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  • International Union of Crystallography (IUCr)  (158)
  • 1
    Electronic Resource
    Electronic Resource
    The application of phase relationships to complex structures. III. The optimum use of phase relationships (1971)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 27 (1971), S. 368-376 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: An improvement is described in the automatic procedure for solving crystal structures incorporated in the computer program LSAM. The development of signs from an initial set containing symbols is carried only as far as is necessary to establish strong relationships between the symbols. The information so gained is used in a fresh beginning of the symbolic-addition process. Some failure of relationships between symbols is allowed to give a multisolution method. A phase-permutation computer program for non-centrosymmetric structures, MULTAN, incorporates a weighted tangent formula. This is of the form {\rm tan}\varphi_{\bf h} = {{\sum_{\bf h'}w_{\bf h'},w_{\bf h-h'}|E_{\bf h'}E_{\bf h-h'}| \sin (\varphi_{\bf h'} + \varphi_{\bf h-h'})}\over{\sum_{\bf h'}w_{\bf h'},w_{\bf h-h'}|E_{\bf h'}E_{\bf h-h'}| \cos (\varphi_{\bf h'} + \varphi_{\bf h-h'})}} = {{T_{\bf h}}\over{B_{\bf h}}} and w_{\bf h} = {\rm tanh}\{ \sigma_3\sigma_2^{-3/2}|E_{\bf h}|(T_{\bf h}^2 + B_{\bf h}^2)^{1/2}\}.All phases are accepted as soon as they are found with the associated weight. This gives a fourfold increase in speed in development of the complete phase set. An absolute figure of merit is described to indicate probably correct phase sets for multisolution methods.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0567739471000822
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  • 2
    Electronic Resource
    Electronic Resource
    On the application of phase relationships to complex structures. XVI. A random approach to structure determination (1978)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 883-892 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: With triple-phase relationships treated as linear equations it is possible to refine a set of phases from given initial values. Phases so obtained are better than those found by refining to self-consistency with the tangent formula. An investigation of the radius of convergence of the least-squares refinement process showed that a substantially correct solution may often be found even starting with random phases. Systems containing up to 300 phases have been investigated and the results and their implications are discussed. It is concluded that the random approach can, at the very least, be used to obtain 70--100 phases as a good starting point for phase development. There is also the possibility of obtaining a sufficient number of phases directly to define a reasonably complex structure, especially with a computer augmented by an array processor. A problem which can arise with linear equations, as with the tangent formula, is that the phases obtained do not adequately define the enantiomorph and give an E map with a pseudo centre of symmetry. Two methods of overcoming this problem are described.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0567739478001837
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  • 3
    Electronic Resource
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    On the application of phase relationships to complex structures. V. Finding the solution (1973)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 29 (1973), S. 231-234 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Multisolution direct methods for solving crystal structures lead to many plausible sets of phases and some means of determining the correct set is necessary. For centrosymmetric structures, figures of merit are usually quite discriminating and the examination of only one or two E maps is necessary. For noncentrosymmetric structures, figures of merit are unreliable and the necessity of examining a large number of E maps can sometime prove to be an almost insuperable obstacle to finding the correct structure. A procedure is described for overcoming this difficulty. The Cooley-Tukey fast-Fourier-transform technique is used to compute E maps and all peaks greater than a certain height are located. A selection of the highest of these peaks, whose number is chosen by the program user, is then analysed with respect to bond lengths and angles. Favourable projections of coherent groups of peaks are output on the line printer in the form of integers representing the ranking order of the peaks and in positions which represent an undistorted projection of the group. Computing time is of the order of one minute per set of phases and the examination of a set of 32 maps and finding the correct solution takes about 30 minutes.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0567739473000616
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  • 4
    Electronic Resource
    Electronic Resource
    On the application of phase relationships to complex structures. VIII. An extension of the magic-integer approach (1975)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 31 (1975), S. 367-372 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A magic-integer approach, called the P-S set method is described. A primary (P) set of reflexions contains some which fix the origin and enantiomorph and others expressed symbolically in magic-integer form. Probable phases for a secondary (S) set of reflexions are derived, also in symbolic form, from single triple-phase relationships containing a pair of P reflexions. Relationships which link the combined P and S sets give rise to the terms of a Fourier map, the peaks of which indicate likely sets of phases for all the reflexions under consideration. These sets of phases are used as starting points for the computer program MULTAN. The process is completely automated and is illustrated by the solution of the structure of cephalotaxine, C18H21O4N, the space group of which is C2 with two molecules in the asymmetric unit.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0567739475000770
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  • 5
    Electronic Resource
    Electronic Resource
    On the application of phase relationships to complex structures. XVII. When MULTAN fails (1979)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 35 (1979), S. 622-626 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Two new multisolution direct-methods procedures are described: MAGIC, which employs the magic-integer concept and YZARC which refines initially random sets of phases by a least-squares approach. Each procedure produces several sets of phases for a number of reflexions, usually in the range 35-100. These are then extended by the tangent formula but with the constraint that the basis phases are not allowed to change until the final cycle. It is shown that for difficult structures these methods, which deal simultaneously with many phase relationships, may have intrinsic advantages over the MUL TAN procedure. Examples of their use are given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0567739479001455
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  • 6
    Electronic Resource
    Electronic Resource
    Structure du di-nitrosométhane cis (1963)
    Copenhagen : International Union of Crystallography (IUCr)
    Acta crystallographica 16 (1963), S. 109-112 
    Details
    ISSN: 0001-5520
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Geosciences
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0365110X63000256
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  • 7
    Electronic Resource
    Electronic Resource
    Direct methods in crystallography edited by H. A. Hauptman (1979)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 35 (1979), S. 701-702 
    Details
    ISSN: 1600-5724
    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/S0567739479001662
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  • 8
    Electronic Resource
    Electronic Resource
    Some ideas on the deconvolution of the Patterson function (1966)
    Copenhagen : International Union of Crystallography (IUCr)
    Acta crystallographica 21 (1966), S. 845-848 
    Details
    ISSN: 0001-5520
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Geosciences
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0365110X66004067
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  • 9
    Electronic Resource
    Electronic Resource
    Two Polymorphs of Bis(4-methoxyphenyl)tellurium(IV) Diiodide (1998)
    Oxford [u.a.] : International Union of Crystallography (IUCr)
    Acta crystallographica 54 (1998), S. 995-1000 
    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/S0108270197016387
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  • 10
    Electronic Resource
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    N-2-(2-Bromo-4,5-dimethoxyphenyl)-1-(2,3,4-trimethoxyphenyl)ethylformamide (1991)
    Oxford [u.a.] : International Union of Crystallography (IUCr)
    Acta crystallographica 47 (1991), S. 2115-2118 
    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/S0108270191003141
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