Quantum mechanics proton ordering

Computer simulations of excess proton conductivity in water have reached a powerful level [8,92,93,102]. Importantly, simulations extend to quantum-mechanical proton dynamic features, so that proton motion can be coupled to details of the molecular environmental dynamics. A recent feature article explored an analytical theory in order to rationalize these complex processes that involve interconversion of proton-bearing clusters and proton transfers [103]. With a simple two-state empirical valence bond model (see below for details), which implements in a classical way the above-mentioned idea of two limiting protonated structures, namely the 11502 and the H30 cluster, it was indeed observed that the two alternative sequences are equivalent with similar life times for both clusters, and that conversions between the two clusters are purely fluctuative. 

We have seen that 10" M s is about the fastest second-order rate constant that we might expect to measure this corresponds to a lifetime of about 10 " s at unit reactant concentration. Yet there is evidence, discussed by Grunwald, that certain proton transfers have lifetimes of the order 10 s. These ultrafast reactions are believed to take place via quantum mechanical tunneling through the energy barrier. This phenomenon will only be significant for very small particles, such as protons and electrons. 

First, we shall discuss reaction (5.7.1), which is more involved than simple electron transfer. While the frequency of polarization vibration of the media where electron transfer occurs lies in the range 3 x 1010 to 3 x 1011 Hz, the frequency of the vibrations of proton-containing groups in proton donors (e.g. in the oxonium ion or in the molecules of weak acids) is of the order of 3 x 1012 to 3 x 1013 Hz. Then for the transfer proper of the proton from the proton donor to the electrode the classical approximation cannot be employed without modification. This step has indeed a quantum mechanical character, but, in simple cases, proton transfer can be described in terms of concepts of reorganization of the medium and thus of the exponential relationship in Eq. (5.3.14). The quantum character of proton transfer occurring through the tunnel mechanism is expressed in terms of the... 

This approach may be possible for small molecules because the gas-phase proton affinity can be obtained quantum mechanically with an accuracy of 1-2 kcal/mol [19]. However, the solvation free energy of H+ cannot be calculated and the experimental value is only known approximately, from 259.5 to 262.5 kcal/mol [60]. Also, because the proton affinity and solvation free energies in Eq. (10-7) are on the order of hundreds of kcal/mol, small percentage errors in the calculation can give rise to large error in AGaqP and pKa. Thus, this method for calculation of absolute pifa s remains impractical at the present time [6],... 

By using this approach, it is possible to calculate vibrational state-selected cross-sections from minimal END trajectories obtained with a classical description of the nuclei. We have studied vibrationally excited H2(v) molecules produced in collisions with 30-eV protons [42,43]. The relevant experiments were performed by Toennies et al. [46] with comparisons to theoretical studies using the trajectory surface hopping model [11,47] (TSHM). This system has also stimulated a quantum mechanical study [48] using diatomics-in-molecule (DIM) surfaces [49] and invoking the infinite-order sudden approximation (IOSA). 

Quantum mechanical calculations of molcular orbitals have been performed on five examples (8-azapurine, -hypoxanthine, -guanine, -adenine, and -xanthine) by two methods (a) a semiempirical approximation, which included contributions from the a electrons of the skeleton, and (b) the CNDO approximation, which included contributions from all the valence electrons of the molecule. The results were tabulated in parallel for each of the three possible positions of the triazole proton. In all 15 entries, the highest occupied and the lowest unoccupied molecular orbitals were calculated and also the dipole moment, the molecular energy, and the UV absorption maxima (the last-named showed only a modest agreement with experimental results). It was concluded that both types of calculation indicated that relative stabilities for the three tautomers (in each of the five sets) should decrease in the order HN-9, HN-7, and HN-8, and that the HN-8 tautomers should be 85 to 125 kJ (20-30 kcal) per mol less stable than the other two. However, it had to be admitted that, in all sets of three isomers examined experimentally, the HN-8 member has never been found inferior in stability. ... 

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