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We propose here a single Pfaffian correlated variational ansatz, thatdramatically improves the accuracy with respect to the single determinant one,while remaining at a similar computational cost. A much larger correlationenergy is indeed determined by the most general two electron pairing function,including both singlet and triplet channels, combined with a many-body Jastrowfactor, including all possible spin-spin spin-density and density-densityterms. The main technical ingredient to exploit this accuracy is the use of thePfaffian for antisymmetrizing an highly correlated pairing function, thusrecovering the Fermi statistics for electrons with an affordable computationalcost. Moreover the application of the Diffusion Monte Carlo, within the fixednode approximation, allows us to obtain very accurate binding energies for thefirst preliminary calculations reported in this study: C$_2$, N$_2$ and O$_2$and the benzene molecule. This is promising and remarkable, considering thatthey represent extremely difficult molecules even for computationally demandingmulti-determinant approaches, and opens therefore the way for realistic andaccurate electronic simulations with an algorithm scaling at most as the fourthpower of the number of electrons.

General correlated geminal ansatz for electronic structure calculations: exploiting Pfaffians in place of determinants