Triatomic molecules minimization

A electronic states, 647—653 II electronic states, 641-646 triatomic molecules, minimal models, 615-618... 

We employ the general scheme presented above as a starting point in our discussion of various approaches for handling the R-T effect in triatomic molecules. We And it reasonable to classify these approaches into three categories according to the level of sophistication at which various aspects of the problem are handled. We call them (1) minimal models (2) pragmatic models (3) benchmark treatments. The criterions for such a classification are given in Table I. 

Hamiltonian equations, 627-628 II electronic states, 632-633 triatomic molecules, 587-598 minimal models, 615-618 Hartree-Fock calculations ... 

Triatomic molecules may be linear or bent (i.e. V-shaped or angular). The shape adopted by any particular molecule is that which is consistent with the minimization of its total energy. 

The simplest possible case will be a triatomic molecule of the type AX2 in which the coordination number (number of bonded atoms X) around the central atom A is 2. What angle between the two A-B bonds will give the greatest possible separation between them, thus minimizing the repulsion between the associated electron clouds It is not very difficult to see that the answer is 180° the two bonds must extend out from the A atom in opposite directions. 

Using the definition of the best loges as the ones which minimize l(P , 12), Daudel et al. (1974) applied this theory to a number of diatomic and triatomic molecules containing up to six electrons, namely, LiH, BeH", BH, and BeH2. 

In a batch forge furnace, the space above the load(s) was held at 2250 F, wall to wall. High-velocity stirring burners were fired between the 8 in. tall piers supporting the load(s). The burners were operated with fuel turndown only to minimize the concentration of triatomic molecules while inducing a high mass of inert gas from above the load. The wall-to-wall temperature drop under the product was very low—a maximum of 6°C (3.3°C). Chapter 8 discusses temperature uniformity in more detail. 

MC-SCF calculations on polyatomic molecules are still rather rare, although there have been many such calculations on triatomic and diatomic molecules. Levy45 has described the results of such calculations using a minimal STO basis set for CH4, C2H4, and CjjHa. A quadratically convergent method was described and the results of localizing the orbitals were investigated. 

Next, consider a reaction between an atom and a diatomic molecule, A + BC. Reactions can differ also in their energetic requirements, but to focus attention on the steric requirements with the energetic effects being equal we take the barrier height Eq to be the same as in the previous reaction. To have minimal steric requirements let us take the transition state, ABC, to be bent. This choice allows A to approach BC within a cone. Because BC has an internal structure, the partition function for the reactants becomes Q = Q Q QvQ - The transition state is a bent triatomic. It has three vibrations, one of which is the reaction coordinate. (As we saw in Section 5.1, this is the asymmetric stretch vibration.) The bent transition state has three planes of rotation, = Q QIQ - Accordingly, for reasons that will become immediately apparent, we write k T) as... 

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