+ All Categories
Home > Documents > A Successful Model for the Condensed Phases of water...

A Successful Model for the Condensed Phases of water...

Date post: 01-Mar-2019
Category:
Upload: vanhanh
View: 218 times
Download: 0 times
Share this document with a friend
28
A Successful Model for the Condensed Phases of water : TIP4P/2005
Transcript

A Successful Model for the Condensed Phases of water : TIP4P/2005

A Successful Model for the Condensed Phases of Water : TIP4P/2005

Departamento de Quımica Fısica

Universidad Complutense

Madrid, SPAIN

Carlos Vega

Jose Luis F. Abascal

Maria M. Conde

Juan L. Aragones

MODELS OF WATER

SPC/E Berendsen et al. 1987

� � � � � �� � � � � �� � � � � �� � � � � �� � � � � �� � � � � �� � � � � �� � � � � �� � � � � �� � � � � �

� � � � � �� � � � � �� � � � � �� � � � � �� � � � � �� � � � � �� � � � � �� � � � � �� � � � � �� � � � � �

� � � � � �� � � � � �� � � � � �� � � � � �� � � � � �� � � � � �� � � � � �� � � � � �� � � � � �� � � � � �

� � � � � �� � � � � �� � � � � �� � � � � �� � � � � �� � � � � �� � � � � �� � � � � �� � � � � �� � � � � �

� � � � � � � � � � �� � � � � � � � � � �� � � � � � � � � � �� � � � � � � � � � �� � � � � � � � � � �� � � � � � � � � � �� � � � � � � � � � �� � � � � � � � � � �� � � � � � � � � � �� � � � � � � � � � �� � � � � � � � � � �� � � � � � � � � � �� � � � � � � � � � �� � � � � � � � � � �� � � � � � � � � � �� � � � � � � � � � �� � � � � � � � � � �� � � � � � � � � � �� � � � � � � � � � �� � � � � � � � � � �� � � � � � � � � � �

� � � � � � � � � � �� � � � � � � � � � �� � � � � � � � � � �� � � � � � � � � � �� � � � � � � � � � �� � � � � � � � � � �� � � � � � � � � � �� � � � � � � � � � �� � � � � � � � � � �� � � � � � � � � � �� � � � � � � � � � �� � � � � � � � � � �� � � � � � � � � � �� � � � � � � � � � �� � � � � � � � � � �� � � � � � � � � � �� � � � � � � � � � �� � � � � � � � � � �� � � � � � � � � � �� � � � � � � � � � �� � � � � � � � � � �

� � � � � � � � � � � � �� � � � � � � � � � � � �� � � � � � � � � � � � �� � � � � � � � � � � � �� � � � � � � � � � � � �� � � � � � � � � � � � �� � � � � � � � � � � � �� � � � � � � � � � � � �� � � � � � � � � � � � �� � � � � � � � � � � � �� � � � � � � � � � � � �� � � � � � � � � � � � �� � � � � � � � � � � � �� � � � � � � � � � � � �� � � � � � � � � � � � �� � � � � � � � � � � � �� � � � � � � � � � � � �� � � � � � � � � � � � �� � � � � � � � � � � � �� � � � � � � � � � � � �� � � � � � � � � � � � �� � � � � � � � � � � � �� � � � � � � � � � � � �

� � � � � � � � � � � � �� � � � � � � � � � � � �� � � � � � � � � � � � �� � � � � � � � � � � � �� � � � � � � � � � � � �� � � � � � � � � � � � �� � � � � � � � � � � � �� � � � � � � � � � � � �� � � � � � � � � � � � �� � � � � � � � � � � � �� � � � � � � � � � � � �� � � � � � � � � � � � �� � � � � � � � � � � � �� � � � � � � � � � � � �� � � � � � � � � � � � �� � � � � � � � � � � � �� � � � � � � � � � � � �� � � � � � � � � � � � �� � � � � � � � � � � � �� � � � � � � � � � � � �� � � � � � � � � � � � �� � � � � � � � � � � � �� � � � � � � � � � � � �

109.5

−2

o

δ /LJ

δ+ δ+

A1o

δ/|e| = 0,4238

σ = 3,16557A

ε/k = 78,2K

µ = 2,35D(1,85)

TIP4P Jorgensen et al. 1983

� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �

� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �

� � �� � �� � �� � �� � �� � �

� � � � � � � � � � �� � � � � � � � � � �� � � � � � � � � � �� � � � � � � � � � �� � � � � � � � � � �� � � � � � � � � � �� � � � � � � � � � �� � � � � � � � � � �� � � � � � � � � � �� � � � � � � � � � �� � � � � � � � � � �� � � � � � � � � � �� � � � � � � � � � �� � � � � � � � � � �� � � � � � � � � � �� � � � � � � � � � �� � � � � � � � � � �� � � � � � � � � � �� � � � � � � � � � �� � � � � � � � � � �� � � � � � � � � � �

� � � � � � � � � � �� � � � � � � � � � �� � � � � � � � � � �� � � � � � � � � � �� � � � � � � � � � �� � � � � � � � � � �� � � � � � � � � � �� � � � � � � � � � �� � � � � � � � � � �� � � � � � � � � � �� � � � � � � � � � �� � � � � � � � � � �� � � � � � � � � � �� � � � � � � � � � �� � � � � � � � � � �� � � � � � � � � � �� � � � � � � � � � �� � � � � � � � � � �� � � � � � � � � � �� � � � � � � � � � �� � � � � � � � � � �

� � � � � � � � � � � � � �� � � � � � � � � � � � � �� � � � � � � � � � � � � �� � � � � � � � � � � � � �� � � � � � � � � � � � � �� � � � � � � � � � � � � �� � � � � � � � � � � � � �� � � � � � � � � � � � � �� � � � � � � � � � � � � �� � � � � � � � � � � � � �� � � � � � � � � � � � � �� � � � � � � � � � � � � �� � � � � � � � � � � � � �� � � � � � � � � � � � � �� � � � � � � � � � � � � �� � � � � � � � � � � � � �� � � � � � � � � � � � � �� � � � � � � � � � � � � �� � � � � � � � � � � � � �� � � � � � � � � � � � � �� � � � � � � � � � � � � �� � � � � � � � � � � � � �� � � � � � � � � � � � � �� � � � � � � � � � � � � �

� � � � � � � � � � � � � �� � � � � � � � � � � � � �� � � � � � � � � � � � � �� � � � � � � � � � � � � �� � � � � � � � � � � � � �� � � � � � � � � � � � � �� � � � � � � � � � � � � �� � � � � � � � � � � � � �� � � � � � � � � � � � � �� � � � � � � � � � � � � �� � � � � � � � � � � � � �� � � � � � � � � � � � � �� � � � � � � � � � � � � �� � � � � � � � � � � � � �� � � � � � � � � � � � � �� � � � � � � � � � � � � �� � � � � � � � � � � � � �� � � � � � � � � � � � � �� � � � � � � � � � � � � �� � � � � � � � � � � � � �� � � � � � � � � � � � � �� � � � � � � � � � � � � �� � � � � � � � � � � � � �� � � � � � � � � � � � � �

δ+ δ+

LJ

0.957

104.5

−2

0.15Α

Αο

ο

ο

δ

δ/|e| = 0,52

σ = 3,154A

ε/k = 78,02K

µ = 2,18D

MODELS OF WATER

TIP5P , Mahoney and Jorgensen , JCP, 2000

δ/|e| = 0,241

σ = 3,12A

ε/k = 80,52K

µ = 2,29D

The phase diagram of water

J.Finney, Phyl.Trans.R.Soc.Lond.B,(2004)

1900 Tammann , 1912 Bridgman, 1968 Whalley , 1998 Finney et al.

Obtaining free energies for the solid (or fluid-solid coexistence)

Cell occupancy W. G. Hoover and F. H. Ree, JCP, 1968

Direct coexistence A. J. C. Ladd and L. V. Woodcock,CPL, 1977.

Constrained fluid lambda-integration

G. Grochola , JCP, 2004, 2005.

D. M. Eike and J. F. Brennecke and E. J. Maginn, JCP, 2005.

Self referential method M. B. Sweatman, PRE, 2005.

Phase switch N. B. Wilding and A. D. Bruce, PRL, 1997, 2000.

Einstein crystal D. Frenkel and A. J. C. Ladd, JCP, 1984.

J. M. Polson and E. Trizac and S. Pronk and D. Frenkel, JCP, 2000.

Water. C.Vega and P. A. Monson, JCP, 1998

Water. E.G.Noya, M.M.Conde and C. Vega , JCP, 2008.

Lattice dynamics Water.G. T. Gao and X. C. Zeng and H. Tanaka, JCP, 2000.

PHASE DIAGRAMS FOR THE TIP4P AND SPC/E MODELSE.Sanz, C.Vega, J.L.F.Abascal and L.G.MacDowell,PRL, 92, 255701, (2004)

Strategy : Free energy calculations + Gibbs Duhem integration (Kofke, 1993)

0.01

0.1

1

10

100 150 200 250 300 350 400 450

P (

GP

a)

T (K)

I

II

VI

VIII VII

liquidV

III

0.01

0.1

1

10

150 200 250 300 350 400 450

P (

GP

a)

T (K)

I

II

VI

VIII VII

liquid

V

III

0.01

0.1

1

10

100 150 200 250 300 350 400 450

P+

0.1

(G

Pa)

T (K)

I

II

VI

VIII VII

liquid

TIP4P Experiment SPC/E

The ideas leading to TIP4P/2005

J.L.F.Abascal and C.Vega, JCP, 123, 234505, (2005)

The model takes from TIP4P the geometry of the charge distribution,

since it reproduces correctly the phase diagram of water (due to a good

balance between dipolar and quadrupolar forces ).

The model takes from SPC/E the idea of reproducing the vaporization

enthalpy after including the vaporization correction.

The model takes from TIP5P the idea of using the maximum in density of

water as a target property.

The model also includes as target properties the density of several ice

polymorphs and the melting point of ice Ih.

Potential models of water

Model dOH H-O-H σ (ε/kB) qH dOM dOL

TIP3P 0.957 104.5 3.150 76.5 0.417 0 -

TIP4P 0.957 104.5 3.154 78.0 0.52 0.15 -

TIP4P/2005 0.957 104.5 3.158 93.2 0.556 0.155 -

TIP5P 0.957 104.5 3.120 80.5 0.241 - 0.70

Does such a small change make any difference ?

Ten properties to be analyzed

1. VLE and critical point.

2. Surface tension.

3. Densities of the different ice polymorphs.

4. Phase diagram calculations.

5. Melting temperature.

6. TMD. α, and κT .

7. Structure of water and ice Ih.

8. EOS at high pressures.

9. Self-diffusion coefficient.

10. Dielectric constant.

Award 0 to 3 points for each property (3=best)

Vapour-liquid equilibrium and surface tension

300

350

400

450

500

550

600

650

0 0.2 0.4 0.6 0.8 1

T (

K)

ρ(g/cm3)

ExptlTIP4P/2005

TIP4PTIP3PTIP5P

200 300 400 500 600 700T / K

0

20

40

60

80

σ

/ (m

N /

m)

Experiment TIP3PTIP5PTIP4PTIP4P/2005

σ =Lz

2[pN − pT ] (1)

σ = lım∆S→0

−kT

2∆S

(

ln⟨

exp(−∆U+/kT )⟩

− ln⟨

exp(−∆U−/kT )⟩)

(2)

TAM. G. J. Gloor , G. Jackson , F. J. Blas and E. de Miguel, JCP, 123, 134703, (2005)

Density predictions for ices

-0.1

-0.05

0

0.05

0.1

ρ−ρ

TIP5P SPC TIP4P TIP3P TIP4P/2005

exp

6.5% 2.2% 2.6% 3.5% 0.9%

IIIV

XIIc

VIXII

IhIX

VIII

Phase diagram of TIP3P and TIP5P

-500

0

500

1000

140 160 180 200 220 240 260 280 300

p (

MP

a)

T (K)

liquid

Ih

II

V

liquidIh

II

TIP3PExpt

-500

0

500

1000

1500

2000

2500

3000

3500

4000

220 240 260 280 300 320 340 360p (

MP

a)

T (K)

liquid

Ih

II

VI

liquidVI

VII

TIP5PExpt

Phase diagram of TIP4P/2005

100 200 300 400 500

T(K)100

1000

10000

1e+05

p(b

ar) Liquid

II

III

I

V

VI

VIIVIII

100 200 300 400 500

T (K)

100

1000

10000

1e+05

p (

bar)

VIIPlastic crystal

(XV?)VIII

VI

V

Ih

IILiquid

III

J.L.Aragones,M.M.Conde,E.G.Noya and C.Vega,Phys.Chem.Chem.Phys., in press,

2008.

Melting properties of ice Ih

Model TIP3P SPC/E TIP4P TIP4P/2005 TIP5P Exptl

Tm(K) 146 215 232 252 274 273.15

ρl 1.017 1.011 1.002 0.993 0.987 0.999

ρIh 0.947 0.950 0.940 0.921 0.967 0.917

∆Hm 0.30 0.74 1.05 1.16 1.75 1.44

dp/dT -66 -126 -160 -135 -708 -137

Tm/Tc 0.25 0.337 0.394 0.394 0.525 0.422

DIRECT DETERMINATION OF THE FLUID-SOLID EQUILIBRIA

R.G. Fernandez, J.L.F.Abascal and C.Vega, JCP, 124, 144506, (2006)

Melting temperatures obtained by direct coexistence are in agreement with those

obtained from free energy calculations

Temperature of maximum density

150 200 250 300 350T (K)

0,97

0,98

0,99

1

1,01

1,02

1,03

1,04

ρ (g

/cm

3 )

TIP3P

TIP4P/2005

TIP5P

TIP4P

O-O radial distribution function : water and ice Ih

2 4 6 8 10r / Å

0

0.5

1

1.5

2

2.5

3

3.5

g (

r)

Experiment TIP4PTIP4P/2005

2 4 6 8 10r / Å

0

1

2

3

4

5

6

7

8

9

g (

r)

Experiment TIP4PTIP4P/2005

Equation of state and diffusion coefficient of water

1.2 1.25 1.3 1.35 1.4

ρ (g/cm3)

10000

12500

15000

17500

20000

22500

p (

bar)

Exp.

TIP4P/2005TIP4PTIP3PTIP5P

1

2

4

8

3.1 3.2 3.3 3.4 3.5 3.6

109 D

(m

2 /s)

103/T (K-1)

TIP3PTIP4PTIP5P

TIP4P/2005Exptl

Property TIP3P TIP4P TIP4P/2005 TIP5P

1. VLE, Tc 1 2 3 0

2. Surface tension 1 2 3 0

3. ρ ices 0 2 3 1

4. Phase diagram 0 2 3 1

5. Tm melting prop. 0 1 2.5 2.5

6. TTMD, α, κT 0 1 3 2

7. Structure 0 1 2.5 2.5

8. EOS (high p) 2 1 3 0

9. D 0 1 3 2

10. ε 2 0 1 3

Total 6 13 27 14

Viscosity of water at room T and p

Model Viscosity (centi Poises)

TIP3P 0,33

SPC/E 0,73

TIP4P/2005 0,86

Experiment 0,89

Variation of the TMD with p, and EOS for supercooled water

0 250 500 750 1000 1250 1500p / bar

220

230

240

250

260

270

280

T /

K TIP4P/2005Experimental

150 175 200 225 250 275 300 325 350 375 400

T / K0,85

0,875

0,9

0,925

0,95

0,975

1

1,025

1,05

den

sit

y /

g c

m -3

TIP4P/2005Experiment

Experiment (confined water): F. Mallamace et al., PNAS, 104, 18387, (2007)

Calculations: H.L.Pi, C.Vega, et al., Mol.Phys. , submitted (J.J.Weiss special issue)

240 260 280 300 320 340 360 380

T (K)

30

40

50

60

70

80

9010

5 κ T (M

Pa

-1)

Expt (100 MPa)

Expt (0.1 MPa)

TIP4P/2005

240 260 280 300 320 340 360 380

T (K)

30

40

50

60

70

80

90

105 κ T

(MP

a-1)

Expt.

TIP4P

SPC/E

TIP5P

0.1 MPa

Isothermal compressibility

Conclusions

The TIP4P/2005 model (designed to be used with Ewald sums) keeps thegeometry of TIP4P, incorporates the polarization correction of Berendsenet al. (as SPC/E) and incorporates the TMD as a target property (as TIP5P)

Since the model does not include polarizability it fails in describing thedielectric constant of water and the properties of the vapor phase.

The model provides a quite good description of the phase diagram ofwater, density of ices, TMD of water , melting point , (by design). Themodel describes quite well D, EOS at high p, VLE, Tc, σ, η, kT andTMD(p).

The model provides an overall improvement (27 points) in the descriptionof water with respect to TIP3P (6 points) , TIP4P (13 points), TIP5P (14points) and SPC/E (21 points). The model is probably close to the best ofwhat can be achieved by a rigid, non-polarizable model , with a LJ centerand three charges.

References.

The model.

J.L.F.Abascal and C.Vega,J.Chem.Phys., 123, 234505, (2005)

Free energy calculations and phase diagram determination.

C.Vega, E.Sanz, J.L.F.Abascal and E.G.Noya , Determination of

phase diagrams via computer simulation: methodology and applications to

water, electrolytes and proteins , J.Phys.Condens.Matter 20, 153101,

(2008).

Comparing TIP4P/2005 with other water models.

C. Vega, J. L. F. Abascal , M. M. Conde and J. L. Aragones What ice

can teach us about water interactions: a critical comparison of the

performance of different water models, Faraday Discussions, 141, 251,

(2009). DOI: 10.1039/b805531a

Dipole and quadrupole moments

Model µ Qxx Qyy Qzz QT µ/QT

SPC 2.27 2.12 -1.82 -0.29 1.97 1.15

SPC/E 2.35 2.19 -1.88 -0.30 2.03 1.15

TIP3P 2.35 1.76 -1.68 -0.08 1.72 1.36

TIP4P 2.18 2.20 -2.09 -0.11 2.15 1.01

TIP4P/2005 2.30 2.36 -2.23 -0.13 2.30 1.00

TIP5P 2.29 1.65 -1.48 -0.17 1.56 1.46

Gas(Expt.) 1.85 2.63 -2.50 -0.13 2.56 0.72

Computing the free energy for solids

A=A Ein−idCM

Λ )3+kTln(V/

Solid

Λ )3−kTln(V/

Solid with one fixedparticle

Ideal Einstein moleculewith one fixed particle

A=A Ein−mol−id

Ideal Einstein molecule

∆Α + ∆Α1 2 ∆Α + ∆Α1 2* *

∆Α 3*

Ideal Einstein crystalwith fixed CM

Solid with fixed CM

Solid

(b)(a)

The Einstein molecule approach

EINSTEINMOLECULEMETHOD

CARRIER( Atom O fixed )

NVT ( T )

ANNEALING ��� ���������

����

2

����� ����� � �� � 1

� �������� 1

�� �������� 2

ANISOTROPIC NpT

U lattice

��� ��� ���� 1

��� � !�! "�" #�# $�$ 2

∆A 1

EVALUATING

∆A 2

EVALUATING% %% %& && &'�' (�( )�) *�* 2

+�+ ,�,- -- -. .. .

1/�/�/ 0�0�0

U sol

U Ein,or

Ein−mol−idU

U Ein,or

Ein−mol−idU 1 11 11 12 22 22 23�3 4�4 56 2

7�789 99 9: :: :

1;�; <�<

U sol=0

E.G.Noya, M.M.Conde and C.Vega, J.Chem.Phys., 129, 104704, (2008)


Recommended