Relative stability symmetry

A comparative study [651] of the relative stabilities of various forms of U03 by DTA methods lists the temperatures of onset of reaction in the sequence a < e < amorphous < 0 < U02.9 < S < 7 (673, 733, 773, 803, 853, 863 and 903 K, respectively). Themal stabilities, as measured by the first-order reaction rate coefficient, magnitudes of E or enthalpies of reaction, increased with increasing structural symmetry. 

Many complex ions, such as NH4+, N(CH3)4+, PtCle", Cr(H20)3+++, etc., are roughly spherical in shape, so that they may be treated as a first approximation as spherical. Crystal radii can then be derived for them from measured inter-atomic distances although, in general, on account of the lack of complete spherical symmetry radii obtained for a given ion from crystals with different structures may show some variation. Moreover, our treatment of the relative stabilities of different structures may also be applied to complex ion crystals thus the compounds K2SnCle, Ni(NH3)3Cl2 and [N(CH3)4]2PtCl3, for example, have the fluorite structure, with the monatomic ions replaced by complex ions and, as shown in Table XVII, their radius ratios fulfil the fluorite requirement. Doubtless in many cases, however, the crystal structure is determined by the shapes of the complex ions. 

Acetals and Related Functions 5 B, and respectively. The remaining conformers , , and F possess a plane of symmetry. Consequently, the acetal function can in principle exist in the six different conformations A-F. Experimental evidence will be described which shows that the relative stabilities of these various conformers depend on stereoelectronic effects and the standard steric interactions. 

Our group has devoted two articles for the study of systems where the chiral subunits are bonded to a boron or to a metallic atom (Scheme 3.28). In both cases, the weakness of the bonds formed can be easily broken. In the first case, a series of bisdiphenylborates and the effect of the fluoro substitution on the relative stability of the homo vs. heterochiral complexes have been studied by means of DFT calculations (B3LYP/6-31G ) [29]. In addition, the corresponding isoelectronic structures, in which the boron has been substituted by a carbon or a positively charged nitrogen, have been considered. In all the cases, the homo and heterochiral complexes present D2 and S4 symmetries, respectively. 

This effect originates in the various f electron configurations of lanthanides and actinides. This effect is based on the correlation observed between the full pattern of the effect and the sequence of values of the L quantum number [52]. The correlation consists of the occurrence of the same double symmetry in (a) the series of L quantum number values of the ground terms of f element ions and (b) the sequence of relatively stabilized or destabilized f electron configurations (i.e.) the double-double effect. Accordingly... 

Applying ab initio quantum-chemical methods and density functional theory in the local density approximation, different (BH) spherical clusters for n — 12,20,32,42 and 92 have been investigated. Most of the clusters show nearly icosahedral symmetry. The hydrogen atoms are bonded to the spherical surface as prickles. The relative stability of the spheres measured as the binding energy per molecule has been analyzed. All the clusters studied are very stable, and the spherical (BH)32 cluster Seems to be the most stable structure. The effect of the hydrogen atoms is to increase the stability of the bare boron clusters. 

The available experimental information does not warrant any definitive distinction between these four possibilities. However, some indirect evidence allows for some choices. Regardless of the 66 kcal/mol of strain embodied in the bicyclobutane ring, it has been shown to be a relatively stable system in the gas phase or in hydrocarbon solvents. Nevertheless, when bicyclobutane is heated at 200 C two of the peripheral C-C bonds are broken, while the central bond remains intact during the purely thermal, symmetry controlled reactions. This relative stability has been associated with the predominantly rr character of this... 

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