Cation bonding strength

All oxygen-based polyhedra with the same Pauling bond strength (cationic charge/coordination number see section 1.10.3) have the same mean polyhedral linear expansion. 

In a general way, the role of the cations depends on the valence, CN, and the related values of the single-bond strength. Cations of higher valence and lower coordination than the alkalis and alkaline earth oxides may also contribute, in part, to the network structure. We can list the cations in three groups. The different types of ion present in oxide glasses are summarized in Table 7.7. 

The IR stretching frequencies o(SN) and o(SF) occur at higher wave numbers and the S-N and S-F distances are significantly shorter in the octahedral cations [M(NSF)6] than those in the free ligand, indicating an increase in S-N and S-F bond strength upon coordination. 

Other measures of nucleophilicity have been proposed. Brauman et al. studied Sn2 reactions in the gas phase and applied Marcus theory to obtain the intrinsic barriers of identity reactions. These quantities were interpreted as intrinsic nucleo-philicities. Streitwieser has shown that the reactivity of anionic nucleophiles toward methyl iodide in dimethylformamide (DMF) is correlated with the overall heat of reaction in the gas phase he concludes that bond strength and electron affinity are the important factors controlling nucleophilicity. The dominant role of the solvent in controlling nucleophilicity was shown by Parker, who found solvent effects on nucleophilic reactivity of many orders of magnitude. For example, most anions are more nucleophilic in DMF than in methanol by factors as large as 10, because they are less effectively shielded by solvation in the aprotic solvent. Liotta et al. have measured rates of substitution by anionic nucleophiles in acetonitrile solution containing a crown ether, which forms an inclusion complex with the cation (K ) of the nucleophile. These rates correlate with gas phase rates of the same nucleophiles, which, in this crown ether-acetonitrile system, are considered to be naked anions. The solvation of anionic nucleophiles is treated in Section 8.3. 

The electrostatic valence rule is satisfied. The bond strength from S7+4, A +3, and Na+ are 1, -, and respectively, since the cations all have the coordination number 4. Each oxygen ion is in contact with 1 Si + i, 1 Al+i, and 1 Na+, giving JbV = 2, and each chlorine ion in contact with 4 Na+, giving Xs = 1, in agreement with their valences. 

In sharp contrast to the stable [H2S. .SH2] radical cation, the isoelectron-ic neutral radicals [H2S.. SH] and [H2S. .C1] are very weakly-bound van der Waals complexes [125]. Furthermore, the unsymmetrical [H2S.. C1H] radical cation is less strongly bound than the symmetrical [H2S.. SH2] ion. The strength of these three-electron bonds was explained in terms of the overlap between the donor HOMO and radical SOMO. In a systematic study of a series of three-electron bonded radical cations [126], Clark has shown that the three-electron bond energy of [X.. Y] decreases exponentially with AIP, the difference between the ionisation potentials (IP) of X and Y. As a consequence, many of the known three-electron bonds are homonuclear, or at least involve two atoms of similar IP. 

Lupinetti, A.J., Jonas, V., Thiel, W., Strauss, S.H. and Frenking, G. (1999) Trends in Molecular Geometries and Bond Strengths of the Homoleptic d Metal Carbonyl Cations [M(CO)J ... 

Hertwig, R.H., Hrusak, J., Schroder, D., Koch, W. and Schwarz, H. (1995) The metal-ligand bond strengths in cationic gold(l) complexes. Application of approximate density functional theory. Chemical Physics Letters, 236, 194-200. 

In a stable ionic structure the valence (ionic charge) of each anion with changed sign is exactly or nearly equal to the sum of the electrostatic bond strengths to it from adjacent cations. The electrostatic bond strength is defined as the ratio of the charge on a cation to its coordination number. 

Let a be the coordination number of an anion. Of the set of its a adjacent cations, let nt be the charge on the i-th cation and kl its coordination number. The electrostatic bond strength of this cation is ... 

Let the cation M2+ in a compound MX2 have coordination number 6. Its electrostatic bond strength is s = 2/6 = The correct charge for the anion, z = -1, can only be obtained when the anion has the coordination number a = 3. 

Let the cation M4+ in a compound MX4 also have coordination number 6 its electrostatic bond strength is s = 4/6 = . For an anion X- having coordination number a = 2 we obtain = + = for an anion with a = 1 the sum is = . For other values of a the resulting p deviate even more from the expected value z = -1. The most favorable structure will have anions with a = 2 and with a = 1, and these in a ratio of 1 1, so that the correct value for z results in the mean. 

The electrostatic valence rule has turned out to be a valuable tool for the distinction of the particles O2-, OH- and OH2. Because H atoms often cannot be localized reliably by X-ray diffraction, which is the most common method for structure determination, O2-, OH- and OH2 cannot be distinguished unequivocally at first. However, their charges must harmonize with the sums pj of the electrostatic bond strengths of the adjacent cations. 

Calculate the electrostatic bond strengths of the cations and determine how well the electrostatic valence rule is fulfilled. Calculate the expected individual V-O bond lengths using data from Table 7.2 and the values d(V4+0) = 189 pm and b(V4+0) = 36 pm. 

The coordination of an O2- ion is three Al3+ ions within an A1404 cube and one Mg2+ ion outside of this cube. This way it fulfills the electrostatic valence rule (Pauling s second rule, cf p. 58), i.e. the sum of the electrostatic bond strengths of the cations corresponds exactly to the charge on an O2- ion ... 

This trend in bond-strength continues with TTeF, but the more polarisable Te p- and d-orbitals allow for greater stabilisation of the cationic charge, giving the order TTF < TTeF < TSF in i/2(1). The difference between the first and second ionisation potentials, A 1/2, follows the trend TTeF < TSF < TTF. Again, the superior polarisability of Te over Se and S reduces intramolecular... 

Why are transition metals well suited for catalysis of this process Certainly the electrophilicity of cationic metal centers is important, as is the relative weakness of transition-metal-carbon bonds. However, similar electrophilicities and bond strengths could be found among main-group cations as well. A key to the effectiveness of Ti catalysts is the presence of two metal-based acceptor orbitals. In effect, two such orbitals are needed to choreograph the reversal of net charge flow at the two alkene carbons as the intermediate alkene complex moves through the transition state toward the final product. 

As one traverses through the lanthanide series, there is a reduction in the cation size as the atomic number increases. This results in small differences in the strength of interactions of the ligand with the lanthanide ions. These trends are reflected in the IR spectra of these complexes in a few cases. Cousins and Hart (203) have observed an increase in Pp Q with decreasing lanthanide ion radius for the complexes of TPPO with lanthanide nitrates. This observation has been attributed to an increase in the Ln—O bond strength with an increase in the atomic number of the lanthanide ion. 

In order to form stable complexes with calcium and iron ions, the activator must have a strong affinity for the cations. The bonding strength can be determined by the group electronegativity as given by the following equation ... 

There are three possible types of three-electron bonds. Oxidation of a u bond leads to a cation-radical with a, u three-electron bond. This bond contains no antibonding electrons, and the total bond strength exceeds that of a double bond by the energy of half a n bond. Olefins can acquire the 2a—In bond on one-electron oxidation, the bond constructed from the electrons 2a and In. Oxidation of organic disulfides, RSSR, to their cation-radicals (RSSR) yields species in which the unpaired electron from the oxidized sulfur interacts with the unbound p-electron pair of the second sulfur (Glass 1999). This establishes a 2n-In bond on top of the already existing o bond. The overall bond strength of this five-electron (2a—2n-In ) bond also exceeds that of the normal... 

In this connection, it is interesting to compare the cation-radicals of 1,2-diphenyl- and 1,1,2,2-tetraphenylethanes in their ability to expel a proton or to cleave the exocyclic C-C bond. The former cation-radical preferentially reacts by deprotonation (Camaioni and Franz 1984, Baciocchi et al. 1986). The C-C bond strength of 121.5 kJ moC in 1,2-diphenylethane cation-radical is too high. At the same time, the C-C scission induced by electron transfer is only feasible if the strength of this bond is lesser than 42 kJ mol In the case of 1,1,2,2-tetraphenylethane cation-radical, this magnitude is equal to 38 kJ mol only, and the C-C scission indeed takes place (Arnold and Lamont 1989). 

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