This paper series aims to establish a complete correspondence between fine-grained (FG) and coarse-grained (CG) dynamics by way of excess entropy scaling (introduced in Paper I). While Paper II successfully captured translational motions in CG systems using a hard sphere mapping, the absence of rotational motions in single-site CG models introduces differences between FG and CG dynamics. In this third paper, our objective is to faithfully recover atomistic diffusion coefficients from CG dynamics by incorporating rotational dynamics. By extracting FG rotational diffusion, we unravel, for the first time reported to our knowledge, a universality in excess entropy scaling between the rotational and translational diffusion. Once the missing rotational dynamics are integrated into the CG translational dynamics, an effective translation-rotation coupling becomes essential. We propose two different approaches for estimating this coupling parameter: the rough hard sphere theory with acentric factor (temperature-independent) or the rough Lennard-Jones model with CG attractions (temperature-dependent). Altogether, we demonstrate that FG diffusion coefficients can be recovered from CG diffusion coefficients by (1) incorporating “entropy-free” rotational diffusion with translation-rotation coupling and (2) recapturing the missing entropy. Our findings shed light on the fundamental relationship between FG and CG dynamics in molecular fluids.

1.
J.
Jin
,
K. S.
Schweizer
, and
G. A.
Voth
,
J. Chem. Phys.
158
(
3
),
034103
(
2023
).
2.
J.
Jin
,
K. S.
Schweizer
, and
G. A.
Voth
,
J. Chem. Phys.
158
(
3
),
034104
(
2023
).
3.
J.
Jin
,
A. J.
Pak
,
A. E. P.
Durumeric
,
T. D.
Loose
, and
G. A.
Voth
,
J. Chem. Theory Comput.
18
(
10
),
5759
5791
(
2022
).
4.
R.
Zwanzig
,
J. Chem. Phys.
33
(
5
),
1338
1341
(
1960
).
7.
H.
Mori
,
Prog. Theor. Phys.
33
(
3
),
423
455
(
1965
).
8.
S.
Izvekov
and
G. A.
Voth
,
J. Chem. Phys.
125
,
151101
(
2006
).
9.
T.
Kinjo
and
S.-a.
Hyodo
,
Phys. Rev. E
75
(
5
),
051109
(
2007
).
10.
C.
Hijón
,
P.
Español
,
E.
Vanden-Eijnden
, and
R.
Delgado-Buscalioni
,
Faraday Discuss.
144
,
301
322
(
2010
).
11.
H.
Lei
,
B.
Caswell
, and
G. E.
Karniadakis
,
Phys. Rev. E
81
(
2
),
026704
(
2010
).
12.
L.
Gao
and
W.
Fang
,
J. Chem. Phys.
135
(
18
),
184101
(
2011
).
13.
S.
Izvekov
,
J. Chem. Phys.
138
(
13
),
134106
(
2013
).
14.
Y.
Yoshimoto
,
I.
Kinefuchi
,
T.
Mima
,
A.
Fukushima
,
T.
Tokumasu
, and
S.
Takagi
,
Phys. Rev. E
88
(
4
),
043305
(
2013
).
15.
Z.
Li
,
X.
Bian
,
B.
Caswell
, and
G. E.
Karniadakis
,
Soft Matter
10
(
43
),
8659
8672
(
2014
).
16.
A.
Davtyan
,
J. F.
Dama
,
G. A.
Voth
, and
H. C.
Andersen
,
J. Chem. Phys.
142
(
15
),
154104
(
2015
).
17.
A.
Davtyan
,
G. A.
Voth
, and
H. C.
Andersen
,
J. Chem. Phys.
145
(
22
),
224107
(
2016
).
18.
Z.
Li
,
X.
Bian
,
X.
Li
, and
G. E.
Karniadakis
,
J. Chem. Phys.
143
(
24
),
243128
(
2015
).
19.
Z.
Li
,
H. S.
Lee
,
E.
Darve
, and
G. E.
Karniadakis
,
J. Chem. Phys.
146
(
1
),
014104
(
2017
).
20.
H.
Lei
,
X.
Yang
,
Z.
Li
, and
G. E.
Karniadakis
,
J. Comput. Phys.
330
,
571
593
(
2017
).
21.
S.
Izvekov
,
J. Chem. Phys.
146
(
12
),
124109
(
2017
).
23.
G.
Jung
,
M.
Hanke
, and
F.
Schmid
,
J. Chem. Theory Comput.
13
(
6
),
2481
2488
(
2017
).
24.
G.
Jung
,
M.
Hanke
, and
F.
Schmid
,
Soft Matter
14
(
46
),
9368
9382
(
2018
).
25.
N.
Bockius
,
J.
Shea
,
G.
Jung
,
F.
Schmid
, and
M.
Hanke
,
J. Phys.: Condens. Matter
33
(
21
),
214003
(
2021
).
26.
F.
Glatzel
and
T.
Schilling
,
Europhys. Lett.
136
(
3
),
36001
(
2021
).
27.
Y.
Han
,
J.
Jin
, and
G. A.
Voth
,
J. Chem. Phys.
154
(
8
),
084122
(
2021
).
28.
P.
Stinis
,
Proc. R. Soc. A
471
(
2176
),
20140446
(
2015
).
29.
Y.
Rosenfeld
,
Phys. Rev. A
15
(
6
),
2545
(
1977
).
30.
Y.
Rosenfeld
,
Chem. Phys. Lett.
48
(
3
),
467
468
(
1977
).
31.
Y.
Rosenfeld
,
J. Phys.: Condens. Matter
11
(
28
),
5415
(
1999
).
32.
M. K.
Nandi
,
A.
Banerjee
,
S.
Sengupta
,
S.
Sastry
, and
S. M.
Bhattacharyya
,
J. Chem. Phys.
143
(
17
),
174504
(
2015
).
33.
K.
Seki
and
B.
Bagchi
,
J. Chem. Phys.
143
(
19
),
194110
(
2015
).
34.
S.
Acharya
and
B.
Bagchi
,
J. Chem. Phys.
153
,
184701
(
2020
).
35.
B.
Sorkin
,
H.
Diamant
, and
G.
Ariel
,
Phys. Rev. Lett.
131
(14), 147101 (
2023
).
36.
J.
Jin
,
Y.
Han
,
A. J.
Pak
, and
G. A.
Voth
,
J. Chem. Phys.
154
(
4
),
044104
(
2021
).
37.
J.
Jin
,
A. J.
Pak
,
Y.
Han
, and
G. A.
Voth
,
J. Chem. Phys.
154
(
4
),
044105
(
2021
).
38.
T. T.
Foley
,
M. S.
Shell
, and
W. G.
Noid
,
J. Chem. Phys.
143
(
24
),
243104
(
2015
).
39.
J.
Jin
,
A. J.
Pak
, and
G. A.
Voth
,
J. Phys. Chem. Lett.
10
(
16
),
4549
4557
(
2019
).
40.
R. W.
Zwanzig
,
J. Chem. Phys.
22
(
8
),
1420
1426
(
1954
).
41.
J. A.
Barker
and
D.
Henderson
,
J. Chem. Phys.
47
(
8
),
2856
2861
(
1967
).
42.
J. A.
Barker
and
D.
Henderson
,
J. Chem. Phys.
47
(
11
),
4714
4721
(
1967
).
43.
J. D.
Weeks
,
D.
Chandler
, and
H. C.
Andersen
,
J. Chem. Phys.
54
(
12
),
5237
5247
(
1971
).
44.
H. C.
Andersen
,
J. D.
Weeks
, and
D.
Chandler
,
Phys. Rev. A
4
(
4
),
1597
(
1971
).
45.
J. D.
Weeks
,
D.
Chandler
, and
H. C.
Andersen
,
J. Chem. Phys.
55
(
11
),
5422
5423
(
1971
).
46.
S.
Mirigian
and
K. S.
Schweizer
,
J. Phys. Chem. Lett.
4
(
21
),
3648
3653
(
2013
).
47.
S.
Mirigian
and
K. S.
Schweizer
,
J. Chem. Phys.
140
(
19
),
194506
(
2014
).
48.
S.
Mirigian
and
K. S.
Schweizer
,
J. Chem. Phys.
140
(
19
),
194507
(
2014
).
49.
J.-P.
Hansen
and
I. R.
McDonald
,
Theory of Simple Liquids
(
Elsevier
,
1990
).
50.
J. V.
Sengers
,
R.
Kayser
,
C.
Peters
, and
H.
White
,
Equations of State for Fluids and Fluid Mixtures
(
Elsevier
,
2000
).
51.
Á.
Mulero
,
Theory and Simulation of Hard-Sphere Fluids and Related Systems
(
Springer
,
2008
).
52.
A.
Santos
,
A Concise Course on the Theory of Classical Liquids
(
Springer
,
Berlin
,
2016
).
53.
N. K.
Ailawadi
,
B. J.
Berne
, and
D.
Forster
,
Phys. Rev. A
3
(
4
),
1462
(
1971
).
54.
N. K.
Ailawadi
,
B. J.
Berne
, and
D.
Forster
,
Phys. Rev. A
3
(
4
),
1472
(
1971
).
55.
N. K.
Ailawadi
and
B. J.
Berne
,
J. Chem. Phys.
54
(
8
),
3569
3571
(
1971
).
56.
A.
Einstein
,
Investigations on the Theory of the Brownian Movement
(
Dover
,
New York
,
1956
).
57.
P. J. W.
Debye
,
Polar Molecules
(
Dover
,
New York
,
1929
).
58.
T.
Lazaridis
and
M.
Karplus
,
J. Chem. Phys.
105
(
10
),
4294
4316
(
1996
).
59.
J.
Zielkiewicz
,
J. Phys. Chem. B
112
(
26
),
7810
7815
(
2008
).
60.
D.
Chandler
,
J. Chem. Phys.
60
(
9
),
3500
3507
(
1974
).
61.
D.
Chandler
,
J. Chem. Phys.
60
(
9
),
3508
3512
(
1974
).
62.
B.
Berne
and
J.
Montgomery
, Jr.
,
Mol. Phys.
32
(
2
),
363
378
(
1976
).
63.
A. R.
Davies
,
G. J.
Evans
, and
M. W.
Evans
,
Faraday Discuss. Chem. Soc.
66
,
231
238
(
1978
).
64.
K.
Singer
,
J. V. L.
Singer
, and
A. J.
Taylor
,
Mol. Phys.
37
(
4
),
1239
1262
(
1979
).
65.
W. A.
Steele
and
W. B.
Streett
,
Mol. Phys.
39
(
2
),
299
310
(
1980
).
66.
D.
Enskog
,
K. Sven. Vetenskapsakad. Handl.
63
(
1–44
),
42
(
1922
).
67.
S.
Chapman
,
T. G.
Cowling
, and
D.
Burnett
,
The Mathematical Theory of Non-Uniform Gases: An Account of the Kinetic Theory of Viscosity, Thermal Conduction and Diffusion in Gases
(
Cambridge University Press
,
1990
).
68.
D.
Chandler
,
J. Chem. Phys.
62
(
4
),
1358
1363
(
1975
).
69.
J.
Dymond
,
J. Chem. Soc., Faraday Trans. 2
68
,
1789
1794
(
1972
).
70.
S. J.
Bertucci
and
W. H.
Flygare
,
J. Chem. Phys.
63
(
1
),
1
9
(
1975
).
71.
J. H.
Dymond
,
Chem. Soc. Rev.
14
(
3
),
317
356
(
1985
).
72.
S. F. Y.
Li
,
R. D.
Trengove
,
W. A.
Wakeham
, and
M.
Zalaf
,
Int. J. Thermophys.
7
(
2
),
273
284
(
1986
).
73.
E.
Ruckenstein
and
H.
Liu
,
Ind. Eng. Chem. Res.
36
(
9
),
3927
3936
(
1997
).
74.
S.
Kämmerer
,
W.
Kob
, and
R.
Schilling
,
Phys. Rev. E
56
(
5
),
5450
(
1997
).
75.
T. B.
Schrøder
,
N. P.
Bailey
,
U. R.
Pedersen
,
N.
Gnan
, and
J. C.
Dyre
,
J. Chem. Phys.
131
(
23
),
234503
(
2009
).
76.
N.
Gnan
,
T. B.
Schrøder
,
U. R.
Pedersen
,
N. P.
Bailey
, and
J. C.
Dyre
,
J. Chem. Phys.
131
(
23
),
234504
(
2009
).
77.
R.
Chopra
,
T. M.
Truskett
, and
J. R.
Errington
,
J. Chem. Phys.
133
(
10
),
104506
(
2010
).
78.
R.
Chopra
,
T. M.
Truskett
, and
J. R.
Errington
,
J. Phys. Chem. B
114
(
32
),
10558
10566
(
2010
).
79.
R.
Chopra
,
T. M.
Truskett
, and
J. R.
Errington
,
Phys. Rev. E
82
(
4
),
041201
(
2010
).
80.
R.
Chopra
,
T. M.
Truskett
, and
J. R.
Errington
,
J. Phys. Chem. B
114
(
49
),
16487
16493
(
2010
).
81.
A.
Chakrabarty
,
A.
Konya
,
F.
Wang
,
J. V.
Selinger
,
K.
Sun
, and
Q.-H.
Wei
,
Phys. Rev. Lett.
111
(
16
),
160603
(
2013
).
82.
A.
Chakrabarty
,
F.
Wang
,
K.
Sun
, and
Q.-H.
Wei
,
Soft Matter
12
(
19
),
4318
4323
(
2016
).
83.
G. G.
Stokes
,
Trans. Cambridge Philos. Soc.
9
,
8
(
1851
).
84.
A.
Einstein
,
Ann. Phys.
322
,
549
560
(
1905
).
85.
D. C.
Wallace
,
Phys. Lett. A
122
(
8
),
418
420
(
1987
).
86.
D. C.
Wallace
,
J. Chem. Phys.
87
(
4
),
2282
2284
(
1987
).
87.
D. C.
Wallace
,
Phys. Rev. A
39
(
9
),
4843
(
1989
).
88.
D. C.
Wallace
,
Proc. R. Soc. London, Ser. A
433
(
1889
),
615
630
(
1991
).
89.
S.-T.
Lin
,
M.
Blanco
, and
W. A.
Goddard
III
,
J. Chem. Phys.
119
(
22
),
11792
11805
(
2003
).
90.
S.-T.
Lin
,
P. K.
Maiti
, and
W. A.
Goddard
III
,
J. Phys. Chem. B
114
(
24
),
8191
8198
(
2010
).
91.
T. A.
Pascal
,
S.-T.
Lin
, and
W. A.
Goddard
III
,
Phys. Chem. Chem. Phys.
13
(
1
),
169
181
(
2011
).
92.
M. A.
McCool
and
L. A.
Woolf
,
J. Chem. Soc., Faraday Trans. 1
68
,
1971
1981
(
1972
).
93.
K. S.
Pitzer
,
J. Am. Chem. Soc.
77
(
13
),
3427
3433
(
1955
).
94.
K. S.
Pitzer
,
D. Z.
Lippmann
,
R. F.
Curl
, Jr.
,
C. M.
Huggins
, and
D. E.
Petersen
,
J. Am. Chem. Soc.
77
(
13
),
3433
3440
(
1955
).
95.
K. S.
Pitzer
,
J. Chem. Phys.
7
(
8
),
583
590
(
1939
).
96.
R. L.
McGreevy
and
L.
Pusztai
,
Mol. Simul.
1
(
6
),
359
367
(
1988
).
97.
A. P.
Lyubartsev
and
A.
Laaksonen
,
Phys. Rev. E
52
(
4
),
3730
(
1995
).
98.
S.
Izvekov
and
G. A.
Voth
,
J. Chem. Phys.
123
(
13
),
134105
(
2005
).
99.
S.
Izvekov
and
G. A.
Voth
,
J. Phys. Chem. B
109
(
7
),
2469
2473
(
2005
).
100.
W. G.
Noid
,
J.-W.
Chu
,
G. S.
Ayton
,
V.
Krishna
,
S.
Izvekov
,
G. A.
Voth
,
A.
Das
, and
H. C.
Andersen
,
J. Chem. Phys.
128
(
24
),
244114
(
2008
).
101.
W. G.
Noid
,
P.
Liu
,
Y.
Wang
,
J.-W.
Chu
,
G. S.
Ayton
,
S.
Izvekov
,
H. C.
Andersen
, and
G. A.
Voth
,
J. Chem. Phys.
128
(
24
),
244115
(
2008
).
102.
M. S.
Shell
,
J. Chem. Phys.
129
(
14
),
144108
(
2008
).
103.
A.
Chaimovich
and
M. S.
Shell
,
J. Chem. Phys.
134
(
9
),
094112
(
2011
).
104.
M. S.
Shell
,
Adv. Chem. Phys.
161
,
395
441
(
2016
).
105.
M. G.
Mazza
,
N.
Giovambattista
,
H. E.
Stanley
, and
F. W.
Starr
,
Phys. Rev. E
76
(
3
),
031203
(
2007
).
106.
E.
Attia
,
J. C.
Dyre
, and
U. R.
Pedersen
,
J. Chem. Phys.
157
(
3
),
034502
(
2022
).
107.
R. C.
Reid
,
J. M.
Prausnitz
, and
B. E.
Poling
,
The Properties of Gases and Liquids
, 4th ed. (McGraw-Hill, New York,
1987
).
108.
J.
Jonas
,
High Pressure NMR
(
Springer
,
1991
).
109.
E. O.
Stejskal
and
J. E.
Tanner
,
J. Chem. Phys.
42
(
1
),
288
292
(
1965
).
110.
R. L.
Hurle
,
A. J.
Easteal
, and
L. A.
Woolf
,
J. Chem. Soc., Faraday Trans. 1
81
(
3
),
769
779
(
1985
).
111.
S.
Meckl
and
M. D.
Zeidler
,
Mol. Phys.
63
(
1
),
85
95
(
1988
).
112.
J. H.
Dymond
,
J. Chem. Phys.
60
(
3
),
969
973
(
1974
).
113.
A. J.
Easteal
,
L. A.
Woolf
, and
D. L.
Jolly
,
Physica A
121
(
1–2
),
286
292
(
1983
).
114.
A. J.
Easteal
and
L. A.
Woolf
,
Physica B+C
124
(
2
),
182
192
(
1984
).
115.
T. F.
Sun
,
J.
Bleazard
, and
A. S.
Teja
,
J. Phys. Chem.
98
(
4
),
1306
1310
(
1994
).
116.
E. W.
Lang
and
H.-D.
Lüdemann
,
High Pressure NMR
(
Springer
,
1991
), pp.
129
187
.
117.
W. J.
Lamb
and
J.
Jonas
,
J. Chem. Phys.
74
(
2
),
913
921
(
1981
).
118.
W. J.
Lamb
,
G. A.
Hoffman
, and
J.
Jonas
,
J. Chem. Phys.
74
(
12
),
6875
6880
(
1981
).
119.
R. J.
Speedy
,
F. X.
Prielmeier
,
T.
Vardag
,
E. W.
Lang
, and
H.-D.
Lüdemann
,
Mol. Phys.
66
(
3
),
577
590
(
1989
).
120.
J.
Jin
and
G. A.
Voth
,
J. Chem. Theory Comput.
14
(
4
),
2180
2197
(
2018
).
121.
J. P.
Garrahan
and
D.
Chandler
,
Proc. Natl. Acad. Sci. U. S. A.
100
(
17
),
9710
9714
(
2003
).
122.
D. S.
Simmons
and
J. F.
Douglas
,
Soft Matter
7
(
22
),
11010
11020
(
2011
).
123.
R. J.
Szukalo
and
W. G.
Noid
,
J. Phys.: Condens. Matter
33
(
15
),
154004
(
2021
).
124.
G.
Tarjus
and
D.
Kivelson
,
J. Chem. Phys.
103
(
8
),
3071
3073
(
1995
).
125.
R. L. C.
Akkermans
and
W. J.
Briels
,
J. Chem. Phys.
114
(
2
),
1020
1031
(
2001
).
126.
J. T.
Padding
and
W. J.
Briels
,
J. Chem. Phys.
117
(
2
),
925
943
(
2002
).
128.
G.
Milano
and
F.
Müller-Plathe
,
J. Phys. Chem. B
109
(
39
),
18609
18619
(
2005
).
129.
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