  Diradical molecules are essential species involved in many organic and
inorganic chemical reactions. The computational study of their electronic
structure is often challenging, because a reliable description of the
correlation, and in particular of the static one, requires multi-reference
techniques. The Jastrow correlated Antisymmetrized Geminal Power (JAGP) is a
compact and efficient wave function ansatz, based on the valence-bond
representation, which can be used within Quantum Monte Carlo (QMC) approaches.
The AGP part can be rewritten in terms of molecular orbitals, obtaining a
multi-determinant expansion with zero-seniority number. In the present work we
demonstrate the capability of the JAGP ansatz to correctly describe the
electronic structure of two diradical prototypes: the orthogonally twisted
ethylene, C2H4, and the methylene, CH2, representing respectively a
homosymmetric and heterosymmetric system. On the other hand, we show that the
simple ansatz of a Jastrow correlated Single Determinant (JSD) wave function is
unable to provide an accurate description of the electronic structure in these
diradical molecules, both at variational level and, more remarkably, in the
fixed-nodes projection schemes showing that a poor description of the static
correlation yields an inaccurate nodal surface. The suitability of JAGP to
correctly describe diradicals with a computational cost comparable with that of
a JSD calculation, in combination with a favorable scalability of QMC
algorithms with the system size, opens new perspectives in the ab initio study
of large diradical systems, like the transition states in cycloaddition
reactions and the thermal isomerization of biological chromophores.
