Rules for estimating the values of triplet phase invariants in multiwavelength anomalous dispersion experiments

Abstract

Table 1 presents a compilation of the standard deviations calculated using the two methods. We decided to redetermine the values reported by RWS since we found some inconsistencies in their original paper [for instance, the ratio tr(rm)/o'(P) for entry v was 1.8 r,,, (rad) while it should be close to 1.0 Zm (rad)]. Since individual tr(0i)'s are not available in the original references, we had to calculate them also. For the calculations we used the original positional parameters and their e.s.d.'s and the method of Shmueli (1974). From a comparison of the standard deviations calculated with the two methods, three cases can be distinguished (Table 1): (i) O'Fs'S and trLs'S are roughly the same (entry ii); (ii) low-precision observations fit the model very well (entry v); and (iii) precise observations give very poor fit (entry vii). ,As discussed above, the O'LS S are a measure of the fit between the real and calculated worlds. Another measure of this agreement in the LS formalism is the conventional R factor. Entries vii and ix of Table ! show that R is sensitive to both systematic and random errors. As pointed out by RWS, the departure of the Ao and A~ coefficients of their Fourier series [see (1) of RWS] from 0 furnishes the FS method with a measure of the deviation from the ideal pseudorotation description. AbstractSeveral simple rules, Rano,4, Rano,5, Rano, 6 and Rano,7, have been derived on the basis of the mathematical and physical characteristics of anomalous dispersion experiments that permit the estimation of values for triplet phase invariants. They apply to twowavelength experiments and concern a variety of values defined in terms of the real and imaginary corrections to atomic scattering factors. The rules apply to the case of a single type of predominant anomalous scatterer. The generalization to more than one type of predominant anomalous scatterer is also described. Test examples show that large numbers of invariants may be evaluated by these means with reliabilities that, in certain circumstances, are at a potentially useful level, but the ultimate applicability depends, of course, on the reliability of the experimental data. The only information required besides the measurements of the diffraction intensities is the chemical composition of the anomalously scattering atoms. If there is more than one type of predominant anomalous scatterer, information concerning the relative proportion of the different types is also required.