  Model off-lattice sequences in two dimensions are constructed so that their
native states are close to an on-lattice target. The Hamiltonian involves the
Lennard-Jones and harmonic interactions. The native states of these sequences
are determined with a high degree of certainty through Monte Carlo processes.
The sequences are characterized thermodynamically and kinetically. It is shown
that the rank-ordering-based scheme of the assignment of contact energies
typically fails in off-lattice models even though it generates high stability
of on-lattice sequences. Similar to the on-lattice case, Go-like modeling, in
which the interaction potentials are restricted to the native contacts in a
target shape, gives rise to good folding properties. Involving other contacts
deteriorates these properties.
