  The Stoermer-Verlet-leapfrog group of integrators commonly used in molecular
dynamics simulations has long become a textbook subject and seems to have been
studied exhaustively. There are, however, a few striking effects in performance
of algorithms which are well-known but have not received adequate attention in
the literature. A closer view of these unclear observations results in
unexpected conclusions. It is shown here that contrary to the conventional
point of view, the leapfrog scheme is distinguished in this group both in terms
of the order of truncation errors and the conservation of the total energy. In
this case the characteristic square growth of fluctuations of the total energy
with the step size, commonly measured in numerical tests, results from
additional interpolation errors with no relation to the accuracy of the
computed trajectory. An alternative procedure is described for checking energy
conservation of leapfrog-like algorithms which is free from interpolation
errors. Preliminary tests on a representative model system suggest that
standard step size values used at present are lower than necessary for accurate
sampling.
