  The self-healing diffusion Monte Carlo algorithm (SHDMC) [Phys. Rev. B {\bf
79}, 195117 (2009), {\it ibid.} {\bf 80}, 125110 (2009)] is shown to be an
accurate and robust method for calculating the ground state of atoms and
molecules. By direct comparison with accurate configuration interaction results
for the oxygen atom we show that SHDMC converges systematically towards the
ground-state wave function. We present results for the challenging N$_2$
molecule, where the binding energies obtained via both energy minimization and
SHDMC are near chemical accuracy (1 kcal/mol). Moreover, we demonstrate that
SHDMC is robust enough to find the nodal surface for systems at least as large
as C$_{20}$ starting from random coefficients. SHDMC is a linear-scaling
method, in the degrees of freedom of the nodes, that systematically reduces the
fermion sign problem.
