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Molecular Modelling usingQuantum Drude Oscillators

by Flaviu Cipcigan(the short version)

In order to understand the properties of substances, we need molecular models that are both accurate and efficient to simulate.

Solving the Schrodinger equation

aim: accurate description of the system(ab initio quantum mechanics)

Solving the Schrodinger equation

aim: accurate description of the systemproblem: inefficient

(ab initio quantum mechanics)

Molecular Modelsaim: efficient description of a system

Begin with efficient building blocks

Begin with efficient building blocksand assemble them

Begin with efficient building blocksand assemble them into molecules

Molecular building blocks are point charges

Molecular building blocks are point charges

Nuclei are point charges

Electrons are not!

electric field

they easily redistributeElectrons are not!

current approaches offer a trade off between accuracy and efficiency

dilemma

(or QDO)The Quantum Drude Oscillatoraim: efficiently model electronic response

harmonic

pseudoelectron

pseudonucleus

electrostatic

van der Waals

damping & repulsion

model the polarisable part of a molecule

but how well?model the polarisable part of a molecule

k

q, m

-q

a QDO only has three free parameters

H Li K RbCs

0.5

—0.5

0

0.5

—0.5

0

0.5

—0.5

0

He Ne Ar Kr Xe

CH4

H2O

Polarisation Invariants(polarisabilities related to each other)

0.5

—0.5

0

0.5

—0.5

0

0.5

—0.5

0

H LiK Rb Cs

He Ne Ar Kr Xe

BH3 CH4 NH3 H2O

Van der Waals Invariants(van der Waals coefficients related to each other)

the response of a QDO matches that of a wide range of atoms & molecules

Since a QDO is a simple quantum mechanical object, it can be efficiently simulated

A QDO model for Argonaim: demonstrate physical validity

why choose argon?

spherical, unpolarisedwhy choose argon?

binds via van der Waals forcesspherical, unpolarisedwhy choose argon?

-0.4

0.0

0.4

distance between atoms / bohr radius

6 7 8 9 10 11 12

inte

ract

ion

en

erg

y /

mH

art

ree Interaction potential between

two Argon QDOs

Modelling the FCC argon solidaim: demonstrate accuracy and transferability

experimental observablesresults

lattice constant binding energy

bulk modulus

compress and expand the solid and calculate its energy

0

—2

—4

—6

—8

—10

—12

—14

0.89 0.92 0.94 0.96 0.98 1.00 1.02

lattice parameter / 5.29 A

en

erg

y p

er

un

it c

ell

/ mH

art

ree

256 atoms

argon QDO parametrised in the gas phase reproduced the equation of state of a solid bound via many body van der Waals forces

key result

but how accurately?

key result

argon QDO parametrised in the gas phase reproduced the equation of state of a solid bound via many body van der Waals forces

5.24

5.2563

32 108 256 500

lattice constant

atoms in cluster

calculated

measured

5.2563 A

5.3296 A± 0.0007

—13.08

—16

32 108 256 500

—14

—15

binding energyper unit cell

atoms in cluster

—13.08 mHartree

—11.80 mHartree± 0.01 per unit cell

per unit cell

—11.90

—14.8

32 108 256 500

—12.8

—13.8

binding energyper unit cell

—11.90 mHartree

—11.80 mHartree± 0.01 per unit cell

per unit cell

atoms in cluster

with nuclear zero point energy

32 108 256 500

5

4.5

4.36

4.36 GPa

2.88 GPa± 0.08

± 0.04

bulk modulus

Argon QDO parametrised in the gas phase reproduced the equation of state of a solid bound via many body van der Waals forces

But how accurately?

key result

Argon QDO parametrised in the gas phase reproduced the equation of state of a solid bound via many body van der Waals forces

As accurately as specialised models

But how accurately?

key result

The future of QDOs

Elastic properties of noble gases

Transferable water model

Biomolecules

Conclusions

Quantum Drude Oscillators capture the essential quantum properties of a molecule resulting in efficient, accurate and transferable molecular models

Image credit

lego: www.flickr.com/photos/donsolo/3706017309/

old building plan: docsouth.unc.edu/unc/unc02-80/unc02-80.html

Autodesk Revit Architecture: www.hagerman.com/products/2010/revitarch2010.htm