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[sdpd] Re: Optimizing optimization

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      <p>--- In <a href="mailto:sdpd%40yahoogroups.com";>sdpd...@yahoogroups.com</a>, &quot;armellebail&quot; &lt;xtal...@...&gt; wrote:<br>
&gt; Discussing recently with an expert in optimizing those<br>
&gt; inaccurate crystal structures refined from powder data,<br>
&gt; telling that he had to re-optimize everything because<br>
&gt; an ultimate set of Rietveld refinement cycles taking<br>
&gt; account of the sycos parameter had slightly changed the<br>
&gt; cell parameters, this remembered me that the opimization<br>
&gt; experts are not structure predictors.<br>
&gt; <br>
&gt; Structure predictors predict everything, including the<br>
&gt; cell parameters.<br>
&gt; <br>
&gt; I you have confidence in your optimizations and think they<br>
&gt; are better than experimental results, why wanting to use<br>
&gt; absolutely the cell parameters obtained from measurements ?<br>
<br>
Strength of crystal structures refined from powder diffraction data:<br>
- unit-cell parameters. It is relatively routine to obtain extremely accurate unit-cell parameters from powder data. The unit-cell parameters are not affected by e.g. preferred orientation, and are not affected as much as other parameters by things like correlation between the background and the Biso parameters, variable slits or absorption.<br>
<br>
Weakness of crystal structures refined from powder diffraction data:<br>
- atomic coordinates, especially of hydrogen atoms. The atomic coordinates are affected by e.g. preferred orientation, correlation between the background and the Biso parameters, variable slits or absorption.<br>
<br>
Strength of crystal structures energy-minimised with quantum-mechanical methods:<br>
- molecular geometry: bond lengths, bond angles, torsion angles, including those for hydrogen atoms.<br>
<br>
Weakness of crystal structures energy-minimised with quantum-mechanical methods without dispersion correction:<br>
- unit-cell parameters. The unit cell expands by 20% (that's twenty percent).<br>
<br>
So combining the strengths of both methods by taking the unit-cell parameters and the starting coordinates from the diffraction data and then energy-minimising the molecular geometry in its crystal environment, keeping the unit cell fixed, is an eminently reasonable route to a decent-quality crystal structure from powder diffraction data.<br>
<br>
Having said that... I myself belong to the crystal-structure prediction community, and when using Density Functional Theory to energy-optimise molecular crystal structures, there is no excuse for not including a dispersion correction. Excellent dispersion corrections for molecular crystals were pioneered by Neumann &amp; Perrin in 2005, and Grimme published a set of dispersion-correction parameters in 2006 (I have never used it, so I cannot comment on their quality, but from what I read in the literature they are pretty good). In May 2010, Grimme published an excellent and complete set of dispersion-correction parameters that can be used for individual molecules, for crystal structures and even for chemical reactions, for the first 94 elements of the periodic table, with analytical first and second derivatives. These are slowly finding their way into software for quantum-mechanical calculations. Whereas the quantum-mechanical calculations take days or weeks, calculating the dispersion correction takes less than a second.<br>
<br>
So, no excuse for not using a dispersion correction, so no excuse for keeping the unit cell fixed.<br>
<br>
(There are some minor technical problems because changing the unit-cell parameters amounts to changing your basis set in subtle ways, both for plane-wave and for atomic orbital calculations, but solutions exist in the literature and the only problem that is left is that calculations with a free unit cell take considerably longer. And in the e-mail I am replying to, it was assumed that the unit cell needed to be fixed because otherwise it would change too much, not because otherwise the calculations would take too long.)<br>
<br>
&gt; And if the cell parameters obtained from optimization<br>
&gt; are so wrong, how and why to be so confident in the optimized<br>
&gt; atomic coordinates ?<br>
<br>
All methods, experimental or computational, have their strengths and their weaknesses. Asking why the atomic coordinates from the quantum-mechanical calculation should be any good if the unit cell is so poor is equivalent to asking why the unit-cell parameters from the powder diffraction should be any good if the coordinates of the hydrogen atoms are so clearly wrong. A theoretical justification is that the lack of dispersion that causes the ridiculous unit-cell expansion mainly plays a role in the *inter*molecular interactions, whereas the *intra*molecular interactions such as chemical bonds (i.e. the interactions that determine the molecular geometry) are hardly affected; the dispersion correction is actually switched off via a damping function for chemically bonded nearest neighbours. Therefore, molecular geometries are fine, and by optimising the entire crystal structure (as opposed to a single molecule in vacuum), the influence of the packing environment on the molecular geometry is taken into account properly. Fixing the unit-cell parameters, which as I argued above are the most accurate pieces of experimental, crystallographic information from a Rietveld refinement, then takes care of the lack of dispersion correction by preventing the unit cell from expanding.<br>
<br>
For a more pragmatic justification, we optimised 241 high-quality single-crystal crystal structures from Acta Cryst. E with DFT with the unit-cell parameters fixed and free, with and without dispersion correction; we published our results in Acta Cryst. B last year (section 3.6 in Van de Streek &amp; Neumann, 2010, Acta Cryst. B66, 544-558; the paper is &quot;open access&quot; and can be found here<br>
<br>
<a href="http://scripts.iucr.org/cgi-bin/paper?S0108768110031873";>http://scripts.iucr.org/cgi-bin/paper?S0108768110031873</a><br>
<br>
). Although including dispersion correction produces systematically better results and leaving the unit-cell parameters free leads to further systematic improvements, our calculations essentially show that for the purpose of optimising the coordinates of molecular crystal structures, the omission of a dispersion correction can be largely compensated for by keeping the unit cell fixed.<br>
<br>
If you have a nagging feeling that &quot;something&quot; must be wrong when optimising a molecular crystal structure with Density Functional Theory without dispersion correction, then you are right. First, the crystal really wants to expand, and fixing the unit-cell parameters causes great pressure within the structure (an alternative to fixing the unit-cell parameters or applying a dispersion correction would be to apply a large hydrostatic pressure of several GPa to counteract this pressure and to keep the unit cell from expanding--but just like fixing the unit cell that would just be covering up the symptoms without really solving the underlying problem). Second, the lattice energy that comes out of the calculation is complete nonsense.<br>
<br>
However, neither of these *thermodynamic* problems affect the *structural* properties of the energy-minimised crystal structure: the atomic coordinates are fine. (If you find it counter-intuitive that a system that is under so much strain [and therefore at first glance cannot be in equilibrium and cannot be in a minimum] can have the correct coordinates, imagine a box with close-packed rubber balls. Now apply hydrostatic pressure until the volume of the box is half the original volume. Clearly, the system is very unhappy, but the relative positions of the balls have not changed and are now consistent with the new dimensions of the box. Also, because of the pressure applied, the system is in equilibrium and is in a minimum.)<br>
<br>
Best wishes,<br>
-- <br>
Dr Jacco van de Streek<br>
Senior Scientist<br>
Avant-garde Materials Simulation<br>
Freiburg im Breisgau, Germany<br>
<br>
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