applications and integration with experimental data checking your results validating your results...

Applications and integration with experimental data

Checking your resultsValidating your resultsStructure determination from powder datacalculations on crystal surfaces

Polymorph predictionchecking 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”



2. The energy function is wrong.

Check with experimentally known structures, or otherexperimental data.



3. The structure is not a true minimum, but ison a saddle point, due to symmetry constraints.example: m

Possible solution:optimize again, after removing(some) symmetry constraints,e.g. in P1.



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.



5. Kinetic factors (over-) rule thermodynamic factors.

Solution: Lengthy MD runs? Isotropy? ….

Polymorph predictionvalidating 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 controlvia the XRPD pattern. One day, something bad appears tohave happened….

yesterday’s pattern

today’s pattern

Are they still making the same polymorph?What is/are the crystal structure(s)?


Input:* An indexable powder pattern* Knowledge of (the major part of ) the cell contents.

Step 1: indexing the powder pattern. Let the computer guesscell 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.P21/c?

Structure solution from X-ray powder dataexample: a=9.0; b=12.0; c=15.0; ==90º; =112ºmonoclinic, Z 4. Guess: P21/c. Why?

spacegroup occurrence N

35.9% 4P -1 13.7% 2

11.6% 46.7% 2

P21/c

P212121

P21

==90º

===90º

==90º

CSD statistics and symmetry restrictions:


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 andposition of the Cl-. Probably….

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

Structure solution from X-ray powder dataStep 2, option2: Determine all parameters that influence thepowder 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 atomiccoordinates, we should get a close match between calculatedand 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 observedpowder pattern.

Simulation of surfacesSimulation of epitaxial growth

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

Simulation of surfacesepitaxial 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:

1 0 01 0 -20 0 2


Approach 1: static energy calculations

1 0 01 0 -20 0 2

* build a representative partof the 100, 10-2, and 002surfaces.

* calculate E() for each surface

1 0 00 0 21 0-2

c

a

Building a representative surface model

5x2x2 5x1x1

10x4x26x4x2

Building a representative surface model

translate dy

translate dz

rotate d

optimize

Print E,

h k l Emin opt

1 0 0 -0.407 45.100 0 2 -0.402 44.991 0-2 -0.559 44.27

Emin: kcal/molÅ2

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)


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?


Approach 2: Molecular Dynamics100x100x12Å NaCl surface (3240 NaCl); 12 anthraquinone.All atoms free to move, except NaCl on sides and bottom:‘swimming pool’-like system.

a) T=300Kb) T=600Kc) T=450K


T=450K, 100ps (2 days CPU)top view

Conclusion: initially too much potential energy,and too little interaction with NaCl


T=450K, 100ps (2 days CPU)side view

Conclusion: some molecules do attach to the surface!


T=450K, 100ps (2 days CPU)side view, detail

Conclusion: carbonyls attach to the Na+ really well.


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...


Another 100 ps of MD…top view


Another 100 ps of MD…close up


Maybe 200 ps is a bit short.Let’s go for 1250 ps

Note‘Row of 3’:• reorients• is immobile

‘Number 4’ getsalmost attached

Molecules that lieflat are mobile


Results from MD:

• Growth in rows as proposed from the static energy calculationsis 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.

applications and integration with experimental data checking your results validating your results...

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