The structure of the 1-propyl cation in the ion pair with the model anion trihydrofluoroborate, proven in earlier work to be appropriate for such studies, was investigated by ab initio calculations at the level previously reported to give the definitive structure of carbocations. In previous work, it was shown that the carbocation structure does not change with the nature of the anion. The cation structure is determined, however, by the distance between the cation and anion, d, and their relative orientation. At infinite interionic distance the only stable chemical species (energy minimum) is the protonated cyclopropane, 1. As the ions move toward each other, the cyclopropane bond opposite to the anion becomes progressively longer and eventually it breaks up in the contact ion pair. Three domains of cation stability are identified as a function of d:  at long distances, ion 1 is the only energy minimum; at intermediate distances 1 and the 1-propyl cation 2 are both energy minima; at short distances, ion 2 is the only energy minimum. Thus, ionization of 1-propyl precursors forms the tight ion pair of 2 as the first intermediate. Isomers 1 and 2 differ in both the C1−C2−C3 angle and the conformation of the C2−C3 bond; the transition structure for their interconversion has been determined by calculations. At the MP4(FC)/6-311G**//MP2/6-311G** level, the two isomers have the same energy content for d = 2.40 Å, but correction for the zero-point energies obtained from the vibrational frequencies calculated at the MP2/6-311G** level reduces the energy of 2 relative to 1, thus requiring a slight upward correction in the value of d for equal stability of isomers. The interconversion of 1 and 2 is observed for a position of the anion essentially in the same plane as the three carbon atoms. Movement of the anion above the same plane results in hydrogen shift with the formation of the 2-propyl cation, 3. Some literature results in which primary carbocations could intervene as intermediates are discussed. In particular, the data on carbon and hydrogen scrambling in 3 in superacid solution are better accounted for by the results of calculations for ion pairs, with both 1 and 2 as intermediates, than by the results of calculations for isolated ions.

The structures, relative energies, and interconversion barriers and pathways for several isomeric C5H11 + carbocations were investigated by high level ab initio MO calculations with inclusion of electron correlation. The energy minima found were two conformations of the tertiary 2-methyl-2-butyl cation (2), bisected (2 b ) and asymmetric (2 as ), and three 1-protonated (corner-protonated) cyclopropanes:  trans-2,3-dimethyl (trans-8), cis-2,3-dimethyl (cis-8), and 1,2-dimethyl (9).The bridged ions trans-8, cis-8, and 9 are higher in energy than the tertiary ion by 8.3, 9.2, and 10.6 kcal/mol, respectively, at the MP4SDTQ(FC)/6-31G**//MP2(FC)/6-31G** level, or 9.6, 10.6 and 12.4 kcal/mol after correcting for the zero-point energies (ZPE). Various conformations of the “open” 3-methyl-2-butyl cation correspond to transition states for the interconversion of the tertiary ion 2 as and the two 1-protonated-2,3-dimethylcyclopropanes. Hydrogen shift in 2 as can lead only to the cis-2,3-dimethyl isomer, cis-8; trans-8 is formed only from the cis isomer by ring opening and reclosure. The 1,3-protonated-1,2-dimethylcyclopropane (10) (edge-protonated) is the transition state for the interconversion of trans-8, and the third corner-protonated cyclopropane isomer (1-protonated-1,2-dimethylcyclopropane, 9). The latter can be regarded as the cyclic form of the 2-pentyl cation or of the 2-methyl-1-butyl cation. The calculations thus agree with the results of the experimental study on the cations generated in trifluoroacetic by predicting the existence of more than one “2-methylbutyl” cation, but disagree on another point, by predicting that the other cation besides 2 has a symmetrical structure, 8.

An investigation of the alkylation reaction of propene with the 2-propyl cation by ab initio density functional methods at the B3LYP/6-31G** level found a distorted trimethyl-1-protonated cyclopropane as an energy minimum along the reaction coordinate (intermediate) and an open ion, the 4-methyl-2-pentyl cation (1), as another energy minimum (product). In contrast, the open ion 1 was not an energy minimum in MP2/6-31G** calculations. Attempts at geometry optimizations of 1 at that level led invariably to the protonated cyclopropane structure (more symmetrical than in the previous case). The ion 1 was in fact a transition structure in the MP2/6-31G** optimizations. A coupled cluster (CCSD/6-31G**) geometry optimization showed, however, the open ion 1 as a true energy minimum. This result brings a note of caution concerning MP2 geometry optimizations of carbocations. In particular, when these calculations find small energy differences between bridged and open structures, but find only the bridged structures as energy minima, the results might be in error. What the level of calculation is at which the predicted carbocation structures can be considered definitive remains an open question.

The geometries of the hydronium and dihydroxonium cations in ion pairs with fluoroborate anions were examined by ab initio calculations at the MP2/6-31G* level. It was found that the representation of the hydronium ion in the field of an anion as an equilateral triangle, employed in the literature for the interpretation of low-temperature broad-band NMR spectra of water in solid acids, is an oversimplification, particularly for the composition H 5 O 2 + (dihydroxonium). Chemical shift calculations (DFT-GIAO-B3LYP at the dzvp, tzp, tz2p, and qz2p levels) were conducted for 17 O in H 3 O + ‚BF 4 -(1) and H 5 O 2 + ‚BF 4 -(2). The signal of 2 was predicted to appear at higher frequency (downfield) than the signal for 1. For experimental verification, the 17 O NMR spectra were recorded for various mixtures of hydronium fluoroborate and water. A nonmonotonic variation of the 17 O chemical shift with the increase in water content was observed; the signal moved first toward higher frequency and had the highest chemical shift for a water-to-hydronium ratio of 1:1 (H 5 O 2 + ), after which a monotonic variation toward lower frequency (upfield) was observed. Along both branches of the δ 17 O vs composition plot (H 3 O + ‚BF 4to H 5 O 2 + ‚BF 4and H 5 O 2 + ‚BF 4to H 2 O) the chemical shift variation was nonlinear. Thus, the experiments and the calculations were in qualitative agreement (the signal for 1 at lower frequency than the signal for 2), but the chemical shift difference predicted by the calculations was larger than the experimental result. Better agreement between the calculated and measured chemical shift differences is obtained for an orientation of ions in 2 with two fluorine atoms hydrogen bonded with the cation. Likewise, a better agreement is obtained for the pyramidal form than for the planar form of 1, in agreement with the geometry optimization results.

DFT calculations at the B3LYP/6-31G** level were conducted on the reaction of the propane molecule with the aluminum hydroxide clusters (HO) 3 Al(OH 2 ) x (x ) 0,1). Weak, physisorbed (van der Waals) complexes were identified. Chemisorption does not involve the Brønsted acidity of the catalyst, as no hydron transfer occurs. Instead, the reaction involves insertion of the aluminum atom into a C-H bond, followed by the migration of the hydrogen atom from aluminum to oxygen, to form the chemisorbed intermediate, (H 2 O) x+1 (HO) 2 Al-CH 2 Et or (H 2 O) x+1 (HO) 2 Al-CHMe 2 , with the latter having a higher energy barrier. The elimination of hydrogen from Cβ and oxygen gives then H 2 and propene, which forms a strong π complex with the aluminum cluster for x ) 0. The first step, chemisorption, has a lower energy barrier than the second, elimination, but still higher than the hydrogen dissociation on the same clusters. Thus, the rate relationship H 2 /D 2 exchange > H 2 /RH exchange > RH dehydrogenation is predicted, as was experimentally observed. The tetracoordinated aluminum cluster (x ) 1) reacts with the hydrocarbon by the same pathway as the tricoordinated aluminum cluster (x ) 0) but with higher barriers for both steps; the barriers are reduced for the larger cluster (HO) 2 (H 2 O)Al-O-Al(OH) 2 (H 2 O). The alternative pathway, forming the alkyl-oxygen adduct (HO) 2 Al(OH 2 ) x (H)-O(R)H is too high in energy to compete. Examination of butane and isobutane establishes the reactivity order: prim C-H > sec-C-H > tert-C-H. For isobutane, essentially only methyl C-H cleavage should occur in the common first step for hydrogen exchange and dehydrogenation. In the second step, i.e., the β C-H cleavage in the Al-alkyl intermediate, the reactivity order is tert-C-H > sec-C-H > prim C-H. "Broken lattice" zeolites and especially extraframework aluminum species present in steamed zeolites should be more reactive than the intact zeolite lattices. Thus, the mechanism is relevant for the activation of alkanes for acid-catalyzed conversions on these catalysts, which have insufficient acid strength to cleave C-H and C-C bonds by hydron transfer.