Angular Momentum Correlation Times Research Articles

(Invited) Synthesis and Properties of Endohedral Open-Cage Fullerenes

Open-cage fullerene derivatives are fascinating molecules because a small molecule can be introduced inside the fullerene cage through the opening. When the NMR active molecules are introduced inside the open-cage fullerene derivatives, the resulting endohedral species are used for the study with the encapsulated molecule as a magnetic probe. First, the regioselectivity in the Diels.Alder reaction of an unsymmetrical open-cage C60 derivative with anthracene was studied. By using an encapsulated H2 molecule as a magnetic probe, the product population was successfully evaluated in detail, indicating the formation of approximately ten compounds as major components. The NICS calculations showed a close resemblance to the observed 1H NMR spectrum, which allowed for a facile characterization of the products. Theoretical studies on the formation of all 29 possible anthracene adducts were also performed. The results indicated that the regioselectivity is strongly governed by steric factors, values of the frontier orbital coefficients, and thermodynamic stabilities. Single-crystal X-ray analysis of the dominant compound revealed the supramolecular architecture between the anthracene moiety and the Π-sphere of a neighboring molecule.[1] Second, The H2O/CH2=CH2-type hydrogen-bonding model was experimentally constructed using a water complex of an open-cage C60 derivative, in which an olefinic double bond and a single molecule of H2O are geometrically confined. To investigate OH/Π-type H-bonding, we performed 1H NMR spectroscopic studies that demonstrated the monotonic downfield shift of the proton signal corresponding to H2O with remarkable rotational perturbation by lowering the temperature. From the temperature dependence of the angular momentum correlation time, the interaction energy was quantitatively estimated to be ca. 0.3 kcal/mol. The computational studies were thoroughly conducted to clarify its inherent nature. As a consequence, the orientation of H2O was found to play a prominent role in varying the bonding strength as well as contribution from the electrostatic attraction and orbital-orbital interaction significantly driven by the favorable orbital overlap.[2][1] Probing the Regioselectivity by Encapsulated H2: Diels-Alder Reaction of a Cage-Opened C60 Derivative with Anthracene, Hashikawa, Y.; Murata, Y. Chem. Eur. J. 2019, 25, 2482-2485.[2] H2O/Olefinic-Π Interaction inside a Carbon Nanocage, Hashikawa, Y.; Murata, Y. J. Am. Chem. Soc. 2019, 141, 12928-12938.

H2O/Olefinic-π Interaction inside a Carbon Nanocage.

The H2O/CH2═CH2-type hydrogen-bonding (H-bonding) model was experimentally constructed using a water complex of an open-cage C60 derivative, in which an olefinic double bond and a single molecule of H2O are geometrically confined. To investigate OH/π-type H-bonding, that is, H2O···(C═C) interaction, we performed 1H NMR spectroscopic studies that demonstrated the monotonic downfield shift of the proton signal corresponding to H2O with remarkable rotational perturbation by lowering the temperature. From the temperature dependence of the angular momentum correlation time (τJ), the interaction energy was quantitatively estimated to be ca. 0.3 kcal/mol. The computational studies were thoroughly conducted to clarify its inherent nature. As a consequence, the orientation of H2O was found to play a prominent role in varying the bonding strength as well as contribution from the electrostatic attraction and orbital-orbital interaction significantly driven by the favorable orbital overlap identified as π(C═C) → σ*(OH) interaction.

Determination of the singlet state lifetime of dissolved nitrous oxide from high field relaxation measurements

Longitudinal spin relaxation due to modulation of dipolar interactions often limits the development of hyperpolarized magnetic tracers. Recently, it has been demonstrated that transferring spin order to a singlet state significantly increases the polarization lifetimes in systems where nitrous oxide is dissolved in a liquid solvent. Additionally, previous studies have suggested that the longitudinal relaxation of nitrous oxide is largely dominated by the spin-rotation interaction. Models of spin-relaxation under Brownian motion naïvely predict the angular momentum reorienting correlation time of the spin rotation interaction to be inversely proportional to the viscosity of the solution. This dependence implies the singlet lifetime can be lengthened by increasing the dissolving solvent's viscosity-an extension which is not observed. Our work formulates a model which describes the relaxation of nitrous oxide dissolved in various solvents. We investigate the effect of altering the temperature of the solvent, as well as the effect of varying solute-solvent interactions on the singlet state as well as the longitudinal polarization lifetime. We predict the singlet lifetime for nitrous oxide dissolved in several solvents by fitting rotational and angular momentum correlation times measured at high magnetic field, and relate singlet relaxation to translational diffusion constants.

Structural study of supercritical water. III. Rotational dynamics

The rotational dynamics of water in super- and subcritical conditions is investigated by measuring the spin-lattice relaxation time T1 of heavy water (D2O). The experimentally determined T1 is shown to be governed by the quadrupolar relaxation mechanism even in the supercritical conditions and to provide the second-order reorientational correlation time τ2R of the O–D axis of a single water molecule. It is then found that while τ2R decreases rapidly with the temperature on the liquid branch of the saturation curve, it remains on the order of several tens of femtoseconds when the density is varied up to twice the critical at a fixed supercritical temperature of 400 °C. The comparison of τ2R with the angular momentum correlation time shows that the rotational dynamics is not diffusive in supercritical water. The dependence of τ2R on the hydrogen bonding state is also examined in combination with molecular dynamics simulations, and the effect of the hydrogen bonding on the rotational dynamics in supercritical water is found to be weaker than but to be on the same order of magnitude as that in ambient water on the relative scale. Actually, although τ2R is divergent in the limit of zero density, it is observed to increase with the density when the density is above ∼1/3 of the critical.

Effect of liquid to solid phase transition on rotational and vibrational broadening of vibrational bands of CF 3CL in Xe solutions

Fundamental and second order bands of CF 3Cl dissolved in Xe solutions have been studied near the melting point by using technique of transparent solid sample growth from the liquid rare gas solution. The widths at half maximum 2 Γ of the bands were noticeably decreased after crystallization, especially in the case of the broadest 2 ν 4( E) band. Experimental data have been interpreted in the framework of Debye limit (〈 ω〉 τ J ≪1) for the J-model of a heavy symmetrical top rotation. Additional broadening, caused by fluctuational mechanisms of vibrational relaxation, was taken into account. Angular momentum correlation times ( τ J⊥ and τ J∥ ) and parts of widths, originated from vibrational relaxation, were estimated for the liquid and solid Xe solutions near the melting point. The results obtained have shown decreasing effect of fluctuational broadening and increasing disturbance of rotational motion of CF 3Cl when going from the liquid Xe solution to the crystal state.

流体のダイナミクス 超臨界水の動的構造解析

The rotational dynamics of water in super- and subcritical conditions is investigated by measuring the spin-lattice relaxation time T1 of heavy water (D2O). The experimentally determined T1 is shown to be governed by the quadrupolar mechanism even in the supercritical conditions and to provide the second-order reorientational correlation time τ2R of the O-D axis. It is then found that while τ2R decreases rapidly with the temperature on the saturation curve, it remains on the order of several tens of femtoseconds when the density is varied at a temperature above the critical. The comparison of τ2R with the angular momentum correlation time shows that the inertial effect is operative in the rotational dynamics of supercritical water. The dependence of τ2R on the hydrogen bonding state is also examined in combination with computer simulations, and the effect of the hydrogen bonding on the rotational dynamics in supercritical water is found to be weaker than but to be on the same order of magnitude as that in ambient water on the relative scale. Actually, although τ2R is divergent in the limit of zero density, it is observed to increase with the density when the density is above ∼1/3 of the critical.

Extended diffusion theory of reorientation of symmetric top molecules with internal rotation: application to mesitylene

Our general extended diffusion theory for the reorientational dynamics of a symmetric top molecule with internal rotation is applied to mesitylene which is an oblate symmetric top. The basic idea of independent extended J-diffusion of both the overall and internal rotations with the different angular momentum correlation times is implemented in the theory. The resulting expressions for the dipole-dipole relaxation times for 13C nuclei are evaluated numerically and compared with NMR experiments on mesitylene. The angular momentum correlation times obtained from the comparison show that internal rotation is much faster than the overall rotation.

Quenched molecular reorientation and angular momentum for liquids confined to nanopores of silica glasses

The results of a theoretical and experimental study of the confinement effects on molecular dynamics of nonpolar liquids in porous silica glasses prepared by the sol-gel process are discussed. The natural abundance 13C and 33S NMR spin-lattice relaxation times of liquid CS2 are reported as a function of pore radius in the range from 15 Å to 102 Å over the temperature range of 168 K to 293 K. Since spin-rotation interactions dominate the 13C relaxation at higher temperatures these experiments allowed us for the first time to follow the confinement effects on angular momentum correlation times. The low-temperature 13C T1 data and the 33S T1 data provide information about reorientational motions. In order to interpret the experimental NMR relaxation data, a theoretical model for anisotropic molecular reorientation and angular velocity, which accounts for the motional behavior of nonpolar liquids confined to nanopores, is proposed. This model predicts an increase of the reorientational and angular momentum correlation times when the pore size is decreased. Application of this theoretical model to the interpretation of the CS2 NMR relaxation data and to earlier relaxation results obtained for confined nonpolar cyclohexane-d12 liquid proved successful.

Extended diffusion theory of reorientation of symmetric top molecules with internal rotation

The extended diffusion (ED) theory for the reorientational dynamics of a symmetric top molecule with internal rotation is reinvestigated. Based on a unified ED picture, we express, by using the convolution theorem of the Laplace transform, the reorientational correlation time with overall and internal free rotor correlation functions. In this work, Bull’s “equal angular momentum correlation time assumption” for both overall and internal rotations is removed. Limiting expressions, for diffusion limit of the overall rotation, are derived and shown to reduce to the results of previous works. As an application, our numerical calculations are compared with experiments on 13C nuclear-magnetic-resonance dipolar relaxation times of toluene. Angular momentum correlation times, thus obtained from the comparison, show that our calculations agree with the previous work of Chung et al.[Chem. Phys. Lett. 93, 499 (1982)].

Study of solvent-solute and solute-solute interaction effects on naphthalene in carbon dioxide by NMR measurement of rotational ang angular momentum correlation times in CO 2 at sub- and supercritical temperatures

The effect of temperature variation from subcritical to supercritical conditions on the rotational and angular momentum correlation times of naphthalene dissolved in carbon dioxide is reported. The rotational correlation time, τ c is found to be only slightly dependent upon solution viscosity, unaffected by the CO 2 phase change at about 32°C and is essentially equal to its value in acetone at the same temperature. τ c is approximately twice its gas phase free rotor time. These results are interpreted to indicate that ground state solute-solute interactions are unimportant. The angular momentum correlation time, τ j , undergoes a dramatic increase at the temperature of the phase change indicating an approximately 3.2 fold solvent density augmentation around the naphthalene compared to the bulk gas phase CO 2 density under the experimental conditions beyond the critical temperature. These results indicate that a substantial solvent density augmentation occurs that does not cause measurable changes in the rotational properties of the solute. The solvent augmentation is found to disappear within approximately 2°C on either side of the critical temperature.

Activated rotational diffusion in solids

Rotation of a molecule in a solid is strongly suppressed due to the corrugated potential created by the crystal and is reduced to small librations around quasistable positions with infrequent jumps between them. We study how the interaction with the crystal vibrations influences the rotational relaxation of the molecule. A simple model, in which the molecular rotation is described by a 1-D Langevin equation, is considered. The analytic expressions for the orientational and angular momentum correlation times are obtained. The Hubbard relation, which was established for dense gases and liquids, is shown to be valid for solids in the intermediate-to-high damping regime and to be violated at sufficiently low damping.

MD simulation of rotational relaxation in liquid nitrogen. Comparison with NMR and Raman data

A simulation of liquid nitrogen has been performed along the coexistence curve. Angular momentum, rotational energy and second-order orientational correlation times τ J , τ E , τ θ,2 were calculated. The first and the last were compared with the available data. The results for τ E were compared with halfwidth data from the isotropic Raman scattering measurements. For the entire coexistence curve, the validity of stochastic perturbation theory was shown: ω Qτ E <1, where ω Q is an average frequency of the Q branch. The rotational contribution to the halfwidth (estimated from the extreme narrowing formula) decreases with cooling, but does not become less than 25% of the whole width. The ratio τ E /τ J varies from 1.7 to 1 in the region between the critical and the triple points, which is inconsistent with the Langevin description of the angular momentum relaxation.

Vibrational and reorientationl relaxation in liquid tert-butyl bromide and tert-butyl bromide- d9

The vibrational and reorientational correlation functions of the ν s(CBr) mode in liquid tert-butyl bromide (TBBr) and in its deuterated analogue (TBBr- d 9) were determined from Raman bandshapes. The Kubo product δτ m obtained by fitting the Rothschild equation to experimental data amounts to 0.36–0.45 for the studied bands, which indicates a fairly fast modulation regime in these systems. The approximation of experimental rotational correlation functions with the help of the J-diffusion model yields values of 0.11–0.12ps for the angular momentum correlation time. The second-order rotational correlation times (1.7–2.0ps) agree well with the NMR results of D.W. Aksnes, K. Ramstad and O.P. Björlykke, Magn. Reson. Chem., 25 (1987) 1063. Selected bandshape parameters for δ(CCC) in both compounds, ϱ(CH 3) in TBBr and ν s(CC) in TBBR- d 9 were also quoted.

Studies of rotational relaxation at low viscosity: Ethane

We have measured the 13C NMR T 1 relaxation time for ethane in the temperature range from 172 to 323 K. From the T 1 data we have extracted the rotational correlation time, τ c, and the angular momentum correlation time, τ J τ c at the lowest viscosities is equal to the free-rotor correlation time for ethane within the experimental error and does not display an increase in the rotational time at extremely low viscosity. As the viscosity increases τ c shows an increase and approaches the Stokes-Einstein-Debye result. τ J decreases with increasing viscosity.

Impact description of the poley absorption

The impact theory is used for spectral band shape description for the liquid phase, the multiplication of averaged rotational frequency and angular momentum correlation time being small. The physical difference between liquid and gas interactions is taken into account by introducing the non-Poisson statistics for the time succession of collisional events and preferable reflection for rotational changes by impact. On this basis, it proved to be possible to propose a quite simple unified explanation for the Poley absorption in dielectric losses and far infrared spectra along with the R(ν) representation of the depolarized Rayleigh scattering.

Nuclear spin relaxation in some phenyl phosphorus compounds

13C and 31P spin-lattice relaxation times ( T1) and nuclear Overhauser effects were measured in triphenylphosphine, triphenylphosphine oxide, triphenylphosphine sulphide, and triphenylphosphine selenide, over a temperature, range −40°C to +55°C. Isotropic reorientation correlation times were calculated from the dipolar relaxation times for phosphorus and that for the para carbon. The spin-rotation mechanism is the dominant relaxation mechanism for phosphorus in triphenylphosphine, whereas the chemical shift anisotropy is the dominant mechanism in triphenylphosphine oxide at low temperatures. In triphenylphosphine sulphide and triphenylphosphine selenide, the dipolar and the chemical shift anisotropy mechanisms are important in phosphorus relaxation. The motional anisotropy of internal rotation of phenyl rings and overall tumbling is determined from the ratio of T 1's of ortho or meta carbon to para carbon, and is found to increase with the decrease in temperature and with the increase in mol. wt. The angular momentum correlation times were calculated from phosphorus spin-rotation relaxation rates. From viscosity data, reduced correlation times were calculated and compared with that calculated using Stokes-Einstein-Debye, Gierer-Wirtz, and Hu-Zwanzig models.

Fokker—Planck—Langevin and extended diffusion models of internal rotation in molecules. I. symmetric internal rotor

The effects of internal rotation in molecules containing a symmetric internal rotor have been investigated using both the Fokker—Planck—Langevin (FPL) and extended diffusion (EDJ) models of collision dynamics. Sample calculations are presented illustrating the effects of the magnitude of the internal barrier to rotation, the magnitude of the internal angular momentum correlation time, and the collision model chosen on correlation times and factors of importance to NMR relaxation. These include second-rank reorientational correlation times, dipole—dipole relaxation spectral densities (including the effects of modulation of the internuclear distance), and spin-rotational correlation factors. The presentation concentrates on the case where internal and overall motions are decoupled, but a general expression for the Liouville operator of an asymmetric molecule with a symmetric internal rotor is derived and the associated collision operators are discussed. The results show that the correlation times and factors are quite sensitive to the size of the barrier and the internal angular momentum correlation time.

Raman study of rotational motions of hydrogen sulphide in the liquid state

Raman spectra of liquid H2S and D2S at various temperatures are analysed. The band profiles have a rotational origin and are compared with those calculated by the J extended diffusion model for an asymmetric rotor. The values obtained for the angular momentum correlation time correspond to a large angle rotational diffusion. The rotational motion is discussed in terms of the Chandler model for translational diffusion.

A nuclear magnetic resonance relaxation study of liquid hydrogen cyanide

The rates of 2H, 13C, and 14N spin-lattice relaxation for liquid deuterium cyanide have been studied as a function of temperature. The quadrupolar nuclei relax exclusively by the quadrupolar relaxation mechanism while the rate of 13C and 15N relaxation is completely dominated by the spin-rotation mechanism. The apparent activation energy that describes the temperature dependence of spin-lattice relaxation for all nuclei studied is approximately 1.6 kcal mol−1. The temperature dependence of the rate of 13C relaxation in liquid HCN was also investigated. Although the determination of very accurate rotational and angular momentum correlation times is hampered by intermolecular effects on the nuclear quadrupolar coupling constants and the appropriately averaged C—H bond separation, the derived correlation times for DCN and HCN are in reasonable agreement (± 15%).

Nuclear relaxation and molecular motion of 1,3,5-trifluorobenzene- d3 in liquid solutions

The 2D and 19F spin-lattice relaxation times of 1,3,5-trifluorobenzene- d 3 in 0.15 mol fraction solutions in various solvents have been measured over the temperature range 270–400 K. The relationship between the reorientational correlation times, τ θ, and the angular momentum correlation times, τ J , obtained from the nuclear relaxation data has been compared with the theoretical relationships predicted by the J-diffusion limit of the extended diffusion (ED J) model and the Fokker-Planck-Langevin (FPL) model for symmetric top molecules. It was found that the rotational motion of 1,3,5-trifluorobenzene- d 3 in most solutions was better described by the FPL model with frictional anisotropy τ ‖/τ · in the range 1–2. (τ ‖ and τ · are the correlation times for the angular velocity components along the axes parallel and perpendicular to the molecular symmetry axis.) The viscosity and temperature dependence of τ θ has been analyzed in terms of a modified Debye equation and values for the anisotropic interaction parameter, κ, in each solvent are reported. The variation in κ with solvent is attributed mainly to the variation in the dipole moment of the solvent molecules. The frictional anisotropy (τ ‖/τ ·) is found to decrease as κ increases. This is interpreted in terms of the effects of molecular shape and electrostatic interactions between CF bond dipole moment and solvent dipole moments.