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->element=element;
264 int destroy_atoms(t_moldyn *moldyn) {
266 if(moldyn->atom) free(moldyn->atom);
271 int thermal_init(t_moldyn *moldyn) {
274 * - gaussian distribution of velocities
275 * - zero total momentum
276 * - velocity scaling (E = 3/2 N k T), E: kinetic energy
281 t_3dvec p_total,delta;
286 random=&(moldyn->random);
288 /* gaussian distribution of velocities */
290 for(i=0;i<moldyn->count;i++) {
291 sigma=sqrt(2.0*K_BOLTZMANN*moldyn->t/atom[i].mass);
293 v=sigma*rand_get_gauss(random);
295 p_total.x+=atom[i].mass*v;
297 v=sigma*rand_get_gauss(random);
299 p_total.y+=atom[i].mass*v;
301 v=sigma*rand_get_gauss(random);
303 p_total.z+=atom[i].mass*v;
306 /* zero total momentum */
307 v3_scale(&p_total,&p_total,1.0/moldyn->count);
308 for(i=0;i<moldyn->count;i++) {
309 v3_scale(&delta,&p_total,1.0/atom[i].mass);
310 v3_sub(&(atom[i].v),&(atom[i].v),&delta);
313 /* velocity scaling */
314 scale_velocity(moldyn);
319 int scale_velocity(t_moldyn *moldyn) {
328 * - velocity scaling (E = 3/2 N k T), E: kinetic energy
331 for(i=0;i<moldyn->count;i++)
332 e+=0.5*atom[i].mass*v3_absolute_square(&(atom[i].v));
333 c=sqrt((2.0*e)/(3.0*moldyn->count*K_BOLTZMANN*moldyn->t));
334 for(i=0;i<moldyn->count;i++)
335 v3_scale(&(atom[i].v),&(atom[i].v),(1.0/c));
340 double get_e_kin(t_moldyn *moldyn) {
348 for(i=0;i<moldyn->count;i++)
349 moldyn->ekin+=0.5*atom[i].mass*v3_absolute_square(&(atom[i].v));
354 double get_e_pot(t_moldyn *moldyn) {
356 return moldyn->energy;
359 double update_e_kin(t_moldyn *moldyn) {
361 return(get_e_kin(moldyn));
364 double get_total_energy(t_moldyn *moldyn) {
366 return(moldyn->ekin+moldyn->energy);
369 t_3dvec get_total_p(t_moldyn *moldyn) {
378 for(i=0;i<moldyn->count;i++) {
379 v3_scale(&p,&(atom[i].v),atom[i].mass);
380 v3_add(&p_total,&p_total,&p);
386 double estimate_time_step(t_moldyn *moldyn,double nn_dist) {
390 /* nn_dist is the nearest neighbour distance */
393 printf("[moldyn] i do not estimate timesteps below %f K!\n",
394 MOLDYN_CRITICAL_EST_TEMP);
398 tau=(0.05*nn_dist*moldyn->atom[0].mass)/sqrt(3.0*K_BOLTZMANN*moldyn->t);
407 /* linked list / cell method */
409 int link_cell_init(t_moldyn *moldyn) {
415 fd=open("/dev/null",O_WRONLY);
419 /* partitioning the md cell */
420 lc->nx=moldyn->dim.x/moldyn->cutoff;
421 lc->x=moldyn->dim.x/lc->nx;
422 lc->ny=moldyn->dim.y/moldyn->cutoff;
423 lc->y=moldyn->dim.y/lc->ny;
424 lc->nz=moldyn->dim.z/moldyn->cutoff;
425 lc->z=moldyn->dim.z/lc->nz;
427 lc->cells=lc->nx*lc->ny*lc->nz;
428 lc->subcell=malloc(lc->cells*sizeof(t_list));
430 printf("[moldyn] initializing linked cells (%d)\n",lc->cells);
432 for(i=0;i<lc->cells;i++)
433 //list_init(&(lc->subcell[i]),1);
434 list_init(&(lc->subcell[i]),fd);
436 link_cell_update(moldyn);
441 int link_cell_update(t_moldyn *moldyn) {
455 for(i=0;i<lc->cells;i++)
456 list_destroy(&(moldyn->lc.subcell[i]));
458 for(count=0;count<moldyn->count;count++) {
459 i=(atom[count].r.x+(moldyn->dim.x/2))/lc->x;
460 j=(atom[count].r.y+(moldyn->dim.y/2))/lc->y;
461 k=(atom[count].r.z+(moldyn->dim.z/2))/lc->z;
462 list_add_immediate_ptr(&(moldyn->lc.subcell[i+j*nx+k*nx*ny]),
469 int link_cell_neighbour_index(t_moldyn *moldyn,int i,int j,int k,t_list *cell) {
488 cell[0]=lc->subcell[i+j*nx+k*a];
489 for(ci=-1;ci<=1;ci++) {
496 for(cj=-1;cj<=1;cj++) {
503 for(ck=-1;ck<=1;ck++) {
510 if(!(ci|cj|ck)) continue;
512 cell[--count2]=lc->subcell[x+y*nx+z*a];
515 cell[count1++]=lc->subcell[x+y*nx+z*a];
527 int link_cell_shutdown(t_moldyn *moldyn) {
534 for(i=0;i<lc->nx*lc->ny*lc->nz;i++)
535 list_shutdown(&(moldyn->lc.subcell[i]));
540 int moldyn_add_schedule(t_moldyn *moldyn,int runs,double tau) {
544 t_moldyn_schedule *schedule;
546 schedule=&(moldyn->schedule);
547 count=++(schedule->content_count);
549 ptr=realloc(moldyn->schedule.runs,count*sizeof(int));
551 perror("[moldyn] realloc (runs)");
554 moldyn->schedule.runs=ptr;
555 moldyn->schedule.runs[count-1]=runs;
557 ptr=realloc(schedule->tau,count*sizeof(double));
559 perror("[moldyn] realloc (tau)");
562 moldyn->schedule.tau=ptr;
563 moldyn->schedule.tau[count-1]=tau;
568 int moldyn_set_schedule_hook(t_moldyn *moldyn,void *hook,void *hook_params) {
570 moldyn->schedule.hook=hook;
571 moldyn->schedule.hook_params=hook_params;
578 * 'integration of newtons equation' - algorithms
582 /* start the integration */
584 int moldyn_integrate(t_moldyn *moldyn) {
587 unsigned int e,m,s,v;
589 t_moldyn_schedule *schedule;
594 schedule=&(moldyn->schedule);
596 /* initialize linked cell method */
597 link_cell_init(moldyn);
599 /* logging & visualization */
605 /* sqaure of some variables */
606 moldyn->tau_square=moldyn->tau*moldyn->tau;
607 moldyn->cutoff_square=moldyn->cutoff*moldyn->cutoff;
609 /* calculate initial forces */
610 potential_force_calc(moldyn);
612 /* zero absolute time */
615 for(sched=0;sched<moldyn->schedule.content_count;sched++) {
617 /* setting amount of runs and finite time step size */
618 moldyn->tau=schedule->tau[sched];
619 moldyn->tau_square=moldyn->tau*moldyn->tau;
620 moldyn->time_steps=schedule->runs[sched];
622 /* integration according to schedule */
624 for(i=0;i<moldyn->time_steps;i++) {
626 /* integration step */
627 moldyn->integrate(moldyn);
629 /* increase absolute time */
630 moldyn->time+=moldyn->tau;
632 /* check for log & visualization */
636 "%.15f %.45f %.45f %.45f\n",
637 moldyn->time,update_e_kin(moldyn),
639 get_total_energy(moldyn));
643 p=get_total_p(moldyn);
645 "%.15f %.45f\n",moldyn->time,
651 snprintf(fb,128,"%s-%f-%.15f.save",moldyn->sfb,
652 moldyn->t,i*moldyn->tau);
653 fd=open(fb,O_WRONLY|O_TRUNC|O_CREAT);
654 if(fd<0) perror("[moldyn] save fd open");
656 write(fd,moldyn,sizeof(t_moldyn));
657 write(fd,moldyn->atom,
658 moldyn->count*sizeof(t_atom));
665 visual_atoms(&(moldyn->vis),moldyn->time,
666 moldyn->atom,moldyn->count);
667 printf("\rsched: %d, steps: %d",sched,i);
674 /* check for hooks */
676 schedule->hook(moldyn,schedule->hook_params);
683 /* velocity verlet */
685 int velocity_verlet(t_moldyn *moldyn) {
688 double tau,tau_square;
695 tau_square=moldyn->tau_square;
697 for(i=0;i<count;i++) {
699 v3_scale(&delta,&(atom[i].v),tau);
700 v3_add(&(atom[i].r),&(atom[i].r),&delta);
701 v3_scale(&delta,&(atom[i].f),0.5*tau_square/atom[i].mass);
702 v3_add(&(atom[i].r),&(atom[i].r),&delta);
703 v3_per_bound(&(atom[i].r),&(moldyn->dim));
706 v3_scale(&delta,&(atom[i].f),0.5*tau/atom[i].mass);
707 v3_add(&(atom[i].v),&(atom[i].v),&delta);
710 /* neighbour list update */
711 link_cell_update(moldyn);
713 /* forces depending on chosen potential */
714 potential_force_calc(moldyn);
715 //moldyn->potential_force_function(moldyn);
717 for(i=0;i<count;i++) {
718 /* again velocities */
719 v3_scale(&delta,&(atom[i].f),0.5*tau/atom[i].mass);
720 v3_add(&(atom[i].v),&(atom[i].v),&delta);
729 * potentials & corresponding forces
733 /* generic potential and force calculation */
735 int potential_force_calc(t_moldyn *moldyn) {
738 t_atom *atom,*btom,*ktom;
740 t_list neighbour[27];
741 t_list *this,*thisk,*neighbourk;
752 printf("DEBUG: count = %d\n",count);
753 for(i=0;i<count;i++) {
756 v3_zero(&(atom[i].f));
758 /* single particle potential/force */
759 if(atom[i].attr&ATOM_ATTR_1BP)
760 moldyn->func1b(moldyn,&(atom[i]));
762 /* 2 body pair potential/force */
763 if(atom[i].attr&(ATOM_ATTR_2BP|ATOM_ATTR_3BP)) {
765 printf("DEBUG: processing atom %d\n",i);
766 link_cell_neighbour_index(moldyn,
767 (atom[i].r.x+moldyn->dim.x/2)/lc->x,
768 (atom[i].r.y+moldyn->dim.y/2)/lc->y,
769 (atom[i].r.z+moldyn->dim.z/2)/lc->z,
775 printf("DEBUG: countn = %d - dnslc = %d\n",countn,dnlc);
776 for(j=0;j<countn;j++) {
778 this=&(neighbour[j]);
781 if(this->start==NULL)
787 btom=this->current->data;
792 if((btom->attr&ATOM_ATTR_2BP)&
793 (atom[i].attr&ATOM_ATTR_2BP))
794 printf("DEBUG: calling func2b\n");
795 moldyn->func2b(moldyn,
800 /* 3 body potential/force */
802 if(!(atom[i].attr&ATOM_ATTR_3BP)||
803 !(btom->attr&ATOM_ATTR_3BP))
806 link_cell_neighbour_index(moldyn,
807 (btom->r.x+moldyn->dim.x/2)/lc->x,
808 (btom->r.y+moldyn->dim.y/2)/lc->y,
809 (btom->r.z+moldyn->dim.z/2)/lc->z,
812 for(k=0;k<lc->countn;k++) {
814 thisk=&(neighbourk[k]);
817 if(thisk->start==NULL)
820 bck=(k<lc->dnlc)?0:1;
824 ktom=thisk->current->data;
826 if(!(ktom->attr&ATOM_ATTR_3BP))
835 moldyn->func3b(moldyn,&(atom[i]),btom,ktom,bck);
837 } while(list_next(thisk)!=\
842 } while(list_next(this)!=L_NO_NEXT_ELEMENT);
851 * periodic boundayr checking
854 int check_per_bound(t_moldyn *moldyn,t_3dvec *a) {
865 if(moldyn->status&MOLDYN_STAT_PBX) {
866 if(a->x>=x) a->x-=dim->x;
867 else if(-a->x>x) a->x+=dim->x;
869 if(moldyn->status&MOLDYN_STAT_PBY) {
870 if(a->y>=y) a->y-=dim->y;
871 else if(-a->y>y) a->y+=dim->y;
873 if(moldyn->status&MOLDYN_STAT_PBZ) {
874 if(a->z>=z) a->z-=dim->z;
875 else if(-a->z>z) a->z+=dim->z;
886 /* harmonic oscillator potential and force */
888 int harmonic_oscillator(t_moldyn *moldyn,t_atom *ai,t_atom *aj,u8 bc) {
891 t_3dvec force,distance;
895 params=moldyn->pot2b_params;
896 sc=params->spring_constant;
897 equi_dist=params->equilibrium_distance;
899 v3_sub(&distance,&(ai->r),&(aj->r));
901 v3_per_bound(&distance,&(moldyn->dim));
902 if(bc) check_per_bound(moldyn,&distance);
903 d=v3_norm(&distance);
904 if(d<=moldyn->cutoff) {
905 /* energy is 1/2 (d-d0)^2, but we will add this twice ... */
906 moldyn->energy+=(0.25*sc*(d-equi_dist)*(d-equi_dist));
907 v3_scale(&force,&distance,-sc*(1.0-(equi_dist/d)));
908 v3_add(&(ai->f),&(ai->f),&force);
914 /* lennard jones potential & force for one sort of atoms */
916 int lennard_jones(t_moldyn *moldyn,t_atom *ai,t_atom *aj,u8 bc) {
919 t_3dvec force,distance;
921 double eps,sig6,sig12;
923 params=moldyn->pot2b_params;
924 eps=params->epsilon4;
926 sig12=params->sigma12;
928 v3_sub(&distance,&(ai->r),&(aj->r));
929 if(bc) check_per_bound(moldyn,&distance);
930 d=v3_absolute_square(&distance); /* 1/r^2 */
931 if(d<=moldyn->cutoff_square) {
935 h1=h2*h2; /* 1/r^12 */
936 /* energy is eps*..., but we will add this twice ... */
937 moldyn->energy+=0.5*eps*(sig12*h1-sig6*h2);
944 v3_scale(&force,&distance,d);
945 v3_add(&(ai->f),&(aj->f),&force);
952 * tersoff potential & force for 2 sorts of atoms
955 /* tersoff 1 body part */
956 int tersoff_mult_1bp(t_moldyn *moldyn,t_atom *ai) {
959 t_tersoff_mult_params *params;
960 t_tersoff_exchange *exchange;
963 params=moldyn->pot1b_params;
964 exchange=&(params->exchange);
967 * simple: point constant parameters only depending on atom i to
971 exchange->beta=&(params->beta[num]);
972 exchange->n=&(params->n[num]);
973 exchange->c=&(params->c[num]);
974 exchange->d=&(params->d[num]);
975 exchange->h=&(params->h[num]);
977 exchange->betan=pow(*(exchange->beta),*(exchange->n));
978 exchange->c2=params->c[num]*params->c[num];
979 exchange->d2=params->d[num]*params->d[num];
980 exchange->c2d2=exchange->c2/exchange->d2;
985 /* tersoff 2 body part */
986 int tersoff_mult_2bp(t_moldyn *moldyn,t_atom *ai,t_atom *aj,u8 bc) {
988 t_tersoff_mult_params *params;
989 t_tersoff_exchange *exchange;
990 t_3dvec dist_ij,force;
992 double A,B,R,S,lambda,mu;
1000 params=moldyn->pot2b_params;
1002 exchange=&(params->exchange);
1007 * we need: f_c, df_c, f_r, df_r
1009 * therefore we need: R, S, A, lambda
1012 v3_sub(&dist_ij,&(ai->r),&(aj->r));
1014 if(bc) check_per_bound(moldyn,&dist_ij);
1016 /* save for use in 3bp */ /* REALLY ?!?!?! */
1017 exchange->dist_ij=dist_ij;
1024 lambda=params->lambda[num];
1025 /* more constants depending of atoms i and j, needed in 3bp */
1026 params->exchange.B=&(params->B[num]);
1027 params->exchange.mu=&(params->mu[num]);
1029 params->exchange.chi=1.0;
1035 lambda=params->lambda_m;
1036 /* more constants depending of atoms i and j, needed in 3bp */
1037 params->exchange.B=&(params->Bmixed);
1038 params->exchange.mu=&(params->mu_m);
1040 params->exchange.chi=params->chi;
1043 d_ij=v3_norm(&dist_ij);
1045 /* save for use in 3bp */
1046 exchange->d_ij=d_ij;
1051 f_r=A*exp(-lambda*d_ij);
1052 df_r=-lambda*f_r/d_ij;
1054 /* f_a, df_a calc + save for 3bp use */
1055 exchange->f_a=-B*exp(-mu*d_ij);
1056 exchange->df_a=-mu*exchange->f_a/d_ij;
1059 /* f_c = 1, df_c = 0 */
1062 v3_scale(&force,&dist_ij,df_r);
1066 arg=M_PI*(d_ij-R)/s_r;
1067 f_c=0.5+0.5*cos(arg);
1068 df_c=-0.5*sin(arg)*(M_PI/(s_r*d_ij));
1069 scale=df_c*f_r+df_r*f_c;
1070 v3_scale(&force,&dist_ij,scale);
1074 v3_add(&(ai->f),&(ai->f),&force);
1075 /* energy is 0.5 f_r f_c, but we will sum it up twice ... */
1076 moldyn->energy+=(0.25*f_r*f_c);
1078 /* save for use in 3bp */
1080 exchange->df_c=df_c;
1082 /* enable the run of 3bp function */
1088 /* tersoff 3 body part */
1090 int tersoff_mult_3bp(t_moldyn *moldyn,t_atom *ai,t_atom *aj,t_atom *ak,u8 bc) {
1092 t_tersoff_mult_params *params;
1093 t_tersoff_exchange *exchange;
1094 t_3dvec dist_ij,dist_ik,dist_jk;
1097 double d_ij,d_ij2,d_ik,d_jk;
1098 double f_c,df_c,b_ij,f_a,df_a;
1099 double f_c_ik,df_c_ik,arg;
1102 double n,c,d,h,beta,betan;
1105 double theta,cos_theta,sin_theta;
1106 double d_theta,d_theta1,d_theta2;
1107 double h_cos,h_cos2,d2_h_cos2;
1108 double frac1,bracket1,bracket2,bracket2_n_1,bracket2_n;
1109 double bracket3,bracket3_pow_1,bracket3_pow;
1112 params=moldyn->pot3b_params;
1114 exchange=&(params->exchange);
1116 if(!(exchange->run3bp))
1120 * we need: f_c, d_fc, b_ij, db_ij, f_a, df_a
1122 * we got f_c, df_c, f_a, df_a from 2bp calculation
1125 d_ij=exchange->d_ij;
1126 d_ij2=exchange->d_ij2;
1128 f_a=params->exchange.f_a;
1129 df_a=params->exchange.df_a;
1131 /* d_ij is <= S, as we didn't return so far! */
1134 * calc of b_ij (scalar) and db_ij (vector)
1136 * - for b_ij: chi, beta, f_c_ik, w(=1), c, d, h, n, cos_theta
1138 * - for db_ij: d_theta, sin_theta, cos_theta, f_c_ik, df_c_ik,
1144 v3_sub(&dist_ik,&(ai->r),&(ak->r));
1145 if(bc) check_per_bound(moldyn,&dist_ik);
1146 d_ik=v3_norm(&dist_ik);
1148 /* constants for f_c_ik calc */
1158 /* calc of f_c_ik */
1163 /* f_c_ik = 1, df_c_ik = 0 */
1169 arg=M_PI*(d_ik-R)/s_r;
1170 f_c_ik=0.5+0.5*cos(arg);
1171 df_c_ik=-0.5*sin(arg)*(M_PI/(s_r*d_ik));
1174 v3_sub(&dist_jk,&(aj->r),&(ak->r));
1175 if(bc) check_per_bound(moldyn,&dist_jk);
1176 d_jk=v3_norm(&dist_jk);
1178 beta=*(exchange->beta);
1179 betan=exchange->betan;
1186 c2d2=exchange->c2d2;
1188 numer=d_ij2+d_ik*d_ik-d_jk*d_jk;
1190 cos_theta=numer/denom;
1191 sin_theta=sqrt(1.0-(cos_theta*cos_theta));
1192 theta=acos(cos_theta);
1193 d_theta=(-1.0/sqrt(1.0-cos_theta*cos_theta))/(denom*denom);
1194 d_theta1=2*denom-numer*2*d_ik/d_ij;
1195 d_theta2=2*denom-numer*2*d_ij/d_ik;
1199 h_cos=(h-cos_theta);
1201 d2_h_cos2=d2-h_cos2;
1203 /* some usefull expressions */
1204 frac1=c2/(d2-h_cos2);
1205 bracket1=1+c2d2-frac1;
1206 bracket2=f_c_ik*bracket1;
1207 bracket2_n_1=pow(bracket2,n-1.0);
1208 bracket2_n=bracket2_n_1*bracket2;
1209 bracket3=1+betan*bracket2_n;
1210 bracket3_pow_1=pow(bracket3,(-1.0/(2.0*n))-1.0);
1211 bracket3_pow=bracket3_pow_1*bracket3;
1213 /* now go on with calc of b_ij and derivation of b_ij */
1214 b_ij=chi*bracket3_pow;
1216 /* derivation of theta */
1217 v3_scale(&force,&dist_ij,d_theta1);
1218 v3_scale(&temp,&dist_ik,d_theta2);
1219 v3_add(&force,&force,&temp);
1221 /* part 1 of derivation of b_ij */
1222 v3_scale(&force,&force,sin_theta*2*h_cos*f_c_ik*frac1);
1224 /* part 2 of derivation of b_ij */
1225 v3_scale(&temp,&dist_ik,df_c_ik*bracket1);
1227 /* sum up and scale ... */
1228 v3_add(&temp,&temp,&force);
1229 scale=bracket2_n_1*n*betan*(1+betan*bracket3_pow_1)*chi*(1.0/(2.0*n));
1230 v3_scale(&temp,&temp,scale);
1232 /* now construct an energy and a force out of that */
1233 v3_scale(&temp,&temp,f_a);
1234 v3_scale(&force,&dist_ij,df_a*b_ij);
1235 v3_add(&temp,&temp,&force);
1236 v3_scale(&temp,&temp,f_c);
1237 v3_scale(&force,&dist_ij,df_c*b_ij*f_a);
1238 v3_add(&force,&force,&temp);
1241 v3_add(&(ai->f),&(ai->f),&force);
1242 /* energy is 0.5 f_r f_c, but we will sum it up twice ... */
1243 moldyn->energy+=(0.25*f_a*b_ij*f_c);