Convergence tests

Use a direct diagonalization method to test the basis set only and vary the:

• Number of spherical regions
• Locations of the spherical regions
• Radii of the spherical regions $R_{\rm {reg}}$
• Energy cutoff $E_{\rm {cut}}$
• Maximum angular momentum component $\ell_{\rm {max}}$

Present results for a selection of simple molecules and crystals.

Results for molecules

• Chlorine ( $R_{\rm {reg}} = 4.0$ Å); LDA/PSP errors: $\delta r_{\rm {opt}} = 1\%$, $\delta f = 17\%$

	$N_{\rm {sphere}} = 2$		$N_{\rm {sphere}} = 3$
$\ell_{\rm {max}}$	$\delta r_{\rm {opt}}$ (%)	$\delta f$ (%)	$\delta r_{\rm {opt}}$ (%)	$\delta f$ (%)
1	10.0	55	2.4	8.1
2	0.6	3.1	0.01	0.03
3	0.07	0.3

• Hydrogen ( $R_{\rm {reg}} = 3.0$ Å); LDA error: $\delta r_{\rm {opt}} = 4\%$, $\delta f = 11\%$

	$N_{\rm {sphere}} = 2$		$N_{\rm {sphere}} = 3$
$\ell_{\rm {max}}$	$\delta r_{\rm {opt}}$ (%)	$\delta f$ (%)	$\delta r_{\rm {opt}}$ (%)	$\delta f$ (%)
2	0.2	0.8	0.01	0.02

• Hydrogen chloride ( $R_{\rm {reg}}^{\rm {H}} = 3.0$ Å, $R_{\rm {reg}}^{\rm {Cl}} = 4.0$ Å); LDA/PSP errors: $\delta r_{\rm {opt}} = 1.6\%$, $\delta f = 6\%$

	$N_{\rm {sphere}} = 2$		$N_{\rm {sphere}} = 3$
$\ell_{\rm {max}}$	$\delta r_{\rm {opt}}$ (%)	$\delta f$ (%)	$\delta r_{\rm {opt}}$ (%)	$\delta f$ (%)
2	0.04	0.2	0.02	0.1