Oscillating barrier method

Lucassen Giles (1975), and Kretzschmar Konig (1984). Fig. 3.24. shows the schematic set-up of the oscillating barrier method as an example. 

The measurements of the characteristics of transverse surface waves are possible when the ratio of oscillation amplitude to wavelength is less than 0.1 % and all perturbations are really small [105]. The potential of relaxation methods was appreciated already by Lucassen (1975) who used the oscillating barrier method [94, 95]. However, for most surfactants the characteristic adsorption times correspond to frequencies, which are inaccessible for this method. The application of surface wave techniques to micellar solutions relates to later time [96 - 105]. 

Fig. 3.24. Method of the oscillating barrier, 1 - compression barrier, 2 - oscillating barrier (0.05 to 1 Hz), 3 - force balnce...

Functions were calculated from the constants given above using the rigid rotator harmonic oscillator method. The entropy was increased by R tn 2 because two rotameric forms are implied by use of the torsional frequency. Small but arbitrary adjustments were made in the assignment of the bending mode frequencies in order to reproduce the vapor pressure data of Scott et al. (1 ) as closely as possible. Calculated values of S (298.15 K) = 57.03 and S (340 K) = 58.70 cal k" raol" may be compared with 56.99 and 58.69, respectively, derived from the data of Scott et al. Internal rotation calculations would require a complex potential function in order to fit the data. The barrier to inversion (990 cm 2.8 kcal mol ) is slightly less than the barrier to... 

By changing the frequency and the intensity of the steady state laser, we can vary the width and the displacement of the excited wave packet. With this example, we want to demonstrate how the space-dependence of a dipole coupling can be used to steer the transfer of a wave packet to an excited molecular potential. However, this is only one example out of many possible. This method is by no means restricted to a model system consisting of harmonic oscillators but can be easily applied to any form of one-dimensional potential curves. Possible applications might be steering of a reaction to one side of a potential barrier by displacing the excited wave packet to the desired side, or coupling to a dissociative state in order to steer the dissociation of a molecule. 

The case of the parabolic barrier can be solved in a similar fashion however, the algebraic procedure becomes cumbersome due to the fact that the corresponding ladder operators are not adjoint to each other. A better approach is to use the concept of the Bargmann-Segal space, whereby avoiding long algebraic derivations [32]. We exemplify this method in the case of the harmonic oscillator. Let us consider the time-dependent Hamiltonian ... 

For example. East and Radom devised a procedure they call El, which calculates from the MP2/6-31G geometry (MP2 calculations are (Uscussed in Section 15.18) and Svib from HF/6-31G scaled vibrational frequencies and the harmonic-oscillator approximation, except that internal rotations with barriers less than 1.4R7 are treated as free rotations [A. L. L. East and L. Radom,/. Chem. Phys., 106,6655 (1997)]. For 19 small molecules with no internal rotors, their El procedure gave gas-phase 5S,298 values with a mean absolute deviation from experiment of only 0.2 J/mol-K and a maximum deviation of 0.6 J/mol-K. The El procedure was in error by up to Ij J/mol-K for molecules with one internal rotor and by up to 2 J/mol-K for molecules with two rotors. An improved procedure called E2 replaces the harmonic-osdllator potential for internal rotors by a cosine potential calculated using the MP2 method and a large basis set, and reduces the error to 1 J/mol-K for one-rotor molecules. 

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