Stable minima

Detailed structural calculations have been carried out for this system. This is because the neutral isomer, C2HsO, which is implicated in the thermochemistry of ethanol, is of interest in pollution control, atmospheric chemistry, and combustion. Also, there is new information available from photoionization experiments with which to compare theoretical calculations. For details of these comparisons, see Curtiss et al.73 In the earlier theoretical studies of Nobes et al.,74 calculations were performed at the MP2 and MP3 levels with basis sets of double plus polarization (6-13G ) with electron correlation. These studies revealed four stable minima for the system protonated acetaldehyde, CHj-C H-OH <-> CH3-CH=0+H the methoxymethyl cation, CH3OCH2 protonated oxirane, (CH2)2OH+ and vinylox-... 

Ah initio calculations on the geometry optimization of the 2 kg state of s-traws-butadiene have shown that the C2h planar structure is not stable since it presents several imaginary frequencies associated to out-of-plane vibrations. Three nonplanar structures are found to be stable minima on the potential energy surface. The nonplanarity of this state makes the out-of-plane vibrations effective accepting modes. This fact strongly increases the rate of 2 kg - 1 kg internal conversion, which would explain the lack of fluorescence in butadiene56. 

Stable adsorption complexes are characterized by local minima on the potential energy hypersurface. The reaction pathway between two stable minima is determined by computation of a transition state structure, a saddle point on the potential energy hypersurface, characterized by a single imaginary vibrational mode. The Cartesian displacements of atoms that participate in this vibration characterize movements of these atoms along the reaction coordinate between sorption complexes. 

For diprotonated isobutane (C4H122+) the structures found as stable minima are analogous to those computed for diprotonated propane (C3H102+). Again, structure 478 (a distonic dication) is 17.7 kcal mol 1 more stable than structure 479 (a gitonic dication), whereas structure 480 is only slightly less stable than 478 (2.6 kcal mol-1).788... 

In the case of the dimethylbromonium cation 46, ab initio calculations have found two stable minima for the protosolvated superelectrophile, the bromine and carbon protonated forms, 51 and 52, respectively (Figure 3).44a Dication 51 is estimated to be more stable than 52 by about 21 kcal/mol at the B3LYP/6-31G //B3LYP/6-31G level. When dimethylbromonium cation (46) is reacted in DF/SbFs in SO2 at —78°C, no deuterium incorporation is observed into the methyl groups. This observation is in accord with the theoretical calculations in that Br-protonation is expected to be the preferred process. 

There is also the possibility of distonic, superelectrophilic bis-carbo-nium ions. Despite the fact that such species may be important in the superacid-catalyzed cracking reactions of aliphatic hydrocarbons, there have been very few studies of such systems. The structures and energies of small distonic alkonium dications have been studied using ab initio calculations.24 For diprotonated -butane (C4Hi22+) two structures were located as stable minima on the potential energy surface. Structure 63 is formed by a protonation of the two terminal C-H bonds, resulting in a pair of two electron-three center bonds. The other structure (64) arises from protonation of the terminal C-H bond and the most distant C-C bond. 

According to the epikernel principle, the symmetry of the stable minima of the corannulene ion is Cs. If corannulene monoanion is a static JT system, the 11 peaks of the hyperhne structure with intensity ratio 1 10 45 120 210 252 210 120 45 10 1 due to the 10 equivalent hydrogens can be split into 3s = 243 peaks. 

The present HF calculations show that there are five and six equivalent minima for the corannulene and the coronene anion, respectively. The symmetry of the stable minima is Cs and C2/l, respectively. The JT potentials are also obtained. The calculated energy barrier between the distorted minima is 7.9 and 0.2 meV for the corannulene ion and the coronene ion, respectively. This is the reason why JT distortion could not be observed in the coronene ion. 

In contrast to the predictions of INDO calculations, however, ab initio calculations232 (3-21 G basis set) on CH2=CH2-, CH CHF-, CH2=CF2 and CF2=CF2- have predicted that planar structures are not stable minima for these radical anions. The planar structures relax to the anti structures upon minimization, and the stabilization due to non-planar distortions, arising from a mixing of the 7r - and the high lying cr -orbitals, increases upon fiuorination. For these four molecules the 90° twisted structures are saddle points, and the CH2CF2 radical anion was predicted to adopt the chair structure. 

Extremum points on a JT energy surface prefer epikernels they prefer maximal epikernels to the lower ranking ones. As a rule stable minima are to be found with the structures of maximal epikernel symmetry. 

Figure 9.2. The location of stable minima in two-dimensional systems. The figure represents how antisymmetrically and symmetrically coupled vibrations affect the position of stable minima - that is reactant and product. The x-axis, s, represents the reaction coordinate, and q the coupled vibration. The points labeled S and A are the positions of the well minima in the two-dimensional system with symmetric and...

A completely rigorous ab initio theory would have no assumptions or approximations [31]. The system would be characterised by a set of N nuclei and n electrons and the method could be used to locate all stable minima and the pathways connecting them. This corresponds to solving the complete Schrodin-ger equation. 

The most recent attempt to extend xenon-nitrogen chemistry has been an investigation of the reactions of XeF2 with HN3, NaN J, and NaOCN in solution in H20, anhydrous HF, or S02C1F. Although no stable xenon—nitrogen compounds were obtained, on the basis of product distribution, FXe(N3) and FXe(NCO) have been postulated as intermediates and ab initio calculations have shown that both possess stable minima (163). 

Thus several spatial configurations which correspond to relatively but not absolutely stable minima may have to be taken into consideration. Each has certain elements of symmetry, but some have more than others. Hence the existence of polymorphic modifications. 

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