Methyl tunnelling in α-crystallised toluene by inelastic neutron scattering: temperature and pressure effects

Calculations of the molecular interactions in 1,3-dibromo-2,4,6-trimethyl-benzene: which methyl groups are quasi-free rotors in the crystal?

Dibromomesitylene (DBMH) is one of the few molecules in which a methyl group is a quasi-free rotor in the crystal state. Density functional theory calculations - using the Born-Oppenheimer approximation (BOa) - indicate that in isolated DBMH, Me4 and Me6 are highly hindered in a 3-fold potential V₃ > 55 meV while Me2 symmetrically located between two Br atoms has a small 6-fold rotation hindering potential: V₆ ∼ 8 meV. Inelastic neutron scattering studies have shown that this is also true in the crystal, the Me2 tunneling gap being 390 μeV at 4.2 K and V₆ ∼ 18 meV. In the monoclinic DBMH crystal, molecules are packed in an anti-ferroelectric manner along the oblique a axis, favoring strong van der Waals interactions, while in the corrugated bc planes each molecule has a quasi hexagonal environment and weaker interactions. This results in the nearby environment of Me2 only being composed of hydrogen atoms. This explains why the Me2 rotation barrier remains small in the crystal and mainly 6-fold. Using the same potentials in the Schrödinger equation for a -CD₃ rotor has allowed predicting a tunneling gap of 69 μeV for deuterated Me2 in very good agreement with inelastic neutron scattering measurements. Therefore, because of a rare and unexpected local symmetry in the crystal, the Me2 rotation barrier remains small and 6-fold and hydrogen nuclei are highly delocalized and not relevant to the Born-Oppenheimer approximation. This and the neglect of spin states explain the failure of density functional theory calculations for finding the rotation energy levels of Me2.

Spectral Addressability in a Modular Two Qubit System

The combination of structural precision and reproducibility of synthetic chemistry is perfectly suited for the creation of chemical qubits, the core units of a quantum information science (QIS) system. By exploiting the atomistic control inherent to synthetic chemistry, we address a fundamental question of how the spin-spin distance between two qubits impacts electronic spin coherence. To achieve this goal, we designed a series of molecules featuring two spectrally distinct qubits, an early transition metal, Ti³⁺, and a late transition metal, Cu²⁺ with increasing separation between the two metals. Crucially, we also synthesized the monometallic congeners to serve as controls. The spectral separation between the two metals enables us to probe each metal individually in the bimetallic species and compare it with the monometallic control samples. Across a range of 1.2-2.5 nm, we find that electron spins have a negligible effect on coherence times, a finding we attribute to the distinct resonance frequencies. Coherence times are governed, instead, by the distance to nuclear spins on the other qubit's ligand framework. This finding offers guidance for the design of spectrally addressable molecular qubits.

Probing Nuclear Spin Effects on Electronic Spin Coherence via EPR Measurements of Vanadium(IV) Complexes

Quantum information processing (QIP) has the potential to transform numerous fields from cryptography, to finance, to the simulation of quantum systems. A promising implementation of QIP employs unpaired electronic spins as qubits, the fundamental units of information. Though molecular electronic spins offer many advantages, including chemical tunability and facile addressability, the development of design principles for the synthesis of complexes that exhibit long qubit superposition lifetimes (also known as coherence times, or T₂) remains a challenge. As nuclear spins in the local qubit environment are a primary cause of shortened superposition lifetimes, we recently conducted a study which employed a modular spin-free ligand scaffold to place a spin-laden propyl moiety at a series of fixed distances from an S = ¹/₂ vanadium(IV) ion in a series of vanadyl complexes. We found that, within a radius of 4.0(4)-6.6(6) Å from the metal center, nuclei did not contribute to decoherence. To assess the generality of this important design principle and test its efficacy in a different coordination geometry, we synthesized and investigated three vanadium tris(dithiolene) complexes with the same ligand set employed in our previous study: K₂[V(C₅H₆S₄)₃] (1), K₂[V(C₇H₆S₆)₃] (2), and K₂[V(C₉H₆S₈)₃] (3). We specifically interrogated solutions of these complexes in DMF-d₇/toluene-d₈ with pulsed electron paramagnetic resonance spectroscopy and electron nuclear double resonance spectroscopy and found that the distance dependence present in the previously synthesized vanadyl complexes holds true in this series. We further examined the coherence properties of the series in a different solvent, MeCN-d₃/toluene-d₈, and found that an additional property, the charge density of the complex, also affects decoherence across the series. These results highlight a previously unknown design principle for augmenting T₂ and open new pathways for the rational synthesis of complexes with long coherence times.

Methyl rotor quantum states and the effect of chemical environment in organic crystals: γ-picoline and toluene

Using a set of first-principles calculations, we have studied the methyl tunnel splitting for molecular crystals of γ-picoline and toluene. The effective rotational potential energy surface of the probe methyl rotor along the tunneling path is evaluated using first-principles electronic structure calculations combined with the nudged elastic band method. The tunnel splitting is calculated by an explicit diagonalization of the one-dimensional time-independent Hamiltonian matrix. The effects of chemical environment and rotor-rotor coupling on the rotational energy barriers were investigated. It is found that more dense packing of the molecules in toluene compared to that in γ-picoline gives rise to a larger rotational barrier which in turn yields a considerably smaller tunnel splitting. Moreover, it turned out that coupled motion of the face-to-face methyl groups in γ-picoline has a significant effect on the reduction of the rotational barrier. Our results are in good agreement with the experimentally observed tunnel splitting.

Spin-symmetry conversion in methyl rotors induced by tunnel resonance at low temperature

Field-cycling NMR in the solid state at low temperature (4.2 K) has been employed to measure the tunneling spectra of methyl (CH3) rotors in phenylacetone and toluene. The phenomenon of tunnel resonance reveals anomalies in (1)H magnetization from which the following tunnel frequencies have been determined: phenylacetone, νt = 6.58 ± 0.08 MHz; toluene, νt(1) = 6.45 ± 0.06 GHz and νt(2) = 7.07 ± 0.06 GHz. The tunnel frequencies in the two samples differ by three orders of magnitude, meaning different experimental approaches are required. In phenylacetone the magnetization anomalies are observed when the tunnel frequency matches one or two times the (1)H Larmor frequency. In toluene, doping with free radicals enables magnetization anomalies to be observed when the tunnel frequency is equal to the electron spin Larmor frequency. Cross-polarization processes between the tunneling and Zeeman systems are proposed and form the basis of a thermodynamic model to simulate the tunnel resonance spectra. These invoke space-spin interactions to drive the changes in nuclear spin-symmetry. The tunnel resonance lineshapes are explained, showing good quantitative agreement between experiment and simulations.

Methyl group dynamics in polycrystalline and liquid ubiquinone Q(0) studied by neutron scattering

We present a quasi-elastic neutron scattering (QENS) study on the methyl group dynamics of ubiquinone Q(0) in the solid and liquid state. For solid ubiquinone Q(0), the dynamics can be described with three Lorentzian functions in the framework of a jump model among three equidistant sites on a circle. According to the known molecular structure of Q(0) in the solid state, this is consistent with three nonequivalent methyl groups in the molecule. From the temperature-dependent analysis of the QENS spectra, the activation energies were determined. The barrier heights could be evaluated from librational bands in the inelastic part of the spectra. The results from neutron spectroscopy are compared to Gaussian 03 calculations leading to an assignment of the activation energies to the different methyl groups in Q(0). The dynamics of Q(0) in the liquid state is evaluated with a scattering function taking into account three different molecular motions. It is demonstrated that the temperature dependence of the long-range diffusion and isotropic rotational diffusion exhibit an Arrhenius-like behavior, whereas the process of methyl group rotation in the liquid phase is virtually free of a barrier.

Quasielastic and inelastic neutron scattering study of methyl group rotation in solid and liquid pentafluoroanisole and pentafluorotoluene

The rotational motion of the methyl group in pentafluoroanisole (PFA) and in pentafluorotoluene (PFT), respectively, was investigated by quasielastic neutron scattering (QENS). For solid PFA, the rotation can be described by a model for uniaxial rotational jumps between three equidistant sites on a circle. Similar to the molecular structure of alpha-toluene, two nonequivalent methyl groups in the unit cell with two different rotational barriers were found for solid PFT. From the analysis of the quasielastic scattering, the activation energies were determined. The barrier heights could be evaluated from bands in the inelastic part of the spectra. The methyl group dynamics in the liquid state is evaluated for both substances using different scattering functions, which are discussed. An empirical model for the description of the contribution of methyl groups in liquids of small organic molecules to the QENS spectra is presented. It is demonstrated that the process of methyl group rotation in the liquid phase is nearly free of a barrier.

Quantitative atom-atom potentials from rotational tunneling: their extraction and their use

Rotational tunneling of small molecular groups has been the subject of considerable theoretical and experimental activity for several decades. Much of this activity has been driven by the promise of exploiting the extreme sensitivity of quantum tunneling to interatomic potentials, but until recently, there was no straightforward means by which quantitative information about these potentials could be extracted. This review explains how a quantitative method, suitable for general application, was developed. It then goes on to show how this has been used to understand tunneling systems for which no previous satisfactory explanation had been found. The application of the methodology, and its results, to other disciplines is discussed.