Chemistry Reference
In-Depth Information
Figure 8
Minimum energy path obtained using the NEB method is shown with the
larger filled circles along the continuous line. The dashed line with smaller filled circles is
a linear interpolation between the initial and final state. The contour plot represents the
potential surface of a 3-atom model coupled to an additional degree of freedom.
(Adapted from J ยด nsson et al.
80
)
A temperature-dependent nudged-elastic-band (NEB) algorithm, also
based on maximizing the flux, was proposed recently.
80-82
In this MaxFlux-
NEB algorithm, based on the differential form of Eq. [25], a discretized
path is constructed with the different neighboring structures maintained
equally spaced by the use of spring forces (Figure 8). The path is then mini-
mized using a modified Verlet algorithm. This methodology has limitations
similar to those of MaxFlux.
Discrete Path Sampling and String Method
Discrete path sampling (DPS)
83-87
is a methodology that samples paths
along the potential energy surface (instead of the Gibbs free energy surface as
in TPS). Fast paths connecting local minima and transition-state conforma-
tions are computed by DPS. The initial path connecting minima and transition
states is computed using the NEB method,
88,89
and the number of paths is
increased by replacing a minimum in the path with a new minimum close to
the original path. That new path is accepted and used to generate additional
paths only if it is faster than the original path (Figure 9). The rate constants are
computed using a harmonic approximation to the local density of states for
