Flaviu Cipcigan, Vlad Sokhan, Jason Crain, Glenn Martyna

Modelling molecules withquantum harmonic oscillators

flickr.com/photos/marittoledo/10398913404

Quantum Drude Oscillators

Path integral molecular dynamics

QDO–waterHow to use Quantum Drude Oscillators to

construct a realistic model of the water molecule

New physics we discovered using QDO–waterInsights into the physics of water

How to represent molecules using electrons on a spring

How to simulate quantum physics using classical molecular dynamics

Quantum Drude OscillatorsModelling electronic response is important to accurately predict materials properties.

Quantum Drude Oscillators are a new modelling method representing molecules via electrons on a spring.

The Quantum Drude Oscillator

schematic ground state is gaussian

Construction

Jones, Crain, Sokhan, Whitfield, Martyna, PRB 87, 144103 (2013)

Polarisation

The Quantum Drude Oscillator

second order correction to

ground state energy

multipole polarisation coefficients

QDO test charge

R

Jones, Crain, Sokhan, Whitfield, Martyna, PRB 87, 144103 (2013)

Dispersion

The Quantum Drude Oscillator

QDO QDO

R

Jones, Crain, Sokhan, Whitfield, Martyna, PRB 87, 144103 (2013)

H LiK Rb Cs

He Ne Ar Kr Xe

BH3 CH4 NH3 H2O

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

The Quantum Drude OscillatorInvariants

Jones, Crain, Sokhan, Whitfield, Martyna, PRB 87, 144103 (2013)

The Quantum Drude OscillatorParameter fitting

Jones, Crain, Sokhan, Whitfield, Martyna, PRB 87, 144103 (2013)

Path integral molecular dynamicsSimulating quantum physics is inefficient.

Path integral molecular dynamics is a method tosimulate quantum physics via classical sampling methods.

Factor the density matrix

Density matrix High temperature “slice”

Partition function

Jones, Crain, Cipcigan, Sokhan, Modani, Martyna, MolPhys 111 (22-23), 3465-3477 (2013)

τ

Approximate the density matrices

external potentialreference density matrix

(harmonic oscillator)

Jones, Crain, Cipcigan, Sokhan, Modani, Martyna, MolPhys 111 (22-23), 3465-3477 (2013)

Diagonalise

Transforming a strongly coupled system to an uncoupled system.

Jones, Crain, Cipcigan, Sokhan, Modani, Martyna, MolPhys 111 (22-23), 3465-3477 (2013)

Change variables while keeping Z(β) constant

Add faux conjugate momenta

faux momenta

Jones, Crain, Cipcigan, Sokhan, Modani, Martyna, MolPhys 111 (22-23), 3465-3477 (2013)

While keeping Z(β) constant

Construct effective classical Hamiltonian

Jones, Crain, Cipcigan, Sokhan, Modani, Martyna, MolPhys 111 (22-23), 3465-3477 (2013)

Sampling this Hamiltonian leads to exact quantum physics

QDO–waterWater is challenging to simulate, with no definitive model.

We constructed a realistic molecular model of water using Quantum Drude Oscillators with excellent predictive power.

The model

Frame gives ground state charge distribution

QDO gives responsesto external fields

= 0.3656 amu

= 0.6287

= -1.1973 e + 0.605 e

- 1.21 e

0.2667 Å0.9572 ÅO

H

M

H 104.52º

Long range

Jones, Cipcigan, Sokhan, Crain, Martyna, PRL 110 (22), 227801 (2013)

Coulomb dampingRepulsion

The modelShort range

Jones, Cipcigan, Sokhan, Crain, Martyna, PRL 110 (22), 227801 (2013)

The modelParameter fitting

QDO

ab initio

empiricalpotential

Sokhan, Jones, Cipcigan, Crain, Martyna, PNAS 112 (20), 6341-6346 (2015)

Liquid–vaopour coexistenceEquation of state matches experiment to 1%

More accurate than models fit to match these densities

Sokhan, Jones, Cipcigan, Crain, Martyna, PNAS 112 (20), 6341-6346 (2015)

Surface tensionImportant quantity for biological interfaces

Matches experiment across a range of temperatures

Cipcigan, Sokhan, Jones, Crain, Martyna, PCCP 17 (14), 8660-8669 (2015)

Liquid radial distribution functionKey quantity determing the structure of a disordered phase

Predictions compare favourably with two independent experiments

Sokhan, Jones, Cipcigan, Crain, Martyna, PNAS 112 (20), 6341-6346 (2015)

QDOX-ray scatteringneutron scattering

High pressure solid (ice II)

6

6.2

6.4

c (Å

)

12.6

12.9

13.2

13.5

100 150

a (Å

)

T (K)

QDO

QDO

neutron scattering

neutron scattering

2%

c

a

Predicted structure matches experimentResults demonstrate excellent transferability of QDO–water

Sokhan, Jones, Cipcigan, Crain, Martyna, PNAS 112 (20), 6341-6346 (2015)

structure of ice II quantified by two lattice constants

Supercritical waterIndustrially important as a green solvent

Isotherms match experiment across range of temperatures

Sokhan, Jones, Cipcigan, Crain, Martyna, PRL 115 (11), 117801 (2015)

673 K773 K

873 K

crossoverdensity

QDO–water is the only model with predictions transferable from high pressure ice to liquid and

supercritical water.

Water has many anomalies essential for life, but some of the physical mechanisms behind these anomalies are still a mystery.

We used QDO–water to understand the link betweenwater’s molecular structure and its condensed phase properties.

Insights into the physics of water

Water is the solvent of life due to its ability to form a network of hydrogen bonds

acceptor

donor

donor

acceptor

These hydrogen bonds are of two types

Water prefers to lose an acceptor bond

Cipcigan, Sokhan, Jones, Crain, Martyna, PCCP 17 (14), 8660-8669 (2015)

dd daa dda ddaa ddaaa

0.0

0.2

0.4

0.6

fre

qu

en

cy

~5% of molecules have 5 hydrogen bonds

Cipcigan, Sokhan, Jones, Crain, Martyna, PCCP 17 (14), 8660-8669 (2015)

0 30 60 90 120 150 180

0

30

60

90

θ / degrees

φ /

degr

ees

The preference for donor bondsorients molecules at the surface of water

Cipcigan, Sokhan, Jones, Crain, Martyna, PCCP 17 (14), 8660-8669 (2015)

gas

liquid

high probability

low probability

Molecular dipole moment is a reporter of local structure in supercritical water

Sokhan, Jones, Cipcigan, Crain, Martyna, PRL 115 (11), 117801 (2015)

Quantum Drude Oscillators

Path integral molecular dynamics

New method to simulate materials over a wide range of conditions.

Easy to parameterise using properties of isolated molecules.

Method to simulate quantum physics via classical sampling methods.

Allows inexpensive treatement of electronic responses.

Water is a grand challange substance essential for life.

QDO–water predicts real water’s properties with splendid accuracy.

QDO–water

Insights into the physics of waterWater prefers to lose an acceptor over a donor bond.This asymmetry leads to a preferential orientation at the surface.The molecular dipole moment is a reporter of local structure.

Next steps Treat biophysical problems

with predictive accuracy

Illustration of Mycoplasma mycoidesDavid S. Goodsell, Scripps Research Institute

Sokhan V, Jones A, Cipcigan F, Crain J, Martyna G (2015) Molecular-scale remnants of the liquid-gas transition in supercritical polar fluidsPhysical Review Letters 115 (11), 117801

VP Sokhan, AP Jones, FS Cipcigan, J Crain, GJ Martyna (2015) Signature properties of water: Their molecular electronic originsProceedings of the National Academy of Sciences 112 (20), 6341-6346

FS Cipcigan, VP Sokhan, AP Jones, J Crain, GJ Martyna (2015) Hydrogen bonding and molecular orientation at the liquid–vapour interface of waterPhysical Chemistry Chemical Physics 17 (14), 8660-8669

A Jones, F Cipcigan, VP Sokhan, J Crain, GJ Martyna (2013) Electronically coarse-grained model for waterPhysical Review Letters 110 (22), 227801

AP Jones, J Crain, FS Cipcigan, VP Sokhan, M Modani, GJ Martyna (2013) Electronically coarse-grained molecular dynamics using quantum Drude oscillatorsMolecular Physics 111 (22-23), 3465-3477