Triplet and quartet relations: their use in direct procedures

Giacovazzo, Carmelo

doi:10.1107/s0567739480000137

Cited by 9 publications

(8 citation statements)

References 11 publications

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“…The tangent procedure has been extensively modified. New criteria were chosen for defining the number of reflections to phase, for modifying the tangent weighting scheme, and for fixing the active use of the psi-0 triplets (Cochran & Douglas, 1957;Giacovazzo, 1993;Cascarano & Giacovazzo, 1995) and of the negative quartet invariants (Giacovazzo, 1975(Giacovazzo, , 1976aGreen & Hauptman, 1976).…”

Section: Modern Tangent Techniques (Mdm)mentioning

confidence: 99%

Crystal structure determination and refinementviaSIR2014

et al. 2015

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SIR2014 is the latest program of the SIR suite for crystal structure solution of small, medium and large structures. A variety of phasing algorithms have been implemented, both ab initio (standard or modern direct methods, Patterson techniques, Vive la Différence) and non-ab initio (simulated annealing, molecular replacement). The program contains tools for crystal structure refinement and for the study of three-dimensional electron-density maps via suitable viewers.

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Section: Modern Tangent Techniques (Mdm)mentioning

confidence: 99%

Crystal structure determination and refinementviaSIR2014

et al. 2015

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“…They can sometimes be useful in situations where there is a deficiency in the number of triplets available, but the use here is somewhat experimental. Positive quartets are correlated with triplets (Giacovazzo, 1980) and this correlation is dependent on the E's involved. It is handled in the way described by Gilmore (Freer & Gilmore, 1980).…”

Section: Tripletsmentioning

confidence: 99%

MITHRIL–an integrated direct-methods computer program

Gilmore¹

1984

J Appl Cryst

897

368

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A new direct-methods computer program, MITHRIL, is described. Written in a neutral subset of Fortran IV, it is built around a heavily modified MULTAN80 system. It incorporates many recent theoretical developments in direct methods including the use of quartet and quintet invariants, a new method for estimating triplets, YZARC and MAGEX, and random-phase tangent refinement. It can be run as a menu-driven interactive real-time package or in the more conventional batch mode. Several levels of user-program interaction are provided.crystallographer to influence the flow of an analysis as it proceeds. These facilities are not readily available in current programs. At the same time, of course, it should be possible to run the package in the more usual batch environment. Cheap low-resolution graphics facilities are also widely available, and a comprehensive program should provide simple graphics facilities, particularly for the interpretation of E maps.Finally, it must be remembered that there are still many structures which present difficulties to direct methods, so that it is essential to have a program at one's disposal that offers as many options as possible.

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“…Without loss of generality we discuss the question in space groups up to orthorhombic following some recent ideas (Giacovazzo, 1980b). Let Rh,,Rh.,Rh,(l+ R),Rh,.h?Rh,R +h2 be the five magnitudes contained in the first phasing shell of 7".…”

Section: The Role Of the W Quartets In Direct Proceduresmentioning

confidence: 99%

The theory of representations: its application to the estimation of the two-phase variants and seminvariants

Giacovazzo¹,

Vicković²

1980

Acta Cryst Sect A

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The theory of representations has been used to obtain probabilistic estimates of the two-phase variants and seminvariants for the non-centrosymmetric space groups up to orthorhombic. Some practical applications show that the phase estimations can be useful in direct procedures, mostly for those crystal structures in which the enantiomorph definition is difficult.Notation h~,h 2 = reciprocal vectors N = number of atoms in the unit cell t = number of atoms in the asymmetric unit E h = normalized structure factor 1 = identity 3 × 3 matrix e=E 2-1 R h = magnitude of the normalized structure factor R v = pth rotation matrix of the point group T v = translation vector associated with the pth rotation matrix in the space group.

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Triplet and quartet relations: their use in direct procedures

Cited by 9 publications

References 11 publications

Crystal structure determination and refinementviaSIR2014

Crystal structure determination and refinementviaSIR2014

MITHRIL–an integrated direct-methods computer program

The theory of representations: its application to the estimation of the two-phase variants and seminvariants

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