Stability and Structure

Most simple metal azides (with the exception of the alkali-metal and some of the alkaline-earth salts) explode readily on application of a thermal, mechanical, photolytic, or electrical impulse. The inorganic fulminates, which are iso-electronic with the corresponding azides, are much more sensitive and even the alkali-metal salts explode easily. Other isoelectronic substances like the cyanates and cyanamides are, however, less sensitive. Many of the azides, fulminates, and cyanamides decompose exothermally, giving in all cases N2 gas. Among the azides the decomposition step is of the following type  

The fact that different metal azides exhibit sizable differences in sensitivity and pseudostability is associated with molecular and solid-state properties and with the decomposition energetics of the individual substances. A great deal of this information is now available for the azides, as discussed in different chapters of this book. Work on isoelectronic substances, reviewed recently by Iqbal [3], has been substantial but not very detailed. However, a qualitative general correlation 

Pauling [4] developed a simple, qualitative theory of the relative stability of the isoelectronic and isomeric ions NCO (cyanate) and CNO (fulminate). Assuming that they have similar electronic structures, with interatomic distances of about 1.16 A, the relative energies of atomic kernel repulsion can be calculated, assuming the charges to be distributed as follows  

The repulsion energy was found to be greater in the fulminate ion by 3e /1.16, or 3624 kJ/mole. Since the atomic kernels are shielded by the valence electrons, the repulsive energy is probably 10% of the above value. The difference in the enthalpy of formation of AgCNO and AgNCO is 270 kJ/mole [3], which is roughly 10% of the calculated number. 

In the spirit of this argument, the bond structures can be discussed in terms of the contribution of resonance to the energy of the molecules. According to Pauling [4,5], the maximum amount of resonance stabilization occurs when alternative valence bond structures are closely equivalent. In NJ and CNO , resonance among the following structures (cf. Chapter 5) occurs  

In polyvalent liquid elements as well as in many metallic glasses and liquid alloys, the first peak in the structure factor S(K) with K = K = k — A is split into two (Figs. 5.2a, 7 and 29a). There is a peak at Kp and another one at Kpe close to 2/cf. The latter is electronically induced [5.8] and essential to the understanding of disordered metals. 

Pseudopotential theory relates rather directly physical properties to 

the perturbation characteristic, is shown in Fig. 5.2d. It is negative and approaches zero for K 2kF. At 2kF, there is a logarithmic singularity responsible for the Friedel oscillations of eff(r)./(X), the local-field correction, takes care of the modifications due to correlation and exchange. For crystalline 

One fascinating aspect of ferrocene chemistry is its extraordinary ability to stabilize carbocations that formally should have their positive charge in a position adjacent to the cyclopentadienyl ring (a-ferrocenylalkyl carbocations). Such cations are so stable that they form quantitatively from appropriate precursors (e.g., alcohols) on treatment with acid and many of them remain unchanged in solution for days and 

As a consequence of the special structure of such cations, the rotation around the bond between the ring carbon and the cationic centre is hindered, due to its partial double bond character. Thus, the cations exist as distinct enantiomers with only a low tendency towards racemization their optical rotations remain constant over long periods and the barrier for hindered rotation of the 1-ferrocenylethylium cation in trifluoroacetic acid was determined to have AH = 81.5kJ/mol and TAS = —22.2 kJ/mol [27] other cations have similar properties [28]. 

The stabilizing effect of ferrocene on positive charges in its neighbourhood is not limited to charges on carbon it has also been observed for phosphenium ions [29]. 

The carbocations being reactive intermediates have short life and so they are unstable. But they have been rendered stable after being trapped in strongest super acids which are mixtures of fluorosulphuric and antimony pentafluoride dissolved in S02 or chlorofluorosulphuric acid S02CIF. Under these conditions their structure and stability have been correlated. 

In general, the greater the resonance and hyper-conjugation the greater is the stability of carbocation. The stability also depends on the field strengths. The following examples illustrate this point. 

We know that among the simple carbocations the order of stability is 

This is because the greater the number of canonical forms, the greater is the stability. Let us see the canonical forms from a tertiary and a primary carbocation. 

Thus a tertiary carbocation like the above will give nine resonating structures while a primary will give only two hyperconjugative forms. This explains why tertiary carbocations are more stable than secondary which in turn is more stable than primary. This also explains why ethyl carbocation (CH3CIlf) is more stable than methyl carbocation (CH )- 

There are three possibilities, any one of which could give the desired product according to Markovnikov s rule. 

What alkenes would you start with to prepare the following products (a) /X Br (b) CH2CH3 (c) Br 

To understand why Markovnikov s rule works, we need to learn more about the stmcture and stability of carbocations and about the general nature of reactions and transition states. The first point to explore involves stmcture. 

The second point to explore involves carbocation stability. 2-Methylpropene might react with H+ to form a carbocation having three alkyl substituents (a tertiary ion, 3°), or it might react to form a carbocation having one alkyl substituent (a primary ion, 1°). Since the tertiary alkyl chloride, 2-chloro-2-methylpropane, is the only product observed, formation of the tertiary cation is evidently favored over formation of the primary cation. Thermodynamic measurements show that, indeed, the stability of carbocations increases with increasing substitution so that the stability order is tertiary secondary primary methyl. 

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The challenges for computational chernislry are to characteri/e and predict the structure and stability of chemical systems, to estimate energy differences between different states, and to explain reaction pathways and mechanisms at the atomic level. Meeting these challenges could eliminate tinie-consiini mg experiments. 

Reactions such as catalytic hydrogenation that take place at the less hindered side of a reactant are common m organic chemistry and are examples of steric effects on reactivity Previously we saw steric effects on structure and stability m the case of CIS and trans stereoisomers and m the preference for equatorial substituents on cyclo hexane rings... 

One explanation for the structure and stability of benzene and other arenes is based on resonance according to which benzene is regarded as a hybrid of the two Kekule structures... 

The many papers in this proceedings are partitioned into very abstruse theoretical analyses of structure and stability of quasicrystals on the one hand, and practical studies of surface structures, mechanical properties and potential applications. The subject shows signs of becoming as deeply divided between theorists and practical investigators, out of touch with each other, as magnetism became in the preceding century. 

In this chapter we present various computational methods for studying the structure and stability regions of various phases within the basic and the extended LG models of the ternary surfactant mixtures. In particular we use ... 

There are notable differences in both structures and stabilities for binary N-O and S-N anions (Section 5.4). The most common oxo-anions of nitrogen are the nitrite [N02] and the nitrate anion [NOs] the latter has a branched chain structure 1.1. The sulfur analogue of nitrite is... 

F. SOLYMOSI, Structure and Stability of Salts of the Halogen Oxyacids in the Solid Phase, Wiley, UK, 1978, 468 pp. 

Tu, A. J., Heller, M. J. Structure and Stability of Metal-Nucleoside Phosphate Complexes, in Metal Ions in Biological Systems Vol. 1 (ed. Sigel, H.), p. 1, Marcel Dekker, Inc. New York 1974... 

Structure and Stability of Benzene Molecular Orbital Theory 521... 

Among the diatomic molecules of the second period elements are three familiar ones, N2,02, and F2. The molecules Li2, B2, and C2 are less common but have been observed and studied in the gas phase. In contrast, the molecules Be2 and Ne2 are either highly unstable or nonexistent. Let us see what molecular orbital theory predicts about the structure and stability of these molecules. We start by considering how the atomic orbitals containing the valence electrons (2s and 2p) are used to form molecular orbitals. 

One of the most important parameters that defines the structure and stability of inorganic crystals is their stoichiometry - the quantitative relationship between the anions and the cations [134]. Oxygen and fluorine ions, O2 and F, have very similar ionic radii of 1.36 and 1.33 A, respectively. The steric similarity enables isomorphic substitution of oxygen and fluorine ions in the anionic sub-lattice as well as the combination of complex fluoride, oxyfluoride and some oxide compounds in the same system. On the other hand, tantalum or niobium, which are the central atoms in the fluoride and oxyfluoride complexes, have identical ionic radii equal to 0.66 A. Several other cations of transition metals are also sterically similar or even identical to tantalum and niobium, which allows for certain isomorphic substitutions in the cation sublattice. 

Lamry R, Biltonen R (1969) in TimasheffSN, Fasman GD (eds) Structure and Stability of Biological Macromolecules. M Dekker, New York, p 7... 

Since a carbanion is what remains when a positive species is removed from a carbon atom, the subject of carbanion structure and stability (Chapter 5) is inevitably related to the material in this chapter. So is the subject of very weak acids and very strong bases (Chapter 8), because the weakest acids are those in which the hydrogen is bonded to carbon. 

The structures and stabilities of several 8 dications are well established. Red, yellow or blue solutions are obtained if sulfur is added to 803-contain-ing sulfuric acid (oleum). Gillespie et al. have suggested that the colours are due to the nonadecasulfur dication 819, octasulfur dication 8g, and tetra-... 

Only the structures of di- and trisulfane have been determined experimentally. For a number of other sulfanes structural information is available from theoretical calculations using either density functional theory or ab initio molecular orbital theory. In all cases the unbranched chain has been confirmed as the most stable structure but these chains can exist as different ro-tamers and, in some cases, as enantiomers. However, by theoretical methods information about the structures and stabilities of additional isomeric sul-fane molecules with branched sulfur chains and cluster-like structures was obtained which were identified as local minima on the potential energy hypersurface (see later). 

F. Takahashi and V. R. Katta, Further studies of the reaction kernel structure and stabilization of jet diffusion flames, Proc. Combust. Inst. 30 383-390, 2005. 

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