An algorithm to sample the exact (within the nodal error) ground stare distribution to find nondifferential properties of multielectron systems is developed and applied to first-row atoms. Calculated properties are the distribution moments and the electronic density at the nucleus (expected value of the delta operator). For this purpose compact trial functions are developed and optimized, and a new estimator for the delta is formulated. A comparison is made with results of highly accurate post-Hartree-Fock calculations, thereby illuminating the nodal error in our estimates. In general, we obtain more accurate estimates for the distribution moments than those obtained previously using Monte Carlo methods, despite the relative crudeness of our trial functions. We confirm the literature values for the electron density at the nucleus for the lighter atoms (Li-C), but disagree with previous (Monte Carlo) estimates for the heavier ones (N-Ne). (C) 1997 American Institute of Physics. [S0021-9606(97)00144-X].