pot(t_moldyn *moldyn) {
355 return moldyn->energy;
358 double update_e_kin(t_moldyn *moldyn) {
360 return(get_e_kin(moldyn));
363 double get_total_energy(t_moldyn *moldyn) {
365 return(moldyn->ekin+moldyn->energy);
368 t_3dvec get_total_p(t_moldyn *moldyn) {
377 for(i=0;i<moldyn->count;i++) {
378 v3_scale(&p,&(atom[i].v),atom[i].mass);
379 v3_add(&p_total,&p_total,&p);
385 double estimate_time_step(t_moldyn *moldyn,double nn_dist,double t) {
389 tau=0.05*nn_dist/(sqrt(3.0*K_BOLTZMANN*t/moldyn->atom[0].mass));
392 printf("[moldyn] warning: time step (%f > %.15f)\n",
402 /* linked list / cell method */
404 int link_cell_init(t_moldyn *moldyn) {
410 fd=open("/dev/null",O_WRONLY);
414 /* partitioning the md cell */
415 lc->nx=moldyn->dim.x/moldyn->cutoff;
416 lc->x=moldyn->dim.x/lc->nx;
417 lc->ny=moldyn->dim.y/moldyn->cutoff;
418 lc->y=moldyn->dim.y/lc->ny;
419 lc->nz=moldyn->dim.z/moldyn->cutoff;
420 lc->z=moldyn->dim.z/lc->nz;
422 lc->cells=lc->nx*lc->ny*lc->nz;
423 lc->subcell=malloc(lc->cells*sizeof(t_list));
425 printf("[moldyn] initializing linked cells (%d)\n",lc->cells);
427 for(i=0;i<lc->cells;i++)
428 //list_init(&(lc->subcell[i]),1);
429 list_init(&(lc->subcell[i]),fd);
431 link_cell_update(moldyn);
436 int link_cell_update(t_moldyn *moldyn) {
450 for(i=0;i<lc->cells;i++)
451 list_destroy(&(moldyn->lc.subcell[i]));
453 for(count=0;count<moldyn->count;count++) {
454 i=(atom[count].r.x+(moldyn->dim.x/2))/lc->x;
455 j=(atom[count].r.y+(moldyn->dim.y/2))/lc->y;
456 k=(atom[count].r.z+(moldyn->dim.z/2))/lc->z;
457 list_add_immediate_ptr(&(moldyn->lc.subcell[i+j*nx+k*nx*ny]),
464 int link_cell_neighbour_index(t_moldyn *moldyn,int i,int j,int k,t_list *cell) {
483 cell[0]=lc->subcell[i+j*nx+k*a];
484 for(ci=-1;ci<=1;ci++) {
491 for(cj=-1;cj<=1;cj++) {
498 for(ck=-1;ck<=1;ck++) {
505 if(!(ci|cj|ck)) continue;
507 cell[--count2]=lc->subcell[x+y*nx+z*a];
510 cell[count1++]=lc->subcell[x+y*nx+z*a];
522 int link_cell_shutdown(t_moldyn *moldyn) {
529 for(i=0;i<lc->nx*lc->ny*lc->nz;i++)
530 list_shutdown(&(moldyn->lc.subcell[i]));
535 int moldyn_add_schedule(t_moldyn *moldyn,int runs,double tau) {
539 t_moldyn_schedule *schedule;
541 schedule=&(moldyn->schedule);
542 count=++(schedule->content_count);
544 ptr=realloc(moldyn->schedule.runs,count*sizeof(int));
546 perror("[moldyn] realloc (runs)");
549 moldyn->schedule.runs=ptr;
550 moldyn->schedule.runs[count-1]=runs;
552 ptr=realloc(schedule->tau,count*sizeof(double));
554 perror("[moldyn] realloc (tau)");
557 moldyn->schedule.tau=ptr;
558 moldyn->schedule.tau[count-1]=tau;
563 int moldyn_set_schedule_hook(t_moldyn *moldyn,void *hook,void *hook_params) {
565 moldyn->schedule.hook=hook;
566 moldyn->schedule.hook_params=hook_params;
573 * 'integration of newtons equation' - algorithms
577 /* start the integration */
579 int moldyn_integrate(t_moldyn *moldyn) {
582 unsigned int e,m,s,v;
584 t_moldyn_schedule *schedule;
589 schedule=&(moldyn->schedule);
591 /* initialize linked cell method */
592 link_cell_init(moldyn);
594 /* logging & visualization */
600 /* sqaure of some variables */
601 moldyn->tau_square=moldyn->tau*moldyn->tau;
602 moldyn->cutoff_square=moldyn->cutoff*moldyn->cutoff;
604 /* calculate initial forces */
605 potential_force_calc(moldyn);
607 /* zero absolute time */
610 for(sched=0;sched<moldyn->schedule.content_count;sched++) {
612 /* setting amount of runs and finite time step size */
613 moldyn->tau=schedule->tau[sched];
614 moldyn->tau_square=moldyn->tau*moldyn->tau;
615 moldyn->time_steps=schedule->runs[sched];
617 /* integration according to schedule */
619 for(i=0;i<moldyn->time_steps;i++) {
621 /* integration step */
622 moldyn->integrate(moldyn);
624 /* increase absolute time */
625 moldyn->time+=moldyn->tau;
627 /* check for log & visualization */
631 "%.15f %.45f %.45f %.45f\n",
632 moldyn->time,update_e_kin(moldyn),
634 get_total_energy(moldyn));
638 p=get_total_p(moldyn);
640 "%.15f %.45f\n",moldyn->time,
646 snprintf(fb,128,"%s-%f-%.15f.save",moldyn->sfb,
647 moldyn->t,i*moldyn->tau);
648 fd=open(fb,O_WRONLY|O_TRUNC|O_CREAT);
649 if(fd<0) perror("[moldyn] save fd open");
651 write(fd,moldyn,sizeof(t_moldyn));
652 write(fd,moldyn->atom,
653 moldyn->count*sizeof(t_atom));
660 visual_atoms(&(moldyn->vis),moldyn->time,
661 moldyn->atom,moldyn->count);
662 printf("\rsched: %d, steps: %d",sched,i);
669 /* check for hooks */
671 schedule->hook(moldyn,schedule->hook_params);
678 /* velocity verlet */
680 int velocity_verlet(t_moldyn *moldyn) {
683 double tau,tau_square;
690 tau_square=moldyn->tau_square;
692 for(i=0;i<count;i++) {
694 v3_scale(&delta,&(atom[i].v),tau);
695 v3_add(&(atom[i].r),&(atom[i].r),&delta);
696 v3_scale(&delta,&(atom[i].f),0.5*tau_square/atom[i].mass);
697 v3_add(&(atom[i].r),&(atom[i].r),&delta);
698 v3_per_bound(&(atom[i].r),&(moldyn->dim));
701 v3_scale(&delta,&(atom[i].f),0.5*tau/atom[i].mass);
702 v3_add(&(atom[i].v),&(atom[i].v),&delta);
705 /* neighbour list update */
706 link_cell_update(moldyn);
708 /* forces depending on chosen potential */
709 potential_force_calc(moldyn);
710 //moldyn->potential_force_function(moldyn);
712 for(i=0;i<count;i++) {
713 /* again velocities */
714 v3_scale(&delta,&(atom[i].f),0.5*tau/atom[i].mass);
715 v3_add(&(atom[i].v),&(atom[i].v),&delta);
724 * potentials & corresponding forces
728 /* generic potential and force calculation */
730 int potential_force_calc(t_moldyn *moldyn) {
733 t_atom *atom,*btom,*ktom;
735 t_list neighbour[27];
736 t_list *this,*thisk,*neighbourk;
747 for(i=0;i<count;i++) {
750 v3_zero(&(atom[i].f));
752 /* single particle potential/force */
753 if(atom[i].attr&ATOM_ATTR_1BP)
754 moldyn->func1b(moldyn,&(atom[i]));
756 /* 2 body pair potential/force */
757 if(atom[i].attr&(ATOM_ATTR_2BP|ATOM_ATTR_3BP)) {
759 link_cell_neighbour_index(moldyn,
760 (atom[i].r.x+moldyn->dim.x/2)/lc->x,
761 (atom[i].r.y+moldyn->dim.y/2)/lc->y,
762 (atom[i].r.z+moldyn->dim.z/2)/lc->z,
768 for(j=0;j<countn;j++) {
770 this=&(neighbour[j]);
773 if(this->start==NULL)
779 btom=this->current->data;
784 if((btom->attr&ATOM_ATTR_2BP)&
785 (atom[i].attr&ATOM_ATTR_2BP))
786 moldyn->func2b(moldyn,
791 /* 3 body potential/force */
793 if(!(atom[i].attr&ATOM_ATTR_3BP)||
794 !(btom->attr&ATOM_ATTR_3BP))
797 link_cell_neighbour_index(moldyn,
798 (btom->r.x+moldyn->dim.x/2)/lc->x,
799 (btom->r.y+moldyn->dim.y/2)/lc->y,
800 (btom->r.z+moldyn->dim.z/2)/lc->z,
803 for(k=0;k<lc->countn;k++) {
805 thisk=&(neighbourk[k]);
808 if(thisk->start==NULL)
811 bck=(k<lc->dnlc)?0:1;
815 ktom=thisk->current->data;
817 if(!(ktom->attr&ATOM_ATTR_3BP))
826 moldyn->func3b(moldyn,&(atom[i]),btom,ktom,bck);
828 } while(list_next(thisk)!=\
833 } while(list_next(this)!=L_NO_NEXT_ELEMENT);
842 * periodic boundayr checking
845 int check_per_bound(t_moldyn *moldyn,t_3dvec *a) {
856 if(moldyn->status&MOLDYN_STAT_PBX) {
857 if(a->x>=x) a->x-=dim->x;
858 else if(-a->x>x) a->x+=dim->x;
860 if(moldyn->status&MOLDYN_STAT_PBY) {
861 if(a->y>=y) a->y-=dim->y;
862 else if(-a->y>y) a->y+=dim->y;
864 if(moldyn->status&MOLDYN_STAT_PBZ) {
865 if(a->z>=z) a->z-=dim->z;
866 else if(-a->z>z) a->z+=dim->z;
877 /* harmonic oscillator potential and force */
879 int harmonic_oscillator(t_moldyn *moldyn,t_atom *ai,t_atom *aj,u8 bc) {
882 t_3dvec force,distance;
886 params=moldyn->pot2b_params;
887 sc=params->spring_constant;
888 equi_dist=params->equilibrium_distance;
890 v3_sub(&distance,&(ai->r),&(aj->r));
892 v3_per_bound(&distance,&(moldyn->dim));
893 if(bc) check_per_bound(moldyn,&distance);
894 d=v3_norm(&distance);
895 if(d<=moldyn->cutoff) {
896 /* energy is 1/2 (d-d0)^2, but we will add this twice ... */
897 moldyn->energy+=(0.25*sc*(d-equi_dist)*(d-equi_dist));
898 v3_scale(&force,&distance,-sc*(1.0-(equi_dist/d)));
899 v3_add(&(ai->f),&(ai->f),&force);
905 /* lennard jones potential & force for one sort of atoms */
907 int lennard_jones(t_moldyn *moldyn,t_atom *ai,t_atom *aj,u8 bc) {
910 t_3dvec force,distance;
912 double eps,sig6,sig12;
914 params=moldyn->pot2b_params;
915 eps=params->epsilon4;
917 sig12=params->sigma12;
919 v3_sub(&distance,&(ai->r),&(aj->r));
920 if(bc) check_per_bound(moldyn,&distance);
921 d=v3_absolute_square(&distance); /* 1/r^2 */
922 if(d<=moldyn->cutoff_square) {
926 h1=h2*h2; /* 1/r^12 */
927 /* energy is eps*..., but we will add this twice ... */
928 moldyn->energy+=0.5*eps*(sig12*h1-sig6*h2);
935 v3_scale(&force,&distance,d);
936 v3_add(&(ai->f),&(aj->f),&force);
943 * tersoff potential & force for 2 sorts of atoms
946 /* tersoff 1 body part */
947 int tersoff_mult_1bp(t_moldyn *moldyn,t_atom *ai) {
950 t_tersoff_mult_params *params;
951 t_tersoff_exchange *exchange;
954 params=moldyn->pot1b_params;
955 exchange=&(params->exchange);
958 * simple: point constant parameters only depending on atom i to
962 exchange->beta=&(params->beta[num]);
963 exchange->n=&(params->n[num]);
964 exchange->c=&(params->c[num]);
965 exchange->d=&(params->d[num]);
966 exchange->h=&(params->h[num]);
968 exchange->betan=pow(*(exchange->beta),*(exchange->n));
969 exchange->c2=params->c[num]*params->c[num];
970 exchange->d2=params->d[num]*params->d[num];
971 exchange->c2d2=exchange->c2/exchange->d2;
976 /* tersoff 2 body part */
977 int tersoff_mult_2bp(t_moldyn *moldyn,t_atom *ai,t_atom *aj,u8 bc) {
979 t_tersoff_mult_params *params;
980 t_tersoff_exchange *exchange;
981 t_3dvec dist_ij,force;
983 double A,B,R,S,lambda,mu;
991 params=moldyn->pot2b_params;
993 exchange=&(params->exchange);
998 * we need: f_c, df_c, f_r, df_r
1000 * therefore we need: R, S, A, lambda
1003 v3_sub(&dist_ij,&(ai->r),&(aj->r));
1005 if(bc) check_per_bound(moldyn,&dist_ij);
1007 /* save for use in 3bp */ /* REALLY ?!?!?! */
1008 exchange->dist_ij=dist_ij;
1015 lambda=params->lambda[num];
1016 /* more constants depending of atoms i and j, needed in 3bp */
1017 params->exchange.B=&(params->B[num]);
1018 params->exchange.mu=&(params->mu[num]);
1020 params->exchange.chi=1.0;
1026 lambda=params->lambda_m;
1027 /* more constants depending of atoms i and j, needed in 3bp */
1028 params->exchange.B=&(params->Bmixed);
1029 params->exchange.mu=&(params->mu_m);
1031 params->exchange.chi=params->chi;
1034 d_ij=v3_norm(&dist_ij);
1036 /* save for use in 3bp */
1037 exchange->d_ij=d_ij;
1042 f_r=A*exp(-lambda*d_ij);
1043 df_r=-lambda*f_r/d_ij;
1045 /* f_a, df_a calc + save for 3bp use */
1046 exchange->f_a=-B*exp(-mu*d_ij);
1047 exchange->df_a=-mu*exchange->f_a/d_ij;
1050 /* f_c = 1, df_c = 0 */
1053 v3_scale(&force,&dist_ij,df_r);
1057 arg=M_PI*(d_ij-R)/s_r;
1058 f_c=0.5+0.5*cos(arg);
1059 df_c=-0.5*sin(arg)*(M_PI/(s_r*d_ij));
1060 scale=df_c*f_r+df_r*f_c;
1061 v3_scale(&force,&dist_ij,scale);
1065 v3_add(&(ai->f),&(ai->f),&force);
1066 /* energy is 0.5 f_r f_c, but we will sum it up twice ... */
1067 moldyn->energy+=(0.25*f_r*f_c);
1069 /* save for use in 3bp */
1071 exchange->df_c=df_c;
1073 /* enable the run of 3bp function */
1079 /* tersoff 3 body part */
1081 int tersoff_mult_3bp(t_moldyn *moldyn,t_atom *ai,t_atom *aj,t_atom *ak,u8 bc) {
1083 t_tersoff_mult_params *params;
1084 t_tersoff_exchange *exchange;
1085 t_3dvec dist_ij,dist_ik,dist_jk;
1088 double d_ij,d_ij2,d_ik,d_jk;
1089 double f_c,df_c,b_ij,f_a,df_a;
1090 double f_c_ik,df_c_ik,arg;
1093 double n,c,d,h,beta,betan;
1096 double theta,cos_theta,sin_theta;
1097 double d_theta,d_theta1,d_theta2;
1098 double h_cos,h_cos2,d2_h_cos2;
1099 double frac1,bracket1,bracket2,bracket2_n_1,bracket2_n;
1100 double bracket3,bracket3_pow_1,bracket3_pow;
1103 params=moldyn->pot3b_params;
1105 exchange=&(params->exchange);
1107 if(!(exchange->run3bp))
1111 * we need: f_c, d_fc, b_ij, db_ij, f_a, df_a
1113 * we got f_c, df_c, f_a, df_a from 2bp calculation
1116 d_ij=exchange->d_ij;
1117 d_ij2=exchange->d_ij2;
1119 f_a=params->exchange.f_a;
1120 df_a=params->exchange.df_a;
1122 /* d_ij is <= S, as we didn't return so far! */
1125 * calc of b_ij (scalar) and db_ij (vector)
1127 * - for b_ij: chi, beta, f_c_ik, w(=1), c, d, h, n, cos_theta
1129 * - for db_ij: d_theta, sin_theta, cos_theta, f_c_ik, df_c_ik,
1135 v3_sub(&dist_ik,&(ai->r),&(ak->r));
1136 if(bc) check_per_bound(moldyn,&dist_ik);
1137 d_ik=v3_norm(&dist_ik);
1139 /* constants for f_c_ik calc */
1149 /* calc of f_c_ik */
1154 /* f_c_ik = 1, df_c_ik = 0 */
1160 arg=M_PI*(d_ik-R)/s_r;
1161 f_c_ik=0.5+0.5*cos(arg);
1162 df_c_ik=-0.5*sin(arg)*(M_PI/(s_r*d_ik));
1165 v3_sub(&dist_jk,&(aj->r),&(ak->r));
1166 if(bc) check_per_bound(moldyn,&dist_jk);
1167 d_jk=v3_norm(&dist_jk);
1169 beta=*(exchange->beta);
1170 betan=exchange->betan;
1177 c2d2=exchange->c2d2;
1179 numer=d_ij2+d_ik*d_ik-d_jk*d_jk;
1181 cos_theta=numer/denom;
1182 sin_theta=sqrt(1.0-(cos_theta*cos_theta));
1183 theta=acos(cos_theta);
1184 d_theta=(-1.0/sqrt(1.0-cos_theta*cos_theta))/(denom*denom);
1185 d_theta1=2*denom-numer*2*d_ik/d_ij;
1186 d_theta2=2*denom-numer*2*d_ij/d_ik;
1190 h_cos=(h-cos_theta);
1192 d2_h_cos2=d2-h_cos2;
1194 /* some usefull expressions */
1195 frac1=c2/(d2-h_cos2);
1196 bracket1=1+c2d2-frac1;
1197 bracket2=f_c_ik*bracket1;
1198 bracket2_n_1=pow(bracket2,n-1.0);
1199 bracket2_n=bracket2_n_1*bracket2;
1200 bracket3=1+betan*bracket2_n;
1201 bracket3_pow_1=pow(bracket3,(-1.0/(2.0*n))-1.0);
1202 bracket3_pow=bracket3_pow_1*bracket3;
1204 /* now go on with calc of b_ij and derivation of b_ij */
1205 b_ij=chi*bracket3_pow;
1207 /* derivation of theta */
1208 v3_scale(&force,&dist_ij,d_theta1);
1209 v3_scale(&temp,&dist_ik,d_theta2);
1210 v3_add(&force,&force,&temp);
1212 /* part 1 of derivation of b_ij */
1213 v3_scale(&force,&force,sin_theta*2*h_cos*f_c_ik*frac1);
1215 /* part 2 of derivation of b_ij */
1216 v3_scale(&temp,&dist_ik,df_c_ik*bracket1);
1218 /* sum up and scale ... */
1219 v3_add(&temp,&temp,&force);
1220 scale=bracket2_n_1*n*betan*(1+betan*bracket3_pow_1)*chi*(1.0/(2.0*n));
1221 v3_scale(&temp,&temp,scale);
1223 /* now construct an energy and a force out of that */
1224 v3_scale(&temp,&temp,f_a);
1225 v3_scale(&force,&dist_ij,df_a*b_ij);
1226 v3_add(&temp,&temp,&force);
1227 v3_scale(&temp,&temp,f_c);
1228 v3_scale(&force,&dist_ij,df_c*b_ij*f_a);
1229 v3_add(&force,&force,&temp);
1232 v3_add(&(ai->f),&(ai->f),&force);
1233 /* energy is 0.5 f_r f_c, but we will sum it up twice ... */
1234 moldyn->energy+=(0.25*f_a*b_ij*f_c);