Weak binding between two aromatic rings: Feeling the van der Waals attraction by quantum Monte Carlo methods

We report a systematic study of the weak chemical bond between two benzene molecules. We first show that it is possible to obtain a very good description of the C-2 dimer and the benzene molecule by using pseudopotentials for the chemically inert 1s electrons and a resonating valence bond wave function as a variational ansatz, expanded on a relatively small Gaussian basis set. We employ an improved version of the stochastic reconfiguration technique to optimize the many-body wave function, which is the starting point for highly accurate simulations based on the lattice regularized diffusion Monte Carlo method. This projection technique provides a rigorous variational upper bound for the total energy, even in the presence of pseudopotentials, and substantially improves the accuracy of the trial wave function, which already yields a large fraction of the dynamical and nondynamical electron correlation. We show that the energy dispersion of two benzene molecules in the parallel displaced geometry is significantly deeper than the face-to-face configuration. However, contrary to previous studies based on post-Hartree-Fock methods, the binding energy remains weak (similar or equal to 2 kcal/mol) also in this geometry, and its value is in agreement with the most accurate and recent experimental findings [H. Krause , Chem. Phys. Lett. 184, 411 (1991)]. (c) 2007 American Institute of Physics.