Molecular dynamics simulations of a simple, bead-spring model of semiflexib
le polyelectrolytes such as DNA are performed. All charges are explicitly t
reated. Starting from extended, noncondensed conformations, condensed struc
tures form in the simulations with tetravalent or trivalent counterions. No
condensates form or are stable for divalent counterions. The mechanism by
which condensates form is described. Briefly, condensation occurs because e
lectrostatic interactions dominate entropy, and the favored coulombic struc
ture is a charge-ordered state. Condensation is a generic phenomenon and oc
curs for a variety of polyelectrolyte parameters. Toroids and rods are the
condensate structures. Toroids form preferentially when the molecular stiff
ness is sufficiently strong.