Energy Landscapes of Model Knotted Polymers

The energy landscape of a model knotted ring polymer, consisting of 100 Lennard-Jones particles connected by harmonic springs, is extensively characterized for three topologies. Basin-hopping global optimization with unrestricted perturbation moves for the geometry can efficiently locate the global minimum of the topologically unconstrained energy landscape. We show that an isotropic radial potential to expand the structure provides a robust way to assign the crossing number and topology of each configuration. The radial potential also provides a way to propose more efficient geometrical perturbations for basin-hopping that preserve the topology, which should be generally applicable to molecular and soft matter systems. All three topologies exhibit multifunnel landscapes with a wide range of relaxation time scales, clearly visible in first passage time distributions. The global minimum corresponds to a particularly favorable, symmetrical packing, which produces a pronounced heat capacity peak. In contrast, the unknotted ring topology supports alternative low-energy minima that constitute remarkable kinetic traps and associated broken ergodicity. Such features may present opportunities for materials design.