Applications of Boolean programming optimisation methodology to the direct solution of crystal structures

Klunk, D.G.; Meyer, Edgar F.

doi:10.1038/248761a0

Cited by 2 publications

(1 citation statement)

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“…This approach, which is described in more detail elsewhere (Klunk & Meyer, 1974), is otherwise known as Boolean programming. It can be formulated by constructing an objective function and inequality constraints as follows" D Maximize CX subject to: AX-b>_'O where all X are zero or one in value.…”

Section: (B) Boolean Programmingmentioning

confidence: 99%

Structure solution by visual packing and optimization techniques. The crystal and molecular structure of spiro[5,5]undeca-1,4,7,10-tetraene-3,9-dione

Cullen¹,

Hass²,

Klunk³

et al. 1976

Acta Crystallogr Sect B

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The structure of spiro [5,5]undeca-l,4,7,10-tetraene-3,9-dione, C~IHsO2, has been determined from three-dimensional X-ray counter data. The crystals have the space group P]" with a= 9.080 (4), b= 13.608 (2), c=7.493 (3)/~, a=91"11 (2), fl=96-91 (4), y= 100.50 (2) ° and four molecules per unit cell. The observed and calculated densities are 1.26 (1) and 1.272 g cm -a respectively. 3180 independent reflections were collected by the 0=20 scan method. The structure was solved independently by two methods. In one method a three-dimensional color television display system was used to search for the most likely packing arrangements in the unit cell. The other method involved an application of Boolean programming. Both methods arrived at the same model, which was refined by least-squares techniques to a conventional R index of 0"048 for the 1485 reflections having I>_ 3at. The two independent molecules in the asymmetric unit are virtually identical and consist of two cyclodienone rings joined by a common spiro C atom. The average C-C bond length for bonds involving the spiro C atom is 1"50 (1)/~. The average bond angle around this atom is 109"4 ° .

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Section: (B) Boolean Programmingmentioning

confidence: 99%