Multiscale Approaches and Perspectives to Modeling Aqueous Electrolytes and Polyelectrolytes - Multiscale Molecular Methods in Applied Chemistry - page 272

of bonded and nonbonded contributions in the CG bonded potential. The potentials
of mean force corresponding to the CG bonded degrees of freedom, obtained from
this sampling procedure, are used as effective potentials to describe bonded degrees
of freedom, including bond stretching, bond angle bending, and torsional rotation in
the CG model. This procedure was performed for PS oligomers with different
stereo-sequences, leading to a set of CG bonded potentials that were used to
describe stereo-regular (isotactic and syndiotactic) and atactic PS conformations
in condensed phase simulations. Effective pair potentials for nonbonded bead-bead
interactions were obtained by computing the free energy of a coupling process that
introduces the atomistic interactions between two groups of atoms corresponding to
the CG beads on two oligomers in vacuum. Figure 9 illustrates this procedure. It
should be noted that the effective nonbonded potentials obtained by this procedure
include effects of multi-body correlations related to steric constraints mediated
by chain backbone atoms surrounding the chemical moieties for which the CG
potential is evaluated. The overall coarse graining procedure of [ 98 ] is very
cheap (sampling in vacuum) and moreover ensures that bonded and nonbonded
interactions are strictly decoupled.

W ( R )

R

R ∞

V eff

( R )

V eff )

R ∞

(

( R )

W off

R

∞

R

( R ) ( R ) = W ( R ) ( R )

V eff -V eff

∞

-W off

Fig. 9 Thermodynamic cycle used to obtain CG nonbonded interactions [ 98 ]. W ( R ) denotes the
reversible work to bring two trimer molecules from infinite distance to distance R computed with a
detailed-atomistic force field. The distance coordinate R between the mass centers of the two
central methylene units, for which a CG interaction potential is being sought, is used as reaction
coordinate. W off ( R ) denotes the reversible work to bring the same two trimer molecules from
infinite distance to distance R , while all direct nonbonded interactions between the atoms belong-
ing to the two central methylene units are switched off. Propane is chosen here for illustration
purposes. In the gas phase, V eff ( R !1 ) ¼ 0. The CG potential function V eff ( R ) ¼ W ( R )
W off ( R ) represents the reversible work (free energy) expended to introduce nonbonded interac-
tions between all atoms of the methylene moieties and can be used as a CG two-body potential for
methylene united atoms in propane