  The excitation energies of parahydrogen clusters have been systematically
calculated by the diffusion Monte Carlo technique in steps of one molecule from
3 to 40 molecules. These clusters possess a very rich spectra, with angular
momentum excitations arriving up to L=13 for the heavier ones. No regular
pattern can be guessed in terms of the angular momenta and the size of the
cluster. Clusters with N=13 and 36 are characterized by a peak in the chemical
potential and a large energy gap of the first excited level, which indicate the
magical character of these clusters. From the calculated excitation energies
the partition function has been obtained, thus allowing for an estimate of
thermal effects. An enhanced production is predicted for cluster sizes N=13, 31
and 36, in agreement with experiment.
