TMS Feb 2010 ZMC: A Tool for Modelling Diffuse Scattering from Single Crystals D.J.Goossens AINSE Fellow Research School of Chemistry Australian National University

TMS Feb 2010 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?  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

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 yes no accept or reject according to some probability

TMS Feb 2010 Within a molecule  conjugation planar geometry. ortho-H repulsion non-planarity.

TMS Feb 2010 Within a molecule d cv =2.4Å

TMS Feb 2010 Within a molecule

TMS Feb 2010 Between molecules To correlate the thermal motions, we connect the molecules with ‘contact vectors’ (cv)

TMS Feb 2010

Key points of approach Describe molecule by z-matrix Allow it to flip/reorient Allow another molecule to substitute for it Allow molecule to flex Put potentials between and within molecules Allow 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-matrix Allow it to flip/reorient Allow another molecule to substitute for it Allow molecule to flex Put potentials between and within molecules Allow 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-matrix Work out which interactions you want Set up a range of input files Establish initial parameter estimates 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

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