Proton transfer dynamics in the hydrogen bond: a direct measurement of the incoherent tunnelling rate by NMR and the quantum-to-classical transition

Hydrogen Bonds: Raman Spectroscopic Study

The work outlines general ideas on how the frequency and the intensity of proton vibrations of X–H···Y hydrogen bonding are formed as the bond evolves from weak to maximally strong bonding. For this purpose, the Raman spectra of different chemical compounds with moderate, strong, and extremely strong hydrogen bonds were obtained in the temperature region of 5 K–300 K. The dependence of the proton vibrational frequency is schematically presented as a function of the rigidity of O-H···O bonding. The problems of proton dynamics on tautomeric O–H···O bonds are considered. A brief description of the N–H···O and C–H···Y hydrogen bonds is given.

Tautomeric Hydrogen Bond in Dimers of Ibuprofen

The Raman spectra of polycrystalline samples of ( RS)-2-(4-isobutylphenyl)-propionic acid of the common name ibuprofen have been measured in the temperature range 5-300 K. In the low-frequency spectrum of the normal C₁₂H₁₇(COOH) and deuterated C₁₂H₁₇(COOD) species, modes with ∼103 and ∼95 cm^-1 wavenumbers were detected, which corresponded to translational vibrations of O-H(D)···O hydrogen bonds of two different tautomers: left L and right R , respectively. At temperatures below 150 K, only the L-tautomer is found, and at T ≥ 150 K, both tautomers are observed. The energy difference Δ E of the ground vibrational state of potential minima for L- and R-tautomers is ∼80 meV for COOH and ∼70 meV for COOD. At T ≥ 150 K, the vibrational frequency of the C═O bond in the COOH moiety exhibits an unusual temperature dependence.

Unusual behavior of benzoic acid at low temperature: Raman spectroscopic study

The Raman spectra of benzoic acid single crystals have been measured in the temperature range of 5-300K. At T<60K the spectra show at least two anomalous features, one of which is of direct relevance to intensity changes of the lattice modes in the low-wavenumber region. The intensity of modes at ∼86 and ∼146cm(-1) tends to zero at T→0K. It is associated with appearance of two H-bonds of different length in the same l-tautomer, and with the loss of the inversion center in the dimer. The modes at ∼86 and ∼146cm(-1) are assigned to symmetric stretching intra-dimer vibrations of the OH⋯O hydrogen bonds of the first and second order, respectively. The assignment is based on the measurements of spectral parameters as function of temperature. The other anomaly is that the series of weak and narrow bands arises in the high-wavenumber region of 2500-3700cm(-1). The bands are assigned to combination tones of O-H hydrogen bonded stretching vibration and intramolecular modes. This effect results from a low-temperature transition of a conventional two wells potential of short H-bond in the l-tautomer to asymmetrical single well potential, and is due to a strong coupling of intramolecular vibrations to O-H stretching.

Proton tunnelling in the hydrogen bonds of the benzoic acid dimer: (18)O substitution and isotope effects of the heavy atom framework

Field-cycling (1)H NMR relaxometry has been used to measure the rate of concerted double proton transfer in the hydrogen bonds of (16)O and (18)O isotopologues of benzoic acid dimers. The experiments have been conducted in the solid state at low temperature 13.3 ≤ T ≤ 80 K where the dynamics are dominated by incoherent proton tunnelling. The low temperature tunnelling rate in the (16)O isotopologue is observed to be approximately 15% faster than in the (18)O isotopologue. The difference is attributed to an isotope effect of the heavy atom framework of the benzoic acid dimer resulting from displacements of the oxygen atoms that accompany the proton transfer. Sources of systematic uncertainty have been minimized in the design of the experimental protocols and the experiments are critically appraised in formally assigning the measured differences to an effect of mass on the tunnelling dynamics.

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.

1H-19F spin-lattice relaxation spectroscopy: proton tunnelling in the hydrogen bond studied by field-cycling NMR

Proton tunnelling in the hydrogen bonds of two fluorine substituted benzoic acid dimers has been investigated using field-cycling NMR relaxometry. The close proximity of the (19)F nuclei to the hydrogen bond protons introduces heteronuclear (19)F-(1)H dipolar interactions into the spin-lattice relaxation processes. This renders the (1)H magnetisation-recovery biexponential and introduces multiple spectral density components into the relaxation matrix characterised by frequencies that are sums and differences of the (19)F and (1)H Larmor frequencies. Using field-cycling NMR pulse sequences that measure the spin-lattice relaxation and cross-relaxation rates we demonstrate how some of these multiple spectral density components can be separately resolved. This leads to an accurate determination of the correlation times that characterise the proton tunnelling motion. A broad spectrum of relaxation behaviour is illustrated and explored in the chosen samples and the investigation is used to explore the theory and practise of field-cycling NMR relaxometry in cases where heteronuclear interactions are significant.

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.

Field-cycling NMR investigations of (13)C-(1)H cross-relaxation and cross-polarisation: the nuclear solid effect and dynamic nuclear polarisation

A field-cycling NMR investigation of (1)H-(13)C polarisation transfer using cross-relaxation and the nuclear solid effect (NSE) is described. Dynamic nuclear polarisation (DNP) of the (13)C spins is observed when forbidden transitions are driven by r.f. irradiation at the sum and difference Larmor frequencies of the two nuclei. When the (1)H spins are pre-polarised, a significant transfer of polarisation to the (13)C nuclei is achieved in a time short compared with the spin-lattice relaxation time of (13)C. The cross-polarisation arising from the NSE is studied as a function of B-field and time. These results are compared with the solutions of the differential equations that govern the coupled system of (1)H-(13)C spins. The effects of cross-relaxation are incorporated into the model for the first time and good agreement between theory and experiment is obtained. The experiments have been conducted at 20K on a (13)C-enriched sample of benzoic acid.

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, T1ρ, 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.

Isotope effects associated with tunneling and double proton transfer in the hydrogen bonds of benzoic acid

The isotope effects associated with double proton transfer in the hydrogen bonds of benzoic acid (BA) dimers have been measured using field-cycling (1)H NMR relaxometry and quasielastic neutron scattering. By studying mixed isotope (hydrogen and deuterium) samples, the dynamics of three isotopologues, BA-HH, BA-HD, and BA-DD, have been investigated. Low temperature measurements provide accurate measurements of the incoherent tunneling rate, k(0). This parameter scales accurately with the mass number, m, according to the formula k(0)=(E/m)e(-Fm) providing conclusive evidence that the proton transfer process is a strongly correlated motion of two hydrons. Furthermore, we conclude that the tunneling pathway is the same for the three isotopologue species. Measurements at higher temperatures illuminate the through barrier processes that are mediated via intermediate or excited vibrational states. In parallel with the investigation of proton transfer dynamics, the theoretical and experimental aspects of studying spin-lattice relaxation in single crystals of mixed isotope samples are investigated in depth. Heteronuclear dipolar interactions between (1)H and (2)H isotopes contribute significantly to the overall proton spin-lattice relaxation and it is shown that these must be modeled correctly to obtain accurate values for the proton transfer rates. Since the sample used in the NMR measurements was a single crystal, full account of the orientation dependence of the spin-lattice relaxation with respect to the applied B field was incorporated into the data analysis.

Proton tunneling in a hydrogen bond measured by cross-relaxation field-cycling NMR

A field-cycling NMR pulse sequence is described for studying cross-relaxation between unlike nuclear spins in the solid state. The technique has been applied to study proton tunneling in the hydrogen bonds of a carboxylic acid containing 19F and 1H spins. By studying the B-field dependence of the off-diagonal element of the relaxation matrix that characterizes the longitudinal polarizations, an accurate measure of the proton transfer rate is obtained.

Extended tunnelling states in the benzoic acid crystal: Infrared and Raman spectra of the OH and OD stretching modes

We compare Raman and infrared spectra of the nuOH/OD modes in benzoic acid crystal powders at 7 K. The extremely sharp Raman bands contrast to the broad infrared profiles and suggest adiabatic separation of hydrogen (deuterium) dynamics from the crystal lattice. There is no evidence of any proton-proton coupling term. The assignment scheme is consistent with a quasisymmetric double-minimum potential, largely temperature independent. Tunnel splitting is a major band shaping mechanism, in addition to anharmonic coupling with lattice modes. The proton/deuteron dynamics are rationalized with nonlocal pseudoparticles and extended states. We propose a symmetry-related damping mechanism to account for the broad infrared profiles, as opposed to the sharp Raman bands. We assign spectral features to distinct interconversion mechanisms based on either pseudoparticle transfer or adiabatic pairwise transfer. We establish close contacts with theoretical models based on first-principles calculations.

Probing Photophysical and Photochemical Processes of Benzoic Acid from ab Initio Calculations

The CASSCF and DFT methods have been used to determine geometric and electronic structures of the benzoic acid monomer in the S(0), S(1), S(2), T(1), and T(2) electronic states. The S(1)/T(2)/T(1) three-surface intersection was found by the state-averaged CASSCF calculations, which, in combination with features of the five lowest electronic states, provides new insights into photophysical processes of the benzoic acid monomer. The potential energy profiles of the alpha C-C and C-O bond fissions as well as decarboxylation reaction in different electronic states have been determined for the benzoic acid monomer. The alpha C-O bond cleavage starts from the T(2) state and leads to the fragments of C(6)H(5)CO(X(2)A') and OH(X(2)Pi) in the ground state, which is predicted to be the most possible channel upon photoexcitation of the benzoic acid monomer at 270 nm or shorter wavelengths.

A 13C field-cycling NMR relaxometry investigation of proton tunnelling in the hydrogen bond: dynamic isotope effects, the influence of heteronuclear interactions and coupled relaxation

Concerted double proton transfer in the hydrogen bonds of a carboxylic acid dimer has been studied using 13C field-cycling NMR relaxometry. Heteronuclear 13C-1H dipolar interactions dominate the 13C spin-lattice relaxation which is significantly influenced by the polarisation state of the 1H Zeeman reservoir. The methodology of field-cycling experiments for such heteronuclear spin-coupled systems is studied experimentally and theoretically, including an investigation of various saturation-recovery and polarisation-recovery pulse sequence schemes. A theoretical model of the spin-lattice relaxation of this coupled system is presented which is corroborated by experiment. Spectral density components with frequencies omega(C), omega(C) + omega(H), and omega(C) - omega(H) are mapped out experimentally from the magnetic field dependence of the 13C and 1H spin-lattice relaxation and the proton transfer rate at low temperature is determined from their widths. Any dynamic isotope effect on the proton tunnelling in the hydrogen bond arising from 13C enrichment in the skeletal framework of the dimer is found to be smaller than experimental uncertainties (approximately 5%).

Tunneling dynamics of double proton transfer in formic acid and benzoic acid dimers

Direct dynamics calculations based on instanton techniques are reported of tunneling splittings due to double proton transfer in formic and benzoic acid dimers. The results are used to assign the observed splittings to levels for which the authors of the high-resolution spectra could not provide a definitive assignment. In both cases the splitting is shown to be due mainly to the zero-point level rather than to the vibrationally or electronically excited level whose spectrum was investigated. This leads to zero-point splittings of 375 MHz for (DCOOH)(2) and 1107 MHz for the benzoic acid dimer. Thus, contrary to earlier calculations, it is found that the splitting is considerably larger in the benzoic than in the formic acid dimer. The calculations are extended to solid benzoic acid where the asymmetry of the proton-transfer potential induced by the crystal can be overcome by suitable doping. This has allowed direct measurement of the interactions responsible for double proton transfer, which were found to be much larger than those in the isolated dimer. To account for this observation both static and dynamic effects of the crystal forces on the intradimer hydrogen bonds are included in the calculations. The same methodology, extended to higher temperatures, is used to calculate rate constants for HH, HD, and DD transfers in neat benzoic acid crystals. The results are in good agreement with reported experimental rate constants measured by NMR relaxometry and, if allowance is made for small structural changes induced by doping, with the transfer matrix elements observed in doped crystals. Hence the method used allows a unified description of tunneling splittings in the gas phase and in doped crystals as well as of transfer rates in neat crystals.

The ground-state tunneling splitting of various carboxylic acid dimers

Carboxylic acid dimers in gas phase reveal ground-state tunneling splittings due to a double proton transfer between the two subunits. In this study we apply a recently developed accurate semiclassical method to determine the ground-state tunneling splittings of eight different carboxylic acid derivative dimers (formic acid, benzoic acid, carbamic acid, fluoro formic acid, carbonic acid, glyoxylic acid, acrylic acid, and N,N-dimethyl carbamic acid) and their fully deuterated analogs. The calculated splittings range from 5.3e-4 to 0.13 cm(-1) (for the deuterated species from 2.8e-7 to 3.3e-4 cm(-1)), thus indicating a strong substituent dependence of the splitting, which varies by more than two orders of magnitude. One reason for differences in the splittings could be addressed to different barriers heights, which vary from 6.3 to 8.8 kcal/mol, due to different mesomeric stabilization of the various transition states. The calculated splittings were compared to available experimental data and good agreement was found. A correlation could be found between the tunneling splitting and the energy barrier of the double proton transfer, as the splitting increases with increased strength of the hydrogen bonds. From this correlation an empirical formula was derived, which allows the prediction of the ground-state tunneling splitting of carboxylic acid dimers at a very low cost and the tunneling splittings for parahalogen substituted benzoic acid dimers is predicted.

Evidence for coherent proton tunneling in a hydrogen bond network

We observed coherent proton tunneling in the cyclic network of four hydrogen bonds in calix[4]arene. The tunneling frequency of 35 megahertz was revealed by a peak in the magnetic field dependence of the proton spin-lattice relaxation rate measured with field-cycling nuclear magnetic resonance in the solid state at temperatures below 80 kelvin. The amplitude of the coherent tunneling peak grows with temperature according to a Boltzmann law with energy D/kB = (125 +/- 10) kelvin (where kB is Boltzmann's constant). The tunneling peak can be interpreted in the context of level crossings in the region where the tunneling frequency matches the proton Larmor frequency. The tunneling spectrum reveals fine structure that we attribute to coupling between the hydrogen bonds in the network. The characteristics of the tunneling peak are interpreted in the context of the potential energy surface experienced by the hydrogen atoms in the network.