Applications and integration with experimental data Checking your results Validating your results Structure determination from powder data calculations on crystal surfaces

Polymorph prediction checking your results Why are most predicted structures not found experimentally, even if they have a low energy? 1. Experimentalists should try harder ;-) “The more time one spends crystallizing, the more polymorphs one will find”

Polymorph prediction checking your results Why are most predicted structures not found experimentally, even if they have a low energy? 2. The energy function is wrong. Check with experimentally known structures, or other experimental data.

Polymorph prediction checking your results Why are most predicted structures not found experimentally, even if they have a low energy? 3. The structure is not a true minimum, but is on a saddle point, due to symmetry constraints. example: m Possible solution: optimize again, after removing (some) symmetry constraints, e.g. in P1.

Polymorph prediction checking your results Why are most predicted structures not found experimentally, even if they have a low energy? 4. The structure is in a very unstable local minimum. Example: two packings which only differ in a methyl rotamer. Solution: do a very short MD simulation on the structure, and optimize again. Combination with (2): run MD on the P1 structure.

Polymorph prediction checking your results Why are most predicted structures not found experimentally, even if they have a low energy? 5. Kinetic factors (over-) rule thermodynamic factors. Solution: Lengthy MD runs? Isotropy? ….

Polymorph prediction validating your results Is the model in line with experimental data? * Powder diffraction: is the XRPD reproduced? * Are structural features from ssNMR, IR, AFM, … reproduced? - number of independent molecules - H-bond scheme - surface features - optical properties

Structure solution from X-ray powder data A company produces a compound, and does quality control via the XRPD pattern. One day, something bad appears to have happened….  yesterday’s pattern today’s pattern  Are they still making the same polymorph? What is/are the crystal structure(s)?

Structure solution from X-ray powder data Input: * An indexable powder pattern * Knowledge of (the major part of ) the cell contents. Step 1: indexing the powder pattern. Let the computer guess cell parameters that correspond to the diffraction angles. Result: cell parameters; Z; possible space groups. example: a=9.0; b=12.0; c=15.0;  =  =90º;  =112º  V=1502; monoclinic. If MV~380  Z=[cell volume] / [molecular volume]  4. P2 1 /c?

Structure solution from X-ray powder data example: a=9.0; b=12.0; c=15.0;  =  =90º;  =112º monoclinic, Z  4. Guess: P2 1 /c. Why? spacegroupoccurrence N 35.9% 4 P % % 4 6.7% 2 P2 1 /c P P2 1  =  =90º  =  =  =90º  =  =90º CSD statistics and symmetry restrictions:

Structure solution from X-ray powder data Step 2, option 1: do a polymorph prediction run in P21/c. What will be the most likely conformer(s)?  CSD search on similar structures. Where will the chloride ion be? * major part of the structure defined as fragment which must be present * Cl - present * no water/other polar solvent present Result: molecular conformation and position of the Cl -. Probably….

Structure solution from X-ray powder data Step 2, option 1: do a polymorph prediction run in P21/c with the complex of the two ions as a single ‘particle’ during MD. Finally, compare the XRPD’s with experiment.

Structure solution from X-ray powder data Step 2, option2: Determine all parameters that influence the powder pattern, but do not depend on the structure: zero-point error, overall temperature factor, peak shape, etc. Result: An ‘ideal’ powder pattern: If we put in the correct atomic coordinates, we should get a close match between calculated and observed diffraction patterns. Step 3: MC search. Create trial structures by varying * molecular position and orientation * conformation (via rotatable torsions) … keeping the unit cell fixed. For each trial structure, compare calculated and observed powder pattern.

Simulation of surfaces Simulation of epitaxial growth Expitaxial growth of anthraquinone on NaCl. Observation: well oriented stripe-pattern on [100]

Simulation of surfaces epitaxial growth of anthraquinone on NaCl [100] Approach 1: assume structure and morphology are not changed compared to single crystal structure. Which anthraquinone surface has the highest affinity for NaCl [1 0 0]? Likely candidates:

Simulation of surfaces epitaxial growth of anthraquinone on NaCl [100] Approach 1: static energy calculations  * build a representative part of the 100, 10-2, and 002 surfaces. * calculate E(  ) for each surface

c a Building a representative surface model

5x2x25x1x1 10x4x26x4x2 Building a representative surface model

translate dy translate dz rotate d  optimize Print E, 

h k l E min  opt E min : kcal/molÅ 2  opt : º Minimum energy as a function of  and [hkl]

These results depend on: * cut-off radius (11-17Å) * anthraquinone system size (6x4x2; 10x1x1; … molecules)

Simulation of surfaces epitaxial growth of anthraquinone on NaCl [100] Conclusions from ‘static’ approach: * growth occurs in single rows single rows give the lowest interaction energy * the “45º” orientation has by far the lowest interaction energy, which explains the two (45º and 135º) observed orientations of the needles on the surface * the 10-2 surface fits best to NaCl: d(O…O) = d(Na…Na) within 0.2%. Will single molecules from the vapor attach to the surface in this way?

Simulation of surfaces epitaxial growth of anthraquinone on NaCl [100] Approach 2: Molecular Dynamics 100x100x12Å NaCl surface (3240 NaCl); 12 anthraquinone. All atoms free to move, except NaCl on sides and bottom: ‘swimming pool’-like system. a) T=300K b) T=600K c) T=450K

Simulation of surfaces epitaxial growth of anthraquinone on NaCl [100] T=450K, 100ps (2 days CPU) top view Conclusion: initially too much potential energy, and too little interaction with NaCl

Simulation of surfaces epitaxial growth of anthraquinone on NaCl [100] T=450K, 100ps (2 days CPU) side view Conclusion: some molecules do attach to the surface!

Simulation of surfaces epitaxial growth of anthraquinone on NaCl [100] T=450K, 100ps (2 days CPU) side view, detail Conclusion: carbonyls attach to the Na + really well.

Simulation of surfaces epitaxial growth of anthraquinone on NaCl [100] To get a more useful simulation: * start from last frame of MD run 1 * bring the ‘evaporated’ molecules closer, but not too close, to the surface. * do another MD run...

Simulation of surfaces epitaxial growth of anthraquinone on NaCl [100] Another 100 ps of MD… top view

Simulation of surfaces epitaxial growth of anthraquinone on NaCl [100] Another 100 ps of MD… close up

Simulation of surfaces epitaxial growth of anthraquinone on NaCl [100] Maybe 200 ps is a bit short. Let’s go for 1250 ps Note ‘Row of 3’: reorients is immobile ‘Number 4’ gets almost attached Molecules that lie flat are mobile

Simulation of surfaces epitaxial growth of anthraquinone on NaCl [100] Results from MD: Growth in rows as proposed from the static energy calculations is indeed well possible. ~1 ns simulation is still very short. The MD T is not directly comparable to the real T. Mobility depends on the orientation of the molecules. Some orientations are very common; we could use the energies as parameters in other calculations.

Molecular Modeling of Crystal Structures Energy function is essential to obtain a reliable result. Visual interpretation of results (MD movies, charge distributions, the shape of a cavity,…) can be essential to understand your system. 30/10/2002: from MM to QM, and how to visualize your results.