  The dynamics of complex systems often involve thermally activated barrier
crossing events that allow these systems to move from one basin of attraction
on the high dimensional energy surface to another. Such events are ubiquitous,
but challenging to simulate using conventional simulation tools, such as
molecular dynamics. Recently, Weinan E et al. [Nonlinearity, 24(6),1831(2011)]
proposed a set of dynamic equations, the gentlest ascent dynamics (GAD), to
describe the escape of a system from a basin of attraction and proved that
solutions of GAD converge to index-1 saddle points of the underlying energy. In
this paper, we extend GAD to enable finite temperature simulations in which the
system hops between different saddle points on the energy surface. An effective
strategy to use GAD to sample an ensemble of low barrier saddle points located
in the vicinity of a locally stable configuration on the high dimensional
energy surface is proposed. The utility of the method is demonstrated by
studying the low barrier saddle points associated with point defect activity on
a surface. This is done for two representative systems, namely, (a) a surface
vacancy and ad-atom pair and (b) a heptamer island on the (111) surface of
copper.
