Manual of VIKAASA: An application capable of computing and graphing viability kernels for simple viability problems

This manual introduces and provides usage details for an application we have developed called VIKAASA, as well as the library of functions underlying it. VIKAASA runs in GNU Octave or MATLAB®, using the numerical computing and graphing capabilities of those packages to approximate, visualise and test viability kernels for viability problems involving a differential inclusion of two or more dynamic variables, a rectangular constraint set and a single scalar control

Carbocations Generated under Stable Conditions by Ionization of Matrix-Isolated Radicals: The Allyl and Benzyl Cations

Carbocations are crucial intermediates in many chemical reactions; hence, considerable effort has gone into investigating their structures and properties, for example, in superacids, in salts, or in the gas phase. However, studies of the vibrational structure of carbocations are not abundant, because their infrared spectra are difficult to obtain in superacids or salts (where furthermore the cations may be perturbed by counterions), and the generation of gas-phase carbocations in discharges usually produces several species. We have applied the technique of ionizing neutral compounds by X-irradiation of cryogenic Ar matrices to radicals embedded in such matrices, thus producing closed-shell cations that can be investigated leisurely, and in the absence of counterions or other perturbing effects, by various forms of spectroscopy. This Article describes the first set of results that were obtained by this approach, the IR spectra of the allyl and the benzyl cation. We use the information obtained in this way, together with previously obtained data, to assess the changes in chemical bonding between the allyl and benzyl radicals and cations, respectively

Carbocations Generated under Stable Conditions by Ionization of Matrix-Isolated Radicals: The Allyl and Benzyl Cations

Carbocations are crucial intermediates in many chemical reactions; hence, considerable effort has gone into investigating their structures and properties, for example, in superacids, in salts, or in the gas phase. However, studies of the vibrational structure of carbocations are not abundant, because their infrared spectra are difficult to obtain in superacids or salts (where furthermore the cations may be perturbed by counterions), and the generation of gas-phase carbocations in discharges usually produces several species. We have applied the technique of ionizing neutral compounds by X-irradiation of cryogenic Ar matrices to radicals embedded in such matrices, thus producing closed-shell cations that can be investigated leisurely, and in the absence of counterions or other perturbing effects, by various forms of spectroscopy. This Article describes the first set of results that were obtained by this approach, the IR spectra of the allyl and the benzyl cation. We use the information obtained in this way, together with previously obtained data, to assess the changes in chemical bonding between the allyl and benzyl radicals and cations, respectively

Influence of Connector Groups on the Interactions of Substituents with Carbon-Centered Radicals

High-level G3X­(MP2)-RAD calculations have been carried out to examine the effect of interposing a “connector” group (W) on the interaction between a substituent (X) and the radical center in carbon-centered radicals (^•CH₂–W–X). The connector groups include −CH₂–, −CHCH–, −CC–, −<i>p-</i>C₆H₄–, −<i>m-</i>C₆H₄–, and −<i>o-</i>C₆H₄–, and the substituents include H, CF₃, CH₃, CHO, NH₂, and CHCH₂. Analysis of the results is facilitated by introducing two new quantities termed radical connector energies and molecule connector energies. We find that the −CH₂– connector effectively turns off π-electron effects but allows the transmission of σ-electron effects, albeit at a reduced level. The effect of a substituent X attached to the −CHCH– and −CC– connector groups is to represent a perturbation of the effect of the connector groups themselves (i.e., CHCH₂ and CCH)

Variations in Rotational Barriers of Allyl and Benzyl Cations, Anions, and Radicals

High accuracy quantum chemical calculations show that the barriers to rotation of a CH₂ group in the allyl cation, radical, and anion are 33, 14, and 21 kcal/mol, respectively. The benzyl cation, radical, and anion have barriers of 45, 11, and 24 kcal/mol, respectively. These barrier heights are related to the magnitude of the delocalization stabilization of each fully conjugated system. This paper addresses the question of why these rotational barriers, which at the Hückel level of theory are independent of the number of nonbonding electrons in allyl and benzyl, are in fact calculated to be factors that are of 2.4 and 4.1 higher in the cations and 1.5 and 1.9 higher in the anions than in the radicals. We also investigate why the barrier to rotation is higher for benzyl than for allyl in the cations and in the anions. Only in the radicals is the barrier for benzyl lower than that for allyl, as Hückel theory predicts should be the case. These fundamental questions in electronic structure theory, which have not been addressed previously, are related to differences in electron–electron repulsions in the conjugated and nonconjugated systems, which depend on the number of nonbonding electrons

Spectroscopic Evidence for Through-Space Arene–Sulfur–Arene Bonding Interaction in <i>m</i>‑Terphenyl Thioether Radical Cations

Electronic absorption spectra and quantum chemical calculations of the radical cations of <i>m</i>-terphenyl <i>tert</i>-butyl thioethers, where the S–<i>t</i>-Bu bond is forced to be perpendicular to the central phenyl ring, show the occurrence of through-space [π···S···π]⁺ bonding interactions which lead to a stabilization of the thioether radical cations. In the corresponding methyl derivatives there is a competition between delocalization of the hole that is centered on a p-AO of the S atom into the π-system of the central phenyl ring or through space into the flanking phenyl groups, which leads to a mixture of planar and perpendicular conformations in the radical cation. Adding a second <i>m</i>-terphenyl <i>tert</i>-butyl thioether moiety does not lead to further delocalization; the spin and charge remain in one of the two halves of the radical cation. These findings have interesting implications with regard to the role of methionines as hopping stations in electron transfer through proteins

The Pyrolysis of Isoxazole Revisited: A New Primary Product and the Pivotal Role of the Vinylnitrene. A Low-Temperature Matrix Isolation and Computational Study

This paper describes the pyrolysis of parent isoxazole and of its 5-methyl and 3,5-dimethyl derivatives by the high-pressure pulsed pyrolysis method, where activation of the precursor molecules occurs predominantly by collisions with the host gas (Ar in our case), rather than with the walls of the pyrolysis tube, where catalyzed processes may occur. The products were trapped at 15 K in Ar matrices and were characterized by vibrational spectroscopy. Thereby, hitherto unobserved primary products of pyrolysis of isoxazole and of its 5-methyl derivative, 3-hydroxypropenenitrile or 3-hydroxybutenenitrile, respectively, were observed. <i>E–Z</i> photoisomerization could be induced in the above hydroxynitriles. On pyrolysis of isoxazole, ketenimine and CO were observed as decomposition products, but this process did not occur when the 5-methyl derivative was pyrolyzed. Instead, the corresponding ketonitrile was formed. In the case of 3,5-dimethylisoxazole, 2-acetyl-3-methyl-2<i>H</i>-azirine was detected at moderate pyrolysis temperatures, whereas at higher temperatures, 2,5-dimethyloxazole was the only observed rearrangement product (next to products of dissociation). These findings are rationalized on the basis of quantum chemical calculations. Thereby it becomes evident that carbonyl-vinylnitrenes play a pivotal role in the observed rearrangements, a role that had not been recognized in previous theoretical studies because it had been assumed that vinylnitrenes are closed-shell singlet species, whereas they are in fact open-shell singlet biradicaloids. Thus, the primary processes had to be modeled by the multiconfigurational CASSCF method, followed by single-point MR-CISD calculations. The picture that emerges from these calculations is in excellent accord with the experimental findings; that is, they explain why some possible products are observed while others are not