An investigation of nodal structures and the construction of trial wave functions

The factors influencing the quality of the nodal surfaces, namely, the atomic basis set, the
single-particle orbitals, and the configurations included in the wave-function expansion, are
examined for a few atomic and molecular systems. The following empirical rules are found: the
atomic basis set must be fairly large, complete active space and natural orbitals are usually better
than Hartree-Fock orbitals, multiconfiguration expansions perform better than single-determinant
wave functions, but only few configurations are effective and their choice is suggested by symmetry
considerations, while too long determinantal expansions spoil the nodal surfaces. These rules allow
us to reduce the nodal error and to compute the best fixed node-diffusion Monte Carlo energies for
a series of dimers of first-row atoms.