double df1dim(double x)
{
int j;
double df1=0.0;
matrix xt=NULL,df=NULL;
alloc_mtx(&xt,dncom,1);
alloc_mtx(&df,dncom,1);
for (j=1;j<=dncom;j++) xt[j][1]=dpcom[j][1]+x*dxicom[j][1];
(*nrdfun)(xt,df);
for (j=1;j<=dncom;j++) df1 += df[j][1]*dxicom[j][1];
free_mtx(&df);
free_mtx(&xt);
return (df1);
}
//calculate energies for isolated molecules
//if we don't know it, calculate it and save the value
double calc_e_iso ( system_t * system, double * sqrtKinv, molecule_t * mptr ) {
int nstart, nsize; // , curr_dimM; (unused variable)
double e_iso; //total vdw energy of isolated molecules
struct mtx * Cm_iso; //matrix Cm_isolated
double * eigvals; //eigenvalues of Cm_cm
molecule_t * molecule_ptr;
atom_t * atom_ptr;
nstart=nsize=0; //loop through each individual molecule
for ( molecule_ptr = system->molecules; molecule_ptr; molecule_ptr=molecule_ptr->next ) {
if ( molecule_ptr != mptr ) { //count atoms then skip to next molecule
for ( atom_ptr = molecule_ptr->atoms; atom_ptr; atom_ptr = atom_ptr->next ) nstart++;
continue;
}
//now that we've found the molecule of interest, count natoms, and calc energy
for ( atom_ptr = molecule_ptr->atoms; atom_ptr; atom_ptr = atom_ptr->next ) nsize++;
//build matrix for calculation of vdw energy of isolated molecule
Cm_iso = build_M(3*(nsize), 3*nstart, system->A_matrix, sqrtKinv);
//diagonalize M and extract eigenvales -> calculate energy
eigvals=lapack_diag(Cm_iso,1); //no eigenvectors
e_iso=eigen2energy(eigvals,Cm_iso->dim,system->temperature);
//free memory
free(eigvals);
free_mtx(Cm_iso);
//convert a.u. -> s^-1 -> K
return e_iso * au2invsec * halfHBAR ;
}
//unmatched molecule
return NAN; //we should never get here
}
//returns interaction VDW energy
double vdw(system_t *system) {
int N; // dimC; (unused variable) //number of atoms, number of non-zero rows in C-Matrix
double e_total, e_iso; //total energy, isolation energy (atoms @ infinity)
double * sqrtKinv; //matrix K^(-1/2); cholesky decomposition of K
double ** Am = system->A_matrix; //A_matrix
struct mtx * Cm; //C_matrix (we use single pointer due to LAPACK requirements)
double * eigvals; //eigenvales
double fh_corr, lr_corr;
N=system->natoms;
//allocate arrays. sqrtKinv is a diagonal matrix. d,e are used for matrix diag.
sqrtKinv = getsqrtKinv(system,N);
//calculate energy vdw of isolated molecules
e_iso = sum_eiso_vdw ( system, sqrtKinv );
//Build the C_Matrix
Cm = build_M (3*N, 0, Am, sqrtKinv);
//setup and use lapack diagonalization routine dsyev_()
eigvals = lapack_diag (Cm, system->polarvdw); //eigenvectors if system->polarvdw == 2
if ( system->polarvdw == 2 )
printevects(Cm);
//return energy in inverse time (a.u.) units
e_total = eigen2energy(eigvals, Cm->dim, system->temperature);
e_total *= au2invsec * halfHBAR; //convert a.u. -> s^-1 -> K
//vdw energy comparison
if ( system->polarvdw == 3 )
printf("VDW Two-Body | Many Body = %lf | %lf\n", twobody(system),e_total-e_iso);
if ( system->feynman_hibbs ) {
if ( system->vdw_fh_2be ) fh_corr = fh_vdw_corr_2be(system); //2be method
else fh_corr = fh_vdw_corr(system); //mpfd
}
else fh_corr=0;
if ( system->rd_lrc ) lr_corr = lr_vdw_corr(system);
else lr_corr=0;
//cleanup and return
free(sqrtKinv);
free(eigvals);
free_mtx(Cm);
return e_total - e_iso + fh_corr + lr_corr;
}
//calculate T matrix element for a particular separation
double e2body(system_t * system, atom_t * atom, pair_t * pair, double r) {
double energy;
double lr = system->polar_damp * r;
double lr2 = lr*lr;
double lr3 = lr*lr2;
double Txx = pow(r,-3)*(-2.0+(0.5*lr3+lr2+2*lr+2)*exp(-lr));
double Tyy = pow(r,-3)*(1-(0.5*lr2+lr+1)*exp(-lr));
double * eigvals;
struct mtx * M = alloc_mtx(6);
//only the sub-diagonals are non-zero
M->val[1]=M->val[2]=M->val[4]=M->val[5]=M->val[6]=M->val[8]=M->val[9]=M->val[11]=0;
M->val[12]=M->val[13]=M->val[15]=M->val[16]=M->val[19]=M->val[20]=M->val[22]=M->val[23]=0;
M->val[24]=M->val[26]=M->val[27]=M->val[29]=M->val[30]=M->val[31]=M->val[33]=M->val[34]=0;
//true diagonals
M->val[0]=M->val[7]=M->val[14]=(atom->omega)*(atom->omega);
M->val[21]=M->val[28]=M->val[35]=(pair->atom->omega)*(pair->atom->omega);
//sub-diagonals
M->val[3]=M->val[18]=
(atom->omega)*(pair->atom->omega)*sqrt(atom->polarizability*pair->atom->polarizability)*Txx;
M->val[10]=M->val[17]=M->val[25]=M->val[32]=
(atom->omega)*(pair->atom->omega)*sqrt(atom->polarizability*pair->atom->polarizability)*Tyy;
eigvals=lapack_diag(M,1);
energy = eigen2energy(eigvals, 6, system->temperature);
//subtract energy of atoms at infinity
// energy -= 3*wtanh(atom->omega, system->temperature);
energy -= 3*atom->omega;
// energy -= 3*wtanh(pair->atom->omega, system->temperature);
energy -= 3*pair->atom->omega;
free(eigvals);
free_mtx(M);
return energy * au2invsec * halfHBAR;
}
