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Quantum Monte Carlo study of the protonated water dimer

We report an extensive theoretical study of the protonated water dimer (Zundel ion) by means of the highly correlated variational Monte Carlo and lattice regularized Monte Carlo approaches. This system represents the simplest model for proton transfer (PT) and a correct description of its properties is essential in order to understand the PT mechanism in more complex acqueous systems. Our Jastrow correlated AGP wave function ensures an accurate treatment of electron correlations. Exploiting the advantages of contracting the primitive basis set over atomic hybrid orbitals, we are able to limit dramatically the number of variational parameters with a systematic control on the numerical precision, crucial in order to simulate larger systems. We investigate energetics and geometrical properties of the Zundel ion as a function of the oxygen-oxygen distance, taken as reaction coordinate. In both cases, our QMC results are found in excellent agreement with coupled cluster CCSD(T) technique, the quantum chemistry "gold standard". Calculations on proton transfer static barriers and dissociation energies display the same agreement. A comparison with density functional theory (DFT) results in the PBE approximation points out the crucial role of electron correlations for a correct description of the PT in the dimer. Our method is able to resolve the tiny energy differences (~ 0.1 Kcal/mol) and the corresponding structural variations at which the proton transfer takes place; it combines these features with a N^3-N^4 scaling with number of particles (favorable with respect to other post-DFT methods), as proven by a benchmark calculation on a larger protonated water cluster. The QMC approach used here represents a promising candidate to provide the first high-level ab initio description of PT in water.