Arrangement channel

Pogrebnya S K, Echave J and Clary D C 1997 Quantum theory of four-atom reactions using arrangement channel hyperspherical coordinates Formulation and application to OH + Hg < HgO + H J. Chem. Phys. 

Now, we are in a position to present the relevant extended approximate BO equation. For this purpose, we consider the set of uncoupled equations as presented in Eq. (53) for the = 3 case. The function icq, that appears in these equations are the eigenvalues of the g matrix and these are coi = 2 (02 = —2, and CO3 = 0. In this three-state problem, the first two PESs are u and 2 as given in Eq. (6) and the third surface M3 is chosen to be similar to M2 but with D3 = 10 eV. These PESs describe a two arrangement channel system, the reagent-arrangement defined for R 00 and a product—anangement defined for R —00. 

Consider a triatomic system with the three nuclei labeled A, Ap, and Ay. Let the arrangement channel -1- A A be called the X arrangement channel, where Xvk is a cyclic permutation of apy. Let Rx,r be the Jacobi vectors associated with this arrangement channel, where r is the vector from A to and the vector from the center of mass of AyA to A . Let R i, rx be the corresponding mass-scaled Jacobi coordinates defined by... 

D. J. Tannor Some years ago we looked at the photodissociation of the ozone molecule [/ Am. Chem. Soc. Ill, 2772 (1989)]. Ozone (O3) can be viewed in much the same way as Naa, in that it has an initial wavepacket with three lobes, one located in each of three symmetrically equivalent wells (see Fig. 1). In the excited state, at the same locations, the potential has saddle points. As a result, each of the component wavepackets bifurcates, and there is a change of alliances The left portion of one wavepacket joins up with the right portion of another wavepacket, and they tunnel into the same product arrangement channel. 

The three-body systems discussed so far contain two identical particles. Another system of interest, C He1, contains three different particles and can decay into two different arrangement channels... 

The different groupings of the atoms are referred to as arrangement channels (or simply channels) we label the reactant channel by a, whereas the different product... 

Long after the scattering several arrangement channels can be populated, with channel Hamiltonians H13 (/ = 1,2,...), and... 

Of particular interest is the probability of being in a complete subspace of state denoted by the label q that is, all m associated with a fixed q, where n = (m, q). greatest concern in chemistry is the case where q labels the chemical identity (i the arrangement channel) of the product of a chemical reaction hence below often explicitly refer to q in this manner. However, it should be clear that the th applies to any other q chosen from the set of n quantum numbers. 

Thus, in this case, the ratio of product into various arrangement channels controlled entirely by the time delay (td — tx) between pulses. 

Here, the superscript R denotes reactive scattering into a specific final arrange channel q q. The total differential cross section, nR(0, cp), for reaction out state in Eq. (7.25) is given by the sum over final states at energy E as... 

One can optimize scattering into arrangement channel q, with the normalization constraint Kl2 = 1, by requiring... 

Here n = m, q where q = 1,2... denotes the product arrangement channel a denotes the remaining quantum numbers other than the energy. 

The hyperspherical coordinate Hamiltonian is suitable for photodissociation with two or more arrangement channels e.g. ABC + hv AB + C or A + BC. The three degrees of freedom are represented by Employing Johnson s... 

In order to keep the presentation as simple as possible, we will limit the discussion to triatomic molecules and motion on a single PES (Born-Oppenheimer approximation). Moreover, only one chemical arrangement channel is considered in the reaction ABC A -F BC. Formal extensions... 

Figure 4 shows the dependence on final rotational state of the C1-hH2(v=0, j =0)—> HCl(v=0jO DCSs at two different coUision energies. We observe that the DCSs all have a very similar shape. Likely, this implies that the overaU shape of the DCS is determined by the reactive probabdity (opacity) as a function of impact parameter and by an overall deflection function (h), while the product final state distribution is governed by the shape of the PES in the exit region of the arrangement channels. We remark also that the determination of fully final-state resolved DCS does not present any particular difficulty for our time-independent method, but would not be feasible with some of the time-dependent methods which have been applied recently to the X-hH2 reactions. [7, 16]... 

Zhang, Z.H. and Kouri. D.J. (1986) Wave-packet solution to the time-dependent arrangement-channel quantum-mechanics equations. Phys. Rev. A 34. 2687-2696. 

As explained above, the hexagonal micellar mould is only present for the micellar solutions that contain between 30 and 65 wt.% of sur ctant. The addition of TMOS probably disturbs this array, leading to a disordered fiamework. However, in the case of less concentrated micellar solutions, where only individual micellar rods exist, it appears that the addition of the silica source plays the key role in the obtention of very regular hexagonally arranged channels. Such a co-operative mechanism could be analogous to the LCT pathway initially proposed by Mobil researchers [2]. 

Hence the resonance width Is a sum of partial widths Into the several arrangement channels. 

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