Truncating the basis set

• In principle, $E_{\rm {cut}}$ determines the maximum angular momentum component $\ell_{\rm {cut}}$
• In practice, we truncate the basis set by introducing a second parameter $\ell_{\rm {max}}$:
  • to reduce the basis set size $\propto (\ell_{\rm {max}} + 1)^2$
  • to reduce the computational cost
  • as in Gaussian and LCAO type basis sets
  • to avoid over-completeness