Beyond Potential Surfaces

Beyond the surface plane is a layer of ions attracted to the surface by specific chemical interactions. The locus of the center of these ions is known as the inner Helmholtz plane (IHP). The charge in this plane, which results from the specifically adsorbed ions is denoted by a2, and the electrostatic potential at the IHP by The species usually assigned to this plane include... 

H. Rabitz The information in the recurrence time alone is minimal. However, the temporal structure of the recurrence signal contains detailed information on the surface explored by the wandering scout wavepacket during its excursion. Further experiments may be necessary to follow (i.e., track) the wavepacket through its excursion over the potential surface. Such pump-probe experiments go beyond conventional spectroscopy. 

Apart from the heat bath mode, the harmonic potential surface model has been used for the molecular vibrations. It is possible to include the generalized harmonic potential surfaces, i.e., displaced-distorted-rotated surfaces. In this case, the mode coupling can be treated within this model. Beyond the generalized harmonic potential surface model, there is no systematic approach in constructing the generalized (multi-mode coupled) master equation that can be numerically solved. The first step to attack this problem would start with anharmonicity corrections to the harmonic potential surface model. Since anharmonicity has been recognized as an important mechanism in the vibrational dynamics in the electronically excited states, urgent realization of this work is needed. 

The electrostatic potential satisfies the Laplace equation within each of the two semi-infinite media which lie beyond the surfaces,... 

The real reasons that the discussion in this chapter has been entirely classical are in part that mechanisms seem to be most easily visualized in terms of classical mechanical concepts — especially the idea of the instantaneous positions of solvent molecules serving as the initial conditions for subsequent dynamics. Beyond that, though, we have limited ourselves to classical mechanics because the localized snapshots of the potential surface that INM ideas so depend on seem difficult to incorporate into standard quantum mechanical calculations. It is tempting to pretend that the INM harmonic modes derived from a classical calculation can be... 

Note in the figures that at potential X, the equilibrium concentration of A at the electrode surface has been reduced to about 80% of its original value, while the equilibrium concentration P has increased by an equivalent amount (that is, cj = ca < a)- At potential Y, which is the half-wave potential, the equilibrium concentrations of the two species at the surface are approximately the same and are equal to CfiJ2. Finally, at potential Z and beyond, the surface concentration of A approaches zero, whereas that of P approaches the original concentration of A, c. At potentials more negative than Z, essentially all A ions approaching the electrode... 

Kratochvil, M., Engkvist, O., Sponer, J., Jungwirth, P., and Hobza, P. (1998) Uracil dimer potential energy and free energy surfaces. Ab initio beyond Hartree-Fock and empirical potential surfaces, J. Phys. Chem. A 102, 6921-6926. 

The potential due to the ionic atmosphere is the same at the distance a/2 as at the distance d, and is therefore constant in the region in between, i.e. in the region beyond the surface of the central ion into which the centre of any other ion cannot penetrate (see Figure 10.5). 

Obviously, the electronic energies E (R) for n 0 corresponds in a similar manner to potential surfaces for electronically excited states. Each PES usually exhibits considerable structure for a polyatomic system and will provide useful pictures with reactant and product valleys, local minima corresponding to stable species, and transition states serving as gateways for the system to travel from one valley to another. However, for the number of nuclear degrees of freedom beyond six, i.e. for more than four-atom systems it becomes extremely cumbersome to produce the PES s and quite complicated to visuahze the topology. Furthermore, when more than one PES is needed, which is not unusual, there is a need for nonadiabatic coupling terms, which also may need interpolation in order to provide useful information. 

Our interest in the photooxidation of Fe " in aqueous solution derives from our more general interest in the effects of solvents on electronic transitions, particularly those in which strong specific interactions with solvent molecules are present (42,45,46). We proceed by performing electronic structure calculations, hquid structure simulations, and spectroscopic calculations for mechanisms 1, 3, and 4, investigating the nature of the photochemical processes of aqueous Fe. In particular, we first require the gas-phase absorption frequencies and intensities of the Fe (H20)6 complex, using both ab initio and semi-empirical (INDO-MRSCI) techniques. Second, we need to determine the structure of water around the Fe " ion in solution. Third, we need to determine the solvent shifts of the absorption bands to evaluate transition energies in solution. This will lead to an estimation of relative importance of all but the charge transfer to solvent process (mechanism 2), calculation of which is beyond die capacity of our present computational facihties. The potential surfaces em-... 

Recent advances in the growth of organic molecular layers suggest that beyond this rather simple kinetically controlled approach a molecular assembly due to directed forces between the deposited entities, which rather creates equilibrium structures, is feasible. This will open the way to an even bigger number of potential surface templates. 

The H- F2 reaction was the first one. beyond H- H2 and Its Isotopes, for which it was meaningful to compare large scale DW calculations with experiment (Clary and Connor [21]). This reaction has the advantage that a reasonable LEPS potential surface Is available (Jonathan et al. [49]) and the product distributions are insensitive to variations in j and Etr for the thermal energy range. This last property allows a fixed energy calculation for H+F2(v=0. j=0) to be meaningfully compared with thermal infrared chemiluminescence data (Polanyi and Sloan [69]. Brandt and Polanyi [11]). 

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