Anisotropic refinement

Partially Dehydrated Ba6 A. Full-matrix least-squares refinement was initiated using the atomic parameters of the framework atoms and of the barium ions (Ba(l), Ba(2), Ba(3), and Ba(4)) in fully hydrated Ba2+-exchanged zeolite A. Full anisotropic refinement converged to the error indices = 0.113 and R2 = 0.088. Simultaneously, the occupancy numbers at Ba(l),... 

The isotropic thermal ellipsoid at Na was very large, indicating the presence of 2 or more nonequivalent Na+ ions at this position. Attempts to separate it into 2 nonequivalent Na+ ion positions failed. The final model (see Table lie) is the result of anisotropic refinement of all positions, except Na which was refined isotropically, with occupancies fixed. The final difference Fourier function, whose estimated standard deviation is 0.06 eA-, was featureless. See Tables lie and III, and Figure 2, for additional information. 

Insufficient data. A good LS refinement requires at least 5, and preferably 10 reflections per refined variable. Each refined atom contributes three coordinates and 1 or 6 displacement parameters (in isotropic or anisotropic refinement, respectively) ... 

Some protein structures can be determined to high resolution and the results of anisotropic refinements have, in a few instances. 

In a few cases very high resolution results (better than 1 A resolution) have been obtained for small proteins, so that there are enough data for a full anisotropic refinement i.e., all six components of the atomic motional tensor, Bj, can be refined independently. One such system is the avian pancreatic... 

Anisotropic refinement, investigation of the H20 sites, and determination of the Si/Al distribution is in progress. 

Two of the three restraints on displacement parameters (DELU, SIMU) take into account the fact that atoms, which are bound to one another, move similarly, both in direction and amount (Hirschfeld 1976 Didisheim and Schwarzenbach 1987). The third one (ISOR) encourages approximate isotropic behaviour for otherwise anisotropically refined atoms. Both SiMU and DELU are based on physically very sensible assumptions and can be used on all or almost all atoms in a model when the data to parameter ratio is low or other problems with the refinement make this seem desirable. SIMU, however, should not be applied to very small ions, isolated atoms and atoms that are part of freely rotating groups. 

ISOR restrains the components of anisotropically refined atoms to behave approximately isotropically within a standard uncertainty of s, or st for terminal atoms (default values 0.1 and 0.2 A ). The syntax is as follows ... 

After 10 cycles of refinement with SHELXL, the model has again improved the R factors are lower than before and all Ueq values are within a reasonable range. On the other hand, the C/eq value for Yb(l) is still a little too low. This finding, together with the two very high residual density peaks (Q(l) and Q(2)) on either side of the metal, make it advisable to try other, even heavier metals. First, however, we should try to refine the model anisotropically. In the presence of much heavier atoms next to lighter ones, it is usually advisable to allow anisotropic refinement for the heavy atoms first. Therefore edit the file si-03. res by adding the line ANIS Yb and save it as si-04. ins. 

In particularly tough cases of disorders, especially for disordered solvent molecules, it can be useful to restrain the anisotropic 17 -values of the atoms to behave more isotropically with ISOR. As with DELU SHELXL ignores ISOR commands for atoms that are refined isotropically. ISOR is helpful for certain special cases (e.g. a disordered atom close to a special position, or anisotropic refinement of a protein against 1.4 A data) and should almost always be applied to the water molecules of a protein model, but is otherwise less appropriate than SiMU or DELU. Figure 5.3 illustrates the effect the restraints DELU, SIMU, and ISOR have on anisotropic displacement parameters. 

Whenever extinction is refined, it is important to check in the. 1st file whether the extinction coefficient refines to sensible values with a reasonably small standard uncertainty. This is the case here, so we will keep EXTI in. Unfortunately, removing the E AD P constraint causes the carbon atom C(6) to be NPD again. This is not unusual for global pseudo-symmetry, as the abovementioned correlation among symmetry-related but not equivalent atoms can lead to problems with anisotropic refinement. Therefore, we decide to live with this constraint and finalize the refinement by adjusting the weighting scheme. The final model in P2 ln is in the file s-05a.res. 

Fig. 10.1 Schematic views of different parameterizations. Isotropic refinement involves 3 parameters for the coordinates and 1 isotropic B-value. In anisotropic refinement, 6 parameters are used to model the probability function for the location of an atom. When an atom needs to be modeled using more than one site, the number of parameters increases accordingly. However, to define the occupancy of two sites only one extra parameter is needed, as the occupancy p2 of the second site can be calculated from the occupancy of the first site,pi, by/ 2 = 1.0—pi.

Schmid, R.L., Felsche, J., and McIntyre, G.J. (1984) Location and anisotropic refinement of deuterium atoms in deuterium sodium silicate-deuterium oxide (1/8) Na2D2Si04.8D20 by neutron diffraction hydrogen bonding at 173K, Acta Cryst, C40,733-736. 

G. laccarino, F. Ham, LES on Cartesian grids with anisotropic Refinement, Lecture Notes in Computational Science and Engineering 56 (2007) 219. 

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