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 moldyn_log_shutdown(moldyn);
45 link_cell_shutdown(moldyn);
46 moldyn_log_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_pbc(t_moldyn *moldyn,u8 x,u8 y,u8 z) {
99 moldyn->status|=MOLDYN_STAT_PBX;
102 moldyn->status|=MOLDYN_STAT_PBY;
105 moldyn->status|=MOLDYN_STAT_PBZ;
110 int set_potential1b(t_moldyn *moldyn,pf_func1b func,void *params) {
113 moldyn->pot1b_params=params;
118 int set_potential2b(t_moldyn *moldyn,pf_func2b func,void *params) {
121 moldyn->pot2b_params=params;
126 int set_potential3b(t_moldyn *moldyn,pf_func3b func,void *params) {
129 moldyn->pot3b_params=params;
134 int moldyn_set_log(t_moldyn *moldyn,u8 type,char *fb,int timer) {
137 case LOG_TOTAL_ENERGY:
138 moldyn->ewrite=timer;
139 moldyn->efd=open(fb,O_WRONLY|O_CREAT|O_TRUNC);
141 perror("[moldyn] efd open");
144 dprintf(moldyn->efd,"# total energy log file\n");
146 case LOG_TOTAL_MOMENTUM:
147 moldyn->mwrite=timer;
148 moldyn->mfd=open(fb,O_WRONLY|O_CREAT|O_TRUNC);
150 perror("[moldyn] mfd open");
153 dprintf(moldyn->efd,"# total momentum log file\n");
156 moldyn->swrite=timer;
157 strncpy(moldyn->sfb,fb,63);
160 moldyn->vwrite=timer;
161 strncpy(moldyn->vfb,fb,63);
162 visual_init(&(moldyn->vis),fb);
165 printf("unknown log mechanism: %02x\n",type);
172 int moldyn_log_shutdown(t_moldyn *moldyn) {
174 if(moldyn->efd) close(moldyn->efd);
175 if(moldyn->mfd) close(moldyn->mfd);
176 if(moldyn->visual) visual_tini(moldyn->visual);
181 int create_lattice(t_moldyn *moldyn,u8 type,double lc,int element,double mass,
182 u8 attr,u8 bnum,int a,int b,int c) {
192 if(type==FCC) count*=4;
194 if(type==DIAMOND) count*=8;
196 atom=malloc(count*sizeof(t_atom));
198 perror("malloc (atoms)");
206 ret=fcc_init(a,b,c,lc,atom,&origin);
209 ret=diamond_init(a,b,c,lc,atom,&origin);
212 printf("unknown lattice type (%02x)\n",type);
218 printf("ok, there is something wrong ...\n");
219 printf("calculated -> %d atoms\n",count);
220 printf("created -> %d atoms\n",ret);
227 atom[count-1].element=element;
228 atom[count-1].mass=mass;
229 atom[count-1].attr=attr;
230 atom[count-1].bnum=bnum;
237 int add_atom(t_moldyn *moldyn,int element,double mass,u8 bnum,u8 attr,
238 t_3dvec *r,t_3dvec *v) {
245 count=++(moldyn->count);
247 ptr=realloc(atom,count*sizeof(t_atom));
249 perror("[moldyn] realloc (add atom)");
257 atom[count-1].element=element;
258 atom[count-1].mass=mass;
259 atom[count-1].bnum=bnum;
260 atom[count-1].attr=attr;
265 int destroy_atoms(t_moldyn *moldyn) {
267 if(moldyn->atom) free(moldyn->atom);
272 int thermal_init(t_moldyn *moldyn) {
275 * - gaussian distribution of velocities
276 * - zero total momentum
277 * - velocity scaling (E = 3/2 N k T), E: kinetic energy
282 t_3dvec p_total,delta;
287 random=&(moldyn->random);
289 /* gaussian distribution of velocities */
291 for(i=0;i<moldyn->count;i++) {
292 sigma=sqrt(2.0*K_BOLTZMANN*moldyn->t/atom[i].mass);
294 v=sigma*rand_get_gauss(random);
296 p_total.x+=atom[i].mass*v;
298 v=sigma*rand_get_gauss(random);
300 p_total.y+=atom[i].mass*v;
302 v=sigma*rand_get_gauss(random);
304 p_total.z+=atom[i].mass*v;
307 /* zero total momentum */
308 v3_scale(&p_total,&p_total,1.0/moldyn->count);
309 for(i=0;i<moldyn->count;i++) {
310 v3_scale(&delta,&p_total,1.0/atom[i].mass);
311 v3_sub(&(atom[i].v),&(atom[i].v),&delta);
314 /* velocity scaling */
315 scale_velocity(moldyn);
320 int scale_velocity(t_moldyn *moldyn) {
329 * - velocity scaling (E = 3/2 N k T), E: kinetic energy
333 printf("[moldyn] no velocity scaling for T = 0 K\n");
338 for(i=0;i<moldyn->count;i++)
339 e+=0.5*atom[i].mass*v3_absolute_square(&(atom[i].v));
340 c=sqrt((2.0*e)/(3.0*moldyn->count*K_BOLTZMANN*moldyn->t));
341 for(i=0;i<moldyn->count;i++)
342 v3_scale(&(atom[i].v),&(atom[i].v),(1.0/c));
347 double get_e_kin(t_moldyn *moldyn) {
355 for(i=0;i<moldyn->count;i++)
356 moldyn->ekin+=0.5*atom[i].mass*v3_absolute_square(&(atom[i].v));
361 double get_e_pot(t_moldyn *moldyn) {
363 return moldyn->energy;
366 double update_e_kin(t_moldyn *moldyn) {
368 return(get_e_kin(moldyn));
371 double get_total_energy(t_moldyn *moldyn) {
373 return(moldyn->ekin+moldyn->energy);
376 t_3dvec get_total_p(t_moldyn *moldyn) {
385 for(i=0;i<moldyn->count;i++) {
386 v3_scale(&p,&(atom[i].v),atom[i].mass);
387 v3_add(&p_total,&p_total,&p);
393 double estimate_time_step(t_moldyn *moldyn,double nn_dist) {
397 /* nn_dist is the nearest neighbour distance */
400 printf("[moldyn] i do not estimate timesteps below %f K!\n",
401 MOLDYN_CRITICAL_EST_TEMP);
405 tau=(0.05*nn_dist*moldyn->atom[0].mass)/sqrt(3.0*K_BOLTZMANN*moldyn->t);
414 /* linked list / cell method */
416 int link_cell_init(t_moldyn *moldyn) {
422 fd=open("/dev/null",O_WRONLY);
426 /* partitioning the md cell */
427 lc->nx=moldyn->dim.x/moldyn->cutoff;
428 lc->x=moldyn->dim.x/lc->nx;
429 lc->ny=moldyn->dim.y/moldyn->cutoff;
430 lc->y=moldyn->dim.y/lc->ny;
431 lc->nz=moldyn->dim.z/moldyn->cutoff;
432 lc->z=moldyn->dim.z/lc->nz;
434 lc->cells=lc->nx*lc->ny*lc->nz;
435 lc->subcell=malloc(lc->cells*sizeof(t_list));
437 printf("[moldyn] initializing linked cells (%d)\n",lc->cells);
439 for(i=0;i<lc->cells;i++)
440 //list_init(&(lc->subcell[i]),1);
441 list_init(&(lc->subcell[i]),fd);
443 link_cell_update(moldyn);
448 int link_cell_update(t_moldyn *moldyn) {
462 for(i=0;i<lc->cells;i++)
463 list_destroy(&(moldyn->lc.subcell[i]));
465 for(count=0;count<moldyn->count;count++) {
466 i=(atom[count].r.x+(moldyn->dim.x/2))/lc->x;
467 j=(atom[count].r.y+(moldyn->dim.y/2))/lc->y;
468 k=(atom[count].r.z+(moldyn->dim.z/2))/lc->z;
469 list_add_immediate_ptr(&(moldyn->lc.subcell[i+j*nx+k*nx*ny]),
476 int link_cell_neighbour_index(t_moldyn *moldyn,int i,int j,int k,t_list *cell) {
495 cell[0]=lc->subcell[i+j*nx+k*a];
496 for(ci=-1;ci<=1;ci++) {
503 for(cj=-1;cj<=1;cj++) {
510 for(ck=-1;ck<=1;ck++) {
517 if(!(ci|cj|ck)) continue;
519 cell[--count2]=lc->subcell[x+y*nx+z*a];
522 cell[count1++]=lc->subcell[x+y*nx+z*a];
534 int link_cell_shutdown(t_moldyn *moldyn) {
541 for(i=0;i<lc->nx*lc->ny*lc->nz;i++)
542 list_shutdown(&(moldyn->lc.subcell[i]));
547 int moldyn_add_schedule(t_moldyn *moldyn,int runs,double tau) {
551 t_moldyn_schedule *schedule;
553 schedule=&(moldyn->schedule);
554 count=++(schedule->content_count);
556 ptr=realloc(moldyn->schedule.runs,count*sizeof(int));
558 perror("[moldyn] realloc (runs)");
561 moldyn->schedule.runs=ptr;
562 moldyn->schedule.runs[count-1]=runs;
564 ptr=realloc(schedule->tau,count*sizeof(double));
566 perror("[moldyn] realloc (tau)");
569 moldyn->schedule.tau=ptr;
570 moldyn->schedule.tau[count-1]=tau;
575 int moldyn_set_schedule_hook(t_moldyn *moldyn,void *hook,void *hook_params) {
577 moldyn->schedule.hook=hook;
578 moldyn->schedule.hook_params=hook_params;
585 * 'integration of newtons equation' - algorithms
589 /* start the integration */
591 int moldyn_integrate(t_moldyn *moldyn) {
594 unsigned int e,m,s,v;
596 t_moldyn_schedule *schedule;
602 schedule=&(moldyn->schedule);
605 /* initialize linked cell method */
606 link_cell_init(moldyn);
608 /* logging & visualization */
614 /* sqaure of some variables */
615 moldyn->tau_square=moldyn->tau*moldyn->tau;
616 moldyn->cutoff_square=moldyn->cutoff*moldyn->cutoff;
618 /* calculate initial forces */
619 potential_force_calc(moldyn);
622 ds=0.5*moldyn->tau_square*v3_norm(&(atom[0].f))/atom[0].mass;
625 /* zero absolute time */
628 for(sched=0;sched<moldyn->schedule.content_count;sched++) {
630 /* setting amount of runs and finite time step size */
631 moldyn->tau=schedule->tau[sched];
632 moldyn->tau_square=moldyn->tau*moldyn->tau;
633 moldyn->time_steps=schedule->runs[sched];
635 /* integration according to schedule */
637 for(i=0;i<moldyn->time_steps;i++) {
639 /* integration step */
640 moldyn->integrate(moldyn);
642 /* increase absolute time */
643 moldyn->time+=moldyn->tau;
645 /* check for log & visualization */
649 "%.15f %.45f %.45f %.45f\n",
650 moldyn->time,update_e_kin(moldyn),
652 get_total_energy(moldyn));
656 p=get_total_p(moldyn);
658 "%.15f %.45f\n",moldyn->time,
664 snprintf(fb,128,"%s-%f-%.15f.save",moldyn->sfb,
665 moldyn->t,i*moldyn->tau);
666 fd=open(fb,O_WRONLY|O_TRUNC|O_CREAT);
667 if(fd<0) perror("[moldyn] save fd open");
669 write(fd,moldyn,sizeof(t_moldyn));
670 write(fd,moldyn->atom,
671 moldyn->count*sizeof(t_atom));
678 visual_atoms(&(moldyn->vis),moldyn->time,
679 moldyn->atom,moldyn->count);
680 printf("\rsched: %d, steps: %d",sched,i);
687 /* check for hooks */
689 schedule->hook(moldyn,schedule->hook_params);
696 /* velocity verlet */
698 int velocity_verlet(t_moldyn *moldyn) {
701 double tau,tau_square;
708 tau_square=moldyn->tau_square;
710 for(i=0;i<count;i++) {
712 v3_scale(&delta,&(atom[i].v),tau);
713 v3_add(&(atom[i].r),&(atom[i].r),&delta);
714 v3_scale(&delta,&(atom[i].f),0.5*tau_square/atom[i].mass);
715 v3_add(&(atom[i].r),&(atom[i].r),&delta);
716 check_per_bound(moldyn,&(atom[i].r));
719 v3_scale(&delta,&(atom[i].f),0.5*tau/atom[i].mass);
720 v3_add(&(atom[i].v),&(atom[i].v),&delta);
723 /* neighbour list update */
724 link_cell_update(moldyn);
726 /* forces depending on chosen potential */
727 potential_force_calc(moldyn);
728 //moldyn->potential_force_function(moldyn);
730 for(i=0;i<count;i++) {
731 /* again velocities */
732 v3_scale(&delta,&(atom[i].f),0.5*tau/atom[i].mass);
733 v3_add(&(atom[i].v),&(atom[i].v),&delta);
742 * potentials & corresponding forces
746 /* generic potential and force calculation */
748 int potential_force_calc(t_moldyn *moldyn) {
751 t_atom *atom,*btom,*ktom;
753 t_list neighbour[27];
754 t_list *this,*thisk,*neighbourk;
765 for(i=0;i<count;i++) {
768 v3_zero(&(atom[i].f));
770 /* single particle potential/force */
771 if(atom[i].attr&ATOM_ATTR_1BP)
772 moldyn->func1b(moldyn,&(atom[i]));
774 /* 2 body pair potential/force */
775 if(atom[i].attr&(ATOM_ATTR_2BP|ATOM_ATTR_3BP)) {
777 link_cell_neighbour_index(moldyn,
778 (atom[i].r.x+moldyn->dim.x/2)/lc->x,
779 (atom[i].r.y+moldyn->dim.y/2)/lc->y,
780 (atom[i].r.z+moldyn->dim.z/2)/lc->z,
786 for(j=0;j<countn;j++) {
788 this=&(neighbour[j]);
791 if(this->start==NULL)
797 btom=this->current->data;
802 if((btom->attr&ATOM_ATTR_2BP)&
803 (atom[i].attr&ATOM_ATTR_2BP))
804 moldyn->func2b(moldyn,
809 /* 3 body potential/force */
811 if(!(atom[i].attr&ATOM_ATTR_3BP)||
812 !(btom->attr&ATOM_ATTR_3BP))
815 link_cell_neighbour_index(moldyn,
816 (btom->r.x+moldyn->dim.x/2)/lc->x,
817 (btom->r.y+moldyn->dim.y/2)/lc->y,
818 (btom->r.z+moldyn->dim.z/2)/lc->z,
821 for(k=0;k<lc->countn;k++) {
823 thisk=&(neighbourk[k]);
826 if(thisk->start==NULL)
829 bck=(k<lc->dnlc)?0:1;
833 ktom=thisk->current->data;
835 if(!(ktom->attr&ATOM_ATTR_3BP))
844 moldyn->func3b(moldyn,&(atom[i]),btom,ktom,bck);
846 } while(list_next(thisk)!=\
851 } while(list_next(this)!=L_NO_NEXT_ELEMENT);
860 * periodic boundayr checking
863 int check_per_bound(t_moldyn *moldyn,t_3dvec *a) {
874 if(moldyn->status&MOLDYN_STAT_PBX) {
875 if(a->x>=x) a->x-=dim->x;
876 else if(-a->x>x) a->x+=dim->x;
878 if(moldyn->status&MOLDYN_STAT_PBY) {
879 if(a->y>=y) a->y-=dim->y;
880 else if(-a->y>y) a->y+=dim->y;
882 if(moldyn->status&MOLDYN_STAT_PBZ) {
883 if(a->z>=z) a->z-=dim->z;
884 else if(-a->z>z) a->z+=dim->z;
895 /* harmonic oscillator potential and force */
897 int harmonic_oscillator(t_moldyn *moldyn,t_atom *ai,t_atom *aj,u8 bc) {
900 t_3dvec force,distance;
904 params=moldyn->pot2b_params;
905 sc=params->spring_constant;
906 equi_dist=params->equilibrium_distance;
908 v3_sub(&distance,&(ai->r),&(aj->r));
910 if(bc) check_per_bound(moldyn,&distance);
911 d=v3_norm(&distance);
912 if(d<=moldyn->cutoff) {
913 /* energy is 1/2 (d-d0)^2, but we will add this twice ... */
914 moldyn->energy+=(0.25*sc*(d-equi_dist)*(d-equi_dist));
915 v3_scale(&force,&distance,-sc*(1.0-(equi_dist/d)));
916 v3_add(&(ai->f),&(ai->f),&force);
922 /* lennard jones potential & force for one sort of atoms */
924 int lennard_jones(t_moldyn *moldyn,t_atom *ai,t_atom *aj,u8 bc) {
927 t_3dvec force,distance;
929 double eps,sig6,sig12;
931 params=moldyn->pot2b_params;
932 eps=params->epsilon4;
934 sig12=params->sigma12;
936 v3_sub(&distance,&(ai->r),&(aj->r));
937 if(bc) check_per_bound(moldyn,&distance);
938 d=v3_absolute_square(&distance); /* 1/r^2 */
939 if(d<=moldyn->cutoff_square) {
943 h1=h2*h2; /* 1/r^12 */
944 /* energy is eps*..., but we will add this twice ... */
945 moldyn->energy+=0.5*eps*(sig12*h1-sig6*h2);
952 v3_scale(&force,&distance,d);
953 v3_add(&(ai->f),&(ai->f),&force);
960 * tersoff potential & force for 2 sorts of atoms
963 /* tersoff 1 body part */
964 int tersoff_mult_1bp(t_moldyn *moldyn,t_atom *ai) {
967 t_tersoff_mult_params *params;
968 t_tersoff_exchange *exchange;
971 params=moldyn->pot1b_params;
972 exchange=&(params->exchange);
975 * simple: point constant parameters only depending on atom i to
979 exchange->beta=&(params->beta[num]);
980 exchange->n=&(params->n[num]);
981 exchange->c=&(params->c[num]);
982 exchange->d=&(params->d[num]);
983 exchange->h=&(params->h[num]);
985 exchange->betan=pow(*(exchange->beta),*(exchange->n));
986 exchange->c2=params->c[num]*params->c[num];
987 exchange->d2=params->d[num]*params->d[num];
988 exchange->c2d2=exchange->c2/exchange->d2;
993 /* tersoff 2 body part */
994 int tersoff_mult_2bp(t_moldyn *moldyn,t_atom *ai,t_atom *aj,u8 bc) {
996 t_tersoff_mult_params *params;
997 t_tersoff_exchange *exchange;
998 t_3dvec dist_ij,force;
1000 double A,B,R,S,lambda,mu;
1008 params=moldyn->pot2b_params;
1010 exchange=&(params->exchange);
1015 * we need: f_c, df_c, f_r, df_r
1017 * therefore we need: R, S, A, lambda
1020 v3_sub(&dist_ij,&(ai->r),&(aj->r));
1022 if(bc) check_per_bound(moldyn,&dist_ij);
1024 /* save for use in 3bp */ /* REALLY ?!?!?! */
1025 exchange->dist_ij=dist_ij;
1032 lambda=params->lambda[num];
1033 /* more constants depending of atoms i and j, needed in 3bp */
1034 params->exchange.B=&(params->B[num]);
1035 params->exchange.mu=&(params->mu[num]);
1037 params->exchange.chi=1.0;
1043 lambda=params->lambda_m;
1044 /* more constants depending of atoms i and j, needed in 3bp */
1045 params->exchange.B=&(params->Bmixed);
1046 params->exchange.mu=&(params->mu_m);
1048 params->exchange.chi=params->chi;
1051 d_ij=v3_norm(&dist_ij);
1053 /* save for use in 3bp */
1054 exchange->d_ij=d_ij;
1059 f_r=A*exp(-lambda*d_ij);
1060 df_r=-lambda*f_r/d_ij;
1062 /* f_a, df_a calc + save for 3bp use */
1063 exchange->f_a=-B*exp(-mu*d_ij);
1064 exchange->df_a=-mu*exchange->f_a/d_ij;
1067 /* f_c = 1, df_c = 0 */
1070 v3_scale(&force,&dist_ij,df_r);
1074 arg=M_PI*(d_ij-R)/s_r;
1075 f_c=0.5+0.5*cos(arg);
1076 df_c=-0.5*sin(arg)*(M_PI/(s_r*d_ij));
1077 scale=df_c*f_r+df_r*f_c;
1078 v3_scale(&force,&dist_ij,scale);
1082 v3_add(&(ai->f),&(ai->f),&force);
1083 /* energy is 0.5 f_r f_c, but we will sum it up twice ... */
1084 moldyn->energy+=(0.25*f_r*f_c);
1086 /* save for use in 3bp */
1088 exchange->df_c=df_c;
1090 /* enable the run of 3bp function */
1096 /* tersoff 3 body part */
1098 int tersoff_mult_3bp(t_moldyn *moldyn,t_atom *ai,t_atom *aj,t_atom *ak,u8 bc) {
1100 t_tersoff_mult_params *params;
1101 t_tersoff_exchange *exchange;
1102 t_3dvec dist_ij,dist_ik,dist_jk;
1105 double d_ij,d_ij2,d_ik,d_jk;
1106 double f_c,df_c,b_ij,f_a,df_a;
1107 double f_c_ik,df_c_ik,arg;
1110 double n,c,d,h,beta,betan;
1113 double theta,cos_theta,sin_theta;
1114 double d_theta,d_theta1,d_theta2;
1115 double h_cos,h_cos2,d2_h_cos2;
1116 double frac1,bracket1,bracket2,bracket2_n_1,bracket2_n;
1117 double bracket3,bracket3_pow_1,bracket3_pow;
1120 params=moldyn->pot3b_params;
1122 exchange=&(params->exchange);
1124 if(!(exchange->run3bp))
1128 * we need: f_c, d_fc, b_ij, db_ij, f_a, df_a
1130 * we got f_c, df_c, f_a, df_a from 2bp calculation
1133 d_ij=exchange->d_ij;
1134 d_ij2=exchange->d_ij2;
1136 f_a=params->exchange.f_a;
1137 df_a=params->exchange.df_a;
1139 /* d_ij is <= S, as we didn't return so far! */
1142 * calc of b_ij (scalar) and db_ij (vector)
1144 * - for b_ij: chi, beta, f_c_ik, w(=1), c, d, h, n, cos_theta
1146 * - for db_ij: d_theta, sin_theta, cos_theta, f_c_ik, df_c_ik,
1152 v3_sub(&dist_ik,&(ai->r),&(ak->r));
1153 if(bc) check_per_bound(moldyn,&dist_ik);
1154 d_ik=v3_norm(&dist_ik);
1156 /* constants for f_c_ik calc */
1166 /* calc of f_c_ik */
1171 /* f_c_ik = 1, df_c_ik = 0 */
1177 arg=M_PI*(d_ik-R)/s_r;
1178 f_c_ik=0.5+0.5*cos(arg);
1179 df_c_ik=-0.5*sin(arg)*(M_PI/(s_r*d_ik));
1182 v3_sub(&dist_jk,&(aj->r),&(ak->r));
1183 if(bc) check_per_bound(moldyn,&dist_jk);
1184 d_jk=v3_norm(&dist_jk);
1186 beta=*(exchange->beta);
1187 betan=exchange->betan;
1194 c2d2=exchange->c2d2;
1196 numer=d_ij2+d_ik*d_ik-d_jk*d_jk;
1198 cos_theta=numer/denom;
1199 sin_theta=sqrt(1.0-(cos_theta*cos_theta));
1200 theta=acos(cos_theta);
1201 d_theta=(-1.0/sqrt(1.0-cos_theta*cos_theta))/(denom*denom);
1202 d_theta1=2*denom-numer*2*d_ik/d_ij;
1203 d_theta2=2*denom-numer*2*d_ij/d_ik;
1207 h_cos=(h-cos_theta);
1209 d2_h_cos2=d2-h_cos2;
1211 /* some usefull expressions */
1212 frac1=c2/(d2-h_cos2);
1213 bracket1=1+c2d2-frac1;
1214 bracket2=f_c_ik*bracket1;
1215 bracket2_n_1=pow(bracket2,n-1.0);
1216 bracket2_n=bracket2_n_1*bracket2;
1217 bracket3=1+betan*bracket2_n;
1218 bracket3_pow_1=pow(bracket3,(-1.0/(2.0*n))-1.0);
1219 bracket3_pow=bracket3_pow_1*bracket3;
1221 /* now go on with calc of b_ij and derivation of b_ij */
1222 b_ij=chi*bracket3_pow;
1224 /* derivation of theta */
1225 v3_scale(&force,&dist_ij,d_theta1);
1226 v3_scale(&temp,&dist_ik,d_theta2);
1227 v3_add(&force,&force,&temp);
1229 /* part 1 of derivation of b_ij */
1230 v3_scale(&force,&force,sin_theta*2*h_cos*f_c_ik*frac1);
1232 /* part 2 of derivation of b_ij */
1233 v3_scale(&temp,&dist_ik,df_c_ik*bracket1);
1235 /* sum up and scale ... */
1236 v3_add(&temp,&temp,&force);
1237 scale=bracket2_n_1*n*betan*(1+betan*bracket3_pow_1)*chi*(1.0/(2.0*n));
1238 v3_scale(&temp,&temp,scale);
1240 /* now construct an energy and a force out of that */
1241 v3_scale(&temp,&temp,f_a);
1242 v3_scale(&force,&dist_ij,df_a*b_ij);
1243 v3_add(&temp,&temp,&force);
1244 v3_scale(&temp,&temp,f_c);
1245 v3_scale(&force,&dist_ij,df_c*b_ij*f_a);
1246 v3_add(&force,&force,&temp);
1249 v3_add(&(ai->f),&(ai->f),&force);
1250 /* energy is 0.5 f_r f_c, but we will sum it up twice ... */
1251 moldyn->energy+=(0.25*f_a*b_ij*f_c);