Proton quantum motion

The bifurcational diagram (fig. 44) shows how the (Qo,li) plane breaks up into domains of different behavior of the instanton. In the Arrhenius region at T> classical transitions take place throughout both saddle points. When T < 7 2 the extremal trajectory is a one-dimensional instanton, which crosses the maximum barrier point, Q = q = 0. Domains (i) and (iii) are separated by domain (ii), where quantum two-dimensional motion occurs. The crossover temperatures, Tci and J c2> depend on AV. When AV Vq domain (ii) is narrow (Tci — 7 2), so that in the classical regime the transfer is stepwise, while the quantum motion is a two-proton concerted transfer. This is the case when the tunneling path differs from the classical one. The concerted transfer changes into the two-dimensional motion at the critical value of parameter That is, when... 

The H+-H2O bond has the special feature that although the bond energy is high, the proton will readily hop from one water molecule in the hydration complex to a neighboring water molecule. This hop is a quantum motion and will occur only when the water molecules have a favorable mutual orientation. It will occur predominantly... 

In the quantum-mechanical description of atoms and molecules, electrons have characteristics of waves as well as particles. In the familiar case of the hydrogen atom, the orbitals Is, 2s, 2p,... describe the different possible standing wave patterns of electron distribution, for a single electron moving in the potential field of a proton. The motion of the electrons in any atom or molecule is described as fully as possibly by a set of wave functions associated with the ground and excited states. 

The quantum Monte Carlo calculations for Fermions have also been applied to a quantitative calculation of the phase diagram of condensed hydrogen. Calculations of the ground state have been carried out as a function of the average volume, treating both the electrons and protons quantum-mechanically, i.e., including the proton zero-point motion. There is only one intrinsic limitation of the method— the finite number of particles which can be included in the many-body ground state. Since the... 

Given the key role of proton transfer, a quantum proton motion treatment is required for a more accurate estimate of the activation energy. In that context, the investigation of H/D kinetic isotope effects would provide a ditect probe of the present mechanism the desorption energy for CI2 is presumably low and it would not mask a quantum motion-influenced reaction barrier, still the rate-determining step. This is different from the CIONO2 hydrolysis, where the HOCl desorption energy far exceeds the reaction barrier and thus would mask any H/D kinetic isotope effect. 

Abstract In the present study, the effect of the potential energy surface representation on the infrared spectra features of the and Df clusters is investigated. For the spectral simulations, we adopted a recently proposed (Sanz-Sanz et al. in Phys Rev A 84 060502-1-4, 2011) two-dimensional adiabatic quantum model to describe the proton-transfer motion between the two H2 or D2 units. The reported calculations make use of a reliable on the fly DFT-based potential surface and the corresponding new dipole moment surface. The results of the vibrational predissociation dynamics are compared with earlier and recent experimental data available from mass-selected photodissociation spectroscopy, as well as with previous theoretical calculations based on an analytical ab initio parameterized surfaces. The role of the potential topology on the spectral features is studied, and general trends are discussed. 

HYNES - You emphasized that the pH depends strongly on the Zundel hydrogen bond polarizability. Since that might depend on proton (presumably quantum) motion in the bond there might be a big (solvent) isotope effect. Can you comment on this and also indicate what is known experimentally for the H O/D O pH ratio ... 

Based on the classical Einstein-Smoluchowski s description [267] of diffusion (as a particular case of Brownian motion) and accounting for the fact that the Brownian and quantum movements are indistinguishable by intermitted measurements in configuration space, there follows an important fact [36,258] that a certain class of self-organized periodic reactions [36] can be realistically characterized by the empirical dispersion relation, MvA. h, which is factually controlled by the Fiirth s quantum diffusion of reactants. In its fundamental sense we can challenge to say that oscillation processes in aqueous solutions are likely caused by quantum motion of protons (while the oscillations in solids are caused by electrons). 

Thus, for a transition between any two vibrational levels of the proton, the fluctuation of the molecular surrounding provides the activation. For each such transition, the motion along the proton coordinate is of quantum (sub-barrier) character. Possible intramolecular activation of the H—O chemical bond is taken into account in the theory by means of the summation of the probabilities of transitions between all the excited vibrational states of the proton with a weighting function corresponding to the thermal distribution.3,36 Incorporation in the theory of the contribution of the excited states enabled us in particular to improve the agreement between the theory and experiment with respect to the independence of the symmetry factor of the potential in a wide region of 8[Pg.135]

By application of proton multiple quantum (MQ) NMR experiments, information about the segmental order parameter, which is directly related to the restrictions on chain motion (cross-links) formed upon gelation of PVA, is obtained.103The quantitative study of rigid phase... 

We can expect to see future research directed at QM/MM and ab initio simulation methods to handle these electronic structure effects coupled with path integral or approximate quantum free energy methods to treat nuclear quantum effects. These topics are broadly reviewed in [32], Nuclear quantum effects for the proton in water have already received some attention [30, 76, 77]. Utilizing the various methods briefly described above (and other related approaches), free energy calculations have been performed for a wide range of problems involving proton motion [30, 67-69, 71, 72, 78-80]. 

The fluorescence emission spectra of TINS in PVA and PVP also show only a single band near 400 nm which is attributable to emission from a non proton-transferred excited state. The similarity between the values of the fluorescence quantum yield, < >fnp, for the non proton-transferred form of TINS in PVA and PVP (12.) indicates that the PVA polymer is unable to behave in an analogous manner to protic, hydrogen-bonding solvents and suggests that no complexation which can facilitate ESIPT occurs in the excited state as a result of the restricted motion of the PVA chains. 

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