void System::quantumForce(mat r, mat &qforce, double wf)
{
int N = Wavefunction->getNumberOfParticles();
int M = Wavefunction->getNumberOfDimensions();
double wf_minus, wf_plus;
mat r_plus, r_minus;
r_plus = mat(N,M);
r_minus = mat(N,M);
r_plus = r_minus = r;
double h = 1e-5;
// compute the first derivative
int i, j;
for (i=0; i<N; i++)
{
for (j=0; j<M; j++)
{
r_plus(i,j) = r(i,j) + h;
r_minus(i,j) = r(i,j) - h;
wf_plus = Wavefunction->evaluateWavefunction(r_plus);
wf_minus = Wavefunction->evaluateWavefunction(r_minus);
qforce(i,j) = (wf_plus-wf_minus);
r_minus(i,j) = r_plus(i,j) = r(i,j);
}
}
qforce = qforce*2.0/(wf*2*h);
}
mat Wavefunction::q_force() {
mat q_f = zeros(n_particles, dim);
//#if NUMERICAL
#if 0
double h = 0.05;
mat r_plus = zeros(n_particles, dim);
mat r_minus = zeros(n_particles, dim);
// Initiating r_plus and r_minus.
r_plus = r_new;
r_minus = r_new;
// Calculating the Quantum Force numerically.
for (int i = 0; i < n_particles; i++) {
for (int j = 0; j < dim; j++) {
r_plus(i, j) += h;
r_minus(i, j) -= h;
q_f(i, j) = 2 * (evaluate(r_plus) - evaluate(r_minus)) / (2 * h * evaluate(r_new));
r_plus(i, j) = r_new(i, j);
r_minus(i, j) = r_new(i, j);
}
}
#else
rowvec gradient_slater;
rowvec gradient_jastrow;
double R = slater->get_ratio();
for (int i = 0; i < n_particles; i++) {
// Finding the Orbitals' gradient.
slater->compute_gradient(i);
gradient_slater = slater->get_gradient();
// Finding the Jastrow's gradient.
jas->compute_gradient(r_new, i);
gradient_jastrow = jas->get_gradient();
q_f.row(i) = 2 * (gradient_jastrow + gradient_slater)/R;
}
#endif
return q_f;
}
/*******************************************************************
*
* NAME : evaluate( double* r)
*
* DESCRIPTION : In progress.
*
*/
double QD_kinetic::evaluate(mat r) {
#if NUMERICAL
// the step length and its squared inverse for the second derivative
double h = 0.001;
double wfminus, wfplus, wfold, e_kinetic;
mat r_plus;
mat r_minus;
wfold = wf->get_wf_old();
r_plus = zeros<mat > (n_particles, dim);
r_minus = zeros<mat > (n_particles, dim);
r_plus = r_minus = r;
// compute the kinetic energy
e_kinetic = 0;
for (int i = 0; i < n_particles; i++) {
for (int j = 0; j < dim; j++) {
r_plus(i, j) = r(i, j) + h;
r_minus(i, j) = r(i, j) - h;
wfminus = wf->evaluate(r_minus);
wfplus = wf->evaluate(r_plus);
e_kinetic += (wfplus - 2 * wfold + wfminus);
r_plus(i, j) = r(i, j);
r_minus(i, j) = r(i, j);
}
}
// include electron mass and hbar squared and divide by wave function
e_kinetic = -0.5 * e_kinetic / (h * h) / wfold;
return e_kinetic;
#else
// Analytic solution with the Jastrow factor.
double e_kin = 0;
e_kin += wf->get_laplacian();
e_kin = -0.5 * e_kin;
return e_kin;
#endif
// Analytic solution without the Jastrow fasctor.
#if 0
double alpha, r_sq, derivative;
alpha = wf->getAlpha();
derivative = 0;
for (int i = 0; i < n_particles; i++) {
r_sq = 0;
for (int j = 0; j < dim; j++) {
r_sq += r(i, j) * r(i, j);
}
derivative += -2 * w * alpha + (w * w) * (alpha * alpha) * r_sq;
}
return -0.5 * derivative;
#endif
}
