TRENDS IN SDPD

Armel Le Bail

Université du Maine, Laboratoire des Fluorures, CNRS ESA 6010, Avenue O. Messiaen, 72085 Le Mans cedex 9, France - email: lebail@univ-lemans.fr

During the last 10 years, the number of structure determinations from powder diffraction (SDPD) increased from 30 to more than 300. A commented bibliography, which is accessible on Internet [1], allows drawing some conclusions on current tendencies in this hot topic. First of all, there is no reason that major trends in crystallography would not affect SDPD. One irreversible tendency is that normal human brains are no longer able to realize the calculations needed for a non-trivial structure determination. More and more fast and powerful computers do the job. Fortunately, humans having not found limit in that domain continue to conceive new software as well as hardware. A trend in SDPD is thus clearly the emergence of sophisticated methods that would not have been applicable if the power of cheap computers had not increased so much. SDPD is a step by step operation where computers are essential at stages of (a) indexation, (b) structure factor extraction, (c) structure factor selection, (d) application of Patterson or direct methods, (e) model completion, and (f) Rietveld method refinement. Beside this classical approach, when initial models are known from other techniques than crystallography (molecule from NMR), stage (d) may be replaced (d') by using methods that try to find an optimum position for a starting model inside the cell. Testing a molecule location is realized by comparison of the corresponding calculated diffraction data either to the extracted "|Fobs|" or to the whole (or large part of) observed powder pattern (suppressing the need of stages b and c). How many times (at least) some methods were applied to experimental SDPD cases is given below under parentheses.

Automatic indexing (a) is not actually a very innovative field. Three main programs traditionally occupy the market: TREOR (107), ITO (88) and DICVOL (40). The next most applied technique is electronic microdiffraction (11).

Mainly the Pawley (36), Le Bail (130) or Rudolf and Clearfield (17) methods realize the structure factor extraction stage (b). A trend is that the two first methods are used also in order to check the correctness of cells proposed at stage (a), rather than using the classical cell parameter refinement from estimated reflection positions.

Variants exist at stage (c). Either the whole data set (132) is used or a selected set of unambiguously indexed reflections (79) is reserved for the next (d) step. Alternative methods try to extrapolate knowledge from this selected set to discriminate the more or less overlapping reflections (using the expected positivity of the Patterson map for instance).

For stage (d), peoples have simply adopted the general trends in structure determination from single crystal data, by using Patterson (103) and direct methods (147), including their most recent improvements. For instance, the new SHELXS-97 included phase annealing direct methods and new Patterson interpretation. SHELX programs are used in well over than 50% of small molecule structure determinations from single crystal as well as from powder data. It should be realized that in many cases, only one or two heavy atoms had to be found for obtaining a partial model which could allow the starting of refinement and the location of the remaining atoms by Fourier difference syntheses.

Locating fragments of known geometry was long ago used in single crystal studies of organic compounds. The PATSEE program has been also applied to solve 1% of experimental powder data cases. It is in this (d') stage that the last ten years of SDPD were particularly innovative. No less than 20 new methods or transposition of existing (single crystal) methods recently emerged for solving structures from powder data. The list, as found in titles of recent papers, is the following: "general Monte Carlo approach; simulated-annealing method and a high degree of molecular flexibility; genetic algorithm; anomalous scattering difference; probablility distributions for estimating the |F|s; new Monte Carlo approach incorporating restrained relaxation of the molecular geometry; Fourier recycling with a specialized topology search specific to zeolites; use of a periodic nodal surface calculated from a few strong, low-index reflections to facilitate structure solution (1997); computer prediction; simultaneous translation and rotation of a structural fragment within the unit cell; combination of high-resolution X-ray powder diffraction and molecular modelling techniques; generalized rigid-body Monte Carlo method (1996); solving crystal structures with the symmetry minimum function; static-structure energy minimization method; computer modelling approach; tangent formula derived from Patterson-function arguments (1995); real-space scavenger; Bayesian approach (1994); optimal symbolic addition program (1993); entropy maximisation and likelihood ranking (1991)". Each of these methods was applied for the solution of 0 to 5 unknown structures. Programs are seldom in the public domain. These could be methods for the future. Most of them are specifically designed for organic compounds and they cannot be applied if at least a large part of the molecular structure is not already known (they concentrate on the finding of the relative position of a fragment of known geometry in the cell). The use of genetic algorithm appears currently to be the most sophisticated approach, giving some freedom to non-rigid molecule parts.

Does complexity is currently increasing? Not really, the world of SDPD is concerned by moderately complex structures. The maximum of atoms simultaneously located by direct methods is not larger than 18. The total number of independent atoms is near of 60 (GSAS (79), FULLPROF (61) and DBW (29) programs dominate the Rietveld refinement last stage). On the other hand, rarely more than one independent molecule was located by non-conventional methods (d'). For organic compounds, the trend is to use geometrical restraints in the final refinement. A kind of limit has been attained recently for C₁₆H₂₂N₆ with 70 atomic coordinates rigid-body-refined from 104 reflections for 3 independent molecules located by Patterson search. Confidence in crystal structure accuracy depends on the reflection/parameter ratio which is admittedly ³ 10 when single crystal data are involved and should be ³ 20 when powder data are concerned (due to overlapping). One could doubt about some details of the structure when this ratio is » 1. Modifying torsion angles would be of little influence on the final fit.

That the most complex structures will soon be solved from synchrotron data is evidence. Anyway, conventional X-rays have not really been outperformed yet by synchrotron radiation in quantity (228 and 63 applications, respectively) nor in quality (no real gap in complexity is observed, although it should be). SDPD from only neutron data are very few (10). After all, the method is of little importance if the structure is determined. It is not risky to predict that the future will very probably see the domination of applications to organic and organometallic compounds against inorganic ones. The 4/1 proportion observed in the CSD/ICSD databanks is unavoidable, although it is the contrary nowadays in SDPD.

1. A. Le Bail, Structure Determination from Powder Diffraction - Database (1994-98) http://fluo.univ-lemans.fr:8001/iniref.html