  Many approaches, which have been developed to express the potential energy of
large systems, exploit the locality of the atomic interactions. A prominent
example are fragmentation methods, in which quantum chemical calculations are
carried out for overlapping small fragments of a given molecule that are then
combined in a second step to yield the system's total energy. Here we compare
the accuracy of the systematic molecular fragmentation approach with the
performance of high-dimensional neural network (HDNN) potentials introduced by
Behler and Parrinello. HDNN potentials are similar in spirit to the
fragmentation approach in that the total energy is constructed as a sum of
environment-dependent atomic energies, which are derived indirectly from
electronic structure calculations. As a benchmark set we use all-trans alkanes
containing up to eleven carbon atoms at the coupled cluster level of theory.
These molecules have been chosen because they allow to extrapolate reliable
reference energies for very long chains, enabling an assessment of the energies
obtained by both methods for alkanes including up to 10 000 carbon atoms. We
find that both methods predict high-quality energies with the HDNN potentials
yielding smaller errors with respect to the coupled cluster reference.
