Spin-lattice relaxation by tunnelling motions of methyl groups in four acetates

Thermal properties of Zn2(C8H4O4)2•C6H12N2 metal-organic framework compound and mirror symmetry violation of dabco molecules

Thermal properties of Zn₂(C₈H₄O₄)₂•C₆H₁₂N₂ metal-organic framework compound at 8-300 K suggest the possibility of subbarrier tunnelling transitions between left-twisted (S) and right-twisted (R) forms of C₆H₁₂N₂ dabco molecules with D₃ point symmetry. The data agree with those obtained for the temperature behavior of nuclear spin-lattice relaxation times. It is shown that there is a temperature range where the transitions are stopped. Therefore, Zn₂(C₈H₄O₄)₂•C₆H₁₂N₂ and related compounds are interesting objects to study the effect of spontaneous mirror-symmetry breaking and stabilization of chiral isomeric molecules in solids at low temperatures.

Complex mechanism of relaxation in solid chloroxylenol (antibacterial/antifungal agent) studied by ¹H NMR spectroscopy and density functional theory calculations

Molecular relaxation in antibacterial/antifungal agent: chloroxylenol (4-chloro-3,5-dimethylphenol, PCMX) in the solid state was studied by the (1)H NMR and quantum chemistry calculations. The temperature dependencies of the proton spin-lattice relaxation time (T1) in the ranges 15-273 K (at 24.667 MHz), 77-295 K (at 15 MHz), and 112-291 K at 90 MHz and the second moment (M2) of (1)H NMR resonant line in the range 106-380 K were measured. The two minima in the temperature dependence of T1 revealed two activation processes, whereas the M2 dependence in the studied range was quite flat and revealed the only significant reduction at 380 K. The low temperature part of T1(T) dependence indicated the occurrence of two processes characteristic of methyl bearing solids; the quantum mechanics governed incoherent tunneling (responsible for the low temperature flattening of T1) and the classical Arrhenius dependence governed hindered rotation (related to the wide low temperature minimum of 0.066 s at 57 K, 24.667 MHz). The 2D potential energy surface obtained using DFT/B3LYP/6-311++G(2d,p) calculations revealed the inequivalence of methyl groups and the lack of their interplay/coupling. The activation energies of classical hindered rotation are 3.35 and 2.5 kJ/mol, whereas temperatures at which the proton tunneling T(tun) finally ceases are 52 and 63 K, for inequivalent methyl groups. C(p)(T) required for the estimation of T(tun) was calculated purely theoretically on the basis of the Einstein and Debye models of specific heat and 51 modes of atomic vibrations, 4 internal rotations, and 3 torsions calculated by DFT. The -CH3 motion (tunneling and classical) results in the reduction in the (1)H NMR line second moment from 17.3 G(2) (rigid) to approximately 11.05 G(2). The pointed high temperature minimum T1(T) of 0.109 s at 89 K, 24.667 MHz, which shifts with frequency, was assigned to small-angle libration jumps, by the Θ2 = ±15° between two positions of equilibrium. The activation energy of this motion estimated on the basis of the fit of the theoretical model to the experimental points is 10.5 kJ/mol. The reduction in the (1)H NMR line second moment assigned to this motion is much lower (due to order parameter s = 0.64) and equal to 1.6 G(2). The high temperature reduction from 9.6 G(2) to 0.9 G(2) at 380 K is a result of the phase transition connected with melting (385-389 K).

Proton dynamics at low and high temperatures in a novel ferroelectric diammonium hypodiphosphate (NH4)2H2P2O6 (ADhP) as studied by 1H spin-lattice relaxation time and second moment of NMR line

Proton spin-lattice relaxation times T1 at 24.7 MHz and 15 MHz and second moment of NMR line have been applied to study molecular dynamics of a novel ferroelectric (NH4)2H2P2O6 (T(c)=178 K) in the temperature range 10-290 K. Low-temperature T1 behaviour below Tc is interpreted in terms of Haupt's theory and Schrödinger correlation time of tunnelling jumps. A shallow T1 minimum observed around 39 K is attributed to the C3 classical motion of "intra" proton-proton vectors of NH3 (ammonium groups NH4(+) may perform stochastic jumps about any of the four C3 symmetry axes). The tunnelling splitting of the ground state vibrational level, (νT)v0, of the same frequency for both ammonium groups was estimated as high as 900 MHz ((ħωT)v0=3.7 μeV). This tunnelling splitting exists only in the ferroelectric phase. Magnetisation recovery is found to be non-exponential in the temperature regime 63-48 K. The temperature of 63 K is the discovered T(tun) above which the probability of stochastic tunnelling jumps equals zero. The T1 relaxation time is temperature independent below 25 K, which is related to a constant value of the correlation time characterising tunnelling jumps according to Schrödinger. The T1 minima observed in the paraelectric phase (204 K at 15 MHz and 213 K at 24.7 MHz) as well as second moment reduction at about 130K are attributed to isotropic motion of all protons.

Complex molecular dynamics of (CH3NH3)5Bi2Br11 (MAPBB) protons from NMR relaxation and second moment of NMR spectrum

Molecular dynamics of a polycrystalline sample of (CH(3)NH(3))(5)Bi(2)Br(11) (MAPBB) is studied on the basis of the proton T(1) (55.2 MHz) relaxation time and the proton second moment of NMR line. The T(1) (55.2 MHz) was measured for temperatures from 20K to 330 K, while the second moment M(2) for those from 40K to 330 K. The proton spin pairs of the methyl and ammonium groups perform a complex stochastic motion being a resultant of four components characterised by the correlation times τ(3)(T), τ(3)(H), τ(2), and τ(iso), referring to the tunnelling and over the barrier jumps in a triple potential, jumps between two equilibrium sites and isotropic rotation. The theoretical expressions for the spectral densities in the cases of the complex motion considered were derived. For τ(3)(H), τ(2), and τ(iso) the Arrhenius temperature dependence was assumed, while for τ(3)(T)-the Schrödinger one. The correlation times τ(3)(H) for CH(3) and NH(3) groups differ, which indicates the uncorrelated motion of these groups. The stochastic tunnelling jumps are not present above the temperature T(tun) at which the thermal energy is higher than the activation energy of jumps over the barrier attributed to the hindered rotation of the CH(3) and NH(3) groups. The T(tun) temperature is 54.6 K for NH(3) group and 46.5 K for CH(3) group in MAPBB crystal. The tunnelling jumps of the methyl and ammonium protons are responsible for the flattening of T(1) temperature dependence at low temperatures. The isotropic tumbling is detectable only from the M(2) temperature dependence. The isotropic tumbling reduces the second moment to 4 G(2) which is the value of the intermolecular part of the second moment. The motion characterised by the correlation time τ(2) is well detectable from both T(1) and M(2) temperature dependences. This motion causes the appearance of T(1) minimum at 130 K and reduction of the second moment to the 7.7 G(2) value. The small tunnelling splitting ω(T) of the same value for the methyl and ammonium groups was estimated as 226 MHz from the Haupt equation or 80 MHz from the corrected by us Haupt equation. These frequencies correspond to 0.93 μeV and 0.34 μeV tunnel splitting energy.

Complex methyl groups dynamics in [(CH3)4P]3Sb2Br9 (PBA) from low to high temperatures by proton spin-lattice relaxation and narrowing of proton NMR spectrum

Molecular dynamics of a polycrystalline sample of [(CH(3))(4)P](3)Sb(2)Br(9) (PBA) has been studied on the basis of the T(1) (24.7 MHz) relaxation time measurement, the proton second moment of NMR and the earlier published T(1) (90 MHz) relaxation times. The study was performed in a wide range of temperatures (30-337 K). The tunnel splitting omega(T) of the methyl groups was estimated as of low frequency (from kHz to few MHz). The proton spin pairs of the methyl group are known to perform a complex internal motion being a resultant of four components. Three of them involve mass transportation over and through the potential barrier and are characterized by the correlation times tau(3) and tau(T)of the jumps over the barrier and tunnel jumps in the threefold potential of the methyl group and tau(iso) the correlation time of isotropic rotation of the whole TMP cation. For tau(3) and tau(iso) the Arrhenius temperature dependence was assumed, while for tau(T)--the Schrödinger one. The fourth motion causes fluctuations of the tunnel splitting frequency, omega(T), and it is related to the lifetime of the methyl spin at the energy level. The correlation function for this fourth motion (tau(omega) correlation time) has been proposed by Müller-Warmuth et al. In this paper a formula for the correlation function and spectral density of the complex motion made of the above-mentioned four components was derived and used in interpretation of the T(1) relaxation time. The second moment of proton NMR line at temperatures below 50K is four times lower than its value for the rigid structure. The three components of the internal motion characterized by tau(T), tau(H), and tau(iso) were proved to reduce the second moment of the NMR line. The tunnel jumps of the methyl group reduce M(2) at almost 0K, the classical jumps over the barrier reduce M(2) in the vicinity of 50K, while the isotropic motion near 150K. Results of the study on the dynamics of CH(3) groups of TMP cation based on the second moment measurements were correlated with those based on T(1) time measurements.

Complex methyl group and hydrogen-bonded proton motions in terms of the Arrhenius and Schrödinger equations

Equations for the temperature dependence of the spectral densities J(is)(m)(momega(I) +/-omega(T)), where m=1, 2, omega(I) and omega(T) are the resonance and tunnel splitting angular frequencies, in the presence of a complex motion, have been derived. The spin pairs of the protons or deuterons of the methyl group perform a complex motion consisting of three component motions. Two of them involve mass transportation over the barrier and through the barrier. They are characterized by k((H)) (Arrhenius) and k((T)) (Schrödinger) rate constants, respectively. The third motion causes fluctuations of the frequencies (nomega(I)+/-omega(T)) and it is related to the lifetime of the methyl spin at the energy level influenced by the rotor-bath interactions. These interactions induce rapid transitions, changing the symmetry of the torsional sublevels either from A to E or from E(a) to E(b). The correlation function for this third motion (k((omega)) rate constant) has been proposed by Müller-Warmuth et al. The spectral densities of the methyl group hindered rotation (k((H)), k((T)) and k((omega)) rate constants) differ from the spectral densities of the proton transfer (k((H)) and k((T)) rate constants) because three compound motions contribute to the complex motion of the methyl group. The recently derived equation [Formula: see text] , where [Formula: see text] and [Formula: see text] are the fraction and energy of particles with energies from zero to E(H), is taken into account in the calculations of the spectral densities. This equation follows from Maxwell's distribution of thermal energy. The spectral densities derived are applied to analyse the experimental temperature dependencies of proton and deuteron spin-lattice relaxation rate in solids containing the methyl group. A wide range of temperatures from zero Kelvin up to the melting point is considered. It has been established that the motion characterized by k((omega)) influences the spin-lattice relaxation up to the temperature T(tun) only. This temperature is directly determined by the equation C(p)T=E(H) (thermal energy=activation energy), where C(p) is the molar heat capacity. Probably the cessation of the third motion is a result of the de Broglie wavelength related to this motion becoming too short. As shown recently, the potential barrier can be an obstacle for the de Broglie wave. The theoretical equations derived in this paper are compared to those known in the literature.

1H NMR study of internal motions and quantum rotational tunneling in (CH3)4NGeCl3

(CH3)4NGeCl3 is prepared, characterized and studied using 1H NMR spin lattice relaxation time and second moment to understand the internal motions and quantum rotational tunneling. Proton second moment is measured at 7 MHz as function of temperature in the range 300-77 K and spin lattice relaxation time (T1) is measured at two Larmor frequencies, as a function of temperature in the range 270-17 K employing a homemade wide-line/pulsed NMR spectrometers. T1 data are analyzed in two temperature regions using relevant theoretical models. The relaxation in the higher temperatures (270-115 K) is attributed to the hindered reorientations of symmetric groups (CH3 and (CH3)4N). Broad asymmetric T1 minima observed below 115 K down to 17 K are attributed to quantum rotational tunneling of the inequivalent methyl groups.

Study of molecular reorientation and quantum rotational tunneling in tetramethylammonium selenate by 1H NMR

1H NMR spin-lattice relaxation time measurements have been carried out in [(CH3)4N]2SeO4 in the temperature range 389-6.6 K to understand the possible phase transitions, internal motions and quantum rotational tunneling. A broad T1 minimum observed around 280 K is attributed to the simultaneous motions of CH3 and (CH3)4N groups. Magnetization recovery is found to be stretched exponential below 72 K with varying stretched exponent. Low-temperature T1 behavior is interpreted in terms of methyl groups undergoing quantum rotational tunneling.

Molecular dynamics in solid pyridoxine as studied by 1H NMR

Spin-lattice relaxation times T1 and T1d as well as NMR second moment were employed to study molecular dynamics of pyridoxine (vitamin B6) in the temperature range 10-350 K. The T1 minimum observed at low temperatures at 200 MHz is attributed to a motion of methyl group. The motion is interpreted in terms of Haupt's theory, which takes into account the tunneling assisted relaxation. At low temperatures, where T1 is temperature independent, occupation of the ground state only is assumed. A motion of proton of the hydroxyl groups or CH2OH groups probably provides additional mechanism of relaxation, in the high-temperature region.

1H and 2H NMR relaxation in hydrogen-bonded solids due to a complex motion: classical jumps over a barrier and incoherent tunneling

Equations for the temperature dependence of proton and deuteron spin-lattice relaxation rates and second moments due to a complex motion consisting of classical jumps over a potential barrier and quantum mechanical tunneling through the barrier have been derived. Asymmetric double and triple potential wells are considered. These equations have been employed to analyze proton spin-lattice relaxation data for solid naphthazarin in the laboratory and rotating frames as a function of temperature. It is shown that tunneling plays an important role in the proton transfer dynamics of this compound.