Least-squares plane

Another aspeet of sterie overerowding whieh has not attraeted mueh attention, although obviously of fairly general potential oeeurrenee, is illustrated by the dipyridothiophene (14). In a hypothetieal planar moleeule the distanee between the two peri-ehlorine atoms would be 2.05 A. In praetiee this is redueed to a more aeeeptable 3.06 A, prineipally as a result of displaeement of the peri-ehlorines by about 0.6 A from the least-squares plane (74JCS(P2)1925). 

If the BF2 groups in Ni(dmg-BF2)2 are substituted by BPh2 units (122), the complex also adopts the saddle-shaped conformation of type D (Fig. 32), in which the two dimethylglyoxime fragments are bent down from the N4 plane with a dihedral angle of about 27° between the two least-squares planes of the dioxime units. The coordination geometry around the nickel ion is distorted square-pyramidal, but there are no intermolecular Ni Ni interactions [167]. 

The trigonal planar zinc phenoxide complex [K(THF)6][Zn(0-2,6-tBu2C6H3)3] is formed by the reaction of a zinc amide complex, via a bis phenoxide, which is then further reacted with potassium phenoxide. TheoX-ray structure shows a nearly perfect planar arrangement of the three ligands with zinc only 0.04 A out of the least squares plane defined by the three oxygen atoms.15 Unlike the bisphenoxide complexes of zinc with coordinated THF molecules, these complexes are not cataly-tically active in the copolymerization of epoxides with C02. The bisphenoxide complex has also been structurally characterized and shown to be an effective polymerization catalyst. 43... 

Both macrocycles display a slight saddle distortion with mean deviation from the least-squares plane of the 24 core atoms of 0.07 A for molecule 147 A and 0.09 A for molecule 147 B. The asymmetry of the periphery is apparent in the macrocyclic core of both molecules in that each is elongated... 

The least-square straight line and least-square plane... 

For a least-square plane, the linear relationship between three data vectors xm, ym and zm can also be written in different ways, such as... 

Figure 2, a) Deviations (AxlO ) from the least squares plane defined by the four nitrogens of the nickel isobacterlochlorln b) An edge-on-view of the molecule that illustrates the puckering of the macrocycle. Substituents have been removed for clarity. (Space group Z 16). 

Differences between the geometrical structures of helicenes concern mainly the angles between the least square planes of subsequent benzene rings and the torsion angles of the bonds of the inner helix. In Table 24 some X-ray data are given. For heptahelicene two different crystals have been obtained. One of the crystals gave two... 

The shift from the least squares plane made by four nitrogen donors. 

A least-squares plane through the four atoms in the Mo2(m2-H)(m2 P) core, as depicted in Figure 3, shows that they are coplanar within 0.02 A. The bridging... 

Fig. 15. Valence Fourier difference map for uracil in the least-squares plane of the C, N, and O atoms. Rearranged from ref. 398.

In general, thiouracils and 2-thiocytosine are planar, but close examination of the least-squares plane through the six atoms of the pyrimidine ring in 2-thiocytidine dihydrate491 shows that the ring atoms C-2 and N-3 are significantly displaced to opposite sides of the plane. The exocyclic atoms S-7 and N-8 show also marked displacements to the same side of the ring. 

Table I) are virtually planar with no atom displaced by more than 0.08 A from the least-squares plane defined by those six atoms. The dihedral angle between the plane formed by the six coordinated carbon atoms (Plane II) and that formed by the uncoordinated olefin (Plane III) are also identical (117°), within experimental error, in all three complexes (Table I). The longest C—F bond distances in 56a and 56b are those on the terminal ends of the coordinated triene, reflecting the considerable rehybridization toward pyramidal geometry at these carbon atoms. Surprisingly, the overall skeletal structure of 57b is not significantly different from those of the fluorinated analogues 56, and the observed differences in air and thermal stability are not manifested in significantly different Mn—C bond distances or in a different mode of metal-ligand bonding in 57b.

Deviations (10 3 A) from Best Least-Squares Planes in Anthracene (taken from Sparks, 1958)... 

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