Tetra-atomic Molecules

Linear Tetra-atomic Molecules.—Acetylene and cyanogen appear to be the only linear tetra-atomic molecules on which calculations have been made. In this case the number of parameters in the general force field becomes 2re + 6/j + ll/3 + 23/i. The problem of determining all of the quartic force constants in the general force field looks unlikely to be well determined, although there are apparently good data on a variety of isotopic species for 

Included in this section are AH3, AB3, HABa, H2AB molecules, and also dimers, and interactions between diatomics or triatomics and atoms or ions. 

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Selected Bases for Highly Excited Vibrations of Tetra-Atomic Molecules. 

In tetra-atomic molecules that are linear, the number of degrees of freedom is F =7, which again considerably complicates the analysis. Nevertheless, the dynamics of such systems can turn out to be tractable if the anharmonicities may be considered as perturbations with respect to the harmonic zero-order Hamiltonian. In such cases, the regular classical motions remain dominant in phase space as compared with the chaotic zones, and the edge periodic orbits of subsystems again form a skeleton for the bulk periodic orbits. 

F. Miscellaneous Tetra-atomic Molecules.—Formaldehyde, HCHO, has received a great deal of attention from theoreticians. Space does not permit more than a brief... 

Figure 2.7-4 Examples of tetra-atomic molecules belonging to different point groups. They can be distinguished by the number of polarized and depolarized Raman active vibrations, the infrared active vibrations and the coincidences of the frequencies of infrared and Raman active bands.

The tetra-atomic molecules of concern throughout this book belong to one of two point groups Cjv or C. The character tables for these groups are reproduced below ... 

A fourth assumption has been that one should start with a periodic system for diatomic molecules. Then, if the results turn out to be promising and if circumstances allow it, the process would go on to use the same approach for linear and cyclic diatomic molecules, for the several structures of tetra-atomic molecules, and possibly for yet larger molecules. This assumption was clearly visible in the successive publications, concerning diatomic and then triatomic periodic systems, by Kong and by Hefferlin and his group. 

One prospect for Kong s elegant construction is that it may be extended to tetra-atomic molecules a proof-of-principle data analysis has already been made. Whether the same can be accomphshed for larger molecules remains to be seen. Another possible prospect is the preparation of tables including all molecules in the compartments of Kong s periodic systems of triatomic and tetra-atomic molecules they should require four and six atom row and column differences, respectively, if the same protocol is used as for diatomic molecules. 

Thus, it seems that the physical periodic systems can be used for predictions of massive numbers of molecules only for diatomic and acyclic triatomic molecules and possibly for one or another structural form of tetra-atomic molecules. This limitation is not due to the method of construction of the periodic system, but to the scarcity of data with which to set up the least-squares or neural-network computing. 

Energy surfaces for chemical reactions involving three main group atoms can be performed with the 12 valence orbitals active. This will cover all possible reaction channels. Tetra-atomic molecules would need 12-16 orbitals depending on whether the ns orbitals have to be included or not. The problem is of course simplified if one or more of the atoms is hydrogen. Additional active orbitals may be needed for excited states surfaces where Rydberg states may become important. 

State geometries involves analysis of the rotational fine structure of the electronic bands. Since the spectra of polyatomic molecules are complex, most analyses of this sort have been carried out on the triatomic or tetra-atomic molecules. For molecules whose spectra contain unresolved fine structure, estimates of the excited state geometry can be obtained by vibrational analyses. 

Kozin, I.N., Law, M.M., Hutson, J.M., Tennyson, J. Calculating energy levels of isomerizing tetra-atomic molecules. 1. The rovibrational bound states of Ar2HF, J. Chem. Phys. 2003,118,4896-904. 

Equation 2.18 shows six possible ionic products that can be formed by simple cleavage of bonds in the molecular ion of a tetra-atomic molecule. 

Simple cleavages of a molecnlar ion conld lead to a rather complex mass spectrum (10 ions for a tetra-atomic molecule 212 ions for an arrangement of 20 atoms). In reality, certain bonds are more likely to break than others, a phenomenon that leads to the formation of relatively few abundant ions. 

Any nonlinear triatomic molecule with three different atoms has only symmetry, e.g., a water molecule with one hydrogen replaced by deuterium. C2 symmetry requires a nonplanar tetra-atomic molecule, such as H2O2. In the free state the dihedral angle of this molecule is almost a right angle (see the figure). To realize Q symmetry, one needs at least six atoms. Since three atoms are always coplanar, the smallest molecule with no symmetry at all has at least four atoms. 

In general, theoretical studies of triatomic and tetra-atomic molecules employ analytical PESs carefully fitted to large grids of ab initio data points, and curvilinear vibrational coordinates, to take into account large-amplitude motions. On the other hand, larger polyatomic molecules are investigated with simple polynomial PES, whose parameters are obtained from ah initio data, and with normal coordinates, possibly considering only the active ones. Finite basis representations (FBR),... 

As discussed in Section 8.2.1, when nonadiabatic couplings cannot be neglected, the BO approximation is not reliable and coupled electronic states must be considered simultaneously with their interactions. For small systems, several full-dimensional approaches based on the vibronic or spin-rovibronic wavefunctions and taking into account simultaneously at least two electronic states have been developed [2, 100-104]. To quote some examples, the full vibronic Hamiltonians have been derived and employed for linear tetra-atomic molecules showing Renner-Teller interactions [103] or CXaY-like molecules of Csv symmetry showing Jahn-Teller interactions [104]. In the following, we will present the computational approaches based on the full rovibronic Carter-Handy Hamiltonian [100], developed for triatomic molecules and expressed in internal coordinates, which allows us to take into account up to three interacting electronic states [2, 100, 101]. 

Dissociation of model triatomic and tetra-atomic molecules 81 - 85... 

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