27 сентября, 2015 
Pokraskin 8.4.1
General Methods
“Are crystal structures predictable? [42]” This question is still a “Holy Grail” for crystallographers, solid-state physicists and solid-state chemists, and has been the subject of controversial discussions for more than a decade.
In order to calculate a crystal packing, it must first be constructed from molecules of specific shape to obtain a maximum of lattice energy, resulting from molecular interactions. To date there is no analytical mathematical solution to this problem.
However, several research groups are even now trying to close this gap and develop methods for the prediction of crystal structures on the basis of chemical composition and molecular structure, without any additional experimental data [43, 45, 70-72]. The main problems here are to locate global energy minima within the numerous possible low-energy crystal packings, and then select possible polymorphs by means of accurately calculated physical criteria, e. g., packing energy or density.
In general, all methods of global minimization follow the same principles. In a first step, possible structures (usually several thousand structures per space group and per molecular conformation) are generated using systematic or random techniques. At this stage many methods take into account only the intermolecular interactions. Secondly, the optimization of the generated structures by energy minimization of a force field leads to possible close packed structures representing local energy minima (with respect to the force field parameters in use). As a rule, the final optimization of the structures using force field methods is the most time-consuming step. Here, depending on the individual problem, either the intermolecular interactions alone in the crystals are taken into account, or the molecular geometry plus the crystal packing are optimized. Instead of force field methods, empirical scoring functions [44] or quantum mechanical methods, or a combination of methods can be used.
Generally, several hundred unique crystal packings remain after optimization. They must then be evaluated with respect to either calculated physical properties such as density and lattice energy, or by means of empirical scoring functions [44].
Absolute predictions of crystal structures require that calculated criteria, i. e., packing energies, are accurate enough and allow for a judgement of the stability order of the virtual polymorphs. At this time, however, no force field method fulfills this requirement. The multipurpose force fields now in use just do not yield reliable predictions of the thermodynamic stability of a crystal packing, and even specifically tailored force fields may lack transferability. Nevertheless, correctly predicted structures can often be found in the top spots of the energy ranking list, which had been calculated using force field methods. This was shown by four blind tests on crystal structure prediction of organic compounds organized by the Cambridge Crystallographic Data Centre [45, 70-72]. These tests revealed that the geometrical accuracy is generally quite good (i. e., the predicted structures are close to the actual ones); but the energetic ranking of the calculated structures is less reliable. Furthermore, it is not possible to judge which of the predicted possible crystal structures could be found experimentally. Nevertheless, the accuracy of the proposed structures is fully sufficient for crystal structure determination from X-ray powder data, if a powder diagram (even of low resolution) is available.
Recently, a combination of elaborated force field and quantum mechanical methods was developed which actually allows the prediction of crystal structures of molecules with moderate complexity [73]. By this method, the crystal structures of all four compounds of the 2007 blind test were correctly predicted. The geometrical accuracy is high. At present (2008) the method still requires considerably computational effort, but this will no longer be a major problem in a few years.
8.4.2
Опубликовано в рубрике 