Carbon-13 spin–lattice relaxation in some polyfluoroaromatic compounds

Carbon-13 chemical shifts, spin-lattice relaxation times and nuclear Overhauser enhancement factors are reported for five polyfluoroaromatic compounds at 28°C. In all cases the relaxation of the fluorine bearing carbon is predominantly dipolar. Effective correlation times are smaller than those of the analogous benzene derivatives by a factor of 3–4, in qualitative agreement with predictions from the Stokes–Einstein diffusion theory. The T₁ values for the para-carbon of monosubstituted fluorobenzenes is clearly shorter than the T₁ values for the ortho- and meta-carbons. This phenomenon was traced to anisotropic tumbling, and D∥ and D⊥ diffusion coefficients were computed using Woessner's equations for molecules assumed to behave like symmetric rotors about their C₂ in-plane principal symmetry axis. Equal tumbling ratios, D∥/D⊥, were found in this way for toluene and perfluorotoluene.     

Carbon-13 spin–lattice relaxation times as a probe for the study of electron donor–acceptor complexes

¹³C spin–lattice relaxation times (T₁'s) are reported for C-3 of 2-methylindole (methyl,3-¹³C₂) as a function of the concentration of added 1,3,5-trinitrobenzene at 35°C in 1,2-dichloroethane. The observed decreases in T₁, with increasing concentrations of 1,3,5-trinitrobenzene, are interpreted in terms of longer time-averaged correlation times which result from (a) the formation of increasing amounts of electron donor–acceptor complex and (b) increases in viscosity. An equation is derived which makes it possible to obtain estimates of the equilibrium constant for complex formation, and the spin–lattice relaxation time of the complex, from the observed T₁'s and viscosity measurements. From the data obtained, values of 6.4 × 10^?12 and 14.1 × 10^?12 s rad^?1 were calculated for the effective correlation times (at 35°C and 0.686 centipoise) and 0.21 and 0.28 nm for the effective radii of free and complexed donor respectively.     

Carbon-13 spin–lattice relaxation of tropane alkaloids. Anisotropic rotational motion of tropine and pseudotropine

The ¹³C spin–lattice relaxation times of tropine and pseudotropine have been measured in CDCl₃ as a function of concentration. The same relative increase in concentration serves to increase the relaxation rates much less in the region 0.9–5.0 wt.% than in the region 5.0–14.3 wt.%. The rotational diffusion coefficients have been calculated from the relaxation data using Woessner's anisotropic rotational diffusion model. Reorientation of both molecules is shown to be moderately anisotropic. The principal axes of the rotational diffusion tensor in the symmetry plane of both molecules are rotationally shifted from the principal axes of the moment of inertia tensor of the free molecules, and the main rotational axis is parallel with a line passing through the centre of mass of the molecule and the nitrogen atom.     

Solid state proton spin–lattice relaxation in four structurally related organic molecules

We report and interpret the temperature dependence of the proton spin–lattice relaxation rate at 8.50 and 22.5 MHz in four polycrystalline solids composed of structurally related molecules: 2-ethylanthracene, 2-t-butylanthracene, 2-ethylanthraquinone, and 2-t-butylanthraquinone. We have been unable to grow single crystals and therefore do not know the crystal structures. Hence, we use the NMR relaxometry data to make predictions about the solid state structures. As expected, we are able to conclude that the ethyl groups do not reorient in the solid state but that the t-butyl groups do. The anthraquinones have a “simpler” structure than the anthracenes. The best dynamical models suggest that there is a unique crystallographic site for the t-butyl groups in 2-t-butylanthraquinone and two sites, each with half the molecules, for the ethyl groups in 2-ethylanthraquinone. There are also two sites in 2-ethylanthracene, but with unequal weights, suggesting four sites in the unit cell with lower symmetry than the two anthraquinones. Finally, the observed relaxation rate data in 2-t-butylanthracene is very complex and its interpretation demonstrates the uniqueness problem that arises in interpreting relaxometry data without the knowledge of the crystal structure.     

NMR spin–lattice relaxation time measurements in organochalcogen compounds

¹H and ⁷⁷Se spin-lattice relaxation times have been measured for the series of organochalcogen compounds MeE(CH₂)nEMe (E=S, Se, n=0–3; E = O, n = 1, 2). The methyl and methylene proton T₁ values decreased with increasing mass/size of the chalcogen and with increasing methylene chain length. The values are primarily due to intra- and inter-molecular dipole-dipole relaxation with proton-proton cross-relaxation effects playing a significant role. ⁷⁷Se T₁ values are dominated by spin rotation and chemical shielding anisotropy mechanisms, their relative importance depending on the size of the molecule and temperature of measurement.     

Carbon-13, 1H spin–spin coupling VI—biphenylene

¹³C, ¹H coupling constants for biphenylene have been obtained from the analysis of the ¹³C NMR spectrum of the natural abundance α-¹³C- and β-¹³C-isotopomers. The various mechanisms responsible for the observed results are discussed.     

Intramolecular interactions and spin–lattice relaxation times of methyl groups

The carbon T₁ values of the alkyl substituents of various compounds have been measured. The salient observation is that the terminal methyl carbon of the n-propyl or a three-carbon chain bonded to an electronegative atom X(or an electron-donating group) has a reduced T₁ value. A net attractive interaction between the methyl hydrogen atoms and X in the gauche conformation is invoked to account for the observed result. In chains longer than three carbons that are not firmly anchored at one end, the γ steric interaction is suggested to be the main steric interaction that causes the reduced T₁ value observed for the terminal methyl carbon.     

13C and 15N spin–lattice relaxation and chemical shift studies of pentane-2,4-diamine

¹³C and ¹⁵N NMR chemical shift and spin–lattice relaxation data have been measured for both meso- and racemic-pentane-2,4-diamine. At high pH (12), relaxation is consistent with hindered rotation of the NH₂ group due, in part, to the formation of intramolecular hydrogen bonds. At low pH (2), relaxation is consistent with relatively unhindered rotation of the NH₃⁺ group. Rotational jump rates and barriers are reported, determined from the NT₁ ratios between ¹⁵N and ¹³C nuclei. In all cases, the ratios for the racemic diastereomer are higher than those of the meso compounds; this is interpreted in terms of conformationally more stable intramolecular hydrogen bond formation in the meso compound. Chemical shifts for the diastereomeric amines show that ¹⁵N shifts move downfield on protonation along with methyl and methylene carbons, while the methine carbon resonances move upfield.     

Carbon-13, proton spin–spin coupling constants in some 2-substituted propanes

Carbon-13, proton coupling constants have been measured in eighteen different 2-substituted propanes. ¹J(C-2,H) shows variations similar to those observed previously for monosubstituted methanes. ²J(C-2,H) is essentially independent of the substituent at C-2, while ²J(C-1,H) varies over a range of at least 5 Hz. The latter coupling constant becomes more positive as the electronegativity of the substituent increases while ³J(CH) decreases as the electronegativity of the substituent increases. The observed trends in ⁿJ(CH) are compared with those calculated using semi-empirical molecular orbital theory at the INDO level of approximation.     

Natural-abundance lithium-6 NMR spin–lattice relaxation in some simple organolithium compounds

⁶Li, ⁷Li and ¹³C spin–lattice relaxation and NOE data are reported for methyllithium, butyllithium and phenyllithium with ⁶Li T₁ values found in the order of tens of seconds and their relaxation 2–3 orders of magnitude less efficient than that for ⁷Li. The data indicate that ⁶Li is substantially relaxed by the intramolecular ⁶Li–¹H mechanism, whereas both quadrupolar and ⁶Li–⁷Li dipolar relaxation are minor processes. The non-linearity of the Arrhenius curve for Me⁶Li is compatible with a small spin–rotation contribution. Since ⁶Li in solution behaves essentially as a spin-1/2 nucleus, it represents, in spite of its lower magnetic moment and overall sensitivity, an attractive alternative to ⁷Li NMR.     

A general survey of the proton spin–lattice relaxation rates of steroids

The spin-lattice relaxation rates of the aromatic, alkene, hydroxyl, methine and methyl protons of 19 steroid derivatives have been measured using the null point method. A simple procedure is described whereby the R₁ values of molecules which have different motional tumbling rates can be directly inter-compared, and it is shown that such ‘normalized’ relaxation data can provide novel insight concerning both the geometry and the local molecular motion of these substances in solution.     

119Sn spin–lattice relaxation times and nuclear Overhauser enhancement factors in some organotin compounds

Dipole-dipole relaxation via non-bonded protons is an important relaxation mechanism for¹¹⁹Sn in tri-n-propyltin and tri-n -butyltin compounds. This causes a negative nuclear Overhauser effect, arising from the negative magnetogyric ratio, which in some cases nulls the signal. The relative contributions from the spin-rotation and dipole-dipole mechanisms vary: larger molecules have lower spin-rotation and higher dipolar relaxation rates. The practical significance of large nuclear Overhauser enhancement factors in recording ¹¹⁹Sn spectra and the relation of the dipole-dipole contribution to the molecular motion and of the spin-rotation contribution to the absolute shift scale for ¹¹⁹Sn are discussed.     

Carbon-13 NMR relaxation and transitions in polymers

High-resolution proton-decoupled carbon-13 nuclear magnetic resonance relaxation parameters have been obtained as a function of temperature for a set of completely amorphous polymers, semicrystalline polymers, and a series of ethylene–vinyl acetate copolymers. With these samples the nature of the glass temperature, other postulated amorphous transitions, and the β transition were investigated. For the completely amorphous polymers, the average correlation times depend on temperature according to the Williams–Landel–Ferry relation. Spectral collapse occurs at temperatures whose ratio to T_g is in the range 1.2–1.4 and corresponds to a correlation time of about 10^?7s. The loss of resolvable spectra is demonstrated to be a consequence of experimental methods and is not due to the occurrence of another amorphous transition. Both the methylene and methine carbons can be resolved for the ethylenevinyl acetate copolymers. Although the correlation time for the methylene carbon is continuous and resolvable through the β transition region, the methine branch-point resonance is lost. The implication of these results to the molecular nature of the β transition is discussed.     

Unexpected proton spin‐lattice relaxation in the solutions of polyolefin and tetrachloroethane

‘Unexpected’ proton spin‐lattice relaxation (T₁) times are reported for the solutions of poly(ethylene‐co‐1‐octene) and tetrachloroethane‐d₂. For the residual protons of the deuterated solvent and the methyl and vinyl protons at the polymer chain ends, their T₁ relaxation times vary significantly with both the polymer concentration and molecular weight over a wide range. The T₁s also decrease with increasing temperature at relative high temperatures. Such behaviors are in contrast to most reported polymer solutions in which the T₁ has nearly no concentration or molecular weight dependence in the dilute and semi‐dilute regime, and normal dependence on temperature. Further investigation revealed that the paramagnetic oxygen effect did shorten the measured proton T₁s, but cannot account for the unexpected T₁ dependences. Spin rotation is proposed to provide a reasonable explanation. Copyright © 2010 John Wiley & Sons, Ltd.     

NMR spin–spin relaxation in solid and molten polyethylene structures

The NMR spin-spin relaxation (T₂) spectra of high-density polyethylene (PE) has been investigated over a wide range of temperatures, both in the solid and molten states. Previous work in these laboratories has shown that the T₂ relaxation spectrum of molten polyethylene differs from that of other polymers studied in that (a) it cannot be decomposed into two relaxation spectra (T_2S and T_2L) and (b) there is some evidence of a memory effect. This paper attempts to elucidate these observations, and compare them with the spin-spin relaxation of polyethylene at lower temperatures. In the solid state, the T₂ decay comprises both a Gaussian distribution for the crystalline region, and an exponential decay for the amorphous component. The effects of crystallization conditions and of temperature were determined. In the molten state the T₂ decay is more complex, but can be resolved into three exponentials. The longest (T_2L) component arises as expected from the most mobile, low molecular weight fraction. The T_2S component is due to an entangled but mobile network, as in other polymers. In addition, a short relaxation component T_2X is observed, which is influenced by previous crystallinity and the processing history of the material, and is ascribed to some vestigial degree of structure in the molten phase.     

Carbon-13–fluorine-19 coupling constants in benzotrifluorides

The carbon–fluorine coupling constants in 33 different substituted benzotrifluorides (trifluoromethyl-benzenes) have been determined. The ³J(CF) to the ortho aromatic ring carbons varied between 1.7 and 5.6 Hz and, in a given molecule, were always larger than the ⁵J(CF) to the para carbon, which ranged between 0.7 and 1.7 Hz. Coupling to the meta carbons, ⁴J(CF), was not observed and is under 0.3 Hz.     

Carbon-13 and aluminium-27 nuclear spin relaxation in triethylaluminum

Carbon-13 spin–lattice relaxation times and nuclear Overhauser enhancement factors are reported for triethylaluminium in toluene-d₈ solution in the temperature interval 208–318 K. Aluminium-27 linewidths are reported for the same solution in the temperature range 212–334 K. The effective correlation times at different positions in the molecule are determined and used for qualitative discussion of internal motions.     

Carbon-13 spin-lattice relaxation study of linear polymers in solution

Proton-decoupled, partially relaxed, Fourier-transform NMR of ¹³C in natural abundance was used to determine spin-lattice relaxation times of individual carbons of polyisobutylene, polyacrylonitrile, poly(vinyl chloride), and poly(vinyl alcohol) in solution. It is shown that the relaxation times are independent of the difference in stereochemical configuration. From the values of the nuclear Overhauser enhancement factor it is shown that the relaxation times are independent of the difference in stereochemical configuration. From the values of the nuclear Overhauser enhancement factor it is shown that the excess spin energy from equilibration of all the ¹³C, even of quaternary carbons, in the polymers dealt with here is transferred to the lattice mainly through ¹³C-¹H dipolar interactions. It is shown that the segmental motions responsible for the spin-lattice relaxation of the polymer skeleton in solution can be described by the isotropic model within a good approximation, except for poly(vinyl alcohol) at low temperature. The activation energies of skeletal and internal methyl motions are estimated from the temperature dependence of the correlation time. Differences in the ¹³C line widths for individual carbons of polyisobutylene are discussed briefly.     

Chemical control of spin–lattice relaxation to discover a room temperature molecular qubit

The second quantum revolution harnesses exquisite quantum control for a slate of diverse applications including sensing, communication, and computation. Of the many candidates for building quantum systems, molecules offer both tunability and specificity, but the principles to enable high temperature operation are not well established. Spin–lattice relaxation, represented by the time constant T₁, is the primary factor dictating the high temperature performance of quantum bits (qubits), and serves as the upper limit on qubit coherence times (T₂). For molecular qubits at elevated temperatures (>100 K), molecular vibrations facilitate rapid spin–lattice relaxation which limits T₂ to well below operational minimums for certain quantum technologies. Here we identify the effects of controlling orbital angular momentum through metal coordination geometry and ligand rigidity via π-conjugation on T₁ relaxation in three four-coordinate Cu²⁺S = ½ qubit candidates: bis(N,N′-dimethyl-4-amino-3-penten-2-imine) copper(ii) (Me₂Nac)₂ (1), bis(acetylacetone)ethylenediamine copper(ii) Cu(acacen) (2), and tetramethyltetraazaannulene copper(ii) Cu(tmtaa) (3). We obtain significant T₁ improvement upon changing from tetrahedral to square planar geometries through changes in orbital angular momentum. T₁ is further improved with greater π-conjugation in the ligand framework. Our electronic structure calculations reveal that the reduced motion of low energy vibrations in the primary coordination sphere slows relaxation and increases T₁. These principles enable us to report a new molecular qubit candidate with room temperature T₂ = 0.43 μs, and establishes guidelines for designing novel qubit candidates operating above 100 K.

Elucidating the role of specific vibrational modes in spin lattice relaxation is a key step to designing room temperature qubits. We executed an experimental and theoretical study on a series of Cu²⁺ qubits to increase their operating temperature.