Functional EntropyOfIdealGas() {
Functional n = Identity();
Functional Veff = -kT*log(n);
Functional nQ = find_nQ();
Functional dnQ_dT = find_dnQ_dT();
// The following is also known as the Sackur-Tetrode equation
return ((Veff/kT + log(nQ) + Functional(2.5))*n).set_name("ideal_gas_entropy");
}
int main(int, char **argv) {
const double myT = water_prop.kT; // room temperature in Hartree
const double R = 2.7;
Functional x(Identity());
Grid n(gd);
n = 0.001*VectorXd::Ones(gd.NxNyNz) + 0.001*(-10*r2(gd)).cwise().exp();
compare_functionals(Sum(), x + kT, myT, n, 2e-13);
compare_functionals(Quadratic(), sqr(x + kT) - x + 2*kT, myT, n, 2e-12);
compare_functionals(Sqrt(), sqrt(x), myT, n, 1e-12);
compare_functionals(SqrtAndMore(), sqrt(x) - x + 2*kT, myT, n, 1e-12);
compare_functionals(Log(), log(x), myT, n, 3e-14);
compare_functionals(LogAndSqr(), log(x) + sqr(x), myT, n, 3e-14);
compare_functionals(LogAndSqrAndInverse(), log(x) + (sqr(x)-Pow(3)) + Functional(1)/x, myT, n, 3e-10);
compare_functionals(LogOneMinusX(), log(1-x), myT, n, 1e-12);
compare_functionals(LogOneMinusNbar(R), log(1-StepConvolve(R)), myT, n, 1e-13);
compare_functionals(SquareXshell(R), sqr(xShellConvolve(R)), myT, n);
Functional n2 = ShellConvolve(R);
Functional n3 = StepConvolve(R);
compare_functionals(n2_and_n3(R), sqr(n2) + sqr(n3), myT, n, 1e-14);
const double four_pi_r2 = 4*M_PI*R*R;
Functional one_minus_n3 = 1 - n3;
Functional phi1 = (-1/four_pi_r2)*n2*log(one_minus_n3);
compare_functionals(Phi1(R), phi1, myT, n, 1e-13);
const double four_pi_r = 4*M_PI*R;
Functional n2x = xShellConvolve(R);
Functional n2y = yShellConvolve(R);
Functional n2z = zShellConvolve(R);
Functional phi2 = (sqr(n2) - sqr(n2x) - sqr(n2y) - sqr(n2z))/(four_pi_r*one_minus_n3);
compare_functionals(Phi2(R), phi2, myT, n, 1e-14);
Functional phi3rf = n2*(sqr(n2) - 3*(sqr(n2x) + sqr(n2y) + sqr(n2z)))/(24*M_PI*sqr(one_minus_n3));
compare_functionals(Phi3rf(R), phi3rf, myT, n, 1e-13);
compare_functionals(AlmostRF(R), myT*(phi1 + phi2 + phi3rf), myT, n, 2e-14);
Functional veff = EffectivePotentialToDensity();
compare_functionals(SquareVeff(R), sqr(veff), myT, Grid(gd, -myT*n.cwise().log()), 1e-12);
compare_functionals(AlmostRFnokT(R), phi1 + phi2 + phi3rf, myT, n, 3e-14);
compare_functionals(AlmostRF(R),
(myT*phi1).set_name("phi1") + (myT*phi2).set_name("phi2") + (myT*phi3rf).set_name("phi3"),
myT, n, 4e-14);
compare_functionals(Phi1Veff(R), phi1(veff), myT, Grid(gd, -myT*n.cwise().log()), 1e-13);
compare_functionals(Phi2Veff(R), phi2(veff), myT, Grid(gd, -myT*n.cwise().log()), 1e-14);
compare_functionals(Phi3rfVeff(R), phi3rf(veff), myT, Grid(gd, -myT*n.cwise().log()), 1e-13);
compare_functionals(IdealGasFast(), IdealGasOfVeff, myT, Grid(gd, -myT*n.cwise().log()),
1e-12);
double mu = -1;
compare_functionals(Phi1plus(R, mu),
phi1(veff) + IdealGasOfVeff + ChemicalPotential(mu)(veff),
myT, Grid(gd, -myT*n.cwise().log()), 1e-12);
if (errors == 0) printf("\n%s passes!\n", argv[0]);
else printf("\n%s fails %d tests!\n", argv[0], errors);
return errors;
}
Functional IdealGas() {
Functional n = Identity();
Functional nQ = find_nQ();
return (kT*n*(log(n/nQ) - Functional(1))).set_name("ideal_gas");
}
Functional find_dnQ_dT() {
Functional mass = Functional(18.01528*1822.8885); // FIXME: molecular weight of water, eventually should be input parameter
// Note: hbar is one in atomic units, yay!
// nQ = (m*kT/(2 pi hbar^2))^3/2
return 1.5*PowAndHalf(3)(mass/Functional(2*M_PI))*sqrt(kT);
}
Functional find_nQ() {
Functional mass = Functional(18.01528*1822.8885); // modified 9/20/11 FIXME: molecular weight of water, eventually should be input parameter
// Note: hbar is one in atomic units, yay!
// nQ = (m*kT/(2 pi hbar^2))^3/2
return PowAndHalf(3)(mass*kT/Functional(2*M_PI));
}
Functional grad(const Functional &, const Functional &, bool) const {
return Functional(0.0);
}
}
Functional grad_T(const Functional &ingrad) const {
return ingrad;
}
void grad(const GridDescription &, double, const VectorXd &, const VectorXd &,
VectorXd *, VectorXd *) const {
}
Expression printme(const Expression &) const {
return Expression("kT").set_type("double");
}
bool append_to_name(const std::string) {
return false;
}
};
Functional kT = Functional(new Temperature(), "kT");
Functional find_nQ() {
Functional mass = Functional(18.01528*1822.8885); // modified 9/20/11 FIXME: molecular weight of water, eventually should be input parameter
// Note: hbar is one in atomic units, yay!
// nQ = (m*kT/(2 pi hbar^2))^3/2
return PowAndHalf(3)(mass*kT/Functional(2*M_PI));
}
Functional find_dnQ_dT() {
Functional mass = Functional(18.01528*1822.8885); // FIXME: molecular weight of water, eventually should be input parameter
// Note: hbar is one in atomic units, yay!
// nQ = (m*kT/(2 pi hbar^2))^3/2
return 1.5*PowAndHalf(3)(mass/Functional(2*M_PI))*sqrt(kT);
}
