Triatomic molecules, stretching vibrations

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. 

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.

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... 

Transient two-photon ionization experiments on trimer systems were, of course, motivated by a need for time-resolved verification of the pseudorotation motion, which can be considered as a superposition of the asymmetric stretch (Qx) and the bending vibration (Qy) [12]. The triatomic molecule with its three modes is quite different from an isolated oscillating dimer, which vibrates in its single mode until eventually it radiates or predissociates. The interplay of vibrational modes in a trimer system can be considered as the prototype of IVR. 

As an illustration of the factors which determine the separability of such group modes, we will consider the stretching vibrations of a linear triatomic molecule, XYZ. Such a molecule has 3x3 — 5 = 4 internal vibrational modes, of which two involve stretching of the X—Y and Y—Z bonds and the other two (which are degenerate, i. e., of the same frequency) bending of the XYZ angle. By the method outlined in section I. 1. we can obtain the frequencies and forms of the stretching modes when the masses and force constants are specified. The secular equation is... 

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. 

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. 

Some examples are given in Figs E.1.1 and E.1.2, for triatomic molecules. A linear triatomic molecule has four (3x3 — 5) vibrational modes two bond-stretching modes and two (degenerate) bending modes. Fig. E.1.2 shows one of the four normal modes... 

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.

Infrared radiation causes excitation of the quantized molecular vibration states. Atoms in a diatomic molecule, e.g. H—H and H—Cl, vibrate in only one way they move, as though attached by a coiled spring, toward and away from each other. This mode is called bond stretching. Triatomic molecules, such as CO2 (0=C=0), possess two different stretching modes. In the symmetrical stretch, each O moves away from the C at the same time. In the antisymmetrical stretch, one O moves toward the C while the other O moves away. 

Eq. 2.5-1 can be applied directly to the calculation of the stretching frequencies of a symmetrical linear triatomic molecule. The molecule contains two bonds, therefore, we expect two stretching vibrations. During the in-phase or symmetric stretching vibration, the middle atom does not move. Therefore, the frequency is equal to that of a ball with the mass mi connected by a spring with the force constant/ to an infinite mass mj (Fig. 2.5-1 a). Therefore, the frequency of the symmetric stretching vibration is given by ... 

Figure 2.5-1 Stretching vibrations of a symmetric linear triatomic molecule, a symmetric (in-phase) stretching vibration, b, antisymmetric (out-of-phase) stretching vibration.

Figure 2.5-2 Stretching vibrations of a symmetric angular triatomic molecule Y-Y-Y, depending on the bond angle a, Y = C /i =/2 = 5 N cm r. symmetric (in-phase), Ua antisymmetric (out-of-phase vibration), the trace - - . shows the frequency of the uncoupled oscillators.

Figure 2.5-3 Stretching vibrations of a linear triatomic molecule, X-Y=Y, X = H, D, T,...

As a linear triatomic molecule, carbon dioxide has four degrees of vibrational motion. These are the symmetrical stretch (vj), the asymmetrical stretch (V3), and the bending mode (V2). The later vibration is doubly degenerate and can be described in two directions perpendicular to the interatomic axis. 

The emerging picture is one in which the quantum-mechanical equivalents of the constants of motion for the two valence electrons in these atoms are like those associated with the near-rigid rotations, bending vibrations, and stretching vibrations we normally associate with linear triatomic molecules. These new results bring into question the range of validity of the nearly-independent-particle model, the quantum-mechanical counterpart of Bohr s planetary model, for atoms with more than one valence electron. 

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