The symbolic addition procedure for phase determination for centrosymmetric and non-centrosymmetric crystals

Karle, J.; Karle, Isabella L.

doi:10.1107/s0365110x66004079

Cited by 702 publications

(351 citation statements)

References 4 publications

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“…An initial attempt to solve the crystal structure of triphenylene from measured three-dimensional electron diffraction data was made by a combination of symbolic addition (Karle & Karle, 1966) (for centrosymmetric zones) and the Sayre (1952) equation or the tangent formula (Karle & Hauptman, 1956) (for extension into the noncentric set). When this was shown to be unsatisfactory, another approach, searching for an optimal molecular packing that would minimize the lattice energy, was employed (Gavezzotti, 1991;Voigt-Martin et al, 1992;Voigt-Martin, Simon et al, 1995).…”

Section: Structure Determinationmentioning

confidence: 99%

Electron Crystallography of Small Organic Molecules: Criteria for Data Collection and Strategies for Structure Solution

Dorset¹,

McCourt²,

Li³

et al. 1998

J Appl Cryst

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By crystallization onto an organic substrate such as naphthalene, thin microcrystals of a small organic molecule, such as triphenylene, can be grown. These crystals are less perturbed by shear and erratic bend disorder than the samples produced by rapid growth from dilute solutions. Selected-area electron diffraction intensities are consistent from specimen to specimen, show the symmetry expected for the crystalline projection and, furthermore, correspond to the Fourier transform of the entire unit cell. However, undersampling of the three-dimensional reciprocal lattice by goniometry can frustrate structure determination if conventional direct methods are used. Nevertheless, the crystal structure may still be solved quite accurately by energy minimization.

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Section: Structure Determinationmentioning

confidence: 99%

Electron Crystallography of Small Organic Molecules: Criteria for Data Collection and Strategies for Structure Solution

Dorset¹,

McCourt²,

Li³

et al. 1998

J Appl Cryst

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“…Crystallographic phases were determined by a procedure termed ''symbolic addition'' by some researchers (22)…”

Section: Discussionmentioning

confidence: 99%

Direct phase determination in protein electron crystallography: The pseudo-atom approximation

Dorset

1997

Proc. Natl. Acad. Sci. U.S.A.

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The crystal structure of halorhodopsin is determined directly in its centrosymmetric projection using 6.0-Å-resolution electron diffraction intensities, without including any previous phase information from the Fourier transform of electron micrographs. The potential distribution in the projection is assumed a priori to be an assembly of globular densities. By an appropriate dimensional re-scaling, these ''globs'' are then assumed to be pseudo-atoms for normalization of the observed structure factors. After this treatment, the structure is determined directly by conventional direct methods, followed by Fourier refinement, leading to a mean phase deviation of only 20؇ (from the values originally found from the image transform) for the 45 most intense ref lections.

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“…Karle & Karle, 1966). The origin was specified by assigning the value of +re/2 to the phases of reflections 1,10,0, 055 and 407 and the enantiomorph was arbitrarily chosen by assigning +z c/2 to reflection 11,0,5.…”

Section: Methodsmentioning

confidence: 99%

On the conformation of naloxone, a narcotic antagonist

Karle¹

1974

Acta Crystallogr Sect B

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The narcotic antagonist naloxone (Ct9H21NO4), the N-allyl derivative of oxymorphone, appears to be 100 to 1000 times more potent than its agonist oxymorphone in enhancing receptor binding in the brain. The conformation of the N-allyl chain, the pertinent feature in this molecule, is not completely extended but has an N-C-C=C torsional angle of -98 °, reminiscent of the N-C-C-C torsional angle of +97 ° in the cyclopropyl methyl chain in cycloazocine. The conformation of the ring system in naloxone is similar to that in morphine and codeine. Hydrogen bonding does not occur directly between alkaloid moieties as in morphine and codeine. The naloxone molecules are separated by layers of CI-ions and water molecules. The space group for naloxone. HCI. 2H20 is P212~2, with a = 13"293 +0.003, b= 18.592+0.015 and c=7.852+0.002 ,~ and Z=4. The R index for 1789 observed reflections is 6.0 %.

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The symbolic addition procedure for phase determination for centrosymmetric and non-centrosymmetric crystals

Cited by 702 publications

References 4 publications

Electron Crystallography of Small Organic Molecules: Criteria for Data Collection and Strategies for Structure Solution

Electron Crystallography of Small Organic Molecules: Criteria for Data Collection and Strategies for Structure Solution

Direct phase determination in protein electron crystallography: The pseudo-atom approximation

On the conformation of naloxone, a narcotic antagonist

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