In triatomic molecules and

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. 

In his classical paper, Renner [7] first explained the physical background of the vibronic coupling in triatomic molecules. He concluded that the splitting of the bending potential curves at small distortions of linearity has to depend on p, being thus mostly pronounced in H electronic state. Renner developed the system of two coupled Schrbdinger equations and solved it for H states in the harmonic approximation by means of the perturbation theory. 

T is a rotational angle, which determines the spatial orientation of the adiabatic electronic functions v / and )/ . In triatomic molecules, this orientation follows directly from symmetry considerations. So, for example, in a II state one of the elecbonic wave functions has its maximum in the molecular plane and the other one is perpendicular to it. If a treatment of the R-T effect is carried out employing the space-fixed coordinate system, the angle t appearing in Eqs. (53)... 

Thus the angle t plays the role analogous to that of the angle defining the orientation of the instantaneous molecular plane in triatomic molecules. Employing the relations (69) and (59) one obtains... 

In this section, we briefly discuss spectroscopic consequences of the R-T coupling in triatomic molecules. We shall restrict ourselves to an analysis of the vibronic and spin-orbit structure, determined by the bending vibrational quantum number o (in the usual spectroscopic notation id) and the vibronic... 

The matrix elements of the operator Ml2 are easy to construct since they are identical to those already encountered in triatomic molecules [Eq. (4.70)]. The corresponding secular equation can be diagonalized, yielding the results shown in Figure 5.5. The main effect of the Majorana term is splitting of the degenerate C-H stretching modes into g and u species, as in the previous triatomic case, Section 4.5. 

Joyeux, M. (1992), The Transition towards Vibrational Chaos in Triatomic Molecules. A Numerical and Analytical Approach, Chem. Phys. 167, 299. 

Figure 9.4. Walsh diagram showing correlation of orhitals between bent and hnear triatomic molecules, and suggesting variation in orbital energy with bond angle.

Force fields up to quartic anharmonic terms are now known with reasonably high accuracy for several triatomic molecules and the results shown in Table 3 for H2O are typical. However, even for these there has had to be an assumption that some of the quartic interaction terms are zero in order that the equations from which the constants are derived shall have unique solutions. It can be seen moreover that some of the cubic and quartic terms have uncertainties which are larger than the values of the constants themselves. 

Translational symmetry. 74 Translawrencium elements, periodicity of. 615-617 Transport, dioxygen, 895-910 Triatomic molecules and ions, molecular orbitals in, 175-182... 

The photofragmentation that occurs as a consequence of absorption of a photon is frequently viewed as a "half-collision" process (16)- The photon absorption prepares the molecule in assorted rovibrational states of an excited electronic pes and is followed by the half-collision event in which translational, vibrational, and rotational energy transfer may occur. It is the prediction of the corresponding product energy distributions and their correlation to features of the excited pes that is a major goal of theoretical efforts. In this section we summarize some of the quantum dynamical approaches that have been developed for polyatomic photodissociation. For ease of presentation we limit consideration to triatomic molecules and, further, follow in part the presentation of Heather and Light (17). 

The principles of electronic spectroscopy have been discussed by Herzberg (1950) for diatomic molecules, and in a classic review by Sponer and Teller (1941) for the more general case of polyatomic structures. Recent developments are described in articles appearing regularly in the Annual Reviews of Physical Chemistry. Triatomic molecules and radicals have been intensively studied, the latter by the powerful method of flash photolysis (Herzberg, 1959). As triatomic structures have been comprehensively reviewed recently (Ramsay, 1962) we include in this article only those triatomic systems that are of particular interest in organic chemistry. Otherwise attention will be directed to molecules of four or more atoms, including all known representatives of the important chromophores. 

The theory outlined above can be used to calculate the exact bound-state energies and wavefunctions for any triatomic molecule and for any value J of the total angular momentum quantum number. We can solve the set of coupled equations (11.7) subject to the boundary conditions Xjfi (R Jp) —> 0 in the limits R —> 0 and R — oo (Shapiro and Balint-Kurti 1979). Alternatively we may expand the radial wavefunctions in a suitable set of one-dimensional oscillator wavefunctions ipm(R),... 

The past three years have seen considerable advances in the study of the electronic structure of triatomic molecules, and calculations of comparable accuracy to those reported on diatomics are now feasible. 

Kohn and Hattig [40] have presented a quite extensive study on the performance of the CC2 method for adiabatic excitation energies, excited state structures, and excited state harmonic frequencies. The systems studied include 7 diatomic molecules, 8 triatomic molecules, and 5 larger molecules. The aug-cc-pVDZ, aug-cc-pVTZ, and aug-cc-pVQZ basis sets were used. The results in general are quite encouraging, and studies of this sort with CCSD and, to the extent that they are possible, with higher level methods would be most welcome. 

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... 

Summarizing, we note that the single-quantum vibrational predissoeiation of a weak van-der-Waals bond in a triatomic molecule and the classical dissociation of the same system do not represent proeesses which can be eompared in the eorrespondenee prineiple limit. Our study explains why the classieal and quantum rates sometimes are elose to each other and show the same trends with a change of the interaction parameters. The underlying logic in comparing of classical and quantum and VP rates is as follows ... 

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