Reactivity Morse potential model

In 1936, de Boer formulated his theory of a stressed bond which, despite its simplicity, still constitutes the basis for most models of chemical reactivity under stress [92], In order to fracture an unstressed bond which, in the absence of any vibration, is approximated by the Morse potential of Fig. 18, an energy D must be supplied. If, however, the bond is under tension due to a constant force feitt pulling on either end, the bond rupture activation energy will be decreased by an amount equivalent to the work performed by the mechanical force over the stretching distance from the equilibrium position. The bond potential energy in the presence of stress is given by ... 

Fig. 4.14. (a) The Morse potential energy curves have the shape of a hook. How does the shape depend on the Morse parameters The figures show the curves for D = 1.2 and a = 1,2. As we can see D controls the well depth and a its width, (b) the Morse oscillator is a kind of compromise between the harmonic oscillator (bl) and a rectangular well (b2). Both potentials correspond to exact solutions of the Schrddinger equation. Model b2 gives the discrete spectrum as well as the continuum and the resonance states. The later ones are only very rarely considered for the Morse oscillator, but they play an important role in scattering phenomena (primarify in reactive collisions). 

Instead of performing the normal mode analysis we have used a more approximate method to take the qr- -coordinates into account. For the Cl - - CH4/CD4 reactions wc have in some work used a tanh-function in the breaking bond to interpolate between the saddle point and the product asymptote to get both the reaction thermicity and AfA" consistent with the ah initio calculations[18]. In addition, if the effective potential energy surface of the system is modeled by the semiempirical London-Eyring-Polanyi-Sato (LEPS) function, the correction is made directly in the Morse parameters for the two reactive bonds by adjusting the Sato parameters) , 19]. 

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