Slawomir Szymanski

Nuclear magnetic resonance line shapes of methyl-like quantum rotors in low-temperature solids

Dissipative dynamics of a tunneling, methyl-like rotor, whose spatial coordinate is weakly coupled to a thermal bath, are described using the reduced density matrix (RDM) approach. It is found that, owing to selection rules imposed on thermally induced transitions by the symmetrization postulate, there are two sorts of coherences between the rotor eigenstates that live long enough to be observed on the nuclear magnetic resonance (NMR) time scale. One comprises degenerate pairs of Kramers sublevels at sequential librational levels of the rotor. The other involves nearly degenerate pairs each of which engages one Kramers sublevel and the remaining sublevel, separated from the Kramers doublet by tunneling quantum. These are the coherences which are seen in the inelastic neutron scattering (INS) patterns of methyl-like rotors. From the RDM equation of motion, augumented with spin-dependent terms relevant in the presence of an external magnetic field, the NMR line shape equation is derived. With no loss of inf...

Theory of thermal effects in nuclear magnetic resonance spectra of metal hydrides undergoing quantum mechanical exchange

Thermal effects in nuclear magnetic resonance spectra of transition metal hydrides exhibiting resolved quantum mechanical exchange splittings are consistently explained. Interactions of the relevant spatial degrees of freedom of the hydride protons with a quantum mechanical thermal bath are described in terms of Wangsness–Bloch–Redfield (WBR) theory. Upon elimination of the vibrational modes which relax too quickly to be observed on the NMR time scale, the WBR equation for the remaining, slowly relaxing modes (exchange modes) is shown to be equivalent to the Alexander–Binsch equation for classically exchanging nuclei, where the standard spin–spin coupling term is replaced by (or augmented with) quantum exchange term. Numerical calculations were performed for a one‐dimensional model of the relevant spatial motions, where the vibrational relaxation effects were described in terms of two adjustable parameters only. The assumed motion includes correlated rotation of a pair of the hydride protons, where the in...

Structure and NMR Spectra of Some (2.2)Paracyclophanes. The Dilemma of (2.2)Paracyclophane Symmetry

Density functional theory (DFT) quantum chemical calculations of the structure and NMR parameters for highly strained hydrocarbon [2.2]paracyclophane 1 and its three derivatives are presented. The calculated NMR parameters are compared with the experimental ones. By least-squares fitting of the (1)H spectra, almost all J(HH) coupling constants could be obtained with high accuracy. Theoretical vicinal J(HH) couplings in the aliphatic bridges, calculated using different basis sets (6-311G(d,p), and Huz-IV) reproduce the experimental values with essentially the same root-mean-square (rms) error of about 1.3 Hz, regardless of the basis set used. These discrepancies could be in part due to a considerable impact of rovibrational effects on the observed J(HH) couplings, since the latter show a measurable dependence on temperature. Because of the lasting literature controversies concerning the symmetry of parent compound 1, D(2h) versus D(2), a critical analysis of the relevant literature data is carried out. The symmetry issue is prone to confusion because, according to some literature claims, the two hypothetical enantiomeric D(2) structures of 1 could be separated by a very low energy barrier that would explain the occurrence of rovibrational effects on the observed vicinal J(HH) couplings. However, the D(2h) symmetry of 1 with a flat energy minimum could also account for these effects.

Nonclassical effects in liquid-phase nuclear magnetic resonance spectra of 9-methyltriptycene derivatives

The dynamics of strongly hindered methyl groups in 9-methyltriptycene derivatives, monitored by liquid-phase nuclear magnetic resonance spectra, were investigated using an iterative, least-squares method of line shape analysis. For two of the compounds, apart from nonclassical effects in the stochastic dynamics, anomalously strong dependence on temperature (ca. 0.05 and 0.08 Hz/K) of the J coupling between the methyl protons was observed. The latter effect was attributed to the occurrence of coherent quantum tunneling of the methyl rotor. For methyl group, this would be the first observation of coherent tunneling above cryogenic temperatures.

Insights into the Tautomerism in meso‐Substituted Corroles: A Variable‐Temperature 1H, 13C, 15N, and 19F NMR Spectroscopy Study

Tris(pentafluorophenyl)corrole and its (15)N-enriched isotopomer were studied in [D8]toluene solution by 1D and 2D variable-temperature NMR techniques to establish the mechanisms of tautomerization of the NH protons inside the interior of the corrole macrocycle. Three such rate processes could be identified of which two modulate the spectral line shapes at temperatures above 205 K and the third is NMR-inaccessible as it is very fast. The latter involves the proton engaged in an unsymmetrical proton sponge unit formed by two pyrrole nitrogen atoms. Temperature and concentration dependences of the two remaining processes were determined. One of them is purely intramolecular and the other is intermolecular at low temperatures, with growing contribution of an intramolecular mechanism at elevated temperatures. The proposed microscopic mechanisms of all these processes are semi-quantitatively confirmed by quantum chemical calculations using density functional theory.

A consistent treatment of coherent and incoherent nuclear exchange in a CD3 group

Abstract Variations with temperature of 2 H NMR single-crystal spectra of a CD 3 group undergoing coherent tunneling and incoherent reorientation are reproduced numerically using a two-parameter NMR lineshape equation involving spin variables only.

Spin-lattice relaxation study of the methyl proton dynamics in solid 9,10-dimethyltriptycene (DMT)

Proton spin-lattice relaxation studies are performed for powder samples of 9,10-dimethyltriptycene (DMT) and its isotopomer DMT-d(12) in which all the non-methyl protons in the molecule are replaced by deuterons. The relaxation data are interpreted in terms of the conventional relaxation theory based on the random jump model in which the Pauli correlations between the relevant spin and torsional states are discarded. The Arrhenius activation energies, obtained from the relaxation data, 25.3 and 24.8 kJ mol(-1) for DMT and DMT-d(12), respectively, are very high as for the methyl groups. The validity of the jump model in the present case is considered from the perspective of Haupt theory in which the Pauli principle is explicitly invoked. To this purpose, the dynamic quantities entering the Haupt model are reinterpreted in the spirit of the damped quantum rotation (DQR) approach introduced recently for the purpose of NMR lineshape studies of hindered molecular rotators. Theoretical modelling of the relevant methyl group dynamics, based on the DQR theory, was performed. From these calculations it is inferred that direct assessments of the torsional barrier heights, based on the Arrhenius activation energies extracted from relaxation data, should be treated with caution.

Structure and dynamics of [3.3]paracyclophane as studied by nuclear magnetic resonance and density functional theory calculations.

Strained cyclophanes with small (-CH(2)-)(n) bridges connecting two benzene rings are interesting objects of basic research, mostly because of the nonplanarity of the rings and of interference of π-electrons of the latter. For title [3.3]paracyclophane, in solutions occurring in two interconverting cis and trans conformers, the published nuclear magnetic resonance (NMR) data are incomplete and involve its partially deuterated isotopomers. In this paper, variable-temperature NMR studies of its perprotio isotopomer combined with DFT quantum chemical calculations provide a complete characterization of the solution structure, NMR parameters, and interconversion of the cis and trans isomers of the title compound. Using advanced methods of spectral analysis, total quantitative interpretation of its proton NMR spectra in both the static and dynamic regimes is conducted. In particular, not only the geminal but also all of the vicinal J(HH) values for the bridge protons are determined, and for the first time, complete Arrhenius data for the interconversion process are reported. The experimental proton and carbon chemical shifts and the (n)J(HH), (1)J(CH), and (1)J(CC) coupling constants are satisfactorily reproduced theoretically by the values obtained from the density functional theory calculations.

Nuclear-spin relaxation in nonrigid molecules: Discrete multisite local dynamics combined with anisotropic molecular reorientation

Nuclear-spin relaxation is considered in a molecular system undergoing two types of dynamic processes: asymmetric-top small-step rotational diffusion and discrete multisite local jumps. The two processes are assumed to be uncorrelated. Time correlation functions for relevant rank-two interactions and corresponding spectral density functions are derived for a general relation between the characteristic rate constants. In addition, limiting cases of fast and slow local motions and of some specific jump conditions are also investigated.

Theory of damped quantum rotation in nuclear magnetic resonance spectra. II. Numerical simulations for the benzene rotor

In Part I of this series of papers, the damped quantum rotation (DQR) theory, formulated originally for hindered threefold molecular rotors in solids, was generalized to the N-fold case. The stochastic dynamics of such objects, evidenced in NMR line shapes, was shown to be more complicated than in the standard model of classical jumps between the wells of the N-fold torsional potential. Actually, it comprises certain quantum rate (i.e., coherence-damping) processes subject to the requirements of the Pauli principle. The jump picture is recovered only when the quantum rates fit specific patterns. In this work, one of the ways of approaching such a classical limit is identified for the benzene rotor. This is inferred from a quantum mechanical model whose validity was earlier confirmed for a methyl group. Based on that model, theoretical calculations for the benzene ring dynamics in a clathrate crystal, 1-(9-anthryloxy)anthraquinone/benzene-d6, confronted with the pertinent literature data, point to possible deviations from the classical limit. However, the predicted DQR effects are too small to be observed in solid echo 2H NMR spectra of the C6D6 isotopomer. The chances of detecting the effects are improved when Carr-Purcell echo 1H spectra of a single crystal of the isotopomer including C6H6 as a guest are considered. The substantial differences in the sensitivity to the DQR effects of the spectra of protonated and deuterated benzene are concerned with different magnitudes of the intramolecular dipolar spin couplings. The dynamic isotope effect (C6D6 vs C6H6), which is small in this case, is only of secondary importance. Legitimacy of the use of the jump model in 2H NMR line shape studies of benzene-d6 is fully confirmed by the present considerations. However, the physical significance of the dynamic parameters extracted from such studies is shown from a new perspective.