Quantum-mechanical calculations of the stabilities of fluxional isomers of C ₄ H\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy}\usepackage{mathrsfs}\setlength{\oddsidemargin}{-69pt}\begin{document}\begin{equation*}{\mathrm{_{7}^{+}}}\end{equation*}\end{document} in solution

Abstract

Although numerous quantum calculations have been made over the years of the stabilities of the fluxional isomers of C 4 H 7 ؉ , none have been reported for other than the gas phase (which is unrealistic for these ionic species) that exhibit exceptional fluxional properties in solution. To be sure, quantum-mechanical calculations for solutions are subject to substantial uncertainties, but nonetheless it is important to see whether the trends seen for the gas-phase C 4H7 ؉ species are also found in calculations for polar solutions. Of the C4H 7 ؉ species, commonly designated bisectedcyclopropylcarbinyl 1, unsym-bicyclobutonium 2, sym-bicyclobutonium 3, allylcarbinyl 4, and pyramidal structure 6, the most advanced gas-phase calculations available thus far suggest that the order of stability is 1 > 2 > 3 Ͼ Ͼ 4 Ͼ Ͼ 6 with barriers of only Ϸ1 kcal͞mol for interconversions among 1, 2, and 3. We report here that, when account is taken of solvation, 2 turns out to be slightly more stable than 1 or 3 in polar solvents. The pattern of the overall results is unexpected, in that despite substantial differences in structures and charge distributions between the primary players in the C 4H7 ؉ equilibria and the large differences in solvation energies calculated for the solvents considered, the differential solvent effects from species to species are rather small.

Nitrenium Ion Analogues of Nonclassical Carbocations: Cyclopropylnitrenium, Allylnitrenium, and Azetidenium Ions and Mechanisms for Their Interconversion

“…4−8 Cation 2 consists of three distinct, rapidly equilibrating isomers, including a bisected cyclopropylcarbinyl cation 2a, a symmetric bicyclobutonium ion 2b, and an unsymmetric bicyclobutonium ion 2c. 9 The equilibration of these structures is so fast that attempts to generate the homoallylic cation, cyclobutylcarbenium ion, or the cyclopropylcarbinyl cation each produce the same mixture of stable products. 10 State of the art calculations are in good general agreement with experimental data on these species.…”

QTAIM-DI-VISAB computational study on the so-called nonclassical bicyclobutonium cation

“…Moreover, it appears that MP2 often tends to overestimate the stability of 'nonclassical' structures. 17 While 1 and 2 were viewed as unsymmetrical species by Casanova et al 4 , we found that OPT=TIGHT calculations yielded geometries that were extremely close to the C S structures. Consequently we fixed the symmetry -in our case using Chemcraft 18 -to C S as did Olah et al…”

“…Computational studies were also carried out in solvent fields. 4 The main focus of the most recent study on 2 and 3 carried out by Olah et al at various levels, including MP4(SDTQ)/cc-pVTZ//MP2/cc-pVTZ + ZPE was the calculation of 13 C NMR chemical shifts at CCSD(T). 1 With the exception of Brown's proposal 5 based on solvolysis data the cation should be viewed as a distorted cyclobutyl cation represented as 5, dashed-line or solid-line structures have been used to represent the bonding of these alleged nonclassical pentacoordinate species in all the studies carried out to this point.…”

The impact of experimental design choices on parameter inference for models of growing cell colonies

“…The ABC-DC algorithm was proposed by Picchini et al [ 25 ], and it uses ABC Markov chain Monte Carlo [ 33 ]. The algorithm works in two stages first the acceptance threshold, ε , is decreased according to a tolerance scheme { ε 1 , ε 2 , … , ε P }, and then the number of clones, K , is increased according to a clone scheme { K P +1 , K P +2 , … , K P + Q }, where subscripts index the population number.…”