Discretization

All discretization schemes rely on Cartesian (all increasing, equally spaced) grids as a foundation. These grids enable fast-Fourier-transform based computations of the derivatives and convolution that are required in many simulations.

The QMol-grid package provides the following types of discretization schemes

• QMol_disc, which defines the Cartesian-grid discretization of the domain, and
• QMol_disc_basis, which expands the wave functions and orbitals as linear combinations of a fixed spatial basis set. For spin-polarized models, the same basis set is used for both the up- and down-spin channels (i.e., QMol_disc_basis defines an unpolarized basis set).

Note that QMol_disc_basis still defines the basis-set components over a Cartesian grid and is therefore almost always slower and less accurate that QMol_disc calculations. QMol_disc_basis can be used to evaluate the effect of basis-set modeling or when a finite number of degrees of freedom is required in calculations.

Besides the domain, discretization objects provide basic functionalities -- like object allocation, arithmetic operations, discretization-dependent low-level computations, etc. -- that are used throughout the rest of the QMol-grid package.