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73949085391
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note
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See also footnote 65.
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56
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73949086912
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note
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j} which are obtained from an atomistic trajectory shall not be confused with the coordinates of a trajectory obtained from coarse-grained simulations
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57
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73949101582
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Note
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Note that here we only consider the special case of a linear relation between the r and R. M is a block-diagonal matrix and to construct it is enough to specify building blocks for each molecule type. For polymers it is enough to specify M for one repeat unit only.
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58
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73949137491
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Note
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Note that this is often a "special" trajectory which is designed to decouple the degrees of freedom of interest, e. g., a single polymer chain in vacuum with appropriate exclusions.
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59
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73949161200
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Note
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Note that, as before, we ignored an irrelevant normalization prefactor Z.
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60
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73949106668
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Note
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52,53 The concept is illustrated in section IV for liquid propane and a single molecule of hexane.
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61
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73949145874
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Note
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2), which is the potential of mean force, eq 2.
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62
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73949111153
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Note
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A formal statistical mechanical framework of force matching applied to a liquid state, or a multiscale coarse-graining method, is given in ref 54.
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73949122835
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http://www.espresso-pp.de.
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64
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73949134764
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Note
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αβ systematically change with the box size.
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65
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73949100956
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Note
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44,45 The latter models map the potentials, which are analytical functions of bonds, angles, and dihedral Coarse-Graining Applications J. Chem. Theory Comput., Vol. 5, No. 12, 2009 3223 dynamic properties of the corresponding substances. In our case coarse-grained potentials are tabulated functions of coarse-grained variables and only the mapping (hydrogens embedded into heavier atoms) is similar to that of the united atom force-fields.
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66
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73949118871
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Note
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For condensed phase systems, the error introduced by the off-plane component of the force might be compensated by some other pair interactions. In this particular case, however, coarse-graining of liquid hexane with both bonded and non-bonded degrees of freedom treated simultaneously results in a very similar angular distribution to that of a single molecule in vacuum.
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