Chemistry Reference
In-Depth Information
where
F
fast
Þ :¼r
r
V
fast
F
slow
i
¼
F
slow
i
ð
r
n
þ1
;
v
n
þ1=2
ð
r
;
v
;
t
ð
r
ð
t
ÞÞ
g
v
ð
t
Þþ
R
ð
t
Þ
;
t
n
þ1
Þ
This method can naturally be extended to include a splitting of more than two
force classes, and it is amenable to other modifications and improvements such
as moving the slow force update to be more symmetrically placed in the inte-
gration loop. It was shown
39
for a three-class force splitting that for typical
molecular systems, the MTS (and hence the frequency of updating the slow
forces) can be extended to 48 fs or longer with resulting computational speed-
ups of at least a factor of 10. The success of Langevin stabilization with extra-
polation MTS methods has led to its use to achieve stable simulations at large
time steps using mollified impulse methods as well.
44-46
A systematic compar-
ison
47
of these methods shows that extrapolation methods hold some advan-
tage among Langevin-stabilized MTS integrators in terms of stability at long
time steps. On the other hand, the argument in favor of mollified impulse
methods is that no stabilization is required at small time steps.
Further Challenges and Recent Advances
The success of Langevin-stabilized methods has yielded, for the first
time, the opportunity to attain the full promise of MTS methods. As in
any field of inquiry, solving one problem often clears the way for the emer-
gence of several others, and MTS integration is no exception. As an example,
the extrapolation method
39
was used successfully with 120-fs slow force
update frequency in simulations of a DNA/polymerase system.
48
Remark-
ably, in this study computational gains were limited to a factor of 5, even
though the longest-range forces were updated less frequently than the fastest
forces by two orders of magnitude. The explanation for this limited gain in
efficiency is due to the extreme sensitivity of DNA systems to electrostatic
interactions, where medium-range forces must be treated with very short
time steps in the range 1-2 fs. This highlights a difficulty with the force-
splitting idea as applied to molecular dynamics of some classes of molecules
such as biological systems: The time and distance scales sometimes do not
naturally fall into well-separated categories. This, in turn, makes it difficult
to identify force classes. For example, the highest frequency motion in a slow
force class might be only marginally slower than the lowest frequency
motion in a fast force class. This feature, more prominent in some systems
than others, can limit the size of time step that can be used for any given force
class severely, hence mitigating the hoped-for computational advantage of
MTS methods.
During the development of long-time-step MTS methods, work pro-
ceeded along another path involving the fundamental problem of costly force
