Carbon dioxide, vibrational modes

Fig. 39. Schematic representation of the fundamental vibrations of carbon dioxide, COji mode Vj is twofold degenerated (Vja.Vjb)...

Let us use the carbon dioxide molecule as an example. It should have 3N - 5 or four modes of vibration. We can represent each mode by the "direction" of the associated normal coordinate, that is, the directions in which each of the atoms move in the course of the vibration. Recall that a normal mode of vibration is the simplest motion of a system of particles, and that for a system vibrating in one mode, all the particles move in phase and at the same frequency. They reach their maximum points of displacement at the same instant, and they pass through their equilibrium positions at the same instant. If we were able to take a "freeze-frame" view of carbon dioxide vibrating purely in one of its normal modes, the directions the atoms move at the instant the particles are at their equilibrium positions would serve to describe the nature of the vibration. We could represent these directions of motion by arrows at each atom, and in fact, this is a very common way of representing molecular normal modes. 

Figure C3.3.12. The energy-transfer-probability-distribution function P(E, E ) (see figure C3.3.2 and figure C3.3.11) for two molecules, pyrazine and hexafluorobenzene, excited at 248 nm, arising from collisions with carbon dioxide molecules. Both collisions that leave the carbon dioxide bath molecule in its ground vibrationless state, OO O, and those that excite the 00 1 vibrational state (2349 cm ), have been included in computing this probability. The spikes in the distribution arise from excitation of the carbon dioxide bath 00 1 vibrational mode.

Michaels C A, Mullin A S, Park J, Chou J Z and Flynn G W 1998 The collisional deactivation of highly vibrationally excited pyrazine by a bath of carbon dioxide excitation of the infrared inactive (10°0), (02°0), and (02 0) bath vibrational modes J. Chem. Phys. 108 2744-55... 

Figure 9.22 Simple vibration modes for carbon dioxide, 0=C=0 (a) a symmetric stretching mode and (b) a scissor mode vibration...

When high-temperature products are in an equilibrium state, many of the constituent molecules dissociate thermally. For example, the rotational and vibrational modes of carbon dioxide are excited and their mohons become very intense. As the temperature is increased, the chemical bonds between the carbon and oxygen atoms are broken. This kind of bond breakage is called thermal dissociation. The dissociahon of H2O becomes evident at about 2000 K and produces H2, OH, O2, H, and O at 0.1 MPa. About 50% of H2O is dissociated at 3200 K, rising to 90% at 3700 K. The products H2, O2, and OH dissociate to H and O as the temperature is increased further. The fraction of thermally dissociated molecules is suppressed as the pressure is increased at constant temperature. 

Exercise 9-13 Carbon dioxide gives two infrared absorption bands but only one Raman line. This Raman line corresponds to a different vibration than the infrared absorptions. Decide which vibrational modes are infrared active (i.e., make the molecule electrically unsymmetrical during at least part of the vibration) and which is Raman active (i.e., occurs so the molecule is electrically symmetrical at all times during the vibration, see Section 9-7A). 

A molecule can only absorb infrared radiation if the vibration changes the dipole moment. Homonuclear diatomic molecules (such as N2) have no dipole moment no matter how much the atoms are separated, so they have no infrared spectra, just as they had no microwave spectra. They still have rotational and vibrational energy levels it is just that absorption of one infrared or microwave photon will not excite transitions between those levels. Heteronuclear diatomics (such as CO or HC1) absorb infrared radiation. All polyatomic molecules (three or more atoms) also absorb infrared radiation, because there are always some vibrations which create a dipole moment. For example, the bending modes of carbon dioxide make the molecule nonlinear and create a dipole moment, hence CO2 can absorb infrared radiation. 

In this chapter, we describe the density- and temperature-dependent behavior of the vibrational lifetime (TO of the asymmetric CO stretching mode of W(CO)6( 2000 cm-1) in supercritical ethane, fluoroform, and carbon dioxide (C02). The studies are performed from low density (well below the critical density) to high density (well above the critical density) at two temperatures one close to the critical temperature and one significantly above the critical temperature (68-70). In addition, experimental results on the temperature dependence of Ti at fixed density are presented. Ti is measured using infrared (IR) pump-probe experiments. The vibrational absorption line positions as a function of density are also reported in the three solvents (68,70) at the two temperatures. 

Figure 3 Vibrational lifetimes for the asymmetric CO stretching mode of W(CO)6 vs. density along two isotherms of three polyatomic supercritical fluids ethane (34°C panel a and 50°C panel b), fluoroform (28°C panel c and 44°C panel d), and carbon dioxide (33°C panel e and 50°C panel f). The upper panel for each solvent is an isotherm at 2°C above the critical temperature. In all six data sets, error bars (representing one standard deviation) are approximately the size of the points.

We have presented experimental and theoretical results for vibrational relaxation of a solute, W(CO)6, in several different polyatomic supercritical solvents (ethane, carbon dioxide, and fluoroform), in argon, and in the collisionless gas phase. The gas phase dynamics reveal an intramolecular vibrational relaxation/redistribution lifetime of 1.28 0.1 ns, as well as the presence of faster (140 ps) and slower (>100 ns) components. The slower component is attributed to a heating-induced spectral shift of the CO stretch. The fast component results from the time evolution of the superposition state created by thermally populated low-frequency vibrational modes. The slow and fast components are strictly gas phase phenomena, and both disappear upon addition of sufficiently high pressures of argon. The vibrational... 

The linear three particle system A—H—X confined to one dimension has in general two fundamental vibrations, both stretching modes, analogous to the two stretching modes of carbon dioxide ... 

Let us now consider in detail the possible modes of vibration of the carbon dioxide molecule. In the deformation vibration, the carbon atom is displaced away from the axis of the molecule in one direction and the oxygen atoms are displaced in the opposite direction (see Figure 33),... 

In tlie above discussion we have considered all the possible modes of vibration of carbon dioxide according to the formula 3 - 5, these should be (3 X 3) — 5=4 in number. The four oscillations will be the symmetrical, the non-symmetrical and two deformation vibrations. The deformation oscillation may occur in any plane passing through the axis of the molecule, but all such vibrations may be described by the projections on to two mutually perpendicular planes passing through the molecular... 

Ideal- s heat capacities increase smoothly with increasing temperature toward an upper limit, which is reached when all translational, rotational, and vibrational modes of molecular motion are fully excited [see Eq. (16.18)]. The influence of temperadireon C p for argon, nitrogen, water, and carbon dioxide is illnstrated m Fig. 4.1. Temperahire dependence is expressed... 

To compensate for the above, the number of theoretical normal vibrations may be reduced by two inherent factors of the molecule. Some vibrations may be degenerate. For example, a Unear triatomic molecule should, by theory, have four vibrational modes. However, the deformational mode of carbon dioxide (see Fig. 2, A, iii) is not uniquely defined, since the motions could take place either in the plane of the paper or in a plane perpendicular to it. If a molecule is highly symmetrical, it is probable that certain vibrations will not be accompanied by a change in the dipole moment, thus the frequency will be forbidden in the infrared. ... 

Unlike the water molecule, carbon dioxide has no dipole moment. How is it possible for any of its vibrational modes to be infrared active ... 

Given that carbon dioxide is a linear molecule, which of its vibrational modes are infrared active, and which, Raman active ... 

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. 

Because of its symmetry with respect to the central carbon atom, carbon dioxide has no net dipole moment. In a symmetrical stretching vibration, the dipole moment of the molecule remains zero. Therefore the Vj mode is not infrared active. However, the electron density along the interatomic axis is alternately elongated and condensed. Thus, the molecular polarizability changes with symmetrical stretching and the vj mode is Raman active. 

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