Ozone and Other 1,3-Dipoles: Toward a Quantitative Measure of Diradical Character

Orbital dependent complications for close vs well-separated electrons in diradicals

We investigate two limits in open-shell diradical systems: O3, in which the interesting orbitals are in close proximity to one another, and (C21H13)2, where there is a significant spatial separation between the two orbitals. In accord with earlier calculations, we find that standard density-functional approximations do not predict the open-shell character for the former case but uniformly predict the open-shell character for the latter case. We trace the qualitatively incorrect behavior in O3 predicted by these standard density functional approximations to self-interaction error and use the Fermi-Löwdin-orbital-self-interaction-corrected formalism to determine accurate triplet, closed-shell singlet, and open-shell broken-spin-symmetry electronic configurations. Analysis of the resulting many-electron overlap matrices allows us to unambiguously show that the broken-spin-symmetry configurations do not participate in the representation of the Ms = 0 triplet states and allows us to reliably extract the singlet-triplet splitting in O3 by analyzing the energy as a function of Fermi-orbital-descriptor permutations. The results of these analyses predict the percentage of open-shell character in O3, which agrees well with conventional wavefunction-based methods. While these techniques are expected to be required in cases near the Coulson-Fischer point, we find that they will be less necessary in diradical systems with well-separated electrons, such as (C21H13)2. Results based on energies from self-interaction-corrected generalized gradient, local density, and Hartree-Fock approximations and experimental results are in generally good agreement for O3. These results help form the basis for deriving extended Heisenberg-like Hamiltonians that are needed for descriptions of molecular magnets when there are competing low-energy electronic configurations.

Computational Studies of Rubber Ozonation Explain the Effectiveness of 6PPD as an Antidegradant and the Mechanism of Its Quinone Formation

The discovery that the commercial rubber antidegradant 6PPD reacts with ozone (O₃) to produce a highly toxic quinone (6PPDQ) spurred a significant research effort into nontoxic alternatives. This work has been hampered by lack of a detailed understanding of the mechanism of protection that 6PPD affords rubber compounds against ozone. Herein, we report high-level density functional theory studies into early steps of rubber and PPD (p-phenylenediamine) ozonation, identifying key steps that contribute to the antiozonant activity of PPDs. In this, we establish that our density functional theory approach can achieve chemical accuracy for many ozonation reactions, which are notoriously difficult to model. Using adiabatic energy decomposition analysis, we examine and dispel the notion that one-electron charge transfer initiates ozonation in these systems, as is sometimes argued. Instead, we find direct interaction between O₃ and the PPD aromatic ring is kinetically accessible and that this motif is more significant than interactions with PPD nitrogens. The former pathway results in a hydroxylated PPD intermediate, which reacts further with O₃ to afford 6PPD hydroquinone and, ultimately, 6PPDQ. This mechanism directly links the toxicity of 6PPDQ to the antiozonant function of 6PPD. These results have significant implications for development of alternative antiozonants, which are discussed.

Multi-center bonds as resonance hybrids: A real space perspective

The concept of distinct bonds within molecules has proven to be successful in rationalizing chemical reactivity. However, bonds are not a well-defined physical concept, but rather vague entities, described by different and often contradicting models. With probability density analysis, which can-in principle-be applied to any wave function, bonds are recovered as spin-coupled positions within most likely electron arrangements in coordinate space. While the wave functions of many systems are dominated by a single electron arrangement that is built from two-center two-electron bonds, some systems require several different arrangements to be well described. In this work, a range of these multi-center bonded molecules are classified and investigated with probability density analysis. The results are compared with valence bond theory calculations and data from collision-induced dissociation experiments.

Dipolar 1,3-cycloaddition of thioformaldehyde S-methylide (CH2 SCH2 ) to ethylene and acetylene. A comparison with (valence) isoelectronic O3 , SO2 , CH2 OO and CH2 SO

Methods rooted in the density functional theory and in the coupled cluster ansatz were employed to investigate the cycloaddition reactions to ethylene and acetylene of 1,3-dipolar species including ozone and the derivatives issued from replacement of the central oxygen atom by the valence-isoelectronic sulfur atom, and/or of one or both terminal oxygen atoms by the isoelectronic CH₂ group. This gives rise to five different 1,3-dipolar compounds, namely ozone itself (O₃ ), sulfur dioxide (SO₂ ), the simplest Criegee intermediate (CH₂ OO), sulfine (CH₂ SO), and thioformaldehyde S-methylide (CH₂ SCH₂ , TSM). The experimental and accurate theoretical data available for some of those molecules were employed to assess the accuracy of two last-generation composite methods employing conventional or explicitly correlated post-Hartree-Fock contributions (jun-Cheap and SVECV-f12, respectively), which were then applied to investigate the reactivity of TSM. The energy barriers provided by both composite methods are very close (the average values for the two composite methods are 7.1 and 8.3 kcal mol^-1 for the addition to ethylene and acetylene, respectively) and comparable to those ruling the corresponding additions of ozone (4.0 and 7.7 kcal mol^-1 , respectively). These and other evidences strongly suggest that, at least in the case of cycloadditions, the reactivity of TSM is similar to that of O₃ and very different from that of SO₂ .

Valence Bond Alternative Yielding Compact and Accurate Wave Functions for Challenging Excited States. Application to Ozone and Sulfur Dioxide

A novel state-averaged version of ab initio nonorthogonal valence bond method is described, for the sake of accurate theoretical studies of excited states in the valence bond framework. With respect to standard calculations in the molecular orbital framework, the state-averaged breathing-orbital valence bond (BOVB) method has the advantage to be free from the penalizing constraint for the ground and excited state(s) to share the same unique set of orbitals. The ability of the BOVB method to faithfully describe excited states and to compute accurate transition energies from the ground state is tested on the five lowest-lying singlet electronic states of ozone and sulfur dioxide, among which 1¹B₂ and 2¹A₁ are the challenging ones. As the 1¹A₂, 1¹B₁, and 1¹B₂ states are of different symmetries than the ground state, they can be calculated at the state-specific BOVB level. On the other hand, the 2¹A₁ states and the 1¹A₁ ground states, which are of like symmetry, are calculated with the state-averaged BOVB technique. In all cases, the calculated vertical energies are close to the experimental values when available, and at par with the most sophisticated calculations in the molecular framework, despite the extreme compactness of the BOVB wave functions, made of no more than 5-9 valence bond structures in all cases. The features that allow the combination of compactness and accuracy in challenging cases are analyzed. For the "ionic" 1¹B₂ states, which are the site of important charge fluctuations, it is because of the built-in dynamic correlation inherent to the BOVB method. For the 2¹A₁ ones, this is the fact that these states have the degree of freedom of having different orbitals than the ground states, even though they are of like symmetry and calculated simultaneously using the newly implemented state-average BOVB algorithm. Finally, the description of the excited states in terms of Lewis structures is insightful, rationalizing the fast ring closure for the 2¹A₁ state of ozone and predicting some diradical character in the so-called "ionic" 1¹B₂ states.

On the connection between probability density analysis, QTAIM, and VB theory

Classification of bonds is essential for understanding and predicting the reactivity of chemical compounds. This classification mainly manifests in the bond order and the contribution of different Lewis resonance structures. Here, we outline a first principles approach to obtain these orders and contributions for arbitrary wave functions in a manner that is both, related to the quantum theory of atoms in molecules and consistent with valence bond theory insight: the Lewis structures arise naturally as attractors of the all-electron probability density |Ψ|2. Doing so, we introduce a valence bond weight definition that does not collapse in the basis set limit.

Captodative Substitution Enhances the Diradical Character of Compounds, Reduces Aromaticity, and Controls Single-Molecule Conductivity Patterns: A Valence Bond Study

The present contribution uses a valence bond (VB) perspective to consider the captodative substitution strategy, a method to enhance the diradical character of (potentially aromatic) compounds. We confirm the qualitative reasoning that has generally been used to rationalize the diradical-character-enhancing effect of captodative substitution: this type of substitution scheme disproportionally stabilizes specific Dewar/diradical(oid) VB structures, thus increasing their weight in the full ground-state wave function. Furthermore, we assess the effect of captodative substitution on the aromaticity of the considered compound. We observe a clear trade-off between diradical character and aromaticity for our model systems: as one of these properties increases, the other decreases. This finding is especially significant within the field of single-molecule electronics because it enables unification of the previously observed inverse proportionality between the aromaticity of a compound and the magnitude of conductance through that molecule, with the observed proportionality between diradical character and the magnitude of conductance associated with a compound. To some extent, both properties, i.e., aromaticity and diradical character, appear to be the flip-sides of the same coin.

Structural diradical character

A reliable first-principles description of singlet diradical character is essential for predicting nonlinear optical and magnetic properties of molecules. As diradical and closed-shell electronic structures differ in their distribution of single, double, triple, and aromatic bonds, modeling electronic diradical character requires accurate bond-length patterns, in addition to accurate absolute bond lengths. We therefore introduce structural diradical character, which we suggest as an additional measure for comparing first-principles calculations with experimental data. We employ this measure to identify suitable exchange-correlation functionals for predicting the bond length patterns and electronic diradical character of a biscobaltocene with the potential for photoswitchable nonlinear optical activity. Out of four popular approximate exchange-correlation functionals with different exact-exchange admixtures (BP86, TPSS, B3LYP, TPSSh), the two hybrid functionals TPSSh and B3LYP perform best for diradical bond length patterns, with TPSSh being best for the organometallic validation systems and B3LYP for the organic ones (for which the D3 dispersion correction was included). Still, none of the functionals is suitable for correctly describing relative bond lengths across the range of molecules studied, so that none can be recommended for predictive studies of (potential) diradicals without reservation. © 2018 Wiley Periodicals, Inc.

Computational investigations of 18-electron triatomic sulfur–nitrogen anions

MRCI-SD/def2-QZVP and PBE0/def2-QZVP calculations have been employed for the analysis of geometries, stabilities, and bonding of isomers of the 18-electron anions N2S2−, NS2−, and NSO−. Isomers of the isoelectronic neutral molecules SO2, S2O, S3, and O3 are included for comparison. The sulfur-centered acyclic NSN2−, NSS−, and NSO− anions are the most stable isomers of their respective molecular compositions. However, the nitrogen-centered isomers SNS− and SNO− lie close enough in energy to their more stable counterparts to allow their occurrence. The experimental structural information, where available, is in good agreement with the optimized bond parameters. The bonding in all investigated species is qualitatively similar, though electron density analyses reveal important quantitative differences that arise from bond polarization. Most of the investigated systems can be described with a single configuration wave function, the two notable exceptions being isomers SSS and OOO that show some diradical character. The computed MRCI-SD/def2-QZVP absorption maxima for SNS− and NSS− are 342 and 327 nm, respectively. The corresponding PBE0/def2-QZVP values in acetonitrile are 353 and 333 nm. These data support the proposed initial formation of SNS− from electrochemical or chemical reduction of SSNS− based on experimental UV–vis spectra. The interconversion of SNS− and NSS− is calculated to be facile and reversible, leading to an equilibrium mixture that also includes the remarkably stable dianion SNSNSS2−. Thus, salts of either SNS− or NSS− with bulky organic cations represent feasible synthetic targets.

QM/MM studies on ozonolysis of α-humulene and Criegee reactions with acids and water at air–water/acetonitrile interfaces

QM/MM electronic structure calculations reveal important mechanistic insights on the ozonolysis of α-humulene and Criegee reactions with acids and water at air–water/acetonitrile interfaces.