// MomentOfInertia()
static void MomentOfInertia(int natom, const double *X_, const double* Mass_, double* pmom)
{
Matrix_3x3 IVEC;
Vec3 eval;
// Center of mass
double cx = 0.0;
double cy = 0.0;
double cz = 0.0;
double sumMass = 0.0;
const double* mass = Mass_;
int natom3 = natom * 3;
for (int i = 0; i < natom3; i+=3) {
sumMass += (*mass);
cx += ( X_[i ] * (*mass) );
cy += ( X_[i+1] * (*mass) );
cz += ( X_[i+2] * (*mass) );
++mass;
}
cx /= sumMass;
cy /= sumMass;
cz /= sumMass;
// Moment of inertia
double xx = 0.0;
double yy = 0.0;
double zz = 0.0;
double xy = 0.0;
double xz = 0.0;
double yz = 0.0;
mass = Mass_;
for (int i = 0; i < natom3; i+=3) {
double dx = X_[i ] - cx;
double dy = X_[i+1] - cy;
double dz = X_[i+2] - cz;
xx += *mass * ( dy * dy + dz * dz );
yy += *mass * ( dx * dx + dz * dz );
zz += *mass * ( dx * dx + dy * dy );
xy -= *mass * dx * dy;
xz -= *mass * dx * dz;
yz -= *(mass++) * dy * dz;
}
IVEC[0] = xx;
IVEC[1] = xy;
IVEC[2] = xz;
IVEC[3] = xy;
IVEC[4] = yy;
IVEC[5] = yz;
IVEC[6] = xz;
IVEC[7] = yz;
IVEC[8] = zz;
// NOTE: Diagonalize sorts evals/evecs in descending order, but
// thermo() expects ascending.
IVEC.Diagonalize_Sort( eval );
pmom[0] = eval[2];
pmom[1] = eval[1];
pmom[2] = eval[0];
}
/** Given the structure of a molecule and its normal mode vibrational
* frequencies this routine uses standard statistical mechanical
* formulas for an ideal gas (in the canonical ensemble, see,
* for example, d. a. mcquarrie, "statistical thermodynamics",
* harper & row, new york, 1973, chapters 5, 6, and 8) to compute
* the entropy, heat capacity, and internal energy.
* The si system of units is used internally. Conversion to units
* more familiar to most chemists is made for output.
*
* \param outfile output file, should already be open.
* \param temp temperature
* \param patm pressure, in atmospheres
*/
int DataSet_Modes::Thermo( CpptrajFile& outfile, int ilevel, double temp, double patm) const
{
// avgcrd_ Contains coordinates in Angstroms
// mass_ Contains masses in amu.
// nmodes_ Number of eigenvectors (already converted to frequencies)
// evalues_ vibrational frequencies, in cm**-1 and in ascending order
double rtemp, rtemp1, rtemp2, rtemp3;
// ----- Constants -------------------
const double thresh = 900.0; // vibrational frequency threshold
const double tokg = 1.660531e-27; // kilograms per amu.
const double boltz = 1.380622e-23; // boltzman constant, in joules per kelvin.
const double planck = 6.626196e-34; // planck constant, in joule-seconds.
// const double avog = 6.022169e+23; // avogadro constant, in mol**(-1).
const double jpcal = 4.18674e+00; // joules per calorie.
const double tomet = 1.0e-10; // metres per Angstrom.
const double hartre = 4.35981e-18; // joules per hartree.
const double pstd = 1.01325e+05; // Standard pressure in pascals
// compute the gas constant, pi, pi**2, and e.
// compute the conversion factors cal per joule and kcal per joule.
// const double gas = avog * boltz;
// pi = four * datan(one)
const double pipi = Constants::PI * Constants::PI;
const double e = exp(1.0);
const double tocal = 1.0 / jpcal;
const double tokcal = tocal / 1000.0;
if (!outfile.IsOpen()) {
mprinterr("Internal Error: DataSet_Modes::Thermo(): output file is not open.\n");
return 1;
}
// print the temperature and pressure.
outfile.Printf("\n *******************\n");
outfile.Printf( " - Thermochemistry -\n");
outfile.Printf( " *******************\n\n");
outfile.Printf("\n temperature %9.3f kelvin\n pressure %9.5f atm\n",temp,patm);
double pressure = pstd * patm;
double rt = Constants::GASK_J * temp;
// compute and print the molecular mass in amu, then convert to
// kilograms.
double weight = 0.0;
for (Darray::const_iterator m = mass_.begin(); m != mass_.end(); ++m)
weight += *m;
outfile.Printf(" molecular mass (principal isotopes) %11.5f amu\n", weight);
weight *= tokg;
//trap non-unit multiplicities.
//if (multip != 1) {
// outfile.Printf("\n Warning-- assumptions made about the electronic partition function\n");
// outfile.Printf( " are not valid for multiplets!\n\n");
//}
// compute contributions due to translation:
// etran-- internal energy
// ctran-- constant v heat capacity
// stran-- entropy
double dum1 = boltz * temp;
double dum2 = pow(Constants::TWOPI, 1.5);
double arg = pow(dum1, 1.5) / planck;
arg = (arg / pressure) * (dum1 / planck);
arg = arg * dum2 * (weight / planck);
arg = arg * sqrt(weight) * exp(2.5);
double stran = Constants::GASK_J * log(arg);
double etran = 1.5 * rt;
double ctran = 1.5 * Constants::GASK_J;
// Compute contributions due to electronic motion:
// It is assumed that the first electronic excitation energy
// is much greater than kt and that the ground state has a
// degeneracy of one. Under these conditions the electronic
// partition function can be considered to be unity. The
// ground electronic state is taken to be the zero of
// electronic energy.
// for monatomics print and return.
if (avgcrd_.size() <= 3){
outfile.Printf("\n internal energy: %10.3f joule/mol %10.3f kcal/mol\n",
etran, etran * tokcal);
outfile.Printf( " entropy: %10.3f joule/k-mol %10.3f cal/k-mol\n",
stran, stran * tocal);
outfile.Printf( " heat capacity cv: %10.3f joule/k-mol %10.3f cal/k-mol\n",
ctran, ctran * tocal);
return 0;
}
Frame AVG;
AVG.SetupFrameXM( avgcrd_, mass_ );
// Allocate workspace memory
// vtemp vibrational temperatures, in kelvin.
// evibn contribution to e from the vibration n.
// cvibn contribution to cv from the vibration n.
// svibn contribution to s from the vibration n.
double* WorkSpace = new double[ 4 * nmodes_ ];
double* vtemp = WorkSpace;
double* evibn = WorkSpace + nmodes_;
double* cvibn = WorkSpace + nmodes_*2;
double* svibn = WorkSpace + nmodes_*3;
// compute contributions due to rotation.
// Compute the principal moments of inertia, get the rotational
// symmetry number, see if the molecule is linear, and compute
// the rotational temperatures. Note the imbedded conversion
// of the moments to SI units.
Matrix_3x3 Inertia;
AVG.CalculateInertia( AtomMask(0, AVG.Natom()), Inertia );
// NOTE: Diagonalize_Sort sorts evals/evecs in descending order, but
// thermo() expects ascending.
// pmom principal moments of inertia, in amu-bohr**2 and in ascending order.
Vec3 pmom;
Inertia.Diagonalize_Sort( pmom );
rtemp = pmom[0];
pmom[0] = pmom[2];
pmom[2] = rtemp;
outfile.Printf("\n principal moments of inertia (nuclei only) in amu-A**2:\n");
outfile.Printf( " %12.2f%12.2f%12.2f\n", pmom[0], pmom[1], pmom[2]);
bool linear = false;
// Symmetry number: only for linear molecules. for others symmetry number is unity
double sn = 1.0;
if (AVG.Natom() <= 2) {
linear = true;
if (AVG.Mass(0) == AVG.Mass(1)) sn = 2.0;
}
outfile.Printf("\n rotational symmetry number %3.0f\n", sn);
double con = planck / (boltz*8.0*pipi);
con = (con / tokg) * (planck / (tomet*tomet));
if (linear) {
rtemp = con / pmom[2];
if (rtemp < 0.2) {
outfile.Printf("\n Warning-- assumption of classical behavior for rotation\n");
outfile.Printf( " may cause significant error\n");
}
outfile.Printf("\n rotational temperature (kelvin) %12.5f\n", rtemp);
} else {
rtemp1 = con / pmom[0];
rtemp2 = con / pmom[1];
rtemp3 = con / pmom[2];
if (rtemp1 < 0.2) {
outfile.Printf("\n Warning-- assumption of classical behavior for rotation\n");
outfile.Printf( " may cause significant error\n");
}
outfile.Printf("\n rotational temperatures (kelvin) %12.5f%12.5f%12.5f\n",
rtemp1, rtemp2, rtemp3);
}
// erot-- rotational contribution to internal energy.
// crot-- rotational contribution to cv.
// srot-- rotational contribution to entropy.
double erot, crot, srot;
if (linear) {
erot = rt;
crot = Constants::GASK_J;
arg = (temp/rtemp) * (e/sn);
srot = Constants::GASK_J * log(arg);
} else {
erot = 1.5 * rt;
crot = 1.5 * Constants::GASK_J;
arg = sqrt(Constants::PI*e*e*e) / sn;
double dum = (temp/rtemp1) * (temp/rtemp2) * (temp/rtemp3);
arg = arg * sqrt(dum);
srot = Constants::GASK_J * log(arg);
}
// compute contributions due to vibration.
// compute vibrational temperatures and zero point vibrational
// energy. only real frequencies are included in the analysis.
// ndof = 3*natoms - 6 - nimag
// if (nimag .ne. 0) write(iout,1210) nimag
// if (linear) ndof = ndof + 1
int ndof = nmodes_;
// (---iff is the first frequency to include in thermo:)
int iff;
if (ilevel != 0)
iff = 0;
else if (linear)
iff = 5;
else
iff = 6;
con = planck / boltz;
double ezpe = 0.0;
for (int i = 0; i < ndof; ++i) {
vtemp[i] = evalues_[i+iff] * con * 3.0e10;
ezpe += evalues_[i+iff] * 3.0e10;
}
ezpe = 0.5 * planck * ezpe;
outfile.Printf("\n zero point vibrational energy %12.1f (joules/mol) \n"
" %12.5f (kcal/mol)\n"
" %12.7f (hartree/particle)\n",
ezpe*Constants::NA, ezpe*tokcal*Constants::NA, ezpe/hartre);
// compute the number of vibrations for which more than 5% of an
// assembly of molecules would exist in vibrational excited states.
// special printing for these modes is done to allow the user to
// easily take internal rotations into account. the criterion
// corresponds roughly to a low frequency of 1.9(10**13) hz, or
// 625 cm**(-1), or a vibrational temperature of 900 k.
int lofreq = 0;
for (int i = 0; i < ndof; ++i)
if (vtemp[i] < thresh)
++lofreq;
if (lofreq != 0) {
outfile.Printf("\n Warning-- %3i vibrations have low frequencies and may represent hindered \n",
lofreq);
outfile.Printf( " internal rotations. The contributions printed below assume that these \n");
outfile.Printf( " really are vibrations.\n");
}
// compute:
// evib-- the vibrational component of the internal energy.
// cvib-- the vibrational component of the heat capacity.
// svib-- the vibrational component of the entropy.
double evib = 0.0;
double cvib = 0.0;
double svib = 0.0;
double scont;
for (int i = 0; i < ndof; ++i) {
// compute some common factors.
double tovt = vtemp[i] / temp;
double etovt = exp(tovt);
double em1 = etovt - 1.0;
// compute contributions due to the i'th vibration.
double econt = tovt * (0.5 + 1.0/em1);
double ccont = etovt * pow(tovt/em1,2.0);
double argd = 1.0 - 1.0/etovt;
if (argd > 1.0e-7)
scont = tovt/em1 - log(argd);
else {
scont = 0.0;
outfile.Printf(" warning: setting vibrational entropy to zero for mode %i with vtemp = %f\n",
i+1, vtemp[i]);
}
// if (lofreq .ge. i) then
evibn[i] = econt * rt;
cvibn[i] = ccont * Constants::GASK_J;
svibn[i] = scont * Constants::GASK_J;
// end if
evib += econt;
cvib += ccont;
svib += scont;
}
evib *= rt;
cvib *= Constants::GASK_J;
svib *= Constants::GASK_J;
// the units are now:
// e-- joules/mol
// c-- joules/mol-kelvin
// s-- joules/mol-kelvin
double etot = etran + erot + evib;
double ctot = ctran + crot + cvib;
double stot = stran + srot + svib;
// print the sum of the hartree-fock energy and the thermal energy.
// call tread(501,gen,47,1,47,1,0)
// esum = gen(32) + etot/avog/hartre
// write(iout,1230) esum
// convert to the following and print
// e-- kcal/mol
// c-- cal/mol-kelvin
// s-- cal/mol-kelvin
etran = etran * tokcal;
ctran = ctran * tocal;
stran = stran * tocal;
erot = erot * tokcal;
crot = crot * tocal;
srot = srot * tocal;
evib = evib * tokcal;
cvib = cvib * tocal;
svib = svib * tocal;
etot = etran + erot + evib;
ctot = ctran + crot + cvib;
stot = stran + srot + svib;
for (int i = 0; i < ndof; ++i) {
evibn[i] *= tokcal;
cvibn[i] *= tocal;
svibn[i] *= tocal;
}
outfile.Printf("\n\n freq. E Cv S\n");
outfile.Printf( " cm**-1 kcal/mol cal/mol-kelvin cal/mol-kelvin\n");
outfile.Printf( "--------------------------------------------------------------------------------\n");
outfile.Printf( " Total %11.3f %11.3f %11.3f\n",etot,ctot,stot);
outfile.Printf( " translational %11.3f %11.3f %11.3f\n",etran,ctran,stran);
outfile.Printf( " rotational %11.3f %11.3f %11.3f\n",erot,crot,srot);
outfile.Printf( " vibrational %11.3f %11.3f %11.3f\n",evib,cvib,svib);
for (int i = 0; i < iff; ++i)
outfile.Printf(" %5i%10.3f\n", i+1, evalues_[i]);
for (int i = 0; i < ndof; ++i) {
outfile.Printf(" %5i%10.3f %11.3f %11.3f %11.3f\n",i+iff+1,
evalues_[i+iff], evibn[i], cvibn[i], svibn[i]);
}
delete[] WorkSpace;
return 0;
}