Cation calculation

The relative weights 8 2-74 for Li and Li+ (= Li-) correspond to 43 % neutral atoms and 28 5 % each of anions and cations. Calculations based on minimizing the energy of the system also indicate similar values for the ratio of atoms to anions and cations. The rule of essential electrical neutrality (Pauling 19486) would require that only the singly-charged ions need be considered. 

Figure 13.3 The n molecular orbitals of the allyl cation. The allyl cation, like the allyl radical, is a conjugated unsaturated system. The shapes of molecular orbitals for the allyl cation calculated using quantum mechanical principles are shown alongside the schematic orbitals. 

Figure 23. Relative enthalpy (AH) for the isomeric butonium cations, calculated by MP4SDTQ/6-311++G //MP2(full)/6-31G (82).

These examples are typical of the effects found in radical ion studies. Ganld and Radom [23] recently showed exactly how wide the variation in calculated properties can be at a series of different levels of ab initio theory for the isomeric CHsF" radical cations. Calculated C-F bond lengths varied from 1.267 to 2.034 A for CHjF, depending on the level of calculation. Such cases are, of... 

Fig. 3. HOMO-LUMO energy gaps of (aza)cyclopentadienyl cation calculated by HMO (adapted from Gompper and Wagner [88AG(E)(24)1437]).

Some systems show NMR coalescence consistent with a rearrangement to an intermediate cation that is less stable. The NMR of the isopropyl cation 9, for example, shows a coalescence of the two proton signals between 0 and 40 °C. The activation barrier is 16 kcal/mol, close to the difference between a secondary and a primary cation. Calculations show that a comer protonated cyclopropane (11) is the only other minimum on the C3H energy surface. " The 1-propyl cation 10 is a transition state. 

The described superelectrophilic activation and fluorene-cyclization is thought to involve a lowered energy of the LUMO and concomitant delocalization of positive charge into the aryl ring(s).32b Calculations at the 4-31G//STO-3G level on a model system (Figure 2) have shown that the amount of positive charge in the phenyl ring increases upon formation of the dication (67) when compared to the monocation (66) and the benzyl cation (calculations are based on fully planar structures). It is well known... 

The sieving effect of the carbon host was also demonstrated by measuring the capacitance values of an AC in a series of solvent-free ionic liquids (ILs) of increasing cation size [17], Since ions are not solvated in pure ILs, it was easy to interpret the electrochemical properties by comparing the nanoporous characteristics of carbon and the size of cations calculated by molecular modeling. It was found that the overall porosity of the carbon is noticeably underused, due to pores smaller than the effective size of the cations. The results with ILs confirm that the optimal pore size depends on the kind of electrolyte, i.e., the dimensions of pores and ions must match each other. 

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