Abstract

Abstract

Under pressure and full of surprises: At very high pressure, oxygen molecules O₂ combine to give—rather than the well-known crown-shaped ring form of elemental sulfur—the novel molecular unit O₈, or (O₂)₄, which exhibits strong bonds in the diatomic units but with much weaker π*–π* bonds between them (see picture).

The structures of a large number of isomers of the sulfur oxides S_nO with n = 4–9 have been calculated at the G3X(MP2) level of theory. In most cases, homocyclic molecules with exocyclic oxygen atoms in an axial position are the global minimum structures. Perfect agreement is obtained with experimentally determined structures of S₇O and S₈O. The most stable S₄O isomer as well as some less stable isomers of S₅O and S₆O are characterized by a strong π*–π* interaction between SO and SS groups, which results in relatively long SS bonds with internuclear distances of 244–262 pm. Heterocyclic isomers are less stable than the global minimum structures, and this energy difference approximately increases with the ring size: 17 (S₄O), 40 (S₅O), 32 (S₆O), 28 (S₇O), 45 (S₈O), and 54 kJ mol⁻¹ (S₉O). Owing to a favorable π*–π* interaction, preference for an axial (or endo) conformation is calculated for the global energy minima of S₇O, S₈O, and S₉O. Vapor-phase decomposition of S_nO molecules to SO₂ and S₈ is strongly exothermic, whereas the formation of S₂O and S₈ is exothermic if n<7, but slightly endothermic for S₇O, S₈O, and S₉O. The calculated vibrational spectra of the most stable isomers of S₆O, S₇O, and S₈O are in excellent agreement with the observed data.

Sauerstoff in Rautenform: Bei sehr hohen Drücken vereinigen sich Sauerstoffmoleküle O₂ zu dem zuvor unbekannten molekularen Gebilde O₈ oder (O₂)₄, das in den parallel angeordneten zweiatomigen Einheiten starke Bindungen enthält, dazwischen aber nur schwache π*-π*-Wechselwirkungen aufweist (siehe Bild).

The complex formation between the Li⁺ cation and the sulfur homocycle S₈ has been studied by ab initio MO calculations at the G3X(MP2) level of theory. Starting with various isomers of S₈, the formation of LiS₈ heterocycles and clusters is preferred over complexes with a monodentate ligand. The binding energies of the cation in the 23 complexes investigated range from –95 to –217 kJ·mol^–1. The global minimum structure of [LiS₈]⁺ is of C_4v symmetry with the S₈ homocycle in the well-known crown conformation and four Li–S bonds of length 254.2 pm (binding energy: –156.5 kJ·mol^–1). The S–S bonds of the various ligands are slightly weakened by the complex formation and a more or less strong bond length alternation is induced. Relatively unstable isomers of S₈ (chair, tub, exo–endo ring, branched rings, triplet chain) are partly stabilized and partly destabilized by complex formation with Li⁺. The interaction between the cation and the S₈ ligands is mainly due to ion–dipole attraction with little to moderate charge transfer (0.04–0.27 electrostatic units). In the four most stable isomers of [LiS₈]⁺, the number of sulfur–sulfur bonds is at a maximum and the coordination number of Li⁺ is either 4 or 3. Complexes of the type [Li(S₄)₂]⁺ are much less stable than isomers with an eight-atomic ligand. The Li–S bond lengths in all of these complex cations (230–273 pm) depend on the coordination number of Li and on the atomic charge of the donating sulfur atom(s). In contrast to [LiS₈]⁺, the complexes of composition [MS₈]⁺ with M = Ca, V, and Cu are more stable as [M(S₄)₂]⁺ than with an eight-atomic crown-shaped ligand. (© Wiley-VCH Verlag GmbH & Co. KGaA, 69451 Weinheim, Germany, 2005)

Complex formation between gaseous Li⁺ ions and sulfur-containing neutral ligands, such as H₂S, Me₂S_n (n = 1–5; Me = CH₃) and various isomers of hexasulfur (S₆), has been studied by ab initio MO calculations at the G3X(MP2) level of theory. Generally, the formation of LiS_n heterocycles and clusters is preferred in these reactions. The binding energies of the cation in the 29 complexes investigated range from −88 kJ mol⁻¹ for [H₂SLi]⁺ to −189 kJ mol⁻¹ for the most stable isomer of [Me₂S₅Li]⁺ which contains three-coordinate Li⁺. Of the various S₆ ligands (chair, boat, prism, branched ring, and triplet chain structures), two isomeric complexes containing the S₅S ligand have the highest binding energies (−163±1 kJ mol⁻¹). However, the global minimum structure of [LiS₆]⁺ is of C_3v symmetry with the six-membered S₆ homocycle in the well-known chair conformation and three LiS bonds with a length of 256 pm (binding energy: −134 kJ mol⁻¹). Relatively unstable isomers of S₆ are stabilized by complex formation with Li⁺. The interaction between the cation and the S₆ ligands is mainly attributed to ion–dipole attraction with a little charge transfer, except in cations containing the six sulfur atoms in the form of separated neutral S₂, S₃, or S₄ units, as in [Li(S₃)₂]⁺ and [Li(S₂)(S₄)]⁺. In the two most stable isomers of the [LiS₆]⁺ complexes, the number of SS bonds is at maximum and the coordination number of Li⁺ is either 3 or 4. A topological analysis of all investigated complexes revealed that the LiS bonds of lengths below 280 pm are characterized by a maximum electron-density path and closed-shell interaction.

Abstract

The structures and relative stabilities of eight S₄ isomers were investigated by G3X(MP2), CCSD(T)/cc-pVTZ and MRCI/CASSCF calculations. The cis-planar (C_2v) structure is confirmed to be the global minimum of S₄, while the rectangular D_2h structure is calculated to be a transition state. The predicted stability order of various singlet S₄ isomers is C_2v>C_2h>C_s>D_2d>D_3h. Calculated electronic absorption spectra [CIS/6-311 + G(3df)] and vibrational spectra [B3LYP/6-31G(2df)] allow a convincing assignment of the observed green absorbing species as the cis-planar (C_2v) structure (global minimum) and the red absorbing species as the trans-planar (C_2h) isomer, in distinct contrast to the previous assignments.

Using high-level ab initio MO methods, we have identified two reaction pathways with different thermodynamic and kinetic properties for the thermal decomposition of the three-membered heterocycle thiirane (C₂H₄S) and related derivatives. A homolytic ring opening, followed by attack of the generated diradical on another thiirane molecule, and subsequent elimination of ethene in a fast radical chain reaction results in the formation of disulfur molecules in their triplet ground state (³S₂) and requires activation enthalpies of ΔH=222 kJ mol⁻¹ and ΔG=212 kJ mol⁻¹. This reaction mechanism would result in a first-order rate law in agreement with one reported gas-phase experiment but does neither match the experimental activation energy nor does it explain the observed retention of the stereochemical configuration in the thermal decomposition of certain substituted thiiranes. Alternatively, sulfur atoms can be transferred from one thiirane molecule to another with the intermediate formation of thiirane 1-sulfide (C₂H₄S₂). This molecule can either decompose unimolecularly to ethene and disulfur in its excited singlet state (¹S₂) or, by means of spin crossover, S₂ in its triplet ground state may be formed. On the other hand, the thiirane 1-sulfide may react with itself and transfer one sulfur atom from one molecule to another with formation of thiirane 1,1-disulfide (C₂H₄S₃), which is an analogue of thiirane sulfone; thiirane is formed as the second product. The 1,1-disulfide may then decompose to ethene and S₃. In still another bimolecular reaction, the thiirane 1-sulfide may react with itself in a strongly exothermic reaction to give S₄ and two equivalents of ethene. This series of reactions results in a second-order rate law and requires activation enthalpies of ΔH=109 kJ mol⁻¹ and ΔG=144 kJ mol⁻¹ for the formation of thiirane 1-sulfide, while the consecutive reactions require less activation enthalpy. Elemental sulfur (S₈) is eventually formed by oligomerization of either S₂, S₃, or S₄ in spin-allowed reactions. These findings are in agreement with most experimental data on the thermal desulfurization of thiirane and its substituted derivatives. Thiirane 1-persulfide (C₂H₄S₃) with a linear arrangement of the three sulfur atoms as well as zwitterions and radicals derived from thiirane are not likely to be intermediates in the thermal decomposition of episulfides.

High level ab initio MO calculations at the G3(MP2) level of theory were employed to study the molecular structures of SF₂, FSSF₃, and SSF₄, as well as the dimerization of gaseous SF₂ to FSSF₃ and the isomerization of FSSF₃ to SSF₄. The dimerization of SF₂ was calculated to be an exothermic process (ΔH°₂₉₈ = −77 kJ·mol⁻¹) with an activation enthalpy (ΔH^≠₂₉₈) of 65 kJ·mol⁻¹. The transition state of the dimerization reaction is characterized by a bridging fluorine atom that undergoes a 1,2-shift, and a weak sulfur-sulfur single bond. The calculated lowest-energy structure of FSSF₃ (2a) is in excellent agreement with the experimentally derived structure, with the −SF group in an equatorial position of the distorted pseudo-trigonal-bipyramid at the central sulfur atom. A significantly less stable FSSF₃ conformer 2b, 76 kJ·mol⁻¹ higher in energy, has the −SF group in an axial position. Unimolecular rearrangement of FSSF₃ (2a) to the trigonal-bipyramidal SSF₄ (3), by a 1,2-fluorine shift (TS2), is endothermic by 37 kJ·mol⁻¹ and is inhibited by a large activation barrier of 267 kJ·mol⁻¹. SSF₄ is predicted to be an observable species in the gas phase. Calculated infrared spectra of 2a and 3 are also reported.

Abstract

A simple formula for extrapolating energies calculated from finite basis sets to the limit of a complete basis set by scaling the basis set extension energies is presented. Combining this basis set extrapolation method with the scaling-all-correlation (SAC) energy method, it is possible to extrapolate correlated electronic structure calculations to the limit of full dynamical correlation with a complete basis set. Based on this combined scaling method, two variants of G3 theory, and G3SCB and G3SCB(MP3), are proposed, with the total mean unsigned errors (MUEs) comparing favourably with those of G3 and G3(MP3).

The properties and reactivities of ketene, thioketene, and selenoketene were studied using the G2(MP2) level of theory. Calculated structures, vibrational frequencies, dipole moments, NMR chemical shifts, and charge distributions strongly suggest that thioketene and selenoketene are best represented by the neutral cumulenic form. Four prototype reactions were examined: ketene-ynol rearrangement, electrophilic and nucleophilic addition, and [2+2] cycloaddition. Thioketene and selenoketene were found to be more reactive than ketene in all reactions. In terms of chemistry, thioketene resembles selenoketene more than ketene. The variation of reactivity can readily be explained in terms of strain energy, electronegativity, and molecular orbital arguments.

Energetisch deutlich höher (24 kJ mol⁻¹) liegt der ¹Δ_g-Zustand im Vergleich zum Triplett-Grundzustand (³Σ_g⁻), den Ethendithion (S=C=C=S) in Übereinstimmung mit der Hundschen Regel hat. Dies ergaben auf einem hohen Niveau durchgeführte Ab-initio-Rechnungen. Den Ergebnissen zufolge kann Ethendithion nicht, wie vorgeschlagen wurde, als das erste Beispiel für die Verletzung der Hundschen Regel in einer Gleichgewichtsstruktur herangezogen werden.

Significantly higher in energy (24 kJ mol⁻¹) than the triplet ground state (³Σ_g⁻) is the ¹Δ_g state of ethenedithione (S=C=C=S), in agreement with Hund's rule. This result was obtained from high-level ab initio calculations. Thus, ethenedithione cannot, as had been proposed, be considered as the first example for the violation of Hund's rule in an equilibrium structure.