  High level ab initio calculations ranging from coupled cluster methods
including explicitly correlated approaches to standard second order
M{\o}ller-Plesset theory using spin scaling (SOS-MP2) have been performed on
sandwich and slipped parallel dimer structures of a series of quasi
one-dimensional acenes and on two-dimensional sheets containing the series
pyrene to coronene encircled with two layers of benzene rings. Sandwich
(graphitic AA type) and slipped parallel (AB type) structures were considered
and, within given symmetry restrictions, full geometry optimizations were
performed. Basis set superposition effects have been considered. The computed
geometries show a significant biconcave deviation of the twodimensional sheets
from planarity with the central intersheet C...C distances considerably smaller
that van der Waals distances. The computed intersheet binding energy per carbon
atom extrapolated for N ->$\infty$ of -74.3 meV (1.713 kcal/mol)/atom agrees
quite well with the experimental defoliation energy of -52 meV (1.199
kcal/mol)/atom (-67 meV (1.545 kcal/mol)/carbon atom without corrections for H
binding contributions) for polyaromatic hydrocarbons (PAHs) from graphite. A
limited investigation of density functional theory (DFT) calculations using
empirical dispersion contributions has been performed also showing a
significant underbinding character of the D3 method. For most of the DFT
variants investigated the graphene sheet models retain a quasi-planar structure
in strong contrast to the aforementioned SOS-MP2 results.
