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 ((hωT)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.

Dynamic processes and chemical composition of Lepidium sativum seeds determined by means of field-cycling NMR relaxometry and NMR spectroscopy.

Proton nuclear magnetic resonance (NMR) techniques, such as field-cycling relaxometry, wide-line NMR spectroscopy, and magic angle spinning NMR spectroscopy, were applied to study the seeds of cress, Lepidium sativum. Field-cycling NMR relaxometry was used for the first time to investigate the properties of the whole molecular system of dry cress seeds. This method not only allowed the dynamics to be studied, but was also successful in the differentiation among the solid (i.e., carbohydrates, proteins, or fats forming a solid form of lipids) and liquid-like (oil compounds) components of the seeds. The (1)H NMR relaxation dispersion of oils was interpreted as a superposition of intramolecular and intermolecular contributions. The intramolecular part was described in terms of a Lorentzian spectral density function, whereas a log-Gaussian distribution of correlation times was applied for the intermolecular dipole-dipole contribution. The models applied led to very good agreement with the experimental data and demonstrate that the contribution of the intermolecular relaxation to the overall relaxation should not be disregarded, especially at low frequencies. A power-law frequency dependence of the proton relaxation dispersion was used for the interpretation of the solid components. From the analysis of the (1)H wide-line NMR spectra of the liquid-like component of hydrated cress seeds, we can conclude that the contribution of oil protons should always be taken into account when evaluating the spin-lattice relaxation times values or measuring the moisture and oil content. The application of (1)H magic angle spinning NMR significantly improves resolution in the liquid-like spectrum of seeds and allows the determination of the chemical composition of cress seeds.

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.

Tunneling molecular dynamics in the light of the corpuscular-wave dualism theory.

This paper presents the experimental demonstration of the corpuscular-wave dualism theory. The correlation between the de Broglie wavelength related to the thermal motion and the potential barrier width and height is reported. The stochastic jumps of light atoms (hydrogen, deuterium) between two equilibrium sites A and B (identical geometry) occur via different pathways; one pathway is over the barrier (classical dynamics), and the other one is through the barrier (tunneling). On the over-the-barrier pathway, there are no obstacles for the de Broglie waves, and this pathway exists from high to low temperatures up to 0 K because the thermal energy is subjected to the Maxwell distribution and a certain number of particles owns enough energy for the hopping over the barrier. On the tunneling pathway, the particles pass through the barrier, or they are reflected from the barrier. Only particles with the energy lower than barrier heights are able to perform a tunneling hopping. The de Broglie waves related to these energies are longer than the barrier width. The Schrödinger equation is applied to calculate the rate constant of tunneling dynamics. The Maxwell distribution of the thermal energy has been taken into account to calculate the tunneling rate constant. The equations for the total spectral density of complex motion derived earlier by us together with the expression for the tunneling rate constant, derived in the present paper, are used in analysis of the temperature dependence of deuteron spin-lattice relaxation of the ammonium ion in the deuterated analogue of ammonium hexachloroplumbate ((ND4)2PbCl6). It has been established that the equation CpTtun = EH (thermal energy equals activation energy), where Cp is the molar heat capacity (temperature-dependent, known from literature), determines directly the low temperature Ttun at which the de Broglie wavelength, lambdadeBroglie, related to the thermal energy, CpT, is equal to the potential barrier width, L. Above Ttun, the lambdadeBroglie wavelength related to the CpT energy is shorter than the potential barrier width and not able to overcome the barrier. The activation energy EH equals 7.5 kJ/mol, and therefore, the Ttun temperature for deuterons in ((ND4)2PbCl6 is 55.7 K. The agreement between the potential barrier width following from the simple geometrical calculations (L = 0.722 A) and de Broglie wavelength at Ttun (L = 0.752 A) is good. The temperature plots of the deuteron correlation times for (ND4)2PbCl6 reveal comparable values of the correlation times of the tunneling, (tau(T)), and over-the-barrier jumps (tau(H)) near 34.8 K. Matsuo, on the basis of the molar heat capacity study, found the first-order phase transition at this temperature.

Application of Schrödinger equation to study the tunnelling dynamics of proton transfer in the hydrogen bond of 2,5-dinitrobenzoic acid: proton T1 T1rho, and deuteron T1 relaxation methods.

Temperature measurements of proton T1 (24.7 MHz), deuteron (deuterated hydroxyl group) T1 (55.2 MHz), and proton T1(rho) (B1 = 9 G) spin-lattice relaxation times of 2,5-dinitrobenzoic acid have been performed. An analysis of present experimental data together with previously published proton T1 (55.2 MHz) data has revealed the following molecular motions: proton/deuteron transfer in the hydrogen bond and two-site hopping of the whole dimer. It is shown that the proton-transfer dynamics are characterized by two correlation times tau(ov) and tau(tu), describing two fundamentally different motional processes, namely, thermally activated jumps over the barrier and tunneling through the barrier. The temperature dependence of 1/tau(tu) is the solution of Schrödinger's equation, which also yields the temperature T(tun), where begins the tunnel pathway for proton transfer. A new equation for the spectral density function of complex motion consisting of the three motions is derived. The third motion (two-site hopping of the whole dimer characterized by tau(lib) correlation time) is responsible for a proton T1(rho) minimum in high temperatures, just below the melting point. Such a minimum is not reached by T1 temperature dependencies. The minimum of T1(rho) assigned to the classical hopping of a hydrogen-bonded proton occurs in the same low-temperature regime in which the flattening of the temperature dependencies of T1 points to the dominance of incoherent tunneling. This experimental fact denies the known theories predicting the intermediate temperature regime where a smooth transition between classical and quantum tunneling dynamics is expected. The fit of the derived theoretical equations to the experimental data T1(rho) and T1 is satisfactory. The correlation times obtained for deuterons indicate deuteron-transfer dynamics much slower than proton-transfer dynamics. It is concluded that the classical proton transfer takes place over the whole temperature regime, while the incoherent tunneling occurs below 46.5 (hydrogen) or 87.2 K (deuterium) only.

The effect of low-temperature dynamics of the dimethylammonium group in [(CH3)2NH2]3Sb2Cl9 on proton spin-lattice relaxation and narrowing of the proton NMR line.

This paper reports the temperature dependence of the relaxation time T1 (55.2 and 90 MHz) and the second moment of the NMR line for protons in a polycrystalline sample of [NH2(CH3)2]3Sb2Cl9 (DMACA). The fundamental aspects of molecular dynamics from quantum tunneling at low temperatures to thermally activated reorientation at elevated temperatures have been studied. The experimentally observed spin-lattice relaxation rate is a consequence of dipolar interactions between the spin pairs inside the methyl group (1/T(1AE) contribution) as well as the spins belonging to neighboring methyl groups and pairs, methyl spin-outer methyl spin (1/T(1EE) contribution). These contributions are considered separately. Two methyl groups in the dimethylammonium (DMA) cations are dynamically inequivalent. The values of the tunnel splitting of separate methyl groups are obtained from the T1 (55.2 MHz) experiment. The tunneling dynamics taking place below the characteristic temperatures 74 and 42 K for separate methyl groups are discussed in terms of the Schrödinger equation. These temperatures point to the one at which thermal energy C(p)T and potential barrier take the same value. It is established that the second moment of the proton NMR line below 74 K up to liquid helium temperature is much lower than the rigid lattice value, which is due to a tunneling stochastic process of the methyl groups.

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.