The Tunnel Effect in Chemistry

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The main emphasis has been on the kinetics of chemical reactions involving the transfer of protons, hydrogen atoms or hydride ions, although Chapter 6 gives an account of the role of the tunnel effect in molecular spectra, and Chapter 7 makes some mention of tunnelling in solid state phenomena, biological processes and. Quantum Effects in a Chemical Reaction? The Tunnel Effect in Chemistry. Eugen Merzbacher. Green's functions are de- emphasized.

The tunnel effect in chemistry. Front Cover.

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Ronald Percy Bell. As for the fitted values, we point out that the determined values of M O 2 are of the expected magnitude 47 , but different for the two compounds.

Quantum tunnelling

The dynamic CF potential can be expressed in terms of equivalent operators, in a fashion analogous to that adopted to express the static CF Hamiltonian. Based on this analysis, we can conclude that the SLR in zero external field is dominated by a resonant spin—phonon process involving the first excited doublet i. The fivefold decrease in the tunneling rate for 2Dy as compared to 1Dy goes along with the close approach to D 4d symmetry and concomitant electronic linearity in the former system vide infra. The relaxation is of pure Orbach character, and the associated parameters are in good agreement with those of the concentrated species.

This observation points to dipolar interactions with neighboring molecules as the dominant source of tunnel-splitting-opening transverse fields in the samples vide infra. In the low-temperature regime above T N , these weak spin-spin interactions will give rise to a distribution of dynamic dipolar fields However, as a tunneling event at a given site will lead to a redistribution of the dipolar fields throughout the crystal, all spins will eventually enter this tunnel window 6. The calculated rates overestimate the experimental values by three orders of magnitude.

However, considering the pronounced Ising nature of the dysprosium spins at low temperature experimentally verified by torque magnetometry and the anisotropic crystal packings Supplementary Fig. It appears that the increased symmetry in 2Dy leads to an approximately threefold reduction of the ground state tunnel splitting as compared to the low-symmetry 1Dy specimen. We emphasize that the reduction of the tunneling splitting predominantly results from the reduction in the value of the perpendicular component of the ground state g -tensor, resulting from the minimization of the off-diagonal B 4 4 CF parameter.

The pronounced effect of dilution in the present case indicates that dipolar interactions dominate the effects of nuclear spins. This opens the possibility that appropriate tailoring of highly anisotropic crystal packings could lead to relatively concentrated magnetic solids where dipolar fields play a minor role in defining the tunnel-splitting-opening transverse field. This prospect could be of importance to the emerging field of molecular spin qubits We note that direct spin—phonon relaxation cannot drive the thermalization of the spins in the tunneling regime the resulting SLR rates would be unphysically small 5.

Hence the modulation of the SLR rate observed for 1Dy at low temperatures cf. This critical slowing down of the tunneling rate has been observed for a few other molecular nanomagnets 5 , 51 , Interestingly, this suggests that if long-range magnetic ordering can be suppressed, the tunneling condition will be very robust. This inhibition is clearly advantageous when seeking control over the timescale of tunneling by means of chemistry. In conclusion, our work demonstrates how the timescale of quantum tunneling of electronic spins can be controlled and manipulated by chemical means through the targeting of structural conformers of high-symmetry lanthanide complexes.

While minimization of tunneling rates through the design of axially symmetric coordination environments has been a long-standing design criterion, our results allow for a quantification of the effect of geometrically imposed electronic linearity, and a comparison with other factors governing the magnitude of ground state tunnel splittings in lanthanide complexes.

Furthermore, the engineering of crystal environments with significant dipolar field anisotropy and suppression of long-range magnetic order serve as interesting second generation design criteria worth pursuing in the quest for further control over spin tunneling in the bulk phase of already symmetry-optimized lanthanide complexes. We propose, that if the conformational change can be induced by external stimuli e.

The solid solution 1Y 0.

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  4. The purity of the solid solution was verified using powder X-ray diffraction Supplementary Fig. The CF modeling based on spectroscopic data, molar magnetization, and molar magnetic susceptibility was performed using the MagProp software In order to allow for an error in the mass of the sample used for magnetization and susceptibility measurements, a model scaling factor was included in the fit.

    As argued elsewhere 33 , the minimal, common point group symmetry at the dysprosium site in 1Dy and 2Dy is C 4. For this reason, the appropriate Hamiltonian of the systems in the Stevens formalism is The definitions of the respective Stevens operators are given elsewhere However, it proved impossible to obtain an unambiguous fit if all the off-diagonal terms were included. According to common practice for tetragonal or near-tetragonal systems 5 , 6 , 57 , the problem was overcome through the exclusion of the sixth order off-diagonal operators i.

    All data were analyzed using the LAMP program package The data were corrected for detector efficiency using data from a vanadium sample, and the data taken on TOFTOF were corrected for the background associated with the sample holder by performing an empty can measurement. Single crystals of 2Dy suitable for cantilever torque magnetometry were prepared using the published method for growing EPR suitable single crystals The temperature dependence of the heat capacity C T , between 1. The magnetization and dc magnetic susceptibility data for 1Dy and 2Dy were reported elsewhere Fitting of the frequency dependent ac magnetic susceptibility was carried out using the CC-fit program developed by Nicholas F.

    Chilton The ac susceptometer was mounted in an Oxford Instruments Kelvinox dilution fridge. One end of the wires was encapsulated along with the sample in the Stycast and the other end was attached to the weak link of the dilution fridge. The raw frequency dependent data suffered from a frequency dependent background, and the imaginary component had to be corrected for this prior to Cole—Cole fitting of the data.

    As it was not feasible to carry out a measurement of a blank, the background was instead determined in the following way. Due to the larger magnitude of the real component of the susceptibility relative to the imaginary one, the former response was much less affected by the background. The so-obtained parameters were used to simulate the corresponding out-of-phase component. By subtracting the simulated response from the experimental one, the background could be determined. This procedure was carried out at different temperatures, and the background response was found to be temperature independent.

    For this reason, a universal background was used for each measured sample.

    Following the background correction, fitting of the frequency dependent data was carried out using the CC-fit program as described above. All other relevant data from this study are available from the authors on request. Gatteschi, D. Quantum tunneling of magnetization and related phenomena in molecular materials. Thomas, L. Macroscopic quantum tunnelling of magnetization in a single crystal of nanomagnets.

    Nature , — Wernsdorfer, W. Exchange-biased quantum tunnelling in a supramolecular dimer of single-molecule magnets. Ishikawa, N. Quantum tunneling of magnetization in lanthanide single-molecule magnets: Bis phthalocyaninato terbium and Bis phthalocyaninato dysprosium anions. Luis, F. B 82 , Gd-based single-ion magnets with tunable magnetic anisotropy: molecular design of spin qubits. Lin, P.

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    A polyuclear lanthanide single-molecule magnet with a record anisotropic barrier. Blagg, R. Magnetic relaxation pathways in lanthanide single-molecule magnets. Pineda, E. Exchange-bias quantum tunnelling in a CO 2 -based Dy 4 -single molecule magnet. Mannini, M. Quantum tunnelling of the magnetization in a monolayer of oriented single-molecule magnets.

    Thiele, S. Electrically driven nuclear spin resonance in single-molecule magnets. Science , — Bogani, L. Molecular spintronics using single-molecule magnets. Cornia, A. Spintronics: the molecular way. Leuenberger, M. Quantum computing in molecular magnets. Stamp, P. Spin-based quantum computers made by chemistry: hows and whys. Sessoli, R. Magnetic bistability in a metal-ion cluster.

    Urdampilleta, M. Supramolecular spin valves. Ganzhorn, M. Quantum Einstein-de Haas effect. Rational design of single-ion magnets and spin qubits based on mononuclear lanthanoid complexes. Woodruff, D. Lanthanide single-molecule magnets. Finn, C. Spin-lattice relaxation in cerium magnesium nitrate at liquid helium temperatures: a new process. Classical and quantum magnetization reversal studied in nanometer-sized particles and clusters. Meihaus, K.

    The Tunnel Effect in Chemistry | Ronald Percy Bell | Springer

    Le Roy, J. A sandwich complex with axial symmetry for harnessing the anisotropy in a prolate erbium III ion. Dalton Trans. Lanthanide double-decker complexes functioning as magnets at the single-molecular level. AlDamen, M. Mononuclear lanthanide single-molecule magnets based on polyoxometalates. Tanaka, D. Proton-induced switching of the single molecule magnetic properties of a porphyrin based Tb III double-decker complex. Chen, Y. Liu, J. Ding, Y. On approaching the limit of molecular magnetic anisotropy: a near-perfect pentagonal bipyramidal dysprosium III single-molecule magnet.

    Switching the anisotropy barrier of a single-ion magnet by symmetry change from quasi- D 5h to quasi- O h. Imposing high-symmetry and tuneable geometry on lanthanide centres with chelating Pt and Pd metalloligands. Sorace, L. Lanthanides in molecular magnetism: old tools in a new field.

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    Cucinotta, G. Gregson, M. A monometallic lanthanide bis methanediide single molecule magnet with a large energy barrier and complex spin relaxation behaviour. Norel, L. A terminal fluoride ligand generates axial magnetic anisotropy in dysprosium complexes. Pedersen, K. Modifying the properties of 4f single-ion magnets by peripheral ligand functionalisation.

    Marx, R. Spectroscopic determination of crystal field splittings in lanthanide double deckers. Vonci, M. Magnetic excitations in polyoxotungstate-supported lanthanoid single-molecule magnets: an inelastic neutron scattering and ab initio study. Perfetti, M. Cantilever torque magnetometry on coordination compounds: from theory to experiments. Cole, K. Dispersion and absorption in dielectrics I. Alternating current characteristics.

    Pointillart, F.

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