  We provide molecular dynamics simulation of heat transport in one-dimensional
molecular chains with different interparticle pair potentials. We show that the
thermal conductivity is finite in the thermodynamic limit in the chains with
the potential, which allows for bond dissociation. The Lennard-Jones, Morse and
Coulomb potentials belong to such type of potentials. The convergence of the
thermal conductivity is provided by phonon scattering on the locally stretched
loose interatomic bonds at low temperature and by the many-particle scattering
at high temperature. On the other hand, the chains with the confining pair
potential, which does not allow for the bond dissociation, posses anomalous
(diverging with the chain length) thermal conductivity. We emphasize that the
chains with the symmetric or asymmetric Fermi-Pasta-Ulam potential or with the
combined potentials containing parabolic confining potential all exhibit
anomalous heat transport.
