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Credit: Peptides and amino acid structures. Source: Wellcome Collection.
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![2100 Henri A. Levy and Robert E. Corey Vol. 63 ture-factor term as a function of the atomic pa rameters. By the use of these plots in a manner already described, 2 significant improvement in the structure factors was gradually accomplished, until a point was reached at which it appeared clear that no further progress could be made with out relinquishing to some extent the restriction placed upon the methyl carbon atom. In fact, it was evident almost at the outset that several serious conflicts among the f-values could readily be resolved by altering the parameters of this atom so as to bring it closer to the peak C (2) in Fig. 1, and hence nearer the two-fold screw axis, but a change of this nature, resulting in an un precedented approach of methyl groups, seemed unjustifiable as long as it could not be convinc ingly demonstrated that it was the only solution to the problem. To provide further evidence re garding a move of this sort, a Fourier projection, p(x,y), was calculated, using 65 non-vanishing structure factors whose signs were then known with reasonable certainty. A plot of this pro jection, Fig. 4, shows a symmetrical, well-resolved peak corresponding to the methyl carbon atom at X = 0.099, y = 0.019, which represents a methyl-methyl approach of 3.7 Â. In the face Fig. 4.—A Fourier projection p(x,y) which showed that the carbon atoms of adjacem t methyl groups must approach closer than 4.0 Â., the distance in the trial structure upon which it was based . The position of the methyl carbon atom in this trial sti ructure is indicated by a cross; its correct position is sho 1 wm by the small circle Cm. of these considerations, we were compelled to relinquish the preconceived restrictions on the position of the methyl radical. It was therefore placed in accordance with the peak of p(x,y), and the resulting structure became a new point of de parture for further refinement by the methods described above. The signs of only two of the structure factors used in this series were reversed by subsequent changes in the atomic positions; their correction served to reduce still further the methyl-methyl separation. The best agreement between calculated and ob served (hk 0) structure factors thus eventually achieved is presented in columns 2 and 3 of Table I. The values of F obsi . (cor.) there listed are obtained from the estimated intensities after correcting them for extinction according to the approximation of Darwin 10 : = W(1 - 2 Ä low.), in which the coefficient 2g was given the value 0.00005. The values of F calcd ., given by the gen eral expression Fm - 2 f, exp [-2«(focf + kyt + fe#)], Aug., 1941 Crystal Structure of ¿/-Alanine 2101 are based upon the x and y parameters for- the carbon, nitrogen, and oxygen atoms listed in columns (B) of Table V. For the atomic scat tering factors, fj, in all calculations, the values of Hartree 11 were used combined with a temperature correction, exp(— B sin 2 0/X 2 ), in which B was given the value 2.23 X 10~ 16 . The structure upon which these calculated F- values are based is consistent with the optical and cleavage properties of the crystal, and in volves no features not in accord with accepted structural principles. Furthermore the agree ment throughout most of the 89 (hk 0) reflections is as good as could be desired. It is probable therefore that within the limits of error imposed by the data this structure is correct. Nevertheless, there are a few serious and apparently insoluble conflicts, particularly among planes of large spacing. Especially disturbing is the pair of planes (320) and (510), which are observed to have F- values of 19.5 and 13.6, respectively, while the calculated quantities are approximately 16 for both. The plots of the structure factors for these planes show conclusively that it is impossible to move any atom in such a way as to improve the agreement of one plane without causing that of the other to become even worse. It was likewise impossible to improve the agreement of (020) either positively or negatively. It occurred to us that these discrepancies might arise from neglect of the contributions to the X-ray scatter ing made by the seven hydrogen atoms of each alanine molecule. In some cases it has been the practice to compensate for the scattering of hy drogen atoms in methyl and amino radicals by making small alterations in the atomic scattering function for carbon and nitrogen. Inspection of the contributions of these atoms to (320), (510), and planes with similar spacing showed that this conflict could not be resolved by any adjustments of this sort. Although, as already stated, the lo cations of the hydrogen atoms cannot be deter mined from X-ray data, in this crystal they can be placed with considerable confidence from purely structural considerations, as discussed in a later section, once the positions of the other atoms are known. Contributions of the hydrogen atoms may therefore be estimated directly using the scattering function for atomic hydrogen. 11 Struc ture factors including these contributions, based upon the assumed parameters for hydrogen listed in Table V, are presented in the final column of Table I. The significant improvement in agree ment obtained, not only for planes of large spacing but for many reflections throughout the assem blage, is confirmatory evidence for both the ex cellence of the (hk 0) data and the correctness of the structure determined. Having established the x and y parameters, the refinement of the z parameters was carried out by similar methods, using agreement of the (Okl) intensities as the criterion for improvement. For this purpose plots of both the real and imaginary parts of the complex structure factors were neces sary. The final assignment of z parameters is con firmed by the intensity agreement of the (AO/) re flections. Comparison of observed and calculated .F-values for the (Okl) and (AO/) planes is shown in Tables II and III. Agreement among 238 non- prism reflections, shown in Table IV, substan tiates the assignment of all the parameters. Calculated structure factors including the con tributions of the hydrogen atoms for the 36 (hkl) planes having sin ê < 0.5 are also listed in Table IV. As in the case of the (hk 0) reflections, many of these planes show decided improvement in their intensity agreement. The significance of Table II Factors |Foh|°](https://iiif.wellcomecollection.org/image/b18186373_PP_CRI_H_2_35_0006.jp2/full/800%2C/0/default.jpg)
