  The Jastrow-modified antisymmetric geminal power (JAGP) ansatz in Hilbert
space successfully overcomes two key failings of other pairing theories, namely
a lack of inter-pair correlations and a lack of multiple resonance structures,
while maintaining a polynomially scaling cost, variational energies, and size
consistency. Here we present efficient quantum Monte Carlo algorithms that
evaluate and optimize the JAGP energy for a cost that scales as the fifth power
of the system size. We demonstrate the JAGP's ability to describe both static
and dynamic correlation by applying it to bond stretching in H2O, C2, and N2 as
well as to a novel, multi-reference transition state of ethene. JAGP's accuracy
in these systems outperforms even the most sophisticated single-reference
methods and approaches that of exponentially-scaling active space methods.
