Post on 13-Apr-2017
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