Berry coordinate

The crystal and molecular structures of two spiroarsoranes of type XXI (R = Ph, R = R" = CH3 and R = OH, R = R" = H) have been determined by single-crystal X-ray diffraction analyses (68, 69). The crystal data for these compounds are summarized in Table V. Both compounds have a geometry at the arsenic atom that lies on the Berry coordinate between rectangular-pyramidal and trigonal-pyramidal. These structures show close parallels between the structures of related arsenic and phosphorus systems. It has been concluded that, since the solid-state structures of these compounds lie close to the Berry coordinate, the dynamic process in solution is distortion along that coordinate (68, 69). 

A single crystal X-ray structural evaluation of the hydrido-phosphorane (117) reveals that the compound lies on the Berry coordinate apparently 50% between tbp and rp structures with the oxygen atoms in apical positions and an O-P-0 bond angle of 166.9°. 

Thus the Berry coordinate represents a viable option for intramolecular exchange in rhodium and iridium complexes, in contrast to platinum and palladium complexes. Nickel complexes, on the other hand, can adopt either tetrahedral or square-planar conformations in the four-coordinate structures, and therefore the fact that these complexes can take on any of the three conformations is not surprising. This analysis is described in detail in Reference 67. 

Table 12 summarises the calculated moments of inertia for hypothetical 5-coordinate molecules chosen to lie along either the Berry or the Turnstile rearrangement coordinates. The initial geometry in both cases is the trigonal bipyramid, and the transition state for the Berry coordinate is a square pyramid with 0 = 100° or 0 = 93°. 

Fig. 8.4. Diagram showing the adherence of 78 nickel complexes to the Berry coordinate (solid line). The origin represents a TBP, the upper right end of the coordinate a SQP...

Bicyclic phosphoranes (87a-d) prepared by the reaction of (85a-d) with (86) were isolated and then characterised by m.s., elemental analysis, i.r. and multinuclear n.m.r. spectroscopy no pseudorotation was observed at ambient temperature. In a related study, tricyclic phosphoranes (89a-d) were obtained from the reaction of (88a-d) with (86). An analogous reaction between (90a-i) and (86) furnished another series of tricyclic phosphoranes (91a-i). The single crystal X-ray structure of (91a) revealed a tbp configuration about phosphorus with a 26% distortion along the Berry coordinate using P-01 as the pivot. 

Fig. 7. Structures of five-coordinate Cu2+ from first principles molecular dynamics. A Berry twist mechanism for the interconversion of the two structures is shown (from left to right) the reorientation of the main axis of a square pyramidal configuration by pseudo-rotations via a trigonal bipyramidal configuration. The grey atoms in the plane of the trigonal bipyramid are all candidates for becoming apical atoms in a square pyramid.

CH3CN, 33-11, 33 H20, 34, 35-jCH3CN, and 37jCH3CN represent nearly ideal or (more or less) distorted square pyramids, with the carbon atom Cl in the apical position. In most cases, the geometries of the Si-coordination polyhedra in the crystal are located on the Berry-pseudorotation coordinate (pivot atom Cl). 

Pseudorotation is well established in 5-coordinated species involving the main group elements and is best described by the Berry mechanism which interconverts two trigonal bipyramids via a square pyramid. Its operation here is difficult to reconcile with the highly stereospecific nature of substitution in Pt(II). Nevertheless, the mechanism has had substantial support. It may very well be that (a) is favored by polar solvents and that (b) is prevalent in nonpolar media. The associated reaction profiles are shown in Fig. 7.11. 

Colorimetric analyses performed in the reflection mode have been used to determine colors of various flowers" as well as the colors and color development of fruits and berries. In an interesting study, the cyclamen red (or pink) colors of some carnation cultivars have been found to be based on the macrocyclic anthocyanin, pelargoni-din 3,5-diglucoside (6",6" -malyl diester).The CIELAB coordinates revealed that these flowers showed similar colors as some rose cultivars, which, however, were mainly based on a very different pigment, cyanidin 3,5-diglucoside. 

Percentage displacement along the Berry pseudorotation coordinate. 

P. Salamon, E. Ihrig, and R. S. Berry. A group of coordinate transformation which preserve the metric of Weinhold. J. Math. Phys. 24, 2515-20 (1983). 

The stability of five-coordinate intermediates also makes possible the ready racemization of optically active silanes by catalytic amounts of base. The base can add readily to form a five-coordinate intermediate. The latter can undergo Berry pseudorotation with complete scrambling of substituents followed by loss of the base to yield the racemized silane. 

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