ZMC: A Tool for Modelling Diffuse Scattering from Single Crystals

1. ZMC: A Tool for Modelling Diffuse Scattering from Single Crystals D.J.Goossens AINSE Fellow Research School of Chemistry Australian National University

2. 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. What’s the problem?

3. 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. What’s the problem?

4. Scope of this program Create a model of the crystal in a computer (Bragg data) Most likely will need to go back to these steps Scripts and other code Model the interactions Do a Monte Carlo simulation to relax the structure Calculate the diffraction pattern of the model Loop over interactions Compare with the observed data (calculate 2) Modify an interaction parameter Get derivatives of 2 with respect to the parameters Repeat until satisfied/model tested Do least squares to get new parameter estimates

5. Create a model of the crystal in a computer (Bragg data) Most likely will need to go back to these steps Model the interactions Do a Monte Carlo simulation to relax the structure Calculate the diffraction pattern of the model Loop over interactions Compare with the observed data (calculate 2) Modify an interaction parameter Get derivatives of 2 with respect to the parameters Repeat until satisfied/model tested Do least squares to get new parameter estimates

6. Randomly select a molecule and calculate its energy Save the new configuration Randomly modify configuration and calculate its energy accept or reject according to some probability no yes Is the new energy less than the old?

7. ortho-H repulsion non-planarity. • conjugation planar geometry. Within a molecule

8. Within a molecule dcv=2.4Å

9. Within a molecule

10. Between molecules To correlate the thermal motions, we connect the molecules with ‘contact vectors’ (cv)

13. 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

14. But first you need to organise the z-matrix Work out which interactions you want Set up a range of input files Establish initial parameter estimates 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

15. Para-terphenyl

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17. Benzocaine

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20. Thanks… Prof. Richard Welberry Dr Aidan Heerdegen Dr Eric Chan Mr Andrew Beasley Prof. W.I.F David AINSE, ARC, AMRFP, ASRP