  We present first-principles, density-functional theory calculations of the
NMR chemical shifts for polycyclic aromatic hydrocarbons, starting with benzene
and increasing sizes up to the one- and two-dimensional infinite limits of
graphene ribbons and sheets. Our calculations are performed using a combination
of the recently developed theory of orbital magnetization in solids, and a
novel approach to NMR calculations where chemical shifts are obtained from the
derivative of the orbital magnetization with respect to a microscopic,
localized magnetic dipole. Using these methods we study on equal footing the
$^1$H and $^{13}$C shifts in benzene, pyrene, coronene, in naphthalene,
anthracene, naphthacene, and pentacene, and finally in graphene, graphite, and
an infinite graphene ribbon. Our results show very good agreement with
experiments and allow us to characterize the trends for the chemical shifts as
a function of system size.
