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add projected hessian for removing translations and rotations
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Signed-off-by: conradhuebler <[email protected]>
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@conradhuebler
conradhuebler committed Aug 20, 2023
1 parent 49b844d commit 4aba1b4
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Showing 2 changed files with 92 additions and 53 deletions.
139 changes: 87 additions & 52 deletions src/core/hessian.cpp
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Original file line number Diff line number Diff line change
Expand Up @@ -22,7 +22,7 @@
// #include <catch2/catch_test_macros.hpp>
// #include <catch2/generators/catch_generators_all.hpp>

// #include <finitediff.hpp>
#include <finitediff.hpp>
// #include <spdlog/spdlog.h>

#include "external/CxxThreadPool/include/CxxThreadPool.h"
Expand All @@ -31,7 +31,7 @@

#include "hessian.h"

// using namespace fd;
using namespace fd;

HessianThread::HessianThread(const std::string& method, const json& controller, int i, int j, int xi, int xj, bool fullnumerical)
: m_method(method)
Expand All @@ -45,7 +45,7 @@ HessianThread::HessianThread(const std::string& method, const json& controller,
setAutoDelete(true);

if (m_fullnumerical)
m_schema = [this]() {
m_schema = [this, i, j, xi, xj]() {
this->Numerical();
};
else
Expand All @@ -71,8 +71,6 @@ int HessianThread::execute()

void HessianThread::Numerical()
{
m_d = 5e-3;

m_geom_ip_jp = m_molecule.Coords();
m_geom_im_jp = m_molecule.Coords();
m_geom_ip_jm = m_molecule.Coords();
Expand Down Expand Up @@ -109,7 +107,6 @@ void HessianThread::Numerical()
}
void HessianThread::Seminumerical()
{
m_d = 5e-3;
m_geom_ip_jp = m_molecule.Coords();
m_geom_im_jp = m_molecule.Coords();

Expand All @@ -127,25 +124,29 @@ void HessianThread::Seminumerical()
energy.updateGeometry(m_geom_im_jp);
double energy_im_jp = energy.CalculateEnergy(true, false);
Matrix gradientm = energy.Gradient();
// std::cout << gradientp << std::endl << std::endl << gradientm << std::endl;
m_gradient = (gradientp - gradientm) / (2 * m_d) / au / au;
// std::cout << m_gradient << std::endl << std::endl;
}

Hessian::Hessian(const std::string& method, const json& controller, int threads)
: m_method(method)
, m_controller(controller)
, m_threads(threads)
{
/* Yeah, thats not really correct, but it works a bit */
if (m_method.compare("gfnff") == 0) {
m_scale_functions = [](double val) -> double {
return val * 2720.57 - 0.0338928;
};
} else {
m_scale_functions = [](double val) -> double {
return val * 2720.57 - 0.0338928;
};
}
}

void Hessian::setMolecule(const Molecule& molecule)
{
m_molecule = molecule;
// std::cout << m_molecule.Centroid().transpose() << std::endl;
// m_molecule.Center(false);
// m_molecule.AlignAxis();
// std::cout << m_molecule.Centroid().transpose() << std::endl;
}

void Hessian::CalculateHessian(int type)
Expand All @@ -157,67 +158,102 @@ void Hessian::CalculateHessian(int type)
else if (type == 3) {
std::cout << "external hessian approach not implemented" << std::endl;
std::cout << "use -hessian 1 or -hessian 2" << std::endl;
// FiniteDiffHess();
FiniteDiffHess();
}
auto eigenvalues = ConvertHessian(m_hessian);
auto hessian2 = ProjectHessian(m_hessian);
auto projected = ConvertHessian(hessian2);

auto freqs = ConvertHessian(m_hessian);
PrintVibrations(eigenvalues, projected);
}

Vector Hessian::ConvertHessian(Matrix& hessian)
Matrix Hessian::ProjectHessian(const Matrix& hessian)
{
// std::cout << hessian << std::endl;
{
Eigen::SelfAdjointEigenSolver<Geometry> diag_I;
diag_I.compute(hessian);
// std::cout << diag_I.eigenvalues().cwiseSqrt() << std::endl;
Matrix D = Eigen::MatrixXd::Random(3 * m_molecule.AtomCount(), 3 * m_molecule.AtomCount());
Eigen::RowVector3d ex = { 1, 0, 0 };
Eigen::RowVector3d ey = { 0, 1, 0 };
Eigen::RowVector3d ez = { 0, 0, 1 };

for (int i = 0; i < 3 * m_molecule.AtomCount(); ++i) {
D(i, 0) = int(i % 3 == 0);
D(i, 2) = int((i + 1) % 3 == 0);
D(i, 1) = int((i + 2) % 3 == 0);
}

for (int i = 0; i < m_molecule.AtomCount(); ++i) {
auto dx = ex.cross(m_molecule.Atom(i).second);
auto dy = ey.cross(m_molecule.Atom(i).second);
auto dz = ez.cross(m_molecule.Atom(i).second);

D(3 * i, 3) = dx(0);
D(3 * i + 1, 3) = dx(1);
D(3 * i + 2, 3) = dx(2);

D(3 * i, 4) = dy(0);
D(3 * i + 1, 4) = dy(1);
D(3 * i + 2, 4) = dy(2);

D(3 * i, 5) = dz(0);
D(3 * i + 1, 5) = dz(1);
D(3 * i + 2, 5) = dz(2);
}

Eigen::MatrixXd XtX = D.transpose() * D;
Eigen::SelfAdjointEigenSolver<Eigen::MatrixXd> es(XtX);
Eigen::MatrixXd S = es.operatorInverseSqrt();
Matrix R = D * S;
Matrix f = R.transpose() * hessian * R;
for (int i = 0; i < 3 * m_molecule.AtomCount(); ++i) {
for (int j = 0; j < 3 * m_molecule.AtomCount(); ++j) {
if (i < 6 || j < 6)
f(i, j) = 0;
}
}
return f;
}

Vector Hessian::ConvertHessian(Matrix& hessian)
{
Vector vector;
constexpr double Eh_to_cm = 27.211386 * 8065.54;
double Eh_to_Ha = 1.0 / 27.211386; // convert from Eh to Ha
double Ha_to_eV = 27.211386; // convert from Ha to eV
double amu_to_kg = 1.66054E-27; // convert from amu to kg
double Angstrom_to_m = 1E-10; // convert from Angstrom to meters
double c = 2.99792E10; // speed of light in cm/s
double h = 6.62607E-34; // Planck's constant in J*s
double eV_to_cm_inv = 8065.54; // convert from eV to cm^-1
const double conv = 1.0e12; // conversion factor from Angstroms to cm
auto amu = m_molecule.Atoms();

for (int i = 0; i < m_molecule.AtomCount() * 3; i++) {
for (int j = 0; j < m_molecule.AtomCount() * 3; j++) {
double mass = 1 / sqrt(Elements::AtomicMass[m_molecule.Atoms()[i / 3]] * Elements::AtomicMass[m_molecule.Atoms()[j / 3]]);

hessian(i, j) *= Ha_to_eV; // convert from Eh/A^2 to eV/A^2
hessian(i, j) /= (Angstrom_to_m * Angstrom_to_m); // from A^2 to m^2
hessian(i, j) *= mass * amu_to_kg; // sqrt(Elements::AtomicMass[amu[i/3]]*Elements::AtomicMass[amu[j/3]]); // convert from Ha/m^2 to Ha/(amu*m^2)
hessian(i, j) *= mass;
}
}

Eigen::SelfAdjointEigenSolver<Geometry> diag_I;
diag_I.compute(hessian);
return diag_I.eigenvalues();
}

vector = diag_I.eigenvalues().cwiseSqrt();
// std::cout << vector.transpose() << std::endl;
/* this conversation factor has to be made pure unit based ... */
vector *= 1.2796e+06; //(2.0 * M_PI * c) * eV_to_cm_inv*conv; // / sqrt(Elements::AtomicMass[amu[i/3]]);
// std::cout << eV_to_cm_inv*conv/(2.0 * M_PI * c) << std::endl;
// vector *= Ha_to_eV*eV_to_cm_inv*conv/(2.0 * M_PI * c);
// std::cout << vector.transpose() << std::endl;

void Hessian::PrintVibrations(Vector& eigenvalues, const Vector& projected)
{
Vector eigval = eigenvalues.cwiseSqrt();
std::cout << std::endl
<< " Frequencies: " << std::endl;

for (int i = 0; i < m_molecule.AtomCount() * 3; ++i) {
if (i % 6 == 0)
std::cout << std::endl;
if (diag_I.eigenvalues()(i) < 0)
std::cout << sqrt(std::abs(diag_I.eigenvalues()(i))) * 1.2796e+06 << "(i)"
if (projected(i) < 0)
std::cout << m_scale_functions(sqrt(std::abs(eigenvalues(i)))) << "(i) "
<< " ";
else
std::cout << vector(i) << " ";
else {
if (projected(i) < 1e-10) {
std::cout << projected(i) << "(*) ";

} else {
if (eigenvalues(i) < 0)
std::cout << m_scale_functions(sqrt(std::abs(eigenvalues(i)))) << "(*) "
<< " ";
else
std::cout << m_scale_functions(eigval(i)) << " ";
}
}
}
std::cout << std::endl;
return vector;
}

void Hessian::CalculateHessianNumerical()
Expand Down Expand Up @@ -295,7 +331,7 @@ void Hessian::CalculateHessianSemiNumerical()

void Hessian::FiniteDiffHess()
{
/*

m_hessian = Eigen::MatrixXd::Ones(3 * m_molecule.AtomCount(), 3 * m_molecule.AtomCount());

EnergyCalculator energy(m_method, m_controller);
Expand All @@ -314,11 +350,10 @@ void Hessian::FiniteDiffHess()
x(3*i + 2) = m_molecule.Atom(i).second[2];

}
Eigen::MatrixXd hess = Eigen::MatrixXd::Zero(3 * m_molecule.AtomCount(), 3 * m_molecule.AtomCount());
// Eigen::MatrixXd hess = Eigen::MatrixXd::Zero(3 * m_molecule.AtomCount(), 3 * m_molecule.AtomCount());

Eigen::MatrixXd fhess;
fd::finite_hessian(x, f, fhess, fd::EIGHTH);
fd::finite_hessian(x, f, fhess, fd::SECOND);

m_hessian = fhess;
*/
m_hessian = fhess / au / au;
}
6 changes: 5 additions & 1 deletion src/core/hessian.h
View file
Original file line number Diff line number Diff line change
Expand Up @@ -57,7 +57,7 @@ class HessianThread : public CxxThread {
int m_i, m_j, m_xi, m_xj;
bool m_fullnumerical = true;
double m_dd = 0;
double m_d = 1e-5;
double m_d = 5e-3;
};

class Hessian {
Expand All @@ -68,11 +68,15 @@ class Hessian {

void CalculateHessian(int type = 1);

void PrintVibrations(Vector& eigenvalues, const Vector& projected);

private:
void CalculateHessianNumerical();
void CalculateHessianSemiNumerical();
void FiniteDiffHess();
std::function<double(double)> m_scale_functions;

Matrix ProjectHessian(const Matrix& hessian);
Vector ConvertHessian(Matrix& hessian);

Matrix m_eigen_geometry, m_eigen_gradient, m_hessian;
Expand Down

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