Tuning the Spin, Aromaticity, and Quantum Tunneling in Computationally Designed Fulvalenes

Quantum Tunneling Instability in Pericyclic Reactions

Several cycloreversion reactions of the retro-Diels-Alder type were computationally assessed to understand their quantum tunneling (QT) reactivity. N2, CO, and other leaving groups were considered based on their strong exothermicity, as it reduces their thermodynamic and kinetic stabilities. Our results indicate that for many of these reactions, it is essential to take into account their QT decomposition rate, which can massively weaken their molecular stability and shorten their half-lives even at deep cryogenic temperatures. In practical terms, this indicates that many supposedly stable molecules will actually be unsynthesizable or unisolable, and therefore trying to prepare or detect them would be a futile attempt. In addition, we discuss the importance of tunneling to correctly understand the enthalpy of activation and the collective atomic effect on the tunneling kinetic isotope effects to test if third-row atoms can tunnel in a chemical reaction. This project raises the question of the importance of in silico chemistry to guide in vitro chemistry, especially in cases where the latter cannot solve its own uncertainties.

Thioxobimanes

Dioxobimanes, colloquially known as bimanes, are a well-established family of N-heterobicyclic compounds that share a characteristic core structure, 1,5-diazabicyclo[3.3.0]octadienedione, bearing two endocyclic carbonyl groups. By sequentially thionating these carbonyls in the syn and anti isomers of the known (Me,Me)dioxobimane, we were able to synthesize a series of thioxobimanes, representing the first heavy-chalcogenide bimane variants. These new compounds were extensively characterized spectroscopically and crystallographically, and their aromaticity was probed computationally. Their potential role as ligands for transition metals was demonstrated by synthesizing a representative gold(I)-thioxobimane complex.

Computational Evidence for Tunneling and a Hidden Intermediate in the Biosynthesis of Tetrahydrocannabinol

Quantum tunneling is computed for a reaction sequence that models the conversion of the ortho-quinone methide of cannabigerolic acid 1 to the decarboxylated product (-)-trans-Δ⁹-tetrahydrocannabinol (THC, 3). This calculation is the first to evaluate multidimensional tunneling in this sequence. Computations were carried out with POLYRATE and GAUSSRATE using B3LYP/6-31G(d,p) to examine the mechanism of THC 3 formation. The pentyl chain on THC 3 and its precursors were replaced with a methyl group to compute tunneling contributions to the rates of four separate steps: (i) initial Diels-Alder reaction of the quinone methide with the trisubstituted alkene end-group of the geranyl 1Z-CH₃ to give 2Z-CH₃, (ii) acid-catalyzed keto-enol tautomerization, which converts 2rZ-CH₃ to 4rZ-CH₃, (iii) carboxyl rotamerization converting 4rZ-CH₃ to 4E-CH₃, and (iv) decarboxylation that converts 4E-CH₃ to 3-CH₃. Tunneling contributions to the rate constants of steps (i)-(iv) are between 19 and 76% at 293 K. In step (ii), nonuniform changes in the zero-point vibrational energy along the reaction path created a shallow minimum in the 0 K free energy. It is a hidden intermediate because it is not a minimum on the potential energy surface and is detectable only when zero-point energy is taken into account along the reaction path. Predicted kinetic isotope effects would be experimentally observable at temperatures that are convenient to use. This is particularly relevant in the decarboxylation stage of the reaction sequence and has important implications because of its role in THC 3 formation.

Boron Tunneling in the "Weak" Bond-Stretch Isomerization of N-B Lewis Adducts

Some nitrile-boron halide adducts exhibit a double-well potential energy surface with two distinct minima: a "long bond" geometry (LB, a van der Waals interaction mostly based on electrostatics, but including a residual charge transfer component) and a "short bond" structure (SB, a covalent dative bond). This behavior can be considered as a "weak" form of bond stretch isomerism. Our computations reveal that complexes RCN-BX₃ (R=CH₃ , FCH₂ , BrCH₂ , and X=Cl, Br) exhibit a fast interconversion from LB to SB geometries even close to the absolute zero thanks to a boron atom tunneling mechanism. The computed half-lives of the meta-stable LB compounds vary between minutes to nanoseconds at cryogenic conditions. Accordingly, we predict that the long bond structures are practically impossible to isolate or characterize, which agrees with previous matrix-isolation experiments.

Quantum mechanical tunnelling: the missing term to achieve sub-kJ mol-1 barrier heights

To predict barrier heights at low temperatures, it is not enough to employ highly accurate electronic structure methods. We discuss the influence of quantum tunnelling on the comparison of experimental and theoretical activation parameters (E_a, ΔH^‡, ΔG^‡, or ΔS^‡), since the slope-based experimental techniques to obtain them completely neglect the tunnelling component. The intramolecular degenerate rearrangement of four fluxional molecules (bullvalene, barbaralane, semibullvalene, and norbornadienylidene) were considered, systems that cover the range between fast deep tunneling and small but significant shallow tunnelling correction. The barriers were computed with the composite W3lite-F12 method at the CCSDT(Q)/CBS level, and the tunnelling contribution with small curvature tunnelling. While at room temperature the effect is small (∼1 kJ mol^-1), at low temperatures it can be considerable (in the order of tens of kJ mol^-1 at ∼80 K).

Switch chemistry at cryogenic conditions: quantum tunnelling under electric fields

While the influence of intramolecular electric fields is a known feature in enzymes, the use of oriented external electric fields (EEF) to enhance or inhibit molecular reactivity is a promising topic still in its infancy. Herein we will explore computationally the effects that EEF can provoke in simple molecules close to the absolute zero, where quantum tunnelling (QT) is the sole mechanistic option. We studied three exemplary systems, each one with different reactivity features and known QT kinetics: π bond-shifting in pentalene, Cope rearrangement in semibullvalene, and cycloreversion of diazabicyclohexadiene. The kinetics of these cases depend both on the field strength and its direction, usually giving subtle but remarkable changes. However, for the cycloreversion, which suffers large changes on the dipole through the reaction, we also observed striking results. Between the effects caused by the EEF on the QT we observed an inversion of the Arrhenius equation, deactivation of the molecular fluxionality, and stabilization or instantaneous decomposition of the system. All these effects may well be achieved, literally, at the flick of a switch.

Adding an external electric field to reactions driven by quantum mechanical tunneling brings a whole new dimension to the idea of switch chemistry.

Fulvalene as a platform for the synthesis of a dimetallic dysprosocenium single-molecule magnet

The dinucleating fulvalenyl ligand [1,1',3,3'-(C5 t Bu2H2)2]2- (Fvtttt) was used to synthesize the dimetallic dysprosocenium cation [{Dy(η5-Cp*)}2(μ-BH4)(η5:η5-Fvtttt)]+ (3) as the salt of [B(C6F5)4]- (Cp* = C5Me5). Compound [3][B(C6F5)4] was obtained using a method in which the double half-sandwich complex [{Dy(BH4)2(THF)}2(Fvtttt)] (1) was reacted with KCp* to give the double metallocene [{Dy(Cp*)(μ-BH4)}2(Fvtttt)] (2), followed by removal of a bridging borohydride ligand upon addition of [(Et3Si)2(μ-H)][B(C6F5)4]. The dimetallic fulvalenyl complexes 1-3 give rise to single-molecule magnet (SMM) behaviour in zero applied field, with the effective energy barriers of 154(15) cm-1, 252(4) cm-1 and 384(18) cm-1, respectively, revealing a significant improvement in performance across the series. The magnetic properties are interpreted with the aid of ab initio calculations, which show substantial increases in the axiality of the crystal field from 1 to 2 to 3 as a consequence of the increasingly dominant role of the Fvtttt and Cp* ligands, with the barrier height and hysteresis properties being attenuated by the equatorial borohydride ligands. The experimental and theoretical results described in this study furnish a blueprint for the design and synthesis of poly-cationic dysprosocenium SMMs with properties that may surpass those of benchmark systems.

Strategies for Design of Potential Singlet Fission Chromophores Utilizing a Combination of Ground-State and Excited-State Aromaticity Rules

Singlet exciton fission photovoltaic technology requires chromophores with their lowest excited states arranged so that 2E(T1) < E(S1) and E(S1) < E(T2). Herein, qualitative theory and quantum chemical calculations are used to develop explicit strategies on how to use Baird's 4n rule on excited-state aromaticity, combined with Hückel's 4n + 2 rule for ground-state aromaticity, to tailor new potential chromophores for singlet fission. We first analyze the E(T1), E(S1), and E(T2) of benzene and cyclobutadiene (CBD) as excited-state antiaromatic and aromatic archetypes, respectively, and reveal that CBD fulfills the criteria on the state ordering for a singlet fission chromophore. We then look at fulvenes, a class of compounds that can be tuned by choice of substituents from Baird-antiaromatic to Baird-aromatic in T1 and S1 and from Hückel-aromatic to Hückel-antiaromatic in S0. The T1 and S1 states of most substituted fulvenes (159 of 225) are described by singly excited HOMO → LUMO configurations, providing a rational for the simultaneous tuning of E(T1) and E(S1) along an approximate (anti)aromaticity coordinate. Key to the tunability is the exchange integral (KH,L), which ideally is constant throughout the compound class, providing a constant ΔE(S1 - T1). This leads us to a geometric model for the identification of singlet fission chromophores, and we explore what factors limit the model. Candidates with calculated E(T1) values of ∼1 eV or higher are identified among benzannelated 4nπ-electron compound classes and siloles. In brief, it is clarified how the joint utilization of Baird's 4n and Hückel's 4n + 2 rules, together with substituent effects (electronic and steric) and benzannelation, can be used to tailor new chromophores with potential use in singlet fission photovoltaics.

Theoretical study on the stability and aromaticity in silapentafulvenes towards triplet ground state species

Pentafulvenes are dipolar hydrocarbons since they shift their π-electrons to achieve Hückel aromaticity and thus the electron donating groups at the exocyclic position can enhance their aromaticity. Silapentafulvenes are analogues of pentafulvene formed by the replacement of the carbon atoms at the exocyclic C[double bond, length as m-dash]C double bond with a silicon atom in pentafulvene. It remains unclear how the aromaticity of 5-silapentafulvenes and 6-silapentafulvenes can be changed due to the polarization of the C[double bond, length as m-dash]Si double bond. Here we perform density functional theory calculations and reveal the increased aromatic character in 6-silapentafulvenes and the reduced aromaticity of 5-silapentafulvenes in the ground state. In addition, the origin of the relative thermodynamic stability of the silapentafulvene isomers can be attributed to the bond dissociation energy (BDE) of the exocyclic bond. More interestingly, some triplet ground state 5-silapentafulvene species are predicted by introducing amino groups on the ring, which is supported by the coupled cluster calculations. Our findings could be useful for experimentalists to realize silaaromatics.

Heavy-atom tunnelling in Cu(ii)N6 complexes: theoretical predictions and experimental manifestation

The degenerate rearrangement on Jahn-Teller distorted metal complexes is a promising reaction for the observation of significant heavy atom quantum mechanical tunnelling. Herein, a family of Cu(ii)-N₆ complexes are theoretically proven to exhibit rapid dynamical Jahn-Teller tunneling even close to the absolute zero. The manifestation of our predictions apparently appeared in solid state EPR experimental measurements on [Cu(en)₃]SO₄ more than 40 years ago, without the authors realizing that it was a quantum outcome.

Heavy atom tunnelling on XeF6 pseudorotation

XeF₆ has multiple C_3v equivalent minima due to the Jahn–Teller effect. Through computational means we prove that the rearrangement between isomers occurs through fluorine quantum mechanical tunnelling.

Calculations Predict That Heavy-Atom Tunneling Dominates Möbius Bond Shifting in [12]- and [16]Annulene

The contribution of heavy-atom tunneling to reactions of [12]- and [16]annulene was probed using small-curvature tunneling rate calculations. At the CCSD(T)/cc-pVDZ//M06-2X/cc-pVDZ level, tunneling is predicted to account for more than 50% of the rate for Möbius bond shifting and ca. 35% of the rate for electrocyclization in [12]annulene, and over 80% of the rate for Möbius bond shifting in [16]annulene, at temperatures at which these reactions have been observed experimentally.

A DFT Study of the Modulation of the Antiaromatic and Open-Shell Character of Dibenzo[a,f]pentalene by Employing Three Strategies: Additional Benzoannulation, BN/CC Isosterism, and Substitution

Dibenzo[a,f]pentalene ([a,f]DBP) is a highly antiaromatic molecule having appreciable open-shell singlet character in its ground state. In this work, DFT calculations at the B3LYP/6-311+G(d,p) level of theory were performed to explore the efficiency of three strategies, that is, BN/CC isosterism, substitution, and (di)benzoannulation of [a,f]DBP, in controlling its electronic state and (anti)aromaticity. To evaluate the type and extent of the latter, the harmonic oscillator model of aromaticity (HOMA) and aromatic fluctuation (FLU) indices were used, along with the nucleus-independent chemical shift NICS-XY-scan procedure. The results suggest that all three strategies could be employed to produce either the closed-shell system or open-shell species, which may be in the singlet or triplet ground state. Triplet states have been characterized as aromatic, which is in accordance with Baird's rule. All the singlet states were found to have weaker global paratropicity than [a,f]DBP. Additional (di)benzo fusion adds local aromatic subunit(s) and mainly retains the topology of the paratropic ring currents of the basic molecule. The substitution of two carbon atoms by the isoelectronic BN pair, or the introduction of substituents, results either in the same type and very similar topology of ring currents as in the parent compound, or leads to (anti)aromatic and nonaromatic subunits. The triplet states of all the examined compounds are also discussed.

Ping-pong tunneling reactions, part 2: boron and carbon bell-clapper rearrangement

Anthracene can be used as a scaffold for intramolecular SN2 degenerate reactions of the “bell clapper” type, where a central boron atom or its isoelectronic carbocation bonds alternatively towards one or the other lateral Lewis bases at the first and eight anthracene positions. This ping-pong bond-switching reaction possesses a symmetrical double-well potential with low activation barrier and relatively narrow barrier width. Herein we show by computational means the active role played by heavy atom quantum tunneling in this degenerate rearrangement reaction at cryogenic temperatures. At these conditions the thermal “over the barrier” reaction is forbidden, whereas the tunneling effect enhances the rate of reaction up to an experimentally measurable half-life. Kinetic isotope effects and cryogenic NMR spectroscopy can, in principle, experimentally demonstrate the tunneling mechanism.

Tunneling by 16 Carbons: Planar Bond Shifting in [16]Annulene

Midsized annulenes are known to undergo rapid π-bond shifting. Given that heavy-atom tunneling plays a role in planar bond shifting of cyclobutadiene, we computationally explored the contribution of heavy-atom tunneling to planar π-bond shifting in the major (CTCTCTCT, 5a) and minor (CTCTTCTT, 6a) known isomers of [16]annulene. UM06-2X/cc-pVDZ calculations yield bond-shifting barriers of ca. 10 kcal/mol. The results also reveal extremely narrow barrier widths, suggesting a high probability of tunneling for these bond-shifting reactions. Rate constants were calculated using canonical variational transition state theory (CVT) as well as with small curvature tunneling (SCT) contributions, via direct dynamics. For the major isomer 5a, the computed SCT rate constant for bond shifting at 80 K is 0.16 s^-1, corresponding to a half-life of 4.3 s, and indicating that bond shifting is rapid at cryogenic temperatures despite a 10 kcal/mol barrier. This contrasts with the CVT rate constant of 8.0 × 10^-15 s^-1 at 80 K. The minor isomer 6a is predicted to undergo rapid bond shifting via tunneling even at 10 K. For both isomers, bond shifting is predicted to be much faster than competing conformation change despite lower barriers for the latter process. The preference for bond shifting represents cases of tunneling control in which the preferred reaction is dominated by heavy-atom motions. At all temperatures below -50 °C, tunneling is predicted to dominate the bond shifting process for both 5a and 6a. Thus, [16]annulene is predicted to be an example of tunneling by 16 carbons. Bond shifting in both isomers is predicted to be rapid at temperatures accessible by solution-phase NMR spectroscopy, and an experiment is proposed to verify these predictions.