Data Reduction, Structure Solution and Refinement

After Lp, absorption and radiation damage decay corrections to the integrated intensities the observed structure factors (Fobs) are obtained. Each measured reflection thus will have the corresponding Fobs- In other words, Fobs is the square root of the measured intensity of a given reflection corrected for effects that come from the properties of the crystal itself. 

In a case where the absorption of X-rays is very small and the crystal does not decompose (the decomposition can be monitored by measuring the intensity of so called standard reflection many times during the data collection, however modern area detector equipped diffractometers are so fast that virtually no X-ray radiation decay is normally observed), the data reduction is just a fast computer calculation of the Lp correction to the measured intensities and Fobs arc obtained. Improperly done data reduction or exclusion of the effects of absorption or decay can render the structure solution impossible, so care must be taken in order to do proper data reduction. 

The unit cell determination, data collection and data reduction contain all the information which can be obtained from experiments and mathematical corrections. The only, and thus the most important, data present in the structure factor that cannot be obtained experimentally is the phase of the reflection. This imposes the so-called Phase Problem , since without phase, the other components of the structure factor cannot be calculated. On the contrary, if we know the phase of the reflection, we can calculate the 3-D coordinates of the atoms contributing to the corresponding structure factor. 

From the well-resolved electron density map, the structural analyst has then to assign the atom types and the 3-D coordinates for the best structure solution (= the phase set, which with given atom types fits best with observed structural factors, viz. the measured reflection data). The assignment is based on the relative height of the peaks in the electron density map coupled with the proposed chemical structure diagram of the studied structure. For compound 1, the structural scheme presented in Fig. 9.9 is used. It turns out that all heavier atoms can be located from the electron density map and assigned unambiguously (Fig. 9.11). 

Frequently, with smaller and well-diffracting structures (W , 700 and dp 10), all atoms of the structure can be written out as the initial model by the program and they just have to be named correctly (as in Fig. 9.11) and refined. The refinement process (see Refs. 110 —1121) uses incremental movement of the atom coordinates and atomic displacement parameters (commonly called as thermal parameters ) of the structure solution model using the so-called least-squares method. The model (the calculated structure factors) is fitted against the measured data (the observed structure factors) and the R-factor (see above. Section 9.2.1) is calculated. With larger structures or if the unit cell contains light atom solvent molecules (C, H, O, N atoms only), some atoms, sometimes even 50% of all atoms, cannot be located from the first very crude electron density map (calculated from the ab initio phase set). However, those atoms which are chemically feasible (based on the proposed molecular structure) can be fed into the calculation of the calculated structure factors Peak ( cafc will approach Fobs when a more accurate model is 

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