Potential integrals#
Real space integrators#
Quadrature rule#
The numerical integrals by creating a table of integrals by using the Gaussian quadrature method , which is designed for accurate results using a minimum number of evaluations for functions with singularities.
The potential of a single atom is localized, but in principle infinite in extent, hence we need to set a reasonable cutoff. The cutoff is calculated by solving the equation
where \(V_{tol}\) is the error at the cut-off. The equation is solved for each species. The use of the cut-off radius creates a discontinuity; hence, abTEM uses a tapering near the cut-off. \(V_{cut}\) can be modified using the cutoff_tolerance
argument of the Potential
or AtomicPotential
objects. abTEM uses a tapering cutoff starting at \(85 \ \%\) of the full cutoff.
from abtem.potentials.integrals import ProjectionQuadratureRule
integrator = ProjectionQuadratureRule()
integrator