Dissecting the Hydrogen Bond: A Quantum Monte Carlo Approach

We present a Quantum Monte Carlo study of the dissociation energy and the dispersion curve of the water dimer, a prototype of hydrogen bonded system. Our calculations are based on a wave function which is a modern and fully correlated implementation of the Pauling’s valence bond idea: the Jastrow Antisymmetrised Geminal Power (JAGP) [Casula et al. J. Chem. Phys. 2003, 119, 6500-6511]. With this variational wave function we obtain a binding energy of -4.5(0.1) kcal/ mol that is only slightly increased to -4.9(0.1) kcal/mol by using the Lattice Regularized Diffusion Monte Carlo (LRDMC). This projection technique allows for the substantial improvement in the correlation energy of a given variational guess and indeed, when applied to the JAGP, yields a binding energy in fair agreement with the value of -5.0 kcal/mol reported by experiments and other theoretical works. The minimum position, the curvature, and the asymptotic behavior of the dispersion curve are well reproduced both at the variational and the LRDMC level. Moreover, thanks to the simplicity and the accuracy of our variational approach, we are able to dissect the various contributions to the binding energy of the water dimer in a systematic and controlled way. This is achieved by appropriately switching off determinantal and Jastrow variational terms in the JAGP. Within this scheme, we estimate that the dispersive van der Waals contribution to the electron correlation is substantial and amounts to 1.5(0.2) kcal/mol, this value being comparable with the intermolecular covalent energy that we find to be 1.1(0.2) kcal/mol. The present Quantum Monte Carlo approach based on the JAGP wave function is revealed as a promising tool for the interpretation and the quantitative description of weakly interacting systems, where both dispersive and covalent energy contributions play an important role.