Anharmonic tunneling

Such a method has recently been developed by Miller. et. al. (28). It uses short lengths of classical trajectory, calculated on an upside-down potential energy surface, to obtain a nonlocal correction to the classical (canonical) equilibrium probability density Peq(p, ) at each point then uses this corrected density to evaluate the rate constant via eq. 4. The method appears to handle the anharmonic tunneling in the reactions H+HH and D+HH fairly well (28), and can... 

Fig. 7. Predicted diffusion coefficients for hydrogen (H) and deuterium (D) in niobium, as calculated by Schober and Stoneham (1988) from a model taking account of tunneling between various states of vibrational excitation and comparison with experimental measurements (solid lines). Theoretical curves are shown both for a model using harmonic vibrational wave functions (dashed lines) and for a model with anharmonic corrections (dashed-dotted lines).

The book thus embraces an extended study on a variety of issues within the theory of orientational ordering and phase transitions in two-dimensional systems as well as the theory of anharmonic vibrations in low-dimensional crystals and dynamic subsystems interacting with a phonon thermostat. For the sake of readability, the main theoretical approaches involved are either presented in separate sections of the corresponding chapters or thoroughly scrutinized in appendices. The latter contain the basic formulae of the theory of local and resonance states for a system of bound harmonic oscillators (Appendix 1), the theory of thermally activated reorientations and tunnel relaxation of orientational... 

This chapter is devoted to tunneling effects observed in vibration-rotation spectra of isolated molecules and dimers. The relative simplicity of these systems permits one to treat them in terms of multidimensional PES s and even to construct these PES s by using the spectroscopic data. Modern experimental techniques permit the study of these simple systems at superlow temperatures where tunneling prevails over thermal activation. The presence of large-amplitude anharmonic motions in these systems, associated with weak (e.g., van der Waals) forces, requires the full power of quantitative multidimensional tunneling theory. 

The LHA is exact for potentials that contain, at most, quadratic terms but obviously an approximation for anharmonic potentials. Thus, a single Gaussian wave packet within a local harmonic approximation can, e.g., not tunnel or bifurcate, i.e., there will be no simultaneously reflected and transmitted part in scattering off barriers. 

All this applies to weak and medium strong H-bonds like those encountered for alcohols and many other systems up to carboxylic acid dimers or about 32-42 kJ/mol. (8 or 10 kcal/mol.) Unfortunately vibrational spectra of systems with very strong H-bonds could, with a few exceptions, only be measured in condensed phases. Factors that come in when such systems are examined are potential surfaces with two minima with, in certain cases, the possibility of tunnelling, or flat single minima Most of these systems are likely to be so anharmonic that second order perturbation theory breaks down and the concept of normal vibrations becomes itself question-nable. Many such systems are highly polarizable and are strongly influenced by the environment yielding extremely broad bands 92). Bratos and Ratajczak 93) has shown that even such systems can be handled by relaxation theories. 

Bunker et have attempted to calculate anharmonicities and tunneling splittings... 

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