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  • 1980-1984  (11)
  • 1
    Electronic Resource
    Electronic Resource
    A general rule and many formulas for the evaluation of triplet phase invariants from isomorphous replacement and anomalous dispersion data (1984)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 40 (1984), S. 374-379 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: On the basis of a common characteristic observed in previously derived formulas for the evaluation of triplet phase invariants from either isomorphous replacement data or anomalous dispersion data, it has been found possible to combine mathematical expressions, certain differences of magnitudes, arising in the analysis of the two techniques to form a myriad of new mixed formulas. The common characteristic is that the various types of differences of magnitudes that are involved in the formulas are all definable in terms of the heavy-atom structure. The formulas involve the mixing of terms arising from several isomorphous derivatives or from a combination of such terms with various types of terms arising in anomalous dispersion or the mixing of various terms arising in anomalous dispersion alone. The evaluation of the triplet phase invariants is facilitated by the use of a simple rule, called the General Rule, that is generally applicable to the case of one predominant type of anomalous scatterer. In the case of more than one predominant type of anomalous scatterer, a slightly more complicated calculation is required and is described. Test calculations show that a very large number of invariants may be evaluated by these means with reliabilities that are potentially high, but depend, of course, on the reliability of the experimental data. A benefit from having the large variety of formulas is that triplet phase invariants can be evaluated at many points throughout the range -π to π and their reliability is enhanced because much information is obtained from only the largest differences of magnitudes.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767384000805
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  • 2
    Electronic Resource
    Electronic Resource
    A simple rule for finding and distinguishing triplet phase invariants with values near 0 or π with isomorphous replacement data (1983)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 39 (1983), S. 800-805 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: On the basis of some mathematical and physical characteristics of isomorphous-replacement experiments, it has been possible to derive a simple rule called Riso that permits the selection of those triplet phase invariants that have values close to zero or π. Test examples show that large numbers of invariants may be evaluated by means of Riso with reliabilities that are potentially high, but depend, of course, on the reliability of the experimental data. In order to apply the rule, it is not necessary to know the chemical nature of the substituent atoms, their positions in the structure or their occupancy. The rule Riso affords new insights into the inter-relationships among isomorphous-replacement data and an alternative selection method to the use of the conditional joint probability distribution. A formula has also been derived for estimating the value of the cosine of triplet phase invariants for the native substance, cos (φhP + φkP + φ(h + k)P), in terms of measured structure factor magnitudes and structure factor magnitudes associated with the contribution from substituent atoms.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767383001579
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  • 3
    Electronic Resource
    Electronic Resource
    Rules for evaluating triplet phase invariants by use of anomalous dispersion data (1984)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 40 (1984), S. 4-11 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: On the basis of some mathematical and physical characteristics of anomalous dispersion experiments, it has been possible to derive simple rules, Rano, 1, Rano, 2 and Rano, 3, that permit the selection of triplet phase invariants, in a single-wavelength experiment, that have values close to π/2, -π/2, 0 and other values in the range from -π to π. The rules, Rano, 1, Rano, 2 and Rano, 3, apply to the case of a single type of predominant anomalous scatterer. The simple 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 are potentially high, but depend, 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. In some cases, even this information is not required if two alternative sets of estimates of the values of the triplet phase invariants are considered.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767384000027
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  • 4
    Electronic Resource
    Electronic Resource
    Triplet phase invariants from an exact algebraic analysis of anomalous dispersion (1984)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 40 (1984), S. 526-531 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: In a previous investigation, a system of exact algebraic equations was derived for any number and type of anomalous scatterers. Solution of the equations provides information concerning intensities of scattering and certain phase differences. In this paper, it is shown that when appropriate combinations of the phase differences and their values are made, the result is the evaluation of the differences of pairs of triplet phase invariants, one associated with the macromolecular structure and the second associated with the structure of the anomalous scatterers. It is usually easy to satisfy the condition that the values of triplet phase invariants associated with the structures of the anomalous scatterers be close to zero.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767384001112
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  • 5
    Electronic Resource
    Electronic Resource
    The relative scaling of multiple-wavelength anomalous dispersion data (1984)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 40 (1984), S. 1-4 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A formula is presented for the calculation of the values of the |Fnh|, the structure-factor magnitudes in the absence of anomalous dispersion, from the observed structure-factor magnitudes, |Fλh| and |Fλh|, that are affected by anomalous dispersion and hence vary with wavelength. Since the values of the |Fnh| are independent of wavelength, the calculation can provide the basis for relatively scaling data that are collected at different wavelengths. Test calculations of the formula with use of accurate data indicate that the formula has the potential to scale relatively experimental data in multiple-wavelength anomalous-dispersion experiments involving heavy-atom-substituted macromolecules to accuracies of 1 or 2% or better.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767384000015
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    Paper (German National Licenses)
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  • 6
    Electronic Resource
    Electronic Resource
    Rules for estimating the values of triplet phase invariants in multiwavelength anomalous dispersion experiments (1984)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 40 (1984), S. 366-373 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Several 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 two-wavelength 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767384000799
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  • 7
    Electronic Resource
    Electronic Resource
    The expected values of triplet invariants: acentric case (1980)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 36 (1980), S. 800-802 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A formula for the expected values of triplet phase invariants is derived in the acentric case from third-order determinantal joint probability distributions. Theoretical calculations based on this and earlier formulae are compared with expected values observed for a roughly equal-atom structure and one containing a heavy atom.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S056773948000160X
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    Paper (German National Licenses)
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  • 8
    Electronic Resource
    Electronic Resource
    Formulas for n-tet phase invariants and embedded seminvariants for all space groups (1982)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 38 (1982), S. 327-333 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Formulas are presented for the calculation of the cosines of n-tet phase invariants and embedded seminvariants in all the space groups. They are shown to be of the form of a particular type of expected value formula that is derivable from the joint probability distribution. In the recent literature, formulas for phase invariants and seminvariants have been given in the form of conditional probability distributions. A detailed comparison of the relative merits of the two types of formulas, expected value and conditional distribution, has not yet been made. The variety of potential applications is quite vast and therefore it may require much effort to make evaluations of current theories. Should it seem worthwhile, the determinantal joint probability distributions employed in this paper could provide the basis for the derivation of additional conditional probability distributions. They are likely to be much more complex, however, than the expected value formulas. Some simple calculations with triplet and quartet invariants involving random structures in space group P1 show a considerable decrease in the reliability of the expected value formulas as the complexity of the structure increases. A comparable observation had been made in the past for conditional probability distributions for triplet phase invariants. Current theories present the possibility of obtaining information in special circumstances, for example, with respect to selected embedded seminvariants. How extensive and how useful such information might be, particularly with respect to the truly difficult structures that occur among the essentially equal-atom, noncentrosymmetric crystals with 100 or more nonhydrogen atoms in the asymmetric unit, remains to be seen.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0567739482000692
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  • 9
    Electronic Resource
    Electronic Resource
    Dithiin tautomers: dimethyl 2,4-diphenyl-2H,4H-1,3-dithiin-5,6-dicarboxylate (I), C20H18O4S2, and dimethyl 2,6-diphenyl-2H,4H-1,3-dithiin-4,5-dicarboxylate (II), C20H18O4S2 (1983)
    Oxford [u.a.] : International Union of Crystallography (IUCr)
    Acta crystallographica 39 (1983), S. 283-287 
    Details
    ISSN: 1600-5759
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108270183004412
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  • 10
    Electronic Resource
    Electronic Resource
    [Leu5]enkephalin: four cocrystallizing conformers with extended backbones that form an antiparallel β-sheet (1983)
    Copenhagen : International Union of Crystallography (IUCr)
    Acta crystallographica 39 (1983), S. 625-637 
    Details
    ISSN: 1600-5740
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108768183003080
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