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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