Symmetry operation Triatomic molecules

Potential fluid dynamics, molecular systems, modulus-phase formalism, quantum mechanics and, 265—266 Pragmatic models, Renner-Teller effect, triatomic molecules, 618-621 Probability densities, permutational symmetry, dynamic Jahn-Teller and geometric phase effects, 705-711 Projection operators, geometric phase theory, eigenvector evolution, 16-17 Projective Hilbert space, Berry s phase, 209-210... 

Figure 6 shows the relation between the several coordinate systems and the molecular conformations for a constant perimeter of the triatomic molecule. Also shown in this figure is the locus of the possible symmetry point groups (we consider the symmetry associated with the group operations applicable to identical nuclei) unless stated otherwise, the symmetry group will be Cs. 

In the case of collisions with triatomic molecules, such as N02, in general the only symmetry operation is the identity operation I. This means that the only requirement of two interacting surfaces is that they have the same multiplicity. 

Let us consider the explicit effect of the Majorana operator on a symmetric triatomic molecule. In light of the symmetry under bond exchange, the Hamiltonian operator (4.23) can be written as... 

Beryllium hydride, BeH2, is the simplest triatomic molecule. This substance has apparently not been shown experimentally to exist, but calculations indicate that it should be a bound linear molecule with two equal Be-H bond distances. We assume this equilibrium conformation and apply the Bom-Oppenheimer approximation. We place the molecule in a Cartesian coordinate system with the Be atom at the origin and with the H atoms on the z axis, as shown in Figure 21.1. We denote one of the H atoms by Ha and the other by Hb. The molecule possesses the same symmetry operations as hJ E, i, ah, Cooz, and infinitely many cr and C2 operations perpendicular to the bond axis. 

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