Cation geometry optimized

Dioxolan-2-ylium cation INDO optimized geometry, 6, 750 total charge density, 6, 750... 

Figure 12. Ab initio optimized cation geometries at UHF/6-31G level of theory, with a constrained to 90°. Bond lengths in A and bond angles in degrees.

The cyclobutenyl cation 92 is one of the first examples demonstrating that electron correlation is required both for geometry optimization and NMR chemical shift calculations.14 The IGLO/6-31G(d,p) calculated 13C NMR chemical shifts of the planar form of a homotropylium cation 94 clearly deviate from the experimental values (mean deviation A = 45.6 ppm) alternating in the seven-membered ring between 122 and 194 ppm, whereas those of the non-planar structure for the homotropylium cation 93 are in good agreement with experiment (mean deviation A = 6.2 ppm).108... 

HF/6-31G(d) geometry optimization for cationic species with vibrational frequencies to determine the zero-point energy. 

Ab initio theoretical calculations for the 4-methylpent-2-yl cation by Farca iu et al.115 have shown both a distorted 1 -protonated 1,1,2-trimethylcyclopropane and the open cation to be energy minima along the reaction coordinate at the B3LYP/ 6-31G level. In contrast, only the protonated cyclopropane was found to be an energy minimum in the MP2/6-31G optimization. Whereas the open cation was a transition structure at this level, a coupled cluster geometry optimization (CCSG/6-31G ) showed that the open ion is also a true energy minimum. 

Theoretical quantum mechanical calculations903-908 have also been performed on the 2-norbornyl cation at various levels. These calculations reveal a significant preference for the o-delocalized nonclassical structure. An extensive calculation by Schaefer and co-workers906 using full geometry optimization for symmetrically and... 

Corma and co-workers152 have performed a detailed theoretical study (B3PW91/6-31G level) of the mechanism of the reactions between carbenium ions and alkanes (ethyl cation with ethane and propane and isopropyl cation with ethane, propane, and isopentane) including complete geometry optimization and characterization of the reactants, products, reaction intermediates, and transition states involved. Reaction enthalpies and activation energies for the various elemental steps and the equilibrium constants and reaction rate constants were also calculated. It was concluded that the interaction of a carbenium ion and an alkane always results in the formation of a carbonium cation, which is the intermediate not only in alkylation but also in other hydrocarbon transformations (hydride transfer, disproportionation, dehydrogenation). 

Both MNDO [340] and ab initio calculations [341] have been performed on the radical cation. The MNDO geometry optimization yields a flap angle of 132° and a Cj— C3 bond distance of 178.6 pm INDO calculations at this geometry give hfcs of 12.0, +18.3, and +78.0G. The ab initio calculations at the 6.31 G level yield a slightly smaller bond distance (174.3 pm) and Fermi contact terms of — 25.7, +14.7, and + 72.0 G. 

The first ionization potential IP V of 43b was calculated. Using the ab initio HF method for geometry optimization and B3LYP for the single point energy calculation, the first IP can be calculated as the energy difference between a molecule and its radical cation. The values of the energies are summarized in Table 5. 

In Equation 6.38, the heat of formation terms, AHf (X) and AHf (X+), refer to the neutral species, X, and the associated radical cation, X+, in their respective ground states they would both usually require separate quantum chemical calculations, including geometry optimizations. 

Fig. 5. (a) Site II cation on a six-membered oxygen ring as the basic unit on types A and X zeolites. T denotes Si or Al. (b) Geometry-optimized cluster model to represent the chemistry of Ag/zeolite. 

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