Unexpected shielding of methyl group protons in some piperidines

High resolution 1H and 13C NMR spectra of four 3-ethyl-4-hydroxy- 4-phenylpiperidines 1-4 have been recorded in CDCl3 and analysed. The conformations of phenyl and hydroxyl groups at C(4) and ethyl group at C(3) were analysed in detail. The chemical shift of the methyl protons in the ethyl group are quite surprising; they are close to TMS in CDCl(3) and even negative in DMSO-d6. These results are interpreted in terms of the magnetic anisotropy of the phenyl rings at C(2) and C(4) which, in turn, depend on the conformations of the ethyl group at C(3) and the hydroxyl group at C(4). Favoured conformations of ethyl group at C(3) and hydroxyl group at C(4) were calculated by AM1 methods.     

Spin-lattice relaxation of radicals in molecular crystals

The mechanism of spin-lattice relaxation of radicals in magnetically diluted molecular crystals caused by delocalization of the unpaired electron is considered.The authors thank I. V. Aleksandrov for a number of helpful remarks during discussions of this investigation.     

Fingerprints of damped quantum rotation observed in solid-state proton NMR spectra.

(1)H NMR spectra of the methyl group in an oriented crystal sample of methylmalonic acid with all three non-methyl protons replaced by deuterons are interpreted in terms of the damped quantum rotation (DQR) theory of NMR line shapes. The DQR approach offers a perfect theoretical reproduction of the observed spectra while the conventional Alexander-Binsch line-shape model shows evident defects in the present case. The temperature trends of the quantities characterizing the coherent and incoherent dynamics of the methyl group in the DQR approach (the effective tunnelling frequency and two coherence-damping rates) derived from the spectra are fairly reproduced using a model reported previously. The present findings provide further evidence of limitations to the validity of the common belief that molecular rate processes in condensed phases are necessarily classical.     

Intramolecular and intermolecular contributions to the barriers for rotation of methyl groups in crystalline solids: electronic structure calculations and solid-state NMR relaxation measurements

The rotation barriers for 10 different methyl groups in five methyl-substituted phenanthrenes and three methyl-substituted naphthalenes were determined by ab initio electronic structure calculations, both for the isolated molecules and for the central molecules in clusters containing 8-13 molecules. These clusters were constructed computationally using the carbon positions obtained from the crystal structures of the eight compounds and the hydrogen positions obtained from electronic structure calculations. The calculated methyl rotation barriers in the clusters (E(clust)) range from 0.6 to 3.4 kcal/mol. Solid-state (1)H NMR spin-lattice relaxation rate measurements on the polycrystalline solids gave experimental activation energies (E(NMR)) for methyl rotation in the range from 0.4 to 3.2 kcal/mol. The energy differences E(clust) - E(NMR) for each of the ten methyl groups range from -0.2 kcal/mol to +0.7 kcal/mol, with a mean value of +0.2 kcal/mol and a standard deviation of 0.3 kcal/mol. The differences between each of the computed barriers in the clusters (E(clust)) and the corresponding computed barriers in the isolated molecules (E(isol)) provide an estimate of the intermolecular contributions to the rotation barriers in the clusters. The values of E(clust) - E(isol) range from 0.0 to 1.0 kcal/mol.     

Theory of damped quantum rotation in NMR spectra. I. Fundamental aspects

The damped quantum rotation (DQR) theory, formulated originally for methyl-like atomic groupings, is now extended to hindered (N>3)-fold molecular rotors, such as the cyclopentadienyl, benzene, and cycloheptatrienyl rings in solid phase environments. It heightens the significance of the Pauli principle in shaping up the stochastic dynamics of such objects, reflected in NMR line shapes. The corresponding NMR line-shape equation is derived; its stochastic part is shown for the first time to have the double commutator form for any values of the quantum-mechanical (coherence-damping) rate constants entering it. Constraints on the relative magnitudes of such constants are determined under which the DQR line-shape equation is converted into the phenomenological Alexander-Binsch equation describing classical jumps of the rotor. When all the quantum rate constants happen to be equal, the phenomenological model of equal jump rates between any two of the N (equivalent) orientations of the rotor is reproduced. On the other hand, the seemingly most plausible (for N>3) nearest-neighbor hopping model does not have any peculiar grounds in the DQR approach. For the special instances of stochastic molecular motions addressed in this work, the extended DQR formalism affords a quantification of the "degree of classicality" represented by a complete set of the relevant quantum rate constants. In view of our earlier experimental findings for the methyl rotors, the very occurrence of the nonclassical DQR effects seems unquestionable even for the objects of the size of benzene. The question of under what circumstances such effects can be big enough to be detected experimentally will be addressed in Part II of this work.     

A heuristic model of damped quantum rotation effects in nuclear magnetic resonance spectra

The damped quantum rotation (DQR) theory describes temperature effects in NMR spectra of hindered molecular rotators composed of identical atoms arranged in regular N-gons. In the standard approach, the relevant coherent dynamics are described quantum mechanically and the stochastic, thermally activated motions classically. The DQR theory is consistent. In place of random jumps over one, two, etc., maxima of the hindering potential, here one has damping processes of certain long-lived coherences between spin-space correlated eigenstates of the rotator. The damping-rate constants outnumber the classical jump-rate constants. The jump picture is recovered when the former cluster appropriately around only as many values as the number of the latter. The DQR theory was confirmed experimentally for hindered methyl groups in solids and even in liquids above 170 K. In this paper it is shown that for three-, four-, and sixfold rotators, the Liouville space equations of NMR line shapes, derived previously with the use of the quantum mechanical reduced density matrix approach, can be be given a heuristic justification. It is based on an equation of motion for the effective spin density matrix, where the relevant spin hamiltonian contains randomly fluctuating terms. The occurrence of the latter can be rationalized in terms of fluctuations of the tunneling splittings between the torsional sublevels of the rotator, including momentary liftings of the Kramers degeneracies. The question whether such degeneracy liftings are physical or virtual is discussed. The random terms in the effective hamiltonian can be Monte Carlo modeled as piecewise constant in time, which affords the stochastic equation of motion to be solved numerically in the Hilbert spin space. For sixfold rotators, this way of calculating the spectra can be useful in the instances where the Liouville space formalism of the original DQR theory is numerically unstable.     

Spin-lattice relaxation in biopolymeric sorbents in the presence of water

The effects of water on relaxation processes in polysaccharides were investigated by the NMR, adsorption, and comparative methods. It was shown that the relaxation vitrification transition that occurred in polysaccharides during the formation of an adsorption layer about two water molecules thick made the largest contribution to the spin-relaxation processes in the polymer-water system.     

Determination of the methyl group rotation energy barrier in some substituted tricyclo [3.1.0.02,6]hexanes by carbon-13 spinlattice relaxation

The resonances in the ¹³C NMR spectra of 1,2,5,6-tetramethyl-3,4-dimethylenetricyclo[3.1.0.0^2,6]hexane and the corresponding enone and dione have been assigned. The rotation energy barriers of the methyl groups have been determined from ¹³C spin-lattice relaxation time measurements; barriers of 6.7–10.9 kJ mol^?1 have been found. Since X-ray data have shown that the skeleton bonds are bent away from the CCH₃ axis by angles of over 120°, only minor interactions occur between adjacent methyl groups. Therefore, these barriers are mainly governed by interactions with the CC skeleton bonds.     

The quenching of isopropyl group rotation in van der Waals molecular solids

X-ray diffraction experiments are employed to determine the molecular and crystal structure of 3-isopropylchrysene. Based on this structure, electronic structure calculations are employed to calculate methyl group and isopropyl group rotational barriers in a central molecule of a ten-molecule cluster. The two slightly inequivalent methyl group barriers are found to be 12 and 15 kJ mol(-1) and the isopropyl group barrier is found to be about 240 kJ mol(-1), meaning that isopropyl group rotation is completely quenched in the solid state. For comparison, electronic structure calculations are also performed in the isolated molecule, determining both the structure and the rotational barriers, which are determined to be 15 kJ mol(-1) for both the isopropyl group and the two equivalent methyl groups. These calculations are compared with, and are consistent with, previously published NMR (1)H spin-lattice relaxation experiments where it was found that the barrier for methyl group rotation was 11+/-1 kJ mol(-1) and that the barrier for isopropyl group rotation was infinite on the solid state NMR time scale.     

Stereospecificity in the proton magnetic relaxation rate of enantiotopic methyls and the methyl rotation barrier

It is proposed that a distinction should be made between stereospecificity of the first kind, which provides spectral (line assignments in the NMR spectrum) and structural (molecular conformations) information, and stereospecificity of the second kind, which only provides spectral information, on the basis of the relaxation times T₁. The nature of the stereospecificity was revealed in detail during analysis of the reasons for the differences in the proton relaxation times of enantiotopic gem-dimethyl groups in the conformationally rigid molecule of 2-oxo-5,5-dimethyl-1,3,2-dioxathiane. It is suggested that the barrier to rotation of the methyl in the geminal CH₃-C-H fragment can be assessed from the temperature dependence of the t₁ time of the methine proton. The experiment was carried out with the stereoisomeric r-2-tert-butyl-4-methyl-trans-7-methyl[2]1,3-dioxepane.Translated from Teoreticheskaya i éksperimental'naya Khimiya, Vol. 22, No. 5, pp. 603–610, September–October, 1986.The authors express their gratitude to Academician B. A. Abruzov for constant interest in the work and to E. N. Klimovitskii for the synthesis of some of the investigated substances.     

Spin-lattice relaxation of radicals in the solid state. Part 3

Some causes of spin-lattice relaxation in the solid state are considered. It is found that anisotropic hyperfine interaction can make an appreciable contribution to the spin-lattice relaxation time, which becomes dependent on the orientation of the radical relative to the external field and on the number of HS components. There is no appreciable contribution from frequency modulation of the vibrations (of the radical as a whole or purely intramolecular) caused by the lattice vibrations.     

Magnetic hyperfine coupling of a methyl group undergoing internal rotation: a case study of methyl formate

The hyperfine structure of methyl formate was recorded in the 2-20 GHz range. A molecular beam coupled to a Fourier transform microwave spectrometer having an instrumental resolution of 0.46 kHz and limited by a Doppler width of a few kHz was used. A-type lines were found split by the magnetic hyperfine coupling while no splittings were observed for E-type lines. Symmetry considerations were used to account for the internal rotation of the methyl top and to derive effective hyperfine coupling Hamiltonians. Neglecting the spin-rotation magnetic coupling, the vanishing splittings of the E-type lines could be understood and analyses of the hyperfine patterns of the A-type lines were performed. The results are consistent with a hyperfine structure dominated by the magnetic spin-spin coupling due to the three hydrogen atoms of the methyl group.