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where the second-order corrections are neglected. Simulation starts from some
initial potential determined by a trial set of parameters and, after running the
simulation, the deviation of computed average properties
A
j
i
from the target
h
values (
) as well as (8) is determined. Then, from (2) the corrections to the
potential parameters
D
h
A
j
i
D
l
i
can be found. The procedure is repeated with the new
parameter set until convergence is reached. In the case where the parameters
lfg
are the values of the pair potential at a number of points covering the whole range of
distances, and the target properties are the values of RDF at the same set of points,
the method becomes equivalent to the inverse Monte Carlo approach [
98
,
99
]. The
method has been used successfully to develop a united atom model for water, a CG
model for an equimolar mixture of
L
- and
D
-proline dissolved in dimethyl sulfoxide,
and a CG model of dimyristoyl phosphatidylcholine lipid molecules. However, the
transferability of the CG potentials needs to be checked in every case [
97
].
3.2 Dynamic-Based CG Model
An alternative way to develop a CG force field is a starting from the dynamic
properties of the system. In this case, the Langevin-equation formalism [
10
,
100
]is
used to describe the dynamic evolution of the system, and the friction coefficients that
partially slow down the dynamics are determined from atomistic reference simula-
tions using force-velocity and velocity-velocity correlation functions [
34
,
71
]. This
method is usually used to study complex liquids [
101
] or biomolecular systems [
85
].
In the same class of methods also fall those that tune the friction coefficients until the
dynamic properties match the atomistic ones [
33
]. In any case, it is of interest to
understand the physical origins of the acceleration of the CG dynamics for specific
cases, to assess the methods mentioned above, and to gain a better understanding
of the effect of coarse graining on the dynamics of a system. However, this class of
method could fail to reproduce the structure of the system, since the developments
of the CG force field only take care of the dynamic properties of the system. There is
currently much research being carried out to investigate, whether it is possible to
derive coarse-grained potentials that are both dynamically and structurally consistent
with the underlying higher-resolution description. In a recent work of Qian et al. [
57
],
the DPD [
55
] and LA [
56
] equations of motion have been applied in CG simulations
to slow down the dynamics of the CG model obtained through the IBI method. The
simulation results showed that both DPD and LA could re-introduce friction into the
system and compensate for the dynamic effects of coarse-graining. Thus, the too-fast
dynamics of CG models in molecular dynamics can be corrected and can be slowed
down to match reality. Empirical rules have been found for the control parameters
(noise strength in DPD and bath collision frequency in LA) in CG simulation of liquid
EB [
57
]. Further work needs to be done to establish how transferable these rules are
among different systems.
The different simulation hierarchies (QM, atomistic MD, and CG simulations)
can be used to address phenomena or properties of a given system at several levels
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