Ronald G. Lawler

Quantum rotation of ortho and para-water encapsulated in a fullerene cage

Inelastic neutron scattering, far-infrared spectroscopy, and cryogenic nuclear magnetic resonance are used to investigate the quantized rotation and ortho–para conversion of single water molecules trapped inside closed fullerene cages. The existence of metastable ortho-water molecules is demonstrated, and the interconversion of ortho-and para-water spin isomers is tracked in real time. Our investigation reveals that the ground state of encapsulated ortho water has a lifted degeneracy, associated with symmetry-breaking of the water environment.

Hydrodynamic theory of CIDEP and CIDNP

The stochastic Liouville method has been applied to the problem of high field CIDEP and CIDNP. The full equation of motion of the density matrix for the pair of free radicals includes: (1) the spatially isotropic Liouville operator; (2) the diffusion operator; (3) selective recombination of radical pairs from the singlet electronic state; (4) the Heisenberg exchange interaction; (5) secular electronic relaxation processes; and (6) radical scavenging processes. The short range character of radical recombination and Heisenberg exchange relative to the long distance of a diffusive trajectory allows these interactions to be treated effectively as delta functions which operate at a distance corresponding to a chemical bond. Using this delta function model, the equation of motion of the density matrix is soluble exactly for: (1) the z component of the electronic magnetization for a single radical fragment, which is proportional to the intensity of an ESR line; and (2) the nuclear spin level populations of the recombination and scavenged products, which are the indirect observables in the NMR experiment. In the limits of weak electronic relaxation and slow scavenging, the solutions of the problem approach those obtained by Adrian using the Noyes molecular pair theory.

Coupled translation-rotation eigenstates of H2 in C60 and C70 on the spectroscopically optimized interaction potential: Effects of cage anisotropy on the energy level structure and assignments

We have developed a quantitatively accurate pairwise additive five-dimensional (5D) potential energy surface (PES) for H(2) in C(60) through fitting to the recently published infrared (IR) spectroscopic measurements of this system for H(2) in the vibrationally excited nu=1 state. The PES is based on the three-site H(2)-C pair potential introduced in this work, which in addition to the usual Lennard-Jones (LJ) interaction sites on each H atom of H(2) has the third LJ interaction site located at the midpoint of the H-H bond. For the optimal values of the three adjustable parameters of the potential model, the fully coupled quantum 5D calculations on this additive PES reproduce the six translation-rotation (T-R) energy levels observed so far in the IR spectra of H(2)@C(60) to within 0.6%. This is due in large part to the greatly improved description of the angular anisotropy of the H(2)-fullerene interaction afforded by the three-site H(2)-C pair potential. The same H(2)-C pair potential spectroscopically optimized for H(2)@C(60) was also used to construct the pairwise additive 5D PES of H(2) (nu=1) in C(70). This PES, because of the lower symmetry of C(70) (D(5h)) relative to that of C(60) (I(h)), exhibits pronounced anisotropy with respect to the direction of the translational motion of H(2) away from the cage center, unlike that of H(2) in C(60). As a result, the T-R energy level structure of H(2) in C(70) from the quantum 5D calculations on the optimized PES, the quantum numbers required for its assignment, and the degeneracy patterns which arise from the T-R coupling for translationally excited H(2) are all qualitatively different from those determined previously for H(2)@C(60) [M. Xu et al., J. Chem. Phys. 128, 011101 (2008).

Electron T1 measurements in short‐lived free radicals by dynamic polarization recovery

A dynamic polarization recovery method for measurement of electron spin T1 relaxation times in free radicals in liquids is described, which is valid even in the presence of chemically induced dynamic electron polarization (CIDEP) and fast chemical decay of the radicals. The method is based on pulsed microwave perturbation and detection of transient magnetization following radical creation in a short pulse. Analysis of the experimental approach and a theoretical description of the method is presented together with a detailed discussion of the advantages and the limitations of the technique. Electron T1 measurements are presented for 14 short‐lived free radicals generated in aqueous solution. The magnitudes of the observed relaxation times, which range from 0.1 to 4 μs, are discussed within the framework of current theories of relaxation for small radicals in liquids. It is tentatively concluded that the spin rotation mechanism is responsible for the very short T1’s in this series of radicals.

Quantum dynamics of coupled translational and rotational motions of H2 inside C60

We report rigorous quantum calculations of the translation-rotation (T-R) eigenstates of the H2 molecule in C60. The resulting level structure can be explained in terms of a few dominant features. These include the coupling between the orbital and the rotational angular momenta of H2 to give the total angular momentum lambda, and the splitting of the sevenfold degeneracy of T-R levels with lambda=3 by the nonsphericity of C60, according to the rules of the icosahedral I h group.

Demonstration of a Chemical Transformation Inside a Fullerene. The Reversible Conversion of the Allotropes of H2@C60

The interconversion of the two allotropes of the hydrogen molecule (para-H2 and ortho-H2) incarcerated inside the fullerene C60 is reported (oH2@C60 and pH2@C60, respectively). For conversion, oH2@C60 was adsorbed at the external surface of the zeolite NaY and immersed into liquid oxygen at 77 K. Equilibrium was reached in less than 0.5 h. Rapid removal of oxygen provides a sample of enriched pH2@C60 that is stable for many days in the absence of paramagnetic catalysts (half-life approximately 15 days). Enriched pH2@C60 is nonvolatile and soluble in organic solvents. At room temperature in the presence of a paramagnetic catalyst (dissolved O2 or the nitroxide Tempo) a slow back conversion into oH2@C60 was observed by 1H NMR. A bimolecular rate constant for conversion of pH2@C60 to oH2@C60 using Tempo of kTempo approximately 4 x 10-5 M-1 s-1 was observed, which is approximately 3 orders of magnitudes slower than that for dissolved pH2 in organic solvents which is not protected by the C60 shell.

Hydrogen Molecules inside Fullerene C70: Quantum Dynamics, Energetics, Maximum Occupancy, And Comparison with C60

Recent synthesis of the endohedral complexes of C(70) and its open-cage derivative with one and two H(2) molecules has opened the path for experimental and theoretical investigations of the unique dynamic, spectroscopic, and other properties of systems with multiple hydrogen molecules confined inside a nanoscale cavity. Here we report a rigorous theoretical study of the dynamics of the coupled translational and rotational motions of H(2) molecules in C(70) and C(60), which are highly quantum mechanical. Diffusion Monte Carlo (DMC) calculations were performed for up to three para-H(2) (p-H(2)) molecules encapsulated in C(70) and for one and two p-H(2) molecules inside C(60). These calculations provide a quantitative description of the ground-state properties, energetics, and the translation-rotation (T-R) zero-point energies (ZPEs) of the nanoconfined p-H(2) molecules and of the spatial distribution of two p-H(2) molecules in the cavity of C(70). The energy of the global minimum on the intermolecular potential energy surface (PES) is negative for one and two H(2) molecules in C(70) but has a high positive value when the third H(2) is added, implying that at most two H(2) molecules can be stabilized inside C(70). By the same criterion, in the case of C(60), only the endohedral complex with one H(2) molecule is energetically stable. Our results are consistent with the fact that recently both (H(2))(n)@C(70) (n = 1, 2) and H(2)@C(60) were prepared, but not (H(2))(3)@C(70) or (H(2))(2)@C(60). The ZPE of the coupled T-R motions, from the DMC calculations, grows rapidly with the number of caged p-H(2) molecules and is a significant fraction of the well depth of the intermolecular PES, 11% in the case of p-H(2)@C(70) and 52% for (p-H(2))(2)@C(70). Consequently, the T-R ZPE represents a major component of the energetics of the encapsulated H(2) molecules. The inclusion of the ZPE nearly doubles the energy by which (p-H(2))(3)@C(70) is destabilized and increases by 66% the energetic destabilization of (p-H(2))(2)@C(60). For these reasons, the T-R ZPE has to be calculated accurately and taken into account for reliable theoretical predictions regarding the stability of the endohedral fullerene complexes with hydrogen molecules and their maximum H(2) content.

The rate of decarboxylation of the benzoyloxy radical as determined by CIDNP

Abstract Analysis of the CIDNP spectrum of ethylbenzoate (BzOEt) and ethylbenzene (PhEt) produced as recombination products of the decomposition of benzoylpropionyl peroxide is reported. Mathematical expressions for the yields and CIDNP intensities of both products are derived using an extension of the radical pair model. Two methods are employed to estimate the decarboxylation rate constant, k, for the benzoyloxy radical: (a) comparison of enhanced and unenhanced intensities of the PhEt quartet, and (b) comparison of the CIDNP intensities of the quartets from BzOEt and PhEt. The two methods give estimates of k agreeing within a factor of three. The lower limit to the value of k so obtained at 130°C in o-dichlorobenzene solution is 1 × 108 s−1. This is 2 to 3 orders of magnitude larger than previous estimates and implies that the lifetime of benzoyloxy radical may be considerably shorter than usually assumed.

A Magnetic Switch for Spin-Catalyzed Interconversion of Nuclear Spin Isomers

The interconversion of ortho-hydrogen (oH(2)) and para-hydrogen (pH(2)), the two nuclear spin isomers of dihydrogen, requires a paramagnetic spin catalyst such as a nitroxide. We report the design and demonstration of spin catalysis of the interconversion of oH(2) and pH(2) incarcerated in an endofullerene based on a reversible nitroxide/hydroxylamine system. The system is an example of a reversible magnetic spin catalysis switch that can increase the rate of interconversion of the nuclear spin isomers of H(2) by a factor of approximately 10(4).

Paramagnet enhanced nuclear relaxation of H2 in organic solvents and in H2@C60.

We have measured the bimolecular contribution (relaxivity) R1 (M(-1) s(-1)) to the spin-lattice relaxation rate for the protons of H2 and H2@C60 dissolved in organic solvents in the presence of paramagnet nitroxide radicals. It is found that the relaxation effect of the paramagnets is enhanced 5-fold in H2@C60 compared to H2 under the same conditions. 13C relaxivity in C60 induced by nitroxide has also been measured. The resulting value of R1 for 13C is substantially smaller relative to the 1H relaxation in H2@C60 than expected solely on the basis of the smaller magnetic moment of 13C. The observed values of R1 have been analyzed quantitatively using an outer-sphere model for bimolecular spin relaxation to extract an encounter distance, d, as the dependent variable. The resulting values of d for H2 and (13)C60 are similar to the sum of the van der Waals radii for the radical and the corresponding molecule. The value of d for (1)H2@C60 is substantially smaller than the corresponding van der Waals estimates, corresponding to larger than expected values of R1. A possible explanation for the enhanced relaxivity is a contribution from hyperfine coupling. Based on the results reported here, it seems that not only is the hydrogen molecule in H2@C60 not insulated from magnetic contact with the outside world but also the interaction with paramagnets is even stronger than expected based on distance alone.