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

TMS Feb 2010

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

TMS Feb 2010

Para-terphenyl

TMS Feb 2010

Information

TMS Feb 2010

Benzocaine

TMS Feb 2010

Information

TMS Feb 2010

Information

TMS Feb 2010

Thanks…

Prof. Richard WelberryDr Aidan HeerdegenDr Eric ChanMr Andrew Beasley

Prof. W.I.F David

AINSE, ARC, AMRFP, ASRP