Electronically coarse grained waterAndrew Jones, Flaviu Cipcigan, Vlad Sokhan, Jason Crain, Glenn Martyna

A. Jones, F. Cipcigan, V. Sokhan, J. Crain, G. Martyna, Electronically coarse grained model for water, PRL 110, 227801 (2013)

A. Jones, Quantum drude oscillators for accurate many-body intermolecular forces, PhD thesis, The University of Edinburgh

Challenge: extending the transferability of empirical potentialsOur solution: coarse grained electronic structure

Free parameters

Response

1. Quantum Drude Oscillator (QDO) Light negative particle tethered harmonicallyto heavy positive, oppositely charged nucleus

: reduced mass : spring constant : charge

Polarisation:

Dispersion:

…

2. Invariants predicted by QDOs

Polarisation: Dispersion:

H Li K RbCs

1.5

0.5

1.0

1.5

0.5

1.0

1.5

0.5

1.0

He Ne Ar Kr Xe

CH4

H2O

H LiK Rb Cs

He Ne Ar Kr Xe

BH3 CH4 NH3 H2O

= 0.3656 amu

= 0.6287

= -1.1973 e

3. QDO-water model

Frame: ground state moments

QDO: molecular response

+ 0.605 e

- 1.21 e

0.2667 Å0.9572 ÅO

H

M

H 104.52º

4. QDO-water model (continued)

Short range interactions

Repulsion

Electrostatic damping Gaussian charges

5. Efficient sampling: APIMD-QDO

1. Write partition function of N particles as path integral, P slices

2. Define effective (classical) potential of N×P particles

3. Approximate resulting high temperature density matrices

(Adiabatic Path Integral Molecular Dynamics applied to QDOs)

6 . Liquid QDO-water

Radial distribution function Vapour pressure

exp: 43.91 kJ/mol

r / Å2 3 4 5 6 7

g OO(r

)

0.0

0.5

1.0

1.5

2.0

2.5Skinner et al. (exp).Exp. (Soper)QDO, N = 300

46 ± 2 kJ / mol

Dielectric constant

exp: 7879 ± 2

Surface tension

exp: 71.73 mN / m72.6 ± 1 mN / m

Density and dipole moment Electronic distribution

7 . Liquid–vapour interface (unoptimised model)

(ground state distribution substracted)

1 Å

13 Å

15 Å

Dip

ole M

om

ent ±

1σ (D

ebye)

Den

sity

± 1σ

(kg

m

)-3

0

200

400

600

800

1000

1 5 10 15 20 13

1.855

2.6

charge loss

charge gain

Surface charge density

8 . Liquid–vapour interface (continued)

1 5 10 15 20 13

Distance from centre (Å)

-1.0

-0.5

0

0.5

1.0Su

rfac

e ch

arge

± 1σ

(e /

Å3 ×

10

-3)

Surface expansion of nearest neighbour distance by 1–2%

9 . Liquid–vapour interface (continued)

2.7

2.75

2.8

2.85

2.9

2.95

3

O-O

dis

tan

ce (Å

)

surfacebulkhydrogen bonded

neighbours

(only classical model with a surface expansion)

neighbours in shell of radius 3.5 Å

nearest neighbour only

Weaker hydrogen bond at the surface

10 . Liquid–vapour interface (continued)

The hydrogen bond forms in the valleys of the PMF (Potential of Mean Force)

How are hydrogen bonds broken?

11 . Liquid–vapour interface (continued)

2 Acceptor: 16%

2 Donor: 4%

1 Donor: 80%

charge loss

charge gain

neighbour oxygen

Tetrahedrality Number of hydrogen bonds

12 . Liquid–vapour interface (continued)

0

0.5

1

1.5

2

2.5

-1 -0.5 0 0.5 1

p(q

)

q

BulkSurface

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 1 2 3 4 5

bulk

surface

Number of hydrogen bondsFr

actio

n of

mol

ecul

es