SupportingInformation: Temperature ... · (a) OPC3 (b) OPC3 Figure S5: Comparison of the Debye...
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Supporting Information: Temperature-Dependence of the Dielectric Relaxation of Water using Non-Polarizable Water Models Piotr Zarzycki * and Benjamin Gilbert * Energy Geosciences Division, Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, California 94720, United States E-mail: [email protected]; [email protected] List of Tables S1 Kirkwood factors, HB-dynamics ......................... S-2 List of Figures S1 Slow convergence of the static dielectric constant (TIP4P-FB) ........ S-3 S2 Convergence of the static dielectric constant (TIP3P-FB) ........... S-4 S3 Stochastic variation in ǫ in Langevin dynamics ................. S-4 S4 DRS: simulations vs experiment (H 2 O-DC, SPC-DC) ............. S-5 S5 DRS: simulations vs experiment (OPC, OPC3) ................. S-6 S6 DRS: simulations vs experiment (TI3P-FB, TIP4P-FB) ............ S-7 S7 DRS: simulations vs experiment (TIP4Q, TIP4P/ǫ) .............. S-8 S-1 Electronic Supplementary Material (ESI) for Physical Chemistry Chemical Physics. This journal is © the Owner Societies 2019
Transcript of SupportingInformation: Temperature ... · (a) OPC3 (b) OPC3 Figure S5: Comparison of the Debye...
Supporting Information:
Temperature-Dependence of the Dielectric
Relaxation of Water using Non-Polarizable Water
Models
Piotr Zarzycki∗ and Benjamin Gilbert∗
Energy Geosciences Division, Lawrence Berkeley National Laboratory, 1 Cyclotron Road,
Berkeley, California 94720, United States
E-mail: [email protected]; [email protected]
List of Tables
S1 Kirkwood factors, HB-dynamics . . . . . . . . . . . . . . . . . . . . . . . . . S-2
List of Figures
S1 Slow convergence of the static dielectric constant (TIP4P-FB) . . . . . . . . S-3
S2 Convergence of the static dielectric constant (TIP3P-FB) . . . . . . . . . . . S-4
S3 Stochastic variation in ǫ in Langevin dynamics . . . . . . . . . . . . . . . . . S-4
S4 DRS: simulations vs experiment (H2O-DC, SPC-DC) . . . . . . . . . . . . . S-5
S5 DRS: simulations vs experiment (OPC, OPC3) . . . . . . . . . . . . . . . . . S-6
S6 DRS: simulations vs experiment (TI3P-FB, TIP4P-FB) . . . . . . . . . . . . S-7
S7 DRS: simulations vs experiment (TIP4Q, TIP4P/ǫ) . . . . . . . . . . . . . . S-8
S-1
Electronic Supplementary Material (ESI) for Physical Chemistry Chemical Physics.This journal is © the Owner Societies 2019
Table S1: Calculated Kirkwood factors, rate constant for the hydrogen-bond breaking, andHB-bond energetics of water at 298K (19 non-polarizable water models).
Water Kirkwood factors Hydrogen-bond network dynamics
Model gK GK τHB [ps] kb[ps−1] n
cycleb
(νD) ∆G[kcal/mol]
three-point modelsSPC 2.515 3.744 6.003 0.167 4.94 2.144SPC/E 2.499 3.722 6.888 0.145 5.17 2.226SPC/EB 2.468 3.676 8.742 0.114 5.36 2.367SPC/FW 2.794 4.166 7.417 0.135 5.66 2.270SPC-DC 2.693 4.015 6.306 0.159 4.97 2.173TIP3P 3.605 5.381 3.658 0.273 5.88 1.851TIP3PF 3.278 4.891 4.959 0.202 6.17 2.031TIP3P-FB 2.678 3.993 7.670 0.130 5.93 2.289H2O-DC 2.670 3.980 7.340 0.136 5.37 2.263OPC3 2.655 3.958 7.539 0.133 4.99 2.279
four-point modelsOPC 2.519 3.755 7.354 0.136 4.87 2.264TIP4P 2.127 3.160 5.353 0.187 3.91 2.076TIP4PEW 2.345 3.491 7.160 0.140 4.76 2.249TIP4P-FB 2.545 3.793 8.493 0.118 4.59 2.350TIP4P2005 2.121 3.154 7.966 0.126 4.31 2.312TIP4Q 2.657 3.961 7.630 0.131 5.58 2.286TIP4P/ǫ 2.618 3.902 7.986 0.125 5.32 2.313
five-point modelsTIP5P 3.485 5.199 6.490 0.154 6.93 2.190TIP5PEW 3.646 5.441 6.173 0.162 6.76 2.161
S-2
30
40
50
60
70
80
90
0 10 20 30 40 50 60 70 80 90 100
ǫ(0) at time t=
Simulation 8 ns 10 ns 30 ns 60 ns 100 ns
0 78.16 78.34 76.781 79.41 78.07 78.68 78.33 79.012 80.59 78.79 77.57 77.16 77.673 80.26 79.18 79.54 78.77 79.414 77.59 76.47 76.98 77.67 77.515 79.17 79.71 78.03 78.10 77.636 79.64 81.00 80.63 78.70 78.647 80.85 82.48 80.83 80.72 80.348 77.54 80.02 79.51 79.67 79.279 79.49 80.01 79.88 79.91 79.50
79.27 79.41 78.84 78.78 78.78Variance σ 1.39 2.76 2.14 1.30 0.98
Average 〈ǫ(0)〉
3.32
4.05
2.83
6.01
3.56
ǫ(0)max − ǫ(0)min︸ ︷︷ ︸
static
dielectricconstan
tǫ(0)
time [ns]
60 ns30 ns
Figure S1: Slow convergence of the static dielectric constant (illustrated for the TIP4P-FB water model at 298 K). The results presented in tables are averages of the dielectricproperties over last nanosecond of 30 ns simulations.
S-3
40
50
60
70
80
90
100
0 10 20 30 40 50 60 70 80 90 100
static
dielectricconstantǫ(0)
time [ns]
81.4281.8583.1 82.0 81.2 81.5
Figure S2: Slow convergence of the static dielectric constant (illustrated for the TIP3P-FBwater model at 298 K).
40
50
60
70
80
90
100
0 5 10 15 20 25 30
40
50
60
70
80
90
100
0 5 10 15 20 25 30
time [ns]time [ns]
static
dielectricconstantǫ(0)
(a) (c)
40
50
60
70
80
90
100
0 5 10 15 20 25 30
(b)
30 ns 30 ns
Self-guided Langevin dynamicscollision frequency γ
γ = 0.1 ps−1 γ = 1.0 ps−1 γ = 2.0 ps−1
Simulation ǫ(0)1 78.51 77.72 77.052 77.26 78.73 80.773 78.15 77.80 79.274 75.88 77.47 78.575 78.56 78.35 80.276 75.89 80.13 76.73
average 77.37 78.37 78.78
std. dev. 1.25 0.98 1.65variance 1.56 0.95 2.74
30 ns
γ = 0.1 ps−1 γ = 1.0 ps−1 γ = 2.0 ps−1
time [ns]
Figure S3: Stochastic variation in ǫ in Langevin dynamics for varying collision frequency γ
in Langevin thermostat (TIP4P-FB water model): (a) 0.1 ps−1, (b) 1.0 ps
−1, (c) 2.0 ps−1.
S-4
0
10
20
30
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60
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90
100
0
10
20
30
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50
(b) H2ODC
dielectricloss
ǫ′′(ν)
dielectricconstan
tǫ′(ν)
0
10
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30
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50
60
70
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90
100
1e+07 1e+08 1e+09 1e+10 1e+11 1e+12
0
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1e+07 1e+08 1e+09 1e+10 1e+11 1e+12
dielectricloss
ǫ′′(ν)
dielectricconstan
tǫ′(ν)
(d) SPCDC
Debye Fit-exp. simulationsT [K]
269.06
293.16
313.16
333.16
Debye Fit-exp. simulationsT [K]
269.06
293.16
313.16
333.16
(c) SPCDC
(a) H2ODC
frequency ν (Hz)frequency ν (Hz)
1
2
3
4
12
31
2
3
4
4
1
2
3
4
Figure S4: Comparison of the Debye function fit to the experimental data and the simulateddielectric spectra obtained for H2ODC and SPCDC water models.S1 The difference betweenexperimental and simulated static dielectric constants are within the simulation error (2-3%). The simulates predict the water relaxation is simulated at higher frequencies andshorter relaxation times (τD) than the Debye-function fitted to the experimental data.
S-5
0
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0
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(d) OPC(c) OPC
dielectricloss
ǫ′′(ν)
dielectricconstantǫ′(ν)
0
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100
1e+07 1e+08 1e+09 1e+10 1e+11 1e+12
0
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1e+07 1e+08 1e+09 1e+10 1e+11 1e+12
dielectricloss
ǫ′′(ν)
dielectricconstan
tǫ′(ν)
frequency ν (Hz)frequency ν (Hz)
Debye Fit-exp. simulationsT [K]
269.06
293.16
313.16
333.16
Debye Fit-exp. simulationsT [K]
269.06
293.16
313.16
333.16
(b) OPC3(a) OPC3
Figure S5: Comparison of the Debye function fit to the experimental data and the simulateddielectric spectra obtained for OPC3 and OPC water models.S2,S3 The difference betweenexperimental and simulated static dielectric constants are within the simulation error (2-3%). The simulates predict the water relaxation is simulated at higher frequencies andshorter relaxation times (τD) than the Debye-function fitted to the experimental data.
S-6
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(a) TIP4Q (b) TIP4Q
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1e+07 1e+08 1e+09 1e+10 1e+11 1e+12
0
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1e+07 1e+08 1e+09 1e+10 1e+11 1e+12
dielectricloss
ǫ′′(ν)
dielectricconstan
tǫ′(ν)
dielectricloss
ǫ′′(ν)
dielectricconstan
tǫ′(ν)
(d) TIP4P/ε
Debye Fit-exp. simulationsT [K]
269.06
293.16
313.16
333.16
Debye Fit-exp. simulationsT [K]
269.06
293.16
313.16
333.16
frequency ν (Hz)frequency ν (Hz)
(c) TIP4P/ε
Figure S6: Comparison of the Debye function fit to the experimental data and the simulateddielectric spectra obtained for TIP3P-FB and TIP4P-FB water models.S4 The differencebetween experimental and simulated static dielectric constants are within the simulationerror (2-3%). The simulates predict the water relaxation is simulated at higher frequenciesand shorter relaxation times (τD) than the Debye-function fitted to the experimental data.
S-7
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0
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dielectricloss
ǫ′′(ν)
dielectricconstantǫ′(ν)
frequency ν (Hz)
0
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1e+07 1e+08 1e+09 1e+10 1e+11 1e+12
0
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1e+07 1e+08 1e+09 1e+10 1e+11 1e+12
frequency ν (Hz)
dielectricloss
ǫ′′(ν)
dielectricconstantǫ′(ν)
(a) TIP3P-FB (b) TIP3P-FB
(c) TIP4P-FB (d) TIP4P-FB
Debye Fit-exp. simulationsT [K]
269.06
293.16
313.16
333.16
Debye Fit-exp. simulationsT [K]
269.06
293.16
313.16
333.16
Figure S7: Comparison of the Debye function fit to the experimental data and the simulateddielectric spectra obtained for TIP4Q and TIP4P/ǫ water models.S5,S6 The difference betweenexperimental and simulated static dielectric constants are within the simulation error (2-3%).The simulates predict the water relaxation is simulated at higher frequencies and shorterrelaxation times (τD) than the Debye-function fitted to the experimental data.
S-8
ACKNOWLEDGEMENTS
This work was supported by funding from U.S. Department of Energy (DOE) Chemical
Sciences, Geosciences, and Biosciences Division under Contract DE-AC02- 05CH11231.
References
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