Symmetric triatomic molecules

Heller E J 1978 Photofragmentation of symmetric triatomic molecules Time dependent pictured. Chem. Phys. 68 3891... 

Figure 9.24 shows part of the laser Stark spectrum of the bent triatomic molecule FNO obtained with a CO infrared laser operating at 1837.430 cm All the transitions shown are Stark components of the rotational line of the Ig vibrational transition, where Vj is the N-F stretching vibration. The rotational symbolism is that for a symmetric rotor (to which FNO approximates) for which q implies that AA = 0, P implies that A/ = — 1 and the numbers indicate that K" = 7 and J" = 8 (see Section 6.2.4.2). In an electric field each J level is split into (J + 1) components (see Section 5.2.3), each specified by its value of Mj. The selection mle when the radiation is polarized perpendicular to the field (as here) is AMj = 1. Eight of the resulting Stark components are shown. 

The simplest intermediate of the nitrogen cation type is the nitronium ion, the active species in most aromatic nitration reactions. There is both cryoscopic and spectroscopic (Raman and infrared) evidence for its existence.802 On the other hand, it has a structure with quaternary rather than electron deficient nitrogen, a structure compatible with the centrosymmetric geometry demanded by the spectra. The Raman line at 1400 cm.-1 has been assigned to the totally symmetric vibration of the linear triatomic molecule. 

Figure 4.3 Vibrational modes of a nonlinear triatomic molecule such as H20. Arrows indicate motion in the plane of the paper, + is towards and - away from the observer, (a) symmetric stretching, (b) asymmetric stretching, (c) out-of-plane wagging, (d) out-of-plane twisting, (e) in-plane scissoring, (f) in-plane rocking.

Calculations of vibrational spectra of bent triatomic molecules with second order Hamiltonians produce results with accuracies of the order of 1-5 cm-1. An example is shown in Table 4.9. These results should again be compared with those of a Dunham expansion with cubic terms [Eq. (0.1)]. An example of such an expansion for the bent S02 molecule is given in Table 0.1. Note that because the Hamiltonian (4.96) has fewer parameters, it establishes definite numerical relations between the many Dunham coefficients similar to the so-called x — K relations (Mills and Robiette, 1985). For example, to the lowest order in l/N one has for the symmetric XY2 case the energies E(vu v2, V3) given by... 

Carbon dioxide is a symmetrical, linear triatomic molecule (0 = C=0) with a zero dipole moment. The carbon-to-hydrogen bond distances are about 1.16A, which is about 0.06A shorter than typical carbonyl double bonds. This shorter bond length was interpreted by Pauling to indicate that greater resonance stabilization occurs with CO2 than with aldehydes, ketones, or amides. When combined with water, carbonic acid (H2CO3) forms, and depending on the pH of the solution, carbonic acid loses one or two protons to form bicarbonate and carbonate, respectively. The various thermodynamic parameters of these reactions are shown in Table I. 

The purpose of this paper is to apply to AB2 and BAC molecules the procedure which in Part I was applied to AH2 molecules. We consider first symmetrical, non-hydride, triatomic molecules AB2. 

Fig. 1. Normal modes of a non-linear triatomic molecule such as H 0 (schematic). v9 symmetric stretching, d symmetric bending, va asymmetric stretching...

When a molecule absorbs energy in the infrared region (1-300 pm), the a bonds of the molecule begin to vibrate. For simple diatomic molecules, such as H. or HC1, the only possible vibration is a movement of the two atoms away from and back to each other. This mode is referred to as a bond stretch. Triatomic molecules such as CO, have two distinct stretching modes—an asymmetrical and a symmetrical mode. In the symmetrical stretch, both oxygen atoms move away from the carbon atom at the same time. Conversely, in the asymmetrical stretch, one oxygen atom moves toward the carbon atom while the second oxygen atom moves away from the carbon atom. 

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. 

The hyperspherical coordinates are simply the polar coordinates in the (R, r)-plane. The Jacobi coordinates (R,r) defined in Figure 2.1 are not appropriate for symmetric molecules because they cannot simultaneously describe both product channels, A + BC and AB + C. The set of Jacobi coordinates appropriate for one dissociation channel is inappropriate for the other one and vice versa. The hyperspherical coordinates, on the other hand, describe both channels equally well and they can be used at short distances as well as in the asymptotic regions. The two-dimensional Hamiltonian for the linear triatomic molecule is given in hyperspherical coordinates by... 

Symmetric triatomic molecules like H2O, 03, and CO2, for example, are good candidates for the discussion of diffuse vibrational structures in absorption spectra. We will first discuss a simple model system and then illustrate the general predictions by realistic examples. 

Fig. 8.2. Typical potential energy surface for a symmetric triatomic molecule ABA. The potential energy surface of H2O in the first excited electronic state for a fixed bending angle has a similar overall shape. The two thin arrows illustrate the symmetric and the anti-symmetric stretch coordinates usually employed to characterize the bound motion in the electronic ground state. The two heavy arrows indicate the dissociation path of the major part of the wavepacket or a swarm of classical trajectories originating in the FC region which is represented by the shaded circle. Reproduced from Schinke, Weide, Heumann, and Engel (1991).

Henriksen, N.E., Engel, V., and Schinke, R. (1987). Test of the Winger method for the photodissociation of symmetric triatomic molecules, J. Chem. Phys. 86, 6862-6870. 

Note that in a non-linear molecule, one of the vibrational modes of the linear molecule has been replaced by a rotational coordinate. As an illustration, let us consider two examples. For the stable linear triatomic molecule CO2, there are 3 x 3 — 5 = 4 internuclear coordinates, which corresponds to the vibrational degrees of freedom, namely the symmetric and antisymmetric stretch and two (degenerate) bending modes (see Appendix E). For the three atoms in the reaction D + H — H—> D — H + H, there are 3 x 3 — 6 = 3 internuclear coordinates. These coordinates can, for example, be chosen as a D H distance, the H H distance, and the I) II H angle. 

Fig. 7.1.1 Photodissociation (at a fixed bending angle) for a symmetric triatomic molecule like ozone. The vibrational ground state is superimposed on the potential energy surface of the electronic ground state an illustration of a true (direct) unimolecular reaction. (Note that in this figure all potential energies above a fixed cut-off value Amax have been replaced by Bmax, in the electronic ground state as well as in the excited electronic state.)...

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. 

Fig. 8.3 Emergence of antisymmetric dipole component da in addition to symmetric component ds in a bent BAB triatomic molecule as a result of an asymmetric stretching vibration, assuming that the dipole is a vectorial sum of bond dipoles, which are proportional -.jo bond lengths.

Figure 1 Vibrational friction on a symmetrical linear triatomic molecule dissolved in high-density supercritical Ar. The figure compares the differing frictions felt by the symmetrical and asymmetrical stretching modes of the triatomic.

Figure 3-48. Bending motion and a sampler of potential energy functions. Top bending vibration of a linear triatomic molecule, where r is the instantaneous distance between the end atoms and re is the equilibrium distance of the linear configuration (r

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