  We report an accurate study of interactions between Benzene molecules using
variational quantum Monte Carlo (VMC) and diffusion quantum Monte Carlo (DMC)
methods. We compare these results with density functional theory (DFT) using
different van der Waals (vdW) functionals. In our QMC calculations, we use
accurate correlated trial wave functions including three-body Jastrow factors,
and backflow transformations. We consider two benzene molecules in the parallel
displaced (PD) geometry, and find that by highly optimizing the wave function
and introducing more dynamical correlation into the wave function, we compute
the weak chemical binding energy between aromatic rings accurately. We find
optimal VMC and DMC binding energies of -2.3(4) and -2.7(3) kcal/mol,
respectively. The best estimate of the CCSD(T)/CBS limit is -2.65(2) kcal/mol
[E. Miliordos et al, J. Phys. Chem. A 118, 7568 (2014)]. Our results indicate
that QMC methods give chemical accuracy for weakly bound van der Waals
molecular interactions, comparable to results from the best quantum chemistry
methods.
