In the hyper-MD method [9–12], a bias or boost potential DV(r)
is added to the true potential V(r) such that, ideally, the potential
surfaces near the minima are raised and those near the barriers,
or saddle points, are left unaffected. A continuous, non-negative
boost potential function DV(r) is defined such that when the true
potential V(r) is below a chosen threshold boost energy E, the simulation
is performed on the modified potential V⁄ (r) = V(r) + DV(r),
and when V(r) is greater than E, the simulation is performed on the
true potential V⁄
(r) = V(r). This approach leads to an enhanced escape
rate for V⁄
(r). The bias potential DV(r) is chosen such that the
derivative of V⁄
(r) has no discontinuity, and the modified potential
reflects the shape of the minima by