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Ab initio phasing
Sheldrick, G. M., Gilmore, C. J., Hauptman, H. A., Weeks, C. M., Miller, R. and Usón, I.  International Tables for Crystallography (2012). Vol. F, ch. 16.1, pp. 413-432 [ doi:10.1107/97809553602060000850 ]
... small-molecule structures have been routinely solved by direct methods, a class of ab initio methods in which probabilistic phase relations ... macromolecular structures in this way has, however, been limited to a few special cases involving relatively small macromolecules, unusually high-resolution ... approaches, including one that does not require high-resolution data, a related molecule as search fragment or heavier atoms and ...

CRUNCH2 - Karle-Hauptman determinants
Sheldrick, G. M., Gilmore, C. J., Hauptman, H. A., Weeks, C. M., Miller, R. and Usón, I.  International Tables for Crystallography (2012). Vol. F, Section 16.1.12.7, p. 429 [ doi:10.1107/97809553602060000850 ]
CRUNCH2 - Karle-Hauptman determinants 16.1.12.7. CRUNCH2 - Karle-Hauptman determinants The program CRUNCH2 is quite different to the other ... of some E-map recycling at the end to complete a substructure, CRUNCH2 operates entirely in reciprocal space by maximizing ...
     [more results from section 16.1.12 in volume F]

Substructure solution for native sulfurs and halide soaks
Sheldrick, G. M., Gilmore, C. J., Hauptman, H. A., Weeks, C. M., Miller, R. and Usón, I.  International Tables for Crystallography (2012). Vol. F, Section 16.1.11, pp. 425-426 [ doi:10.1107/97809553602060000850 ]
... the incorporation of heavy-metal ions by soaking crystals with a low concentration of the metal salt for several hours. The ... not work well for all expression systems; the second had a low success rate. The improved quality of modern diffraction data ... sulfur atoms or from halide ions introduced by soaking with a high concentration of a halide (iodide or bromide) for ...

Substructure applications
Sheldrick, G. M., Gilmore, C. J., Hauptman, H. A., Weeks, C. M., Miller, R. and Usón, I.  International Tables for Crystallography (2012). Vol. F, Section 16.1.10.4, p. 425 [ doi:10.1107/97809553602060000850 ]
... known for some time that conventional direct methods can be a valuable tool for locating the positions of heavy-atom substructures ... when applied to such data. Dual-space direct methods provide a more robust foundation for handling such data, which are often ... care in data processing, especially if the values resulting from a MAD experiment are to be used. SHELXD is frequently ...
     [more results from section 16.1.10 in volume F]

Recognizing solutions
Sheldrick, G. M., Gilmore, C. J., Hauptman, H. A., Weeks, C. M., Miller, R. and Usón, I.  International Tables for Crystallography (2012). Vol. F, Section 16.1.9.3, pp. 421-422 [ doi:10.1107/97809553602060000850 ]
... progress of current SnB jobs can be followed by monitoring a figure-of-merit histogram for the trial structures that have been processed (Fig. 16.1.9.2). A clear bimodal distribution of figure-of-merit values is a strong indication that a solution has, in fact, been ...
     [more results from section 16.1.9 in volume F]

Utilizing Pattersons for better starts
Sheldrick, G. M., Gilmore, C. J., Hauptman, H. A., Weeks, C. M., Miller, R. and Usón, I.  International Tables for Crystallography (2012). Vol. F, Section 16.1.8, pp. 419-420 [ doi:10.1107/97809553602060000850 ]
... are present, it is possible to start recycling procedures from a set of atomic positions that are consistent with the Patterson ... This filter is currently implemented as follows in SHELXD. First, a sharpened Patterson function (Sheldrick et al., 1993) is calculated, and ... the top 200 (for example) non-Harker peaks further than a given minimum distance from the origin are selected, in ...

Resolution enhancement: the `free lunch' algorithm
Sheldrick, G. M., Gilmore, C. J., Hauptman, H. A., Weeks, C. M., Miller, R. and Usón, I.  International Tables for Crystallography (2012). Vol. F, Section 16.1.7, p. 419 [ doi:10.1107/97809553602060000850 ]
... 16.1.7. Resolution enhancement: the `free lunch' algorithm Direct methods take a set of phases, refine them and also determine new ones. ... to predict new amplitudes as well. If density modification of a real-space map is performed, then any process of real-space density modification will, following a Fourier transformation, give structure-factor amplitudes for reflections that ...

Fourier refinement
Sheldrick, G. M., Gilmore, C. J., Hauptman, H. A., Weeks, C. M., Miller, R. and Usón, I.  International Tables for Crystallography (2012). Vol. F, Section 16.1.6, p. 419 [ doi:10.1107/97809553602060000850 ]
... that can only be generated using the larger E magnitudes, a limited number of reflections are phased during the actual dual-space cycles. Working with a limited amount of data has the added advantage that less ... current trial structure is the `best' so far based on a figure of merit (either the minimal function or a ...

Random omit maps
Sheldrick, G. M., Gilmore, C. J., Hauptman, H. A., Weeks, C. M., Miller, R. and Usón, I.  International Tables for Crystallography (2012). Vol. F, Section 16.1.5.3, p. 419 [ doi:10.1107/97809553602060000850 ]
Random omit maps 16.1.5.3. Random omit maps A third peak-picking strategy involves selecting approximately of the top ... the common practice in macromolecular crystallography of omitting part of a structure from a Fourier calculation in the hope of finding an improved ...
     [more results from section 16.1.5 in volume F]

Parameter shift
Sheldrick, G. M., Gilmore, C. J., Hauptman, H. A., Weeks, C. M., Miller, R. and Usón, I.  International Tables for Crystallography (2012). Vol. F, Section 16.1.4.3, p. 418 [ doi:10.1107/97809553602060000850 ]
... be used to minimize by varying the phases. So far, a seemingly simple algorithm, known as parameter shift (Bhuiya & Stanley, 1963 ... to reduce the value of the minimal function. For example, a typical phase-refinement stage consists of three iterations or scans through the reflection list, with each phase being shifted a maximum of two times by 90° in either the ...
     [more results from section 16.1.4 in volume F]

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