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FC.cxx
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FC.cxx
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/*
* FC is a program to calculate Franck-Condon factors
Copyright (C) 1999,2006, 2020 Pierre-Nicholas Roy
This program is free software; you can redistribute it and/or
modify it under the terms of the GNU General Public License
as published by the Free Software Foundation; either version 2
of the License, or (at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program; if not, write to the Free Software
Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
*/
#include "FC.h"
double int00=1.;
int factrl(int n);
vector triplelmn(int ni,int nj,int nk,int nl,int nm,int nn,
int modei,int modej,int modek,int model,
int modem,int moden,
matrix& Pmat,matrix &Qmat,matrix &Rmat,
diagmat& II,vector& delta);
vector tripleij(int ni,int nj,int nk,int nl,int nm,
int modei,int modej,int modek,int model,int modem,
matrix& Pmat,matrix &Qmat,matrix &Rmat,
diagmat& II,vector& delta);
vector triplei(int ni,int nj,int nk,int nl,
int modei,int modej,int modek,int model,
matrix& Pmat,matrix &Qmat,matrix &Rmat,
diagmat& II,vector& delta);
vector triplelm(int ni,int nj,int nk,int nl,int nm,
int modei,int modej,int modek,int model,int modem,
matrix& Pmat,matrix &Qmat,matrix &Rmat,
diagmat& II,vector& delta);
vector triple(int ni,int nj,int nk,int modei,int modej,int modek,
matrix& Pmat,diagmat& II,vector& delta);
complex HermiteH(int n,complex x);
complex sigma(int k,matrix &Qmat,matrix &Rmat,vector &delta);
complex tau(int k,matrix &Pmat,diagmat &II,vector &delta);
double oi0(int k,int n,double int00,matrix &Pmat,diagmat &II,vector &delta);
double o0i(int k,int n,double int00,matrix& Qmat,matrix& Rmat,vector&
delta);
double o11(int k,int i,double int00,matrix& Rmat,diagmat& II,
matrix& Pmat,matrix& Qmat,vector& delta);
double o21(int k,int i,double int00,matrix& Rmat,diagmat& II,
matrix& Pmat,matrix& Qmat,vector& delta);
double boltzman(double EoverT);
double oki(int nkp1,int ni,int k,int i,double int00,matrix& Rmat,diagmat&
II,matrix& Pmat,matrix& Qmat,vector& delta);
double okl00(int nkp1,int nl,int k,int l,double int00,diagmat& II,
matrix& Pmat,vector& delta);
double lorentz(double omega,double w0,double gamma);
vector lor(double pos,double signal,int size,double gamma,vector grid);
double oklk0(int nk,int nl,int nkp1p,int k,int l,double int00,diagmat II,
matrix Pmat, matrix &Qmat, matrix& Rmat,vector& delta);
double oklkl(int nk,int nl,int nkp1p,int nlp,int k,int l,
double int00,diagmat II,matrix Pmat, matrix &Qmat, matrix& Rmat,
vector& delta);
double o00ij(int nip1,int nj,int i,int j,double int00,matrix& Qmat,
matrix& Rmat,vector& delta);
double position(int modei,int modej,int modek,
int model,int modem,int moden,
int cati,int catj,int catk,
int neul,int neum,int neun,
vector &omegaion,vector &omega);
vector triplehot(int ni,int nj,int nk,int modei,int modej,int modek,
matrix& Qmat,matrix &Rmat,diagmat &II,vector& delta);
vector singlecold(int ni,int modei,matrix& Pmat,diagmat& II,vector& delta);
vector singlehot(int ni,int modei,matrix& Qmat,matrix &Rmat,vector& delta);
vector doublecold(int ni,int nj,int modei,int modej,
matrix& Pmat,diagmat& II,vector& delta);
vector doublehot(int ni,int nj,int modei,int modej,
matrix& Qmat,matrix &Rmat,vector& delta);
vector ijhot(int ni,int nj,int modei,int modej,matrix &Pmat,matrix &Qmat,
matrix &Rmat,diagmat &II,vector &delta);
vector ijkhot(int ni,int nj,int nk,int modei,int modej,int modek,
matrix &Pmat,matrix &Qmat,matrix &Rmat,diagmat &II,
vector &delta);
vector triplel(int ni,int nj,int nk,int nl,
int modei,int modej,int modek,int model,
matrix& Pmat,matrix &Qmat,matrix &Rmat,
diagmat& II,vector& delta);
vector ijklhot(int ni,int nj,int nk,int nl,
int modei,int modej,int modek,int model,
matrix &Pmat,matrix &Qmat,matrix &Rmat,diagmat &II,
vector &delta);
vector iklhot(int ni,int nk,int nl,int modei,int modek,int model,
matrix &Pmat,matrix &Qmat,matrix &Rmat,diagmat &II,
vector &delta);
double const speedofl=137.0359895;
int main(int argc,char** argv)
{
if (argc!=3) {
std::cerr<<"usage: "<<argv[0]<<" <using nomal modes: 0=yes; 1=No (using Force constants instead)> <input filename>"<<std::endl;
exit(0);
}
int usingnormalmodes=atoi(argv[1]);
std::strstream filenamein;
filenamein<<argv[2]<<std::ends;
ifstream file(filenamein.str());
int i,j,k,l,lp,m,n,natom;
int modei;
int modej;
int modek;
int model;
int modem;
int moden;
double pos;
char Units;
file >> Units;
file >> natom;
int N=3*natom-6;
vector massvec(natom);
diagmat sqmass(3*natom);
diagmat invsqmass(3*natom);
for (i=0;i<natom;i++) file >> massvec(i);
/* get masses */
massvec=(1./autoamu)*massvec;
for (i=0;i<natom;i++) {
for (j=0;j<3;j++) {
sqmass(i*3+j)=sqrt(massvec(i));
invsqmass(i*3+j)=1./sqrt(massvec(i));
}
}
vector geon(3*natom);
vector geoc(3*natom);
vector omega(3*natom-6);
vector omegaion(3*natom-6);
matrix Lmat(3*natom,3*natom-6);
matrix Lmation(3*natom,3*natom-6);
matrix FCMn(3*natom,3*natom);
matrix FCMc(3*natom,3*natom);
for (i=0;i<2;i++) {
/*loop over species
get geometries */
if (i==0) {
for (l=0;l<(3*natom);l++) file >> geon(l);
}
if (i==1) {
for (l=0;l<(3*natom);l++) file >> geoc(l);
}
if (usingnormalmodes == 0) {
for (j=0;j<(3*natom-6);j++) {
if (i==0) {
file >> omega(j);
omega(j)/=hatocm;
}
if (i==1) {
file >> omegaion(j);
omegaion(j)/=hatocm;
}
for (k=0;k<(3*natom);k++) {
if (i==0) file >> Lmat(k,j);
if (i==1) file >> Lmation(k,j);
}
}
}
else {
// get force constant matrix
if (i==0) {
for (l=0;l<(3*natom)/4;l++) {
for (lp=0;lp<(3*natom);lp++) {
for (j=0;j<4;j++) {
file >> FCMn(lp,j+l*4);
// std::cout.width(12);std::cout.precision(6);
// std::cout<<FCMn(lp,j+l*4)<<" ";
}
//std::cout<<std::endl;
}
//std::cout<<std::endl;
}
for (lp=0;lp<(3*natom);lp++) {
for (j=0;j<(3*natom)%4;j++) {
file >> FCMn(lp,(3*natom)-1+j);
// std::cout<<FCMn(lp,(3*natom)-1+j)<<" ";
// std::cout<<std::endl;
}
}
}
if (i==1) {
for (l=0;l<(3*natom)/4;l++) {
for (lp=0;lp<(3*natom);lp++) {
for (j=0;j<4;j++) {
file >> FCMc(lp,j+l*4);
// std::cout.width(12);std::cout.precision(6);
// std::cout<<FCMc(lp,j+l*4)<<" ";
}
//std::cout<<std::endl;
}
//std::cout<<std::endl;
}
for (lp=0;lp<(3*natom);lp++) {
for (j=0;j<(3*natom)%4;j++) {
file >> FCMc(lp,(3*natom)-1+j);
// std::cout<<FCMc(lp,(3*natom)-1+j)<<" ";
// std::cout<<std::endl;
}
}
}
}
}
// for (l=0;l<(3*natom);l++) {
// for (lp=0;lp<(3*natom);lp++) {
// std::cout.width(6);std::cout.precision(3);
// std::cout<<FCMn(l,lp)<<" ";
// }
// std::cout<<std::endl;
// }
double wmin,wmax,fwhm,gamma,v00;
double T;
double res;
/* resolution of output data file */
int cationquanta;
int neutralquanta;
file >> wmin;
file >> wmax;
file >>T;
file >>fwhm;
file >>res;
file >>v00;
/* neutral quanta */
file >>neutralquanta;
/* cation quanta */
file >>cationquanta;
double labellimit;
file >>labellimit;
int numberofactivemodes=3;
file>>numberofactivemodes;
// adjust center of mass
vector CMi(3);
vector CMf(3);
double totalmass=0.;
for (i=0;i<natom;i++) {
totalmass+=massvec(i);
for (j=0;j<3;j++) {
CMi(j)+=massvec(i)*geon(i*3+j);
CMf(j)+=massvec(i)*geoc(i*3+j);
}
}
CMi=(1./totalmass)*CMi;
CMf=(1./totalmass)*CMf;
for (i=0;i<natom;i++) {
for (j=0;j<3;j++) {
geon(i*3+j)-=CMi(j);
geoc(i*3+j)-=CMf(j);
}
}
//input read
// setup rotation matrix
// matrix Rx(3,3),Ry(3,3),Rz(3,3);
// Rx(0,0)=1.;Rx(0,1)=0.;Rx(0,2)=0.;
// Rx(1,0)=0.;Rx(1,1)=cos(anglex);Rx(1,2)=sin(anglex);
// Rx(2,0)=0.;Rx(2,1)=-sin(anglex);Rx(2,2)=cos(anglex);
// Ry(0,0)=cos(angley);Ry(0,1)=0.;Ry(0,2)=-sin(angley);
// Ry(1,0)=0.;Ry(1,1)=1.;Ry(1,2)=0.;
// Ry(2,0)=sin(angley);Ry(2,1)=0.;Ry(2,2)=cos(angley);
// Rz(0,0)=cos(anglez);Rz(0,1)=sin(anglez);Rz(0,2)=0.;
// Rz(1,0)=-sin(anglez);Rz(1,1)=cos(anglez);Rz(1,2)=0.;
// Rz(2,0)=0.;Rz(2,1)=0.;Rz(2,2)=1.;
// matrix Rwhole=Rx*Ry*Rz;
//rotate the geometry
// int ip,jp;
// matrix RotateCartesian(3*natom,3*natom);
// matrix RotateCartesianMW(3*natom,3*natom);
// for (i=0;i<natom;i++)
// for (ip=0;ip<3;ip++)
// for (jp=0;jp<3;jp++) {
// RotateCartesian(i*3+ip,i*3+jp)=Rwhole(ip,jp);
// RotateCartesianMW(i*3+ip,i*3+jp)=Rwhole(ip,jp);
// }
// geoc=RotateCartesian*geoc;
// Lmation=RotateCartesianMW*Lmation;
/* perform orthogonalisation or not? */
char ortho_of_S='N';
char ortho_of_L;
if (usingnormalmodes == 0)
ortho_of_L='Y';
else
ortho_of_L='N';
/* set limits */
int ni,nj,nk,nl,nm,nn;
/* definition of gamma */
gamma=fwhm;
vector Rvec=geoc-geon;
//Rvec=.5*Rvec;
/* vector Rvec=geon-geoc; //makes more sense */
/* uncomment the foolowing line for geometries in Angstrom */
if (Units == 'A') Rvec=(1./.529177)*Rvec;
if (Units != 'A' && Units !='B') std::cerr<<"wrong Units flag"<<std::endl;
/* Rvec=geoc-geonfix;
no difference under translation */
vector Rvecmass=sqmass*Rvec;
/* modified Gram-Schmidt orthogonalisation on both L's */
// massweight the force constant matrices and diagonalize
if (usingnormalmodes != 0) {
matrix mwHn=invsqmass*FCMn*invsqmass;
matrix mwHc=invsqmass*FCMc*invsqmass;
mwHn=.5*(mwHn+transpose(mwHn));
mwHc=.5*(mwHc+transpose(mwHc));
vector NMn=diag(mwHn);
vector NMc=diag(mwHc);
std::strstream vibreportoutname;
vibreportoutname<<filenamein.str()<<".vibanalysis.stat"<<ends;
ofstream vibreportout(vibreportoutname.str());
vibreportout<<"mode";
vibreportout<<" initial state (1/CM)";
vibreportout<<" final state (1/CM)"<<std::endl;
for (k=0;k<(3*natom);k++)
vibreportout<<k<<" "<<sqrt(complex(NMn(k),0.))*hatocm<<" "<<sqrt(complex(NMc(k),0.))*hatocm<<std::endl;
// inertia tensor
matrix In(3,3);
for (i=0;i<natom;i++) {
In(0,0)+=massvec(i)*(geon(i*3+1)*geon(i*3+1)+geon(i*3+2)*geon(i*3+2));
In(1,1)+=massvec(i)*(geon(i*3+0)*geon(i*3+0)+geon(i*3+2)*geon(i*3+2));
In(2,2)+=massvec(i)*(geon(i*3+1)*geon(i*3+1)+geon(i*3+0)*geon(i*3+0));
In(0,1)+=-massvec(i)*(geon(i*3+0)*geon(i*3+1));
In(0,2)+=-massvec(i)*(geon(i*3+0)*geon(i*3+2));
In(1,2)+=-massvec(i)*(geon(i*3+1)*geon(i*3+2));
}
In(1,0)=In(0,1);
In(2,0)=In(0,2);
In(2,1)=In(1,2);
vector Ival=diag(In);
// translation vectors
vector D1(3*natom);
vector D2(3*natom);
vector D3(3*natom);
vector D4(3*natom);
vector D5(3*natom);
vector D6(3*natom);
for (i=0;i<natom;i++) {
D1(i*3+0)=sqrt(massvec(i));
D2(i*3+1)=sqrt(massvec(i));
D3(i*3+2)=sqrt(massvec(i));
}
// D4j;i = ((Py)i Xj;3 - (Pz)i Xj;2) sqrt(mi)
// D5j;i = ((Pz)i Xj;1 - (Px)i Xj;3) sqrt(mi)
// D6j;i = ((Px)i Xj;2 - (Py)i Xj;1) sqrt(mi)
/* where j = x; y; z; i is over all atoms and P is the dot product of R
(the coordinates of the atoms with respect to the center of mass)
and the corresponding row of X, the matrix used to diagonalize the
moment of inertia tensor I.
*/
vector Pvec(natom*3);
for (i=0;i<natom;i++) {
for (j=0;j<3;j++) {
Pvec(i*3+0)+=geon(i*3+j)*In(j,0);
Pvec(i*3+1)+=geon(i*3+j)*In(j,1);
Pvec(i*3+2)+=geon(i*3+j)*In(j,2);
}
}
for (i=0;i<natom;i++) {
D4(i*3+0)=(Pvec(i*3+1)*In(0,2)-Pvec(i*3+2)*In(0,1))*sqrt(massvec(i));
D4(i*3+1)=(Pvec(i*3+1)*In(1,2)-Pvec(i*3+2)*In(1,1))*sqrt(massvec(i));
D4(i*3+2)=(Pvec(i*3+1)*In(2,2)-Pvec(i*3+2)*In(2,1))*sqrt(massvec(i));
D5(i*3+0)=(Pvec(i*3+2)*In(0,0)-Pvec(i*3+0)*In(0,2))*sqrt(massvec(i));
D5(i*3+1)=(Pvec(i*3+2)*In(1,0)-Pvec(i*3+0)*In(1,2))*sqrt(massvec(i));
D5(i*3+2)=(Pvec(i*3+2)*In(2,0)-Pvec(i*3+0)*In(2,2))*sqrt(massvec(i));
D6(i*3+0)=(Pvec(i*3+0)*In(0,1)-Pvec(i*3+1)*In(0,0))*sqrt(massvec(i));
D6(i*3+1)=(Pvec(i*3+0)*In(1,1)-Pvec(i*3+1)*In(1,0))*sqrt(massvec(i));
D6(i*3+2)=(Pvec(i*3+0)*In(2,1)-Pvec(i*3+1)*In(2,0))*sqrt(massvec(i));
}
normalise(D1);
normalise(D2);
normalise(D3);
normalise(D4);
normalise(D5);
normalise(D6);
std::cout<<D4*D5<<" "<<D5*D6<<" "<<D4*D6<<std::endl;
for (k=0;k<(3*natom-6);k++) {
omegaion(k)=sqrt(NMc(k+6));
omega(k)=sqrt(NMn(k+6));
//std::cout<<omega(k)*hatocm<<" "<<omegaion(k)*hatocm<<std::endl;
for (j=0;j<(3*natom);j++) {
Lmat(j,k)=mwHn(j,k+6);
Lmation(j,k)=mwHc(j,k+6);
}
}
// phase correction
matrix Stest=transpose(Lmation)*Lmat;
for (k=0;k<(3*natom-6);k++) {
if (Stest(k,k) < 0) {
for (j=0;j<(3*natom);j++)
Lmation(j,k)=-mwHc(j,k+6);
}
}
}
matrix oLmat=Lmat;
matrix oLmation=Lmation;
for (k=0;k<(3*natom-6);k++) {
double proj1=0.0;
double proj2=0.0;
for (i=0;i<(3*natom);i++) {
proj1+=oLmat(i,k)*oLmat(i,k);
proj2+=oLmation(i,k)*oLmation(i,k);
}
proj1=sqrt(proj1);
proj2=sqrt(proj2);
for (i=0;i<(3*natom);i++) {
oLmat(i,k)=oLmat(i,k)/proj1; oLmation(i,k)=oLmation(i,k)/proj2; }
for (j=k+1;j<(3*natom-6);j++) {
proj1=0.0; proj2=0.0;
for (i=0;i<(3*natom);i++) {
proj1+=oLmat(i,k)*oLmat(i,j);
proj2+=oLmation(i,k)*oLmation(i,j);
}
for (i=0;i<(3*natom);i++) {
oLmat(i,j)=oLmat(i,j)-oLmat(i,k)*proj1;
oLmation(i,j)=oLmation(i,j)-oLmation(i,k)*proj2;
}
}
}
/* matrix diff=Lmat-oLmat; */
if (ortho_of_L == 'Y') {
Lmat=oLmat;
Lmation=oLmation;
}
// matrix projectorion=Lmation*transpose(Lmation);
// matrix projector=Lmat*transpose(Lmat);
// matrix projectorU=projector;
// matrix projectorionU=projectorion;
// vector singval=diag(projectorU);
// vector singvalion=diag(projectorionU);
// matrix nonsingularvectors(3*natom,N);
// matrix nonsingularvectorsion(3*natom,N);
// diagmat inversesingvalion(N);
// diagmat inversesingval(N);
// for (i=0;i<N;i++) {
// inversesingvalion(i)=1./singvalion(6+i);
// inversesingval(i)=1./singval(6+i);
// }
// for (i=0;i<3*natom;i++) {
// for (j=0;j<N;j++) {
// nonsingularvectors(i,j)=projectorU(i,j+6);
// nonsingularvectorsion(i,j)=projectorionU(i,j+6);
// }
// }
// matrix inverseprojectorion=
// nonsingularvectorsion*inversesingvalion*transpose(nonsingularvectorsion);
// matrix inverseprojector=
// nonsingularvectors*inversesingval*transpose(nonsingularvectors);
// matrix inverseofLmation=transpose(Lmation)*inverseprojectorion;
// matrix inverseofLmat=transpose(Lmat)*inverseprojector;
// if (inverseofL ==1) {
// inverseofLmation=transpose(Lmation);
// inverseofLmat=transpose(Lmat);
// }
diagmat lambda(3*natom-6);
diagmat lambdaion(3*natom-6);
for (j=0;j<(3*natom-6);j++) {
lambda(j)=sqrt(omega(j)); lambdaion(j)=sqrt(omegaion(j));
}
matrix OSmat=transpose(Lmation)*Lmat;
//matrix OSmat=inverseofLmation*Lmat;
matrix Smat=OSmat;
/* orthogonalisation of S */
for (k=0;k<(3*natom-6);k++) {
double proj1=0.0;
for (i=0;i<(3*natom-6);i++) {
proj1+=Smat(i,k)*Smat(i,k);
} proj1=sqrt(proj1);
for (i=0;i<(3*natom-6);i++) {
Smat(i,k)=Smat(i,k)/proj1;
}
for (j=k+1;j<(3*natom-6);j++) {
proj1=0.0;
for (i=0;i<(3*natom-6);i++) {
proj1+=Smat(i,k)*Smat(i,j);
} for (i=0;i<(3*natom-6);i++) {
Smat(i,j)=Smat(i,j)-Smat(i,k)*proj1;
}
}
}
if (ortho_of_S == 'N') Smat=OSmat;
matrix orthoS=transpose(Smat)*Smat;
matrix orthoL=transpose(Lmat)*Lmat;
matrix orthoLion=transpose(Lmation)*Lmation;
/* output of the S matrix */
std::strstream Smatrixname;
Smatrixname <<filenamein.str()<<".S.mat"<<ends;
ofstream Smatrix(Smatrixname.str());
std::strstream OrSname;
OrSname<<filenamein.str()<<".OrS.mat"<<ends;
ofstream OrS(OrSname.str());
for (i=0;i<(3*natom-6);i++) {
for (j=0;j<(3*natom-6);j++) {
Smatrix.precision(2);
Smatrix.width(8);
Smatrix<<Smat(i,j)<<" ";
OrS.precision(2);
OrS.width(8);
OrS<<orthoS(i,j)<<" ";
}
Smatrix<<std::endl;
OrS<<std::endl;
}
OrS<<"L^t L"<<std::endl;
for (i=0;i<(3*natom-6);i++) {
for (j=0;j<(3*natom-6);j++) {
OrS.precision(2);
OrS.width(8);
OrS<<orthoL(i,j)<<" ";
}
OrS<<std::endl;
}
OrS<<"L^t L (ion)"<<std::endl;
for (i=0;i<(3*natom-6);i++) {
for (j=0;j<(3*natom-6);j++) {
OrS.precision(2);
OrS.width(8);
OrS<<orthoLion(i,j)<<" ";
}
OrS<<std::endl;
}
//vector dvec=inverseofLmation*Rvecmass;
vector dvec=transpose(Lmation)*Rvecmass;
std::strstream dvecfilename;
dvecfilename<<filenamein.str()<<".d.vec"<<ends;
ofstream dvecfile(dvecfilename.str());
for (i=0;i<(3*natom-6);i++) {
dvecfile.precision(2);
dvecfile.width(8);
dvecfile<<dvec(i)<<" ";
}
dvecfile<<std::endl;
/* for sharp initial in terms of final */
matrix Jmat=transpose(Lmat)*Lmation;
//matrix Jmat=inverseofLmat*Lmation;
vector K=transpose(Lmat)*sqmass*(geoc-geon);
//vector K=inverseofLmat*sqmass*(geoc-geon);
diagmat II(3*natom-6);
for (j=0;j<(3*natom-6);j++) II(j)=1.;
matrix JJ=lambdaion*(Smat*inverse(lambda));
matrix Qmat=inverse((II+transpose(JJ)*JJ));
matrix Pmat=JJ*Qmat*transpose(JJ);
matrix Rmat=Qmat*transpose(JJ);
vector delta=lambdaion*dvec;
Smatrix<<std::endl;
Smatrix<<"J"<<std::endl;
for (i=0;i<(3*natom-6);i++) {
for (j=0;j<(3*natom-6);j++) {
Smatrix.precision(2);
Smatrix.width(8);
Smatrix<<JJ(i,j)<<" ";
}
Smatrix<<std::endl;
}
Smatrix<<std::endl;
Smatrix<<"P"<<std::endl;
for (i=0;i<(3*natom-6);i++) {
for (j=0;j<(3*natom-6);j++) {
Smatrix.precision(2);
Smatrix.width(8);
Smatrix<<Pmat(i,j)<<" ";
}
Smatrix<<std::endl;
}
Smatrix<<"Q"<<std::endl;
for (i=0;i<(3*natom-6);i++) {
for (j=0;j<(3*natom-6);j++) {
Smatrix.precision(2);
Smatrix.width(8);
//Smatrix<<Qmat(i,j)<<" ";
Smatrix<<(II+transpose(JJ)*JJ)(i,j)<<" ";
}
Smatrix<<std::endl;
}
Smatrix<<"R"<<std::endl;
for (i=0;i<(3*natom-6);i++) {
for (j=0;j<(3*natom-6);j++) {
Smatrix.precision(2);
Smatrix.width(8);
Smatrix<<Rmat(i,j)<<" ";
}
Smatrix<<std::endl;
}
Smatrix<<"delta"<<std::endl;
for (i=0;i<(3*natom-6);i++) {
Smatrix.precision(2);
Smatrix.width(8);
Smatrix<<delta(i)<<" ";
}
Smatrix<<std::endl;
/* <0|0> transition */
for (j=0;j<(3*natom-6);j++) int00*=(omegaion(j)/omega(j));
int00=pow(int00,.25);
int00*=exp(log(sqrt(det(Qmat)))+((double) ((3*natom-6)) /2.)*log(2.));
int00*=exp(-.5*delta*((II-Pmat)*delta));
std::cout<<"00 band "<<int00<<std::endl;
/* spectrum */
/* definition of the spectral window */
double signal,fcfac;
double o;
double length=wmax-wmin;
int size=(int) ceil(length/res);
vector sumlor(size);
vector grid(size);
for (i=0;i<size;i++) grid(i)=((double) i)*res+wmin;
int temperature=(int) T;
std::strstream specname;
std::strstream specfname;
specname<<filenamein.str()<<".sticks.out"<<ends;
specfname<<filenamein.str()<<".spec.out"<<ends;
ofstream spec(specname.str());
ofstream specf(specfname.str());
std::strstream fcfilename;
fcfilename<<filenamein.str()<<".fc.tex"<<ends;
ofstream fcfile(fcfilename.str());
fcfile<<"\\documentstyle[preprint,aps]{revtex}"<<std::endl;
fcfile<<"\\begin{document}"<<std::endl;
fcfile<<"\\include{epsf}"<<std::endl;
fcfile<<"\\unitlength1in"<<std::endl;
fcfile<<"\\renewcommand{\\baselinestretch}{1.5}"<<std::endl;
fcfile<<"\\begin{table}"<<std::endl;
fcfile<<"\\begin{tabular}{rcrrr}"<<std::endl;
fcfile<<"Peak& Assignment&Position (cm$^{-1}$)";
fcfile<<"& Rel. FC factor& Signal\\\\"<<std::endl;
fcfile<<"\\hline"<<std::endl;
fcfile.precision(3);
fcfile.setf(ios::fixed,ios::floatfield);
labellimit/=(int00*int00);
/* <0|0> band */
int fccount=0;
pos=v00;
if (pos <wmax && pos >wmin) {
signal=1.;
//modification below and to all signal output to spec file
spec<<pos<<" "<<signal*(int00*int00)<<std::endl;
fccount+=1;
fcfile<<fccount<<"& $1^0_0$&"<<pos<<"&1&1\\\\"<<std::endl;
sumlor=sumlor+lor(pos,signal,size,gamma,grid);
}
std::cout<<"start recursive calculation"<<std::endl;
int istart=1;
int jstart=1;
int kstart=1;
int lstart=1;
int mstart=1;
int nstart=1;
for (modei=0;modei<(numberofactivemodes);modei++) {
/* <i|0> */
ni=cationquanta;
vector t=singlecold(ni,
modei,
Pmat,II,delta);
moden=0; n=0;
modem=0; m=0;
model=0; l=0;
modek=0; k=0;
modej=0; j=0;
for (i=istart;i<ni;i++) {
pos=position(
modei,modej,modek,
model,modem,moden,
i,j,k,l,m,n,
omegaion,omega);
pos+=v00;
if (pos <wmax && pos >wmin) {
o=t(((((i)))));
fcfac=o*o/(int00*int00);
signal=fcfac*
boltzman((omega(model)*((double) l)/T
+omega(modem)*((double) m)/T
+omega(moden)*((double) n)/T));
sumlor=sumlor+lor(pos,signal,size,gamma,grid);
if (signal >= labellimit ) {
spec<<pos<<" "<<signal*(int00*int00)<<std::endl;
fccount+=1;
fcfile<<fccount<<"&$";
fcfile<<modei+1<<"_"<<l<<"^"<<i<<"$& ";
fcfile<<pos;
fcfile<<"& "<<fcfac<<"& "<<signal<<"\\\\"<<std::endl;
}
}
}
/* <0|i> */
ni=neutralquanta;
vector thot=singlehot(ni,
modei,
Qmat,Rmat,delta);
moden=0; n=0;
modem=0; m=0;
model=0; l=0;
modek=0; k=0;
modej=0; j=0;
for (i=istart;i<ni;i++) {
pos=position(
modej,modej,modek,
modei,modem,moden,
j,j,k,i,m,n,
omegaion,omega);
pos+=v00;
if (pos <wmax && pos >wmin) {
o=thot(((((i)))));
fcfac=o*o/(int00*int00);
signal=fcfac*
boltzman((omega(modei)*((double) i)/T
+omega(modem)*((double) m)/T
+omega(moden)*((double) n)/T));
sumlor=sumlor+lor(pos,signal,size,gamma,grid);
if (signal >= labellimit ) {
spec<<pos<<" "<<signal*(int00*int00)<<std::endl;
fccount+=1;
fcfile<<fccount<<"&$";
fcfile<<modei+1<<"_"<<i<<"^"<<l<<"&$ ";
fcfile<<pos;
fcfile<<"& "<<fcfac<<"& "<<signal<<"\\\\"<<std::endl;
}
}
}
for (modej=0;modej<(numberofactivemodes);modej++) {
/* <i|j> */
ni=cationquanta;
nj=neutralquanta;
vector t=ijhot(ni,nj,modei,modej,Pmat,Qmat,Rmat,II,delta);
moden=0; n=0;
modem=0; m=0;
model=0; l=0;
modek=0; k=0;
for (i=istart;i<ni;i++) {
for (j=jstart;j<nj;j++) {
pos=position(
modei,modek,modek,
modej,modem,moden,
i,k,k,j,m,n,
omegaion,omega);
pos+=v00;
if (pos <wmax && pos >wmin) {
o=t(((((i*nj+j)))));
fcfac=o*o/(int00*int00);
signal=fcfac*
boltzman((omega(modej)*((double) j)/T
+omega(modem)*((double) m)/T
+omega(moden)*((double) n)/T));
sumlor=sumlor+lor(pos,signal,size,gamma,grid);
if (signal >= labellimit ) {
spec<<pos<<" "<<signal*(int00*int00)<<std::endl;
fccount+=1;
fcfile<<fccount<<"&$";
fcfile<<modei+1<<"_"<<l<<"^"<<i<<" ";
fcfile<<modej+1<<"_"<<j<<"^"<<l<<"$& ";
fcfile<<pos;
fcfile<<"& "<<fcfac<<"& "<<signal<<"\\\\"<<std::endl;
}
}
}
}
}
for (modej=(modei+1);modej<numberofactivemodes;modej++) {
/* <ij|0> */
ni=cationquanta/2+1;
nj=cationquanta/2+1;
vector t=doublecold(ni,nj,
modei,modej,
Pmat,II,delta);
moden=0; n=0;
modem=0; m=0;
model=0; l=0;
modek=0; k=0;
for (i=istart;i<ni;i++) {
for (j=jstart;j<nj;j++) {
pos=position(
modei,modej,modek,
model,modem,moden,
i,j,k,l,m,n,
omegaion,omega);
pos+=v00;
if (pos <wmax && pos >wmin) {
o=t(((((i*nj+j)))));
fcfac=o*o/(int00*int00);
signal=fcfac*
boltzman((omega(model)*((double) l)/T
+omega(modem)*((double) m)/T
+omega(moden)*((double) n)/T));
sumlor=sumlor+lor(pos,signal,size,gamma,grid);
if (signal >= labellimit ) {
spec<<pos<<" "<<signal*(int00*int00)<<std::endl;
fccount+=1;
fcfile<<fccount<<"&$";
fcfile<<modei+1<<"_"<<l<<"^"<<i<<" ";
fcfile<<modej+1<<"_"<<m<<"^"<<j<<"$& ";
fcfile<<pos;
fcfile<<"& "<<fcfac<<"& "<<signal<<"\\\\"<<std::endl;
}
}
}
}
/* <0|ij> */
ni=neutralquanta/2+1;
nj=neutralquanta/2+1;
vector t2=doublehot(ni,nj,
modei,modej,
Qmat,Rmat,delta);
moden=0; n=0;
modem=0; m=0;
model=0; l=0;
modek=0; k=0;
for (i=istart;i<ni;i++) {
for (j=jstart;j<nj;j++) {
pos=position(
modek,modek,modek,
modei,modej,moden,
k,k,k,i,j,n,
omegaion,omega);
pos+=v00;
if (pos <wmax && pos >wmin) {
o=t2(((((i*nj+j)))));
fcfac=o*o/(int00*int00);
signal=fcfac*
boltzman((omega(modei)*((double) i)/T
+omega(modej)*((double) j)/T
+omega(moden)*((double) n)/T));
sumlor=sumlor+lor(pos,signal,size,gamma,grid);
if (signal >= labellimit ) {
spec<<pos<<" "<<signal*(int00*int00)<<std::endl;
fccount+=1;
fcfile<<fccount<<"&$";
fcfile<<modei+1<<"_"<<i<<"^"<<l<<" ";
fcfile<<modej+1<<"_"<<j<<"^"<<l<<"$& ";
fcfile<<pos;
fcfile<<"& "<<fcfac<<"& "<<signal<<"\\\\"<<std::endl;
}
}
}
}
for (modek=0;modek<(numberofactivemodes);modek++) {
/* <ij|k> */
ni=cationquanta/2 +1;
nj=cationquanta/2 +1;
nk=neutralquanta;
vector t=ijkhot(ni,nj,nk,
modei,modej,modek,Pmat,Qmat,Rmat,II,delta);
moden=0; n=0;
modem=0; m=0;
model=0; l=0;
for (i=istart;i<ni;i++) {
for (j=jstart;j<nj;j++) {
for (k=kstart;k<nk;k++) {
pos=position(
modei,modej,model,
modek,modem,moden,
i,j,l,k,m,n,
omegaion,omega);
pos+=v00;
if (pos <wmax && pos >wmin) {
o=t(((((i*nj+j)*nk+k))));
fcfac=o*o/(int00*int00);
signal=fcfac*
boltzman((omega(modek)*((double) k)/T
+omega(modem)*((double) m)/T
+omega(moden)*((double) n)/T));
sumlor=sumlor+lor(pos,signal,size,gamma,grid);
if (signal >= labellimit ) {
spec<<pos<<" "<<signal*(int00*int00)<<std::endl;
fccount+=1;
fcfile<<fccount<<"&$";
fcfile<<modei+1<<"_"<<l<<"^"<<i<<" ";
fcfile<<modej+1<<"_"<<m<<"^"<<j<<" ";
fcfile<<modek+1<<"_"<<k<<"^"<<l<<"$& ";
fcfile<<pos;
fcfile<<"& "<<fcfac<<"& "<<signal<<"\\\\"<<std::endl;
}
}
}
}
}
/* <k|ij> */
nk=cationquanta;
nj=neutralquanta/2+1;
ni=neutralquanta/2+1;
vector t3=iklhot(nk,ni,nj,modek,modei,modej,Pmat,Qmat,Rmat,II,delta);
moden=0; n=0;
modem=0; m=0;
model=0; l=0;
for (i=istart;i<ni;i++) {
for (j=jstart;j<nj;j++) {
for (k=kstart;k<nk;k++) {
pos=position(
modek,model,model,
modei,modej,moden,
k,l,l,i,j,n,
omegaion,omega);
pos+=v00;
if (pos <wmax && pos >wmin) {
o=t3(((((k*ni+i)*nj+j))));
fcfac=o*o/(int00*int00);
signal=fcfac*
boltzman((omega(modei)*((double) i)/T
+omega(modej)*((double) j)/T
+omega(moden)*((double) n)/T));
sumlor=sumlor+lor(pos,signal,size,gamma,grid);
if (signal >= labellimit ) {
spec<<pos<<" "<<signal*(int00*int00)<<std::endl;
fccount+=1;
fcfile<<fccount<<"&$";
fcfile<<modei+1<<"_"<<i<<"^"<<l<<" ";
fcfile<<modej+1<<"_"<<j<<"^"<<l<<" ";
fcfile<<modek+1<<"_"<<n<<"^"<<k<<"$& ";
fcfile<<pos;
fcfile<<"& "<<fcfac<<"& "<<signal<<"\\\\"<<std::endl;
}
}
}
}
}
for (model=(modek+1);model<(numberofactivemodes);model++) {
/* <ij|kl> */
ni=cationquanta/2 +1;
nj=cationquanta/2 +1;
nk=neutralquanta/2+1;
nl=neutralquanta/2+1;
vector t=ijklhot(ni,nj,nk,nl,modei,modej,modek,model,
Pmat,Qmat,Rmat,II,delta);
moden=0; n=0;
modem=0; m=0;
for (i=istart;i<ni;i++) {
for (j=jstart;j<nj;j++) {
for (k=kstart;k<nk;k++) {
for (l=lstart;l<nl;l++) {
pos=position(
modei,modej,moden,
modek,model,moden,
i,j,n,k,l,n,
omegaion,omega);
pos+=v00;
if (pos <wmax && pos >wmin) {
o=t(((((i*nj+j)*nk+k)*nl+l)));
fcfac=o*o/(int00*int00);
signal=fcfac*
boltzman((omega(modek)*((double) k)/T
+omega(model)*((double) l)/T
+omega(moden)*((double) n)/T));
sumlor=sumlor+lor(pos,signal,size,gamma,grid);
if (signal >= labellimit ) {
spec<<pos<<" "<<signal*(int00*int00)<<std::endl;
fccount+=1;
fcfile<<fccount<<"&$";
fcfile<<modei+1<<"_"<<m<<"^"<<i<<" ";
fcfile<<modej+1<<"_"<<m<<"^"<<j<<" ";
fcfile<<modek+1<<"_"<<k<<"^"<<n<<" ";
fcfile<<model+1<<"_"<<l<<"^"<<n<<"$& ";
fcfile<<pos;
fcfile<<"& "<<fcfac<<"& "<<signal<<"\\\\"<<std::endl;
}
}
}
}
}
}
}