Modelling molecules with quantum harmonic oscillators
-
Upload
flaviu-cipcigan -
Category
Science
-
view
282 -
download
2
Transcript of Modelling molecules with quantum harmonic oscillators
![Page 1: Modelling molecules with quantum harmonic oscillators](https://reader034.fdocuments.in/reader034/viewer/2022051404/58a02c2b1a28ab4e768b674d/html5/thumbnails/1.jpg)
Flaviu Cipcigan, Vlad Sokhan, Jason Crain, Glenn Martyna
Modelling molecules withquantum harmonic oscillators
![Page 2: Modelling molecules with quantum harmonic oscillators](https://reader034.fdocuments.in/reader034/viewer/2022051404/58a02c2b1a28ab4e768b674d/html5/thumbnails/2.jpg)
flickr.com/photos/marittoledo/10398913404
![Page 3: Modelling molecules with quantum harmonic oscillators](https://reader034.fdocuments.in/reader034/viewer/2022051404/58a02c2b1a28ab4e768b674d/html5/thumbnails/3.jpg)
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
![Page 4: Modelling molecules with quantum harmonic oscillators](https://reader034.fdocuments.in/reader034/viewer/2022051404/58a02c2b1a28ab4e768b674d/html5/thumbnails/4.jpg)
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.
![Page 5: Modelling molecules with quantum harmonic oscillators](https://reader034.fdocuments.in/reader034/viewer/2022051404/58a02c2b1a28ab4e768b674d/html5/thumbnails/5.jpg)
The Quantum Drude Oscillator
schematic ground state is gaussian
Construction
Jones, Crain, Sokhan, Whitfield, Martyna, PRB 87, 144103 (2013)
![Page 6: Modelling molecules with quantum harmonic oscillators](https://reader034.fdocuments.in/reader034/viewer/2022051404/58a02c2b1a28ab4e768b674d/html5/thumbnails/6.jpg)
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)
![Page 7: Modelling molecules with quantum harmonic oscillators](https://reader034.fdocuments.in/reader034/viewer/2022051404/58a02c2b1a28ab4e768b674d/html5/thumbnails/7.jpg)
Dispersion
The Quantum Drude Oscillator
QDO QDO
R
Jones, Crain, Sokhan, Whitfield, Martyna, PRB 87, 144103 (2013)
![Page 8: Modelling molecules with quantum harmonic oscillators](https://reader034.fdocuments.in/reader034/viewer/2022051404/58a02c2b1a28ab4e768b674d/html5/thumbnails/8.jpg)
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)
![Page 9: Modelling molecules with quantum harmonic oscillators](https://reader034.fdocuments.in/reader034/viewer/2022051404/58a02c2b1a28ab4e768b674d/html5/thumbnails/9.jpg)
The Quantum Drude OscillatorParameter fitting
Jones, Crain, Sokhan, Whitfield, Martyna, PRB 87, 144103 (2013)
![Page 10: Modelling molecules with quantum harmonic oscillators](https://reader034.fdocuments.in/reader034/viewer/2022051404/58a02c2b1a28ab4e768b674d/html5/thumbnails/10.jpg)
Path integral molecular dynamicsSimulating quantum physics is inefficient.
Path integral molecular dynamics is a method tosimulate quantum physics via classical sampling methods.
![Page 11: Modelling molecules with quantum harmonic oscillators](https://reader034.fdocuments.in/reader034/viewer/2022051404/58a02c2b1a28ab4e768b674d/html5/thumbnails/11.jpg)
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
![Page 12: Modelling molecules with quantum harmonic oscillators](https://reader034.fdocuments.in/reader034/viewer/2022051404/58a02c2b1a28ab4e768b674d/html5/thumbnails/12.jpg)
Approximate the density matrices
external potentialreference density matrix
(harmonic oscillator)
Jones, Crain, Cipcigan, Sokhan, Modani, Martyna, MolPhys 111 (22-23), 3465-3477 (2013)
![Page 13: Modelling molecules with quantum harmonic oscillators](https://reader034.fdocuments.in/reader034/viewer/2022051404/58a02c2b1a28ab4e768b674d/html5/thumbnails/13.jpg)
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
![Page 14: Modelling molecules with quantum harmonic oscillators](https://reader034.fdocuments.in/reader034/viewer/2022051404/58a02c2b1a28ab4e768b674d/html5/thumbnails/14.jpg)
Add faux conjugate momenta
faux momenta
Jones, Crain, Cipcigan, Sokhan, Modani, Martyna, MolPhys 111 (22-23), 3465-3477 (2013)
While keeping Z(β) constant
![Page 15: Modelling molecules with quantum harmonic oscillators](https://reader034.fdocuments.in/reader034/viewer/2022051404/58a02c2b1a28ab4e768b674d/html5/thumbnails/15.jpg)
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
![Page 16: Modelling molecules with quantum harmonic oscillators](https://reader034.fdocuments.in/reader034/viewer/2022051404/58a02c2b1a28ab4e768b674d/html5/thumbnails/16.jpg)
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.
![Page 17: Modelling molecules with quantum harmonic oscillators](https://reader034.fdocuments.in/reader034/viewer/2022051404/58a02c2b1a28ab4e768b674d/html5/thumbnails/17.jpg)
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)
![Page 18: Modelling molecules with quantum harmonic oscillators](https://reader034.fdocuments.in/reader034/viewer/2022051404/58a02c2b1a28ab4e768b674d/html5/thumbnails/18.jpg)
Coulomb dampingRepulsion
The modelShort range
Jones, Cipcigan, Sokhan, Crain, Martyna, PRL 110 (22), 227801 (2013)
![Page 19: Modelling molecules with quantum harmonic oscillators](https://reader034.fdocuments.in/reader034/viewer/2022051404/58a02c2b1a28ab4e768b674d/html5/thumbnails/19.jpg)
The modelParameter fitting
QDO
ab initio
empiricalpotential
Sokhan, Jones, Cipcigan, Crain, Martyna, PNAS 112 (20), 6341-6346 (2015)
![Page 20: Modelling molecules with quantum harmonic oscillators](https://reader034.fdocuments.in/reader034/viewer/2022051404/58a02c2b1a28ab4e768b674d/html5/thumbnails/20.jpg)
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)
![Page 21: Modelling molecules with quantum harmonic oscillators](https://reader034.fdocuments.in/reader034/viewer/2022051404/58a02c2b1a28ab4e768b674d/html5/thumbnails/21.jpg)
Surface tensionImportant quantity for biological interfaces
Matches experiment across a range of temperatures
Cipcigan, Sokhan, Jones, Crain, Martyna, PCCP 17 (14), 8660-8669 (2015)
![Page 22: Modelling molecules with quantum harmonic oscillators](https://reader034.fdocuments.in/reader034/viewer/2022051404/58a02c2b1a28ab4e768b674d/html5/thumbnails/22.jpg)
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
![Page 23: Modelling molecules with quantum harmonic oscillators](https://reader034.fdocuments.in/reader034/viewer/2022051404/58a02c2b1a28ab4e768b674d/html5/thumbnails/23.jpg)
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
![Page 24: Modelling molecules with quantum harmonic oscillators](https://reader034.fdocuments.in/reader034/viewer/2022051404/58a02c2b1a28ab4e768b674d/html5/thumbnails/24.jpg)
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
![Page 25: Modelling molecules with quantum harmonic oscillators](https://reader034.fdocuments.in/reader034/viewer/2022051404/58a02c2b1a28ab4e768b674d/html5/thumbnails/25.jpg)
QDO–water is the only model with predictions transferable from high pressure ice to liquid and
supercritical water.
![Page 26: Modelling molecules with quantum harmonic oscillators](https://reader034.fdocuments.in/reader034/viewer/2022051404/58a02c2b1a28ab4e768b674d/html5/thumbnails/26.jpg)
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
![Page 27: Modelling molecules with quantum harmonic oscillators](https://reader034.fdocuments.in/reader034/viewer/2022051404/58a02c2b1a28ab4e768b674d/html5/thumbnails/27.jpg)
Water is the solvent of life due to its ability to form a network of hydrogen bonds
![Page 28: Modelling molecules with quantum harmonic oscillators](https://reader034.fdocuments.in/reader034/viewer/2022051404/58a02c2b1a28ab4e768b674d/html5/thumbnails/28.jpg)
acceptor
donor
donor
acceptor
These hydrogen bonds are of two types
![Page 29: Modelling molecules with quantum harmonic oscillators](https://reader034.fdocuments.in/reader034/viewer/2022051404/58a02c2b1a28ab4e768b674d/html5/thumbnails/29.jpg)
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
![Page 30: Modelling molecules with quantum harmonic oscillators](https://reader034.fdocuments.in/reader034/viewer/2022051404/58a02c2b1a28ab4e768b674d/html5/thumbnails/30.jpg)
~5% of molecules have 5 hydrogen bonds
Cipcigan, Sokhan, Jones, Crain, Martyna, PCCP 17 (14), 8660-8669 (2015)
![Page 31: Modelling molecules with quantum harmonic oscillators](https://reader034.fdocuments.in/reader034/viewer/2022051404/58a02c2b1a28ab4e768b674d/html5/thumbnails/31.jpg)
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
![Page 32: Modelling molecules with quantum harmonic oscillators](https://reader034.fdocuments.in/reader034/viewer/2022051404/58a02c2b1a28ab4e768b674d/html5/thumbnails/32.jpg)
Molecular dipole moment is a reporter of local structure in supercritical water
Sokhan, Jones, Cipcigan, Crain, Martyna, PRL 115 (11), 117801 (2015)
![Page 33: Modelling molecules with quantum harmonic oscillators](https://reader034.fdocuments.in/reader034/viewer/2022051404/58a02c2b1a28ab4e768b674d/html5/thumbnails/33.jpg)
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.
![Page 34: Modelling molecules with quantum harmonic oscillators](https://reader034.fdocuments.in/reader034/viewer/2022051404/58a02c2b1a28ab4e768b674d/html5/thumbnails/34.jpg)
Next steps Treat biophysical problems
with predictive accuracy
Illustration of Mycoplasma mycoidesDavid S. Goodsell, Scripps Research Institute
![Page 35: Modelling molecules with quantum harmonic oscillators](https://reader034.fdocuments.in/reader034/viewer/2022051404/58a02c2b1a28ab4e768b674d/html5/thumbnails/35.jpg)
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