There is no energy cut off test for calculations that employ atomic basis sets, in general: the calculation is well-defined with just the atomic basis set.
For comparison, the Gaussian-basis PySCF program implements four ways to compute the Coulomb interactions in crystalline systems:
- Gaussian-basis density fitting
- mixed Gaussian-plane wave density fitting
- plane-wave density fitting
- exact Gaussian integrals through a range separated approach (https://arxiv.org/abs/2012.07929)
As to your question, SIESTA employs pseudopotentials, and option 3 is what they use. If you look at the newest paper on the code, J. Chem. Phys. 152, 204108 (2020)
The auxiliary real-space grid is an essential ingredient of the method as it allows the efficient representation of charge densities and potentials as well as the computation of the matrix elements of the Hamiltonian that cannot be handled as two-center integrals. This grid can be seen as the reciprocal space of a set of plane waves, and its fineness is most conveniently parameterized by an energy cutoff (the “density” cutoff of plane-wave methods). There are limits to the softness of the functions that can be described with such a grid, so core electrons are not considered (although semi-core electrons usually
are), and their effect is incorporated into pseudopotentials. The real-space grid is also used to solve the Poisson equation involved in the computation of the electrostatic potential from the charge density through the use of a fast-Fourier-transform method. This means that SIESTA uses periodic boundary conditions (PBC). Non-periodic systems, such as molecules, tubes, or slabs, are treated using appropriate supercells.
This means that the plane-wave cutoff in SIESTA affects the evaluation of the Coulomb interaction. The higher the cutoff, the better SIESTA is able to describe the interaction of the atomic basis functions. With $E_\text{cut} \to \infty$ you recover the exact solution in the used atomic basis set.
