Polyatomic system parameters

The concept of a reaction co-ordinate in organic chemistry is one that is not simply defined, since for a polyatomic system of n atoms it may depend on as many as 3n — 6 parameters for complete characterization. The reaction co-ordinate used by organic chemists in their representation of a reaction profile has only a qualitative significance. For example, that for an SN2 process on a methyl derivative is generally equated with the change in either the... 

We may now ask how the method performs when only a small number of points is affordable since this is a critical issue for large polyatomic systems. This has been investigated by comparing the CHIPR form (fit I) obtained above with another obtained from fit II to a grid of 420 distinct points, also with 345 (= 337 - - 8) parameters. Note that no points have been considered for Z.HHH —60°, with an extra 75 points added to avoid solving a non-linear system of equations. Interestingly, fit II shows no unphysical features and an... 

In the reaction volume approach the reference frame is a function of three parameters taken to be the hyperspherical variables defining the size and shape of the reaction center of the polyatomic system. Thus each atom in the system has a reference position a,(p, 9,4>) which is defined by minimizing the gradient, i.e., the force on each individual atom of the system. That is the gradient is minimized subject to the three... 

The accurate representation of multidimensional potential energy surfaces is a formidable problem. A common approach is to employ an expression that incorporates as much physical insight as possible in the functional form and which has a number of parameters that are adjusted to empirical data. Examples of this approach are found in applications of the London-Eyring-Polyani-Sato (LEPS), valence-bond (VB), diatomics-in-molecules (DIM), and many-body expansion methods to polyatomic systems. 

Figure C3.5.6 compares the result of this ansatz to the numerical result from the Wiener-Kliintchine theorem. They agree well and the ansatz exliibits the expected exponential energy-gap law (VER rate decreases exponentially with Q). The ansatz was used to detennine the VER rate with no quantum correction Q= 1), with the Bader-Beme hannonic correction [61] and with a correction based [83, M] on Egelstaff s method [62]. The Egelstaff corrected results were within a factor of five of experiment, whereas other corrections were off by orders of magnitude. This calculation represents the present state of the art in computing VER rates in such difficult systems, inasmuch as the authors used only a model potential and no adjustable parameters. However the ansatz procedure is clearly not extendible to polyatomic molecules or to diatomic molecules in polyatomic solvents.

The nuclear spin-rotation interaction becomes very simple for a diatomic molecule. The principal components of the tensor a for a polyatomic molecule were described in equation (8.163) this expression reveals that for a diatomic system the axial component (c/)zz is zero and, of course, the two perpendicular components are equal. The nuclear spin rotation interaction for a diatomic molecule is therefore described by a single parameter c/. The appropriate term in the effective Hamiltonian, first presented in equation (8.7), is... 

A number of diatomic and polyatomic inorganic radicals have been produced in photochemical systems. Some of these radicals are listed in Table 2. Recently Martin and Swift (189) observed, during the photolysis of ceric perchlorate acid glass, ESR spectra similar to those of methyl radicals and intuitively assigned them to H O radicals. Given that these spectra have been correctly analyzed, it is difficult to understand how their ESR parameters could relate to the 6 radical H O. Confirmation of the assignment must await further detailed study. 17... 

In sununary, we have presented a new theoretical perspective of adsorption of polyatomics. The approach simplifies the inherent complexity of this kind of adsorption systems in a statistical exclusion parameter which hass a physical meaning traced to the adsorption configuration on the lattice sites. 

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