  In view of the continuous theoretical efforts aimed at an accurate
microscopic description of the strongly correlated transition metal oxides and
related materials, we show that with continuum quantum Monte Carlo (QMC)
calculations it is possible to obtain the value of the spin superexchange
coupling constant of a copper oxide in a quantitatively excellent agreement
with experiment. The variational nature of the QMC total energy allows us to
identify the best trial wave function out of the available pool of wave
functions, which makes the approach essentially free from adjustable parameters
and thus truly ab initio. The present results on magnetic interactions suggest
that QMC is capable of accurately describing ground state properties of
strongly correlated materials.
