Protonation dynamics

It seems that surface hopping (also called Molecular Dynamics with Quantum Transitions, MDQT) is a rather heavy tool to simulate proton dynamics. A recent and promising development is path integral centroid dynamics [123] that provides approximate dynamics of the centroid of the wavefunctions. Several improvements and applications have been published [123, 124, 125, 126, 127, 128). 

Ye, G., Hayden, C. A. and Coward, G. R. 2007. Proton dynamics of nation and Nafion/Si02 composites by solid state NMR and pulse field gradient NMR. Macromolecules 40 1529-1537. 

For the partially deuterated benzoic acid (C6D5COOH), the solid state H NMR spectrum is dominated by the intra-dimer H- H dipole-dipole interaction. In a single crystal, both tautomers A and B are characterised by a well-defined interproton vector with respect to the direction of the magnetic field (Fig. 1). Proton motion modulates the H- H dipole-dipole interactions, which in turn affects the H NMR lineshape and the spin-lattice relaxation time. It has been shown that spin-lattice relaxation times are sensitive to the proton dynamics over the temperature range from 10 K to 300 K, and at low temperatures incoherent quantum tunnelling characterises the proton dynamics. A dipolar splitting of about 16 kHz is observed at 20 K. From the orientation dependence of the dipolar splitting, the... 

In order to confirm the proton transfer mechanism proposed previously [160], the results of IQNS on terephthalic acid were reported [164]. The jump distance is calculated to be 0.7 A for the proton transfer model and 2.1 A for the 180° rotation model - the latter process was ruled out on the basis of the experimental IQNS results, leading to the conclusion that the mechanism of the proton dynamics is indeed a double proton exchange. IQNS results for terephthalic acid and acetylene dicarboxylic acid have also been reported [165]. For both samples, the jump distance was found to be less than 1 A. For acetylene dicarboxylic acid, single crystal measurements yielded a jump distance of 0.73 A. The Q-depen-dence was found to be in excellent agreement with the 2-site jump model. From these results, the 180° rotation model can be ruled out in favour of the proton transfer model. 

It is interesting to note that, for malonic acid (which is structurally related to DMMA), the activation energy measured from XH NMR Tx measurements [170] is 5.6 kj mol-1, which is significantly lower than in DMMA and is assigned to proton jumps between the two minima of an asymmetric double well potential. This emphasises the importance of the effect of the crystal packing on the asymmetry of the potential function, which defines the mechanism of the proton dynamics in carboxylic acid dimers. 

Mizuno, M. and Hayashi, S., Proton dynamics in phase II of CSHSO4 studied by H-1 NMR, Solid State Ionics, 167, 317-323 (2004). 

However—and this is the third aspect—the characteristic lifetime of a hydrogen bond is very short (between 10 and 10 s) and this is why viscoelastic properties of a gel structure will never be observed even in short characteristic time experiments. The explanation of such a short time is that hydrogen bond lifetimes are determined by the proton dynamics [3,8]. In particular, large-amplitude librational movements take easily the proton from the region, between two oxygens, where the energy of the bond is sufficiently large. 

Inelastic neutron scattering studies have shown [7-11] that many hydrogen-bonded crystals [potassium carbonate (i.e., KHCO3), various polyanilines, Ca(OH)2, and others] are characterized by the proton dynamics that is very decoupled from the backbone lattice. 

Vibrational spectroscopy measures atomic oscillations practically on the scale as the scale of proton dynamics, 10-15 to 10 12 s. Fillaux et al. [110] note that optical spectroscopies, infrared and Raman, have disadvantages for the study of proton transfer that preclude a complete characterization of the potential. (However, the infrared and Raman techniques are useful to observe temperature effects inelastic neutron spectra are best observed at low temperature.) As mentioned in Ref. 110, the main difficulties arise from the nonspecific sensitivity for proton vibrations and the lack of a rigorous theoretical framework for the interpretation of the observed intensities. 

What is the reason for decoupling the proton dynamics from the crystal lattice revealed in a great number of compounds Fillaux [119] has investigated the reason for this decoupling, supposing that the proton dynamics could be... 

Let us treat the proton dynamics starting from the modified Hamiltonian (153), that is [149,150],... 

The principal structure of the outlet proton channel is now considered as being composed of water molecules and the terminal —OH group of Asp 212, Glu 204 and, possibly, tyrosine(s). In contrast, the inlet channel has hydrophobic side chains of amino acid residues, except for the polar side chain of Asp 96 which is positioned about 0.1 nm from the Schiff base and about 0.6 nm from the cytoplasmic end of the C segment [224]. One or two water molecules close to the Schiff base [256-258] perhaps play a structure forming role and promote the proton dynamics. 

Terms To and T describe unordered proton configurations in the bonds, so that the probability of single-domain chain oscillations becomes a+lV- 2 cos [(Ei — Eo)tjh. When To and Ti are small in comparison with the a terms, one can treat the chain repolarization as that of a single domain. Contribution of To and Ti in (442) becomes more appreciable at the increasing of the integral J that leads to the destroying the correlated proton dynamics. For example, in the case of a chain consisting only of two bonds, which is characterized by periodical boundary conditions, we have... 

Let us calculate the tunneling rate of correlated proton dynamics associated with oscillations of the chain s total polarization using the quasi-classical (WKB)... 

However, the model by Stasyuk et al. [135] described in Section II.A is more attractive because it allows an estimation of the frequency of coherent orientational tunnel transitions taking into account both the proton dynamics of the hydrogen bonds and the reorientational processes of A H groups. Let us... 

Thus starting from the simplest pseudo-spin model of proton dynamics in the hydrogen bond, we have studied a possibility of spontaneous tunnel oscillations of the polarization of a short hydrogen-bonded chain. The phenomenon can be affected by two reasons (a) the coherent motion of protons along the hydrogen bonds and (b) the coherent motion of protons around heavy backbone atoms. 

Particular emphasis has been placed on two antithetical urgent problems proton transfer incorporating acoustic phonons, which is intensively studied by Trommsdorf and co-workers [15,16,21,22,78-84], and the proton dynamics that is very decoupled from the backbone lattice, which is investigated by Fillaux and collaborators [1,7-11,14,49,110-114]. 

S. Takeda, H. Chihara, T. Inabe, T. Mitani, and Y. Mamyama, NMR study of proton dynamics in the NHO hydrogen bonds in the thermochromic crystals of IV-salicylideneanilines, Chem. Phys. Lett 189(1), 13-17(1992). 

Keywords Proton dynamics, neutron scattering, hydrogen bond, proton transfer, decoherence-... 

---