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TMS Feb 2010
ZMC: A Tool for Modelling Diffuse Scattering from Single Crystals
ZMC: A Tool for Modelling Diffuse Scattering from Single Crystals
D.J.Goossens
AINSE FellowResearch School of ChemistryAustralian National University
TMS Feb 2010
What’s the problem?What’s the problem?
Modelling Bragg data -- use unit cell (asymmetric unit + symmetry)
But the whole point of diffuse scattering is SRO.
Means you cannot treat unit cells as the same
Looking for the population of local configurations.
So you need a model big enough to contain a statistically useful population of local configurations (around 32 32 32 unit cells).
Too many atoms to fit their positions directly.
TMS Feb 2010
What’s the problem?What’s the problem?
Too many atoms to fit their positions directly.
So instead work with the interactions that determine the positions.
Parameterise these interactions
These parameters become the parameters of the model.
In this case, we are interested in modelling the diffuse scattering from flexible molecular crystals.
TMS Feb 2010
Create a model of the crystal in a computer (Bragg data)
Model the interactions
Do a Monte Carlo simulation to relax the structure
Calculate the diffraction pattern of the model
Compare with the observed data (calculate 2)
Modify an interaction parameter
Get derivatives of 2 with respect to the parameters
Do least squares to get new parameter estimates
Loop over interactions
Repeat until satisfied/model tested
Most likely will need to go back to these steps
Scope of this program
Scripts and other code
TMS Feb 2010
Create a model of the crystal in a computer (Bragg data)
Model the interactions
Do a Monte Carlo simulation to relax the structure
Calculate the diffraction pattern of the model
Compare with the observed data (calculate 2)
Modify an interaction parameter
Get derivatives of 2 with respect to the parameters
Do least squares to get new parameter estimates
Loop over interactions
Repeat until satisfied/model tested
Most likely will need to go back to these steps
Randomly select amolecule and
calculate its energy
Randomly modifyconfiguration and
calculate its energy
Is the new energyless than the old?
Save the newconfiguration
yesno
accept or rejectaccording to some
probability
TMS Feb 2010
Randomly select a molecule and
calculate its energy
Randomly modify configuration and
calculate its energy
Is the new energy less than the old?
Save the new configuration
yesno
accept or reject according to some
probability
TMS Feb 2010
Within a moleculeWithin a molecule
€
E = kcv dcvi − dcv( )2
+cv
∑ ktorsion Δϕ torsion( )torsions
∑2
conjugation
planar geometry.
ortho-H repulsion
non-planarity.
TMS Feb 2010
0
1
2
3
4
5
6
7
8
9
10
-50 -30 -10 10 30 50
Twist angle
Energy
Within a moleculeWithin a molecule
€
E = kcv dcvi − dcv( )2
+cv
∑ ktorsion Δϕ torsion( )torsions
∑2
0
5
10
15
20
25
30
-100 -50 0 50 100
Twist angle
Energy
dcv=2.4Å
TMS Feb 2010
1.5
2
2.5
3
3.5
4
4.5
5
5.5
6
-50 -30 -10 10 30 50
Twist angle
Energy
Within a moleculeWithin a molecule
€
E = kcv dcvi − dcv( )2
+cv
∑ ktorsion Δϕ torsion( )torsions
∑2
TMS Feb 2010
Between moleculesBetween molecules
To correlate the thermal motions, we connect the molecules with ‘contact vectors’ (cv)
€
E = kcv dcvi − dcv( )2
cv
∑
TMS Feb 2010
Key points of approach
Describe molecule by z-matrixAllow it to flip/reorientAllow another molecule to substitute for itAllow molecule to flexPut potentials between and within moleculesAllow for interaction of occupancy and displacement
Then do MC
Then calculate diffuse scattering
Then interrogate the model
TMS Feb 2010
Key points of approach
Describe molecule by z-matrixAllow it to flip/reorientAllow another molecule to substitute for itAllow molecule to flexPut potentials between and within moleculesAllow for interaction of occupancy and displacement
Then do MC
Then calculate diffuse scattering
Then interrogate the model
But first you need to organise the z-matrixWork out which interactions you wantSet up a range of input filesEstablish initial parameter estimates
But first you need to organise the z-matrixWork out which interactions you wantSet up a range of input filesEstablish initial parameter estimates