Triatomic molecules symmetry

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)... 

ABA symmetry, Renner-Teller effect, triatomic molecules, 618-621 ABBA molecules, Renner-Teller effect, tetraatomic 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... 

An important problem of molecular spectroscopy is the assignment of quantum numbers. Quantum numbers are related to conserved quantities, and a full set of such numbers is possible only in the case of dynamical symmetries. For the problem at hand this means that three vibrational quantum numbers can be strictly assigned only for local molecules (f = 0) and normal molecules ( , = 1). Most molecules have locality parameters that are in between. Near the two limits the use of local and normal quantum numbers is still meaningful. The most difficult molecules to describe are those in the intermediate regime. For these molecules the only conserved vibrational quantum number is the multiplet number n of Eq. (4.71). A possible notation is thus that in which the quantum number n and the order of the level within each multiplet are given. Thus levels of a linear triatomic molecules can be characterized by... 

The Hamiltonians of the previous sections describe realistic vibrational spectra of linear triatomic molecules except when accidental degeneracies (resonances, cf. Section 3.3) occur. A particularly important case is that in which the bending overtone (02°0) is nearly degenerate with the stretching fundamental (10°0) of the same symmetry Fermi, 1929, resonance). This situation occurs when the coefficient in Eq. (4.67) is nearly equal to -A (Figure 4.13). The Majorana... 

Cooper, I. L., and Levine, R. D. (1991), Computed Overtone Spectra of Linear Triatomic Molecules by Dynamical Symmetry, /. Mol. Spectr. 148, 391. 

The idea that distortion of a triatomic molecule from a linear to a bent shape occurs if the HOMO and LUMO are of the same symmetry representation, so that electrons in the HOMO are stabilized, was discussed as a tentative general approach to molecular shape. 

Fig. 4.12 The normalized eigenvalues, , of the triatomic molecule AH2 as a function of the bond angle, 2/3, for the particular choice of normalized atomic energy level mismatch, 5 = 1. The symmetries of the eigenfunctions are also shown for the bent and linear configurations.

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

Triatomic fragments involving boron and carbon, such as those found in many borocarbide structures,16 show typical valence electron counts ranging between 12 and 16 electrons. These counts are unusual for isolated triatomic molecules, which usually have 16 or more electrons, unless one of the terminal atoms is FI (12 electrons).17 Within the boron-carbon family, four of six possible arrangements for the trimeric fragments have been observed (1) C—C-C, (2) C-B-C, (3) B-B—C, and (4) B-C-B. Coincident-ally, only those with D,h point symmetry occur in metal borocarbides. They include (1) CCC units in Sc3C4 18 (2) CBC units in Si BCj 19,20... 

The photodissociation of symmetric triatomic molecules of the type ABA is particularly interesting because they can break apart into two identical ways ABA — AB + A and ABA — A + BA. Figure 7.18(a) shows a typical PES as a function of the two equivalent bond distances. It represents qualitatively the system IHI which we will discuss in some detail below. We consider only the case of a collinear molecule as illustrated in Figure 2.1. The potential is symmetric with respect to the C -symmetry line 7 IH = i HI and has a comparatively low barrier at short distances. The minimum energy path smoothly connects the two product channels via the saddle point. A trajectory that starts somewhere in the inner region can exit in either of the two product channels. However, the branching ratio ctih+i/cti+hi obtained by averaging over many trajectories or from the quantum mechanical wavepacket must be exactly unity. 

Both HCN and CO2, with Coov and symmetry, respectively, have two bonds and, hence, have two stretching modes and one (doubly degenerate) bending mode. In C02, the two bonds are equivalent and they may couple in a symmetric and an antisymmetric way, giving rise to symmetric and asymmetric stretching modes. However, for HCN, we simply have the C-H and C=N stretching modes. The observed frequencies and their assignments for these two triatomic molecules are summarized in Tables 7.3.1 and 7.3.2. 

Xenon difluoride XeF2 and calcium carbide (form I) CaC2 are isomorphous with Z = 2, the linear triatomic molecule occupies Wyckoff position 2(a) of site symmetry 4/mmm. Hg2Cl2 (calomel) has a very similar crystal structure, although it is tetraatomic. The molecular structure and crystal packing of XeF2 and Hg2Cl2 are compared in Fig. 9.6.15. 

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