Vibration diatomic molecule

In rare gas crystals [77] and liquids [78], diatomic molecule vibrational and vibronic relaxation have been studied. In crystals, VER occurs by multiphonon emission. Everything else held constant, the VER rate should decrease exponentially with the number of emitted phonons (exponential gap law) [79, 80] The number of emitted phonons scales as, and should be close to, the ratio O/mQ, where is the Debye frequency. A possible complication is the perturbation of the local phonon density of states by the diatomic molecule guest [77]. 

We have seen in Section 6.1.3.2 that, for diatomic molecules, vibrational energy levels, other than those with v = 1, in the ground electronic state are very often obtained not from... 

We previously found the selection rule A7 = 1 for a 2 diatomic-molecule vibration-rotation or pure-rotation transition. The rule (4.138) forbids A/ = 1 for homonuclear diatomics this gives us no new information as far as vibration-rotation spectra are concerned, since the absence of a dipole moment insures the absence of a vibration-rotation or pure-rotation spectrum, anyway. 

Figure 14.8 Schematic representation of the electronic ground state and an excited state of a diatomic molecule. Vibrational levels of the ground state are shown in red, those of the excited state, in blue. The rotational levels for u = 0 are also shown.

Figure 9.3 Potential energy (E) of diatomic molecule vibration. For a small displacement vibration (Ar), the vibration motion can be treated as harmonic. Quantum theory divides the potential energy of vibration into several levels as v0, v, v2, v3,. ..

The harmonic potential is a model of last resort for diatomic molecules. Its behavior at R = 0 and R = oo is unphysical, as is the sign of ae. Exact diatomic molecule vibrational wavefunctions for levels above v = 0, except for their number of nodes, differ from harmonic oscillator eigenfunctions (Hermite polynomials with an exponential factor) in that they are not symmetric about Re and, increasingly so at high v, are skewed toward the outer turning point. 

Fig. 4. Potential curves for the i " and electronic states of a diatomic molecule. Vibrational substates and their wavefunctions are also included. [Note The shape of the potential curve for the state is usually flatter and its equilibrium inter-nuclear distance is greater due to weaker bonding. A more detailed discussion of this will be found in the text.]...

M is a typical nuclear mass and is the electron mass, taken to be unity. For a diatomic molecule vibrating... 

A diatomic molecule vibrates like a harmonic oscillator with mass equal to the reduced mass of the nuclei of the molecule. 

As with diatomic molecules, vibrational and rotational transitions in polyatomic molecules take place along with electronic transitions. The Franck-Condon principle applies, so that the final state will usually be an excited vibrational state as well as an excited electronic state. Since there are several normal modes in any polyatomic molecule the simultaneous electronic, vibrational, and rotational transitions can give very complicated spectra. The most important selection rule is the same for all molecules and atoms The total spin quantum number is the same for the final as for the initial state ... 

In contrast to diatomic molecules vibrating in a single mode only, polyatomic molecules can vibrate in many modes. A molecule containing N atoms has 3N 6 vibrational degrees of freedom (linear molecules 3N — 5), which correspond to the number of possible fundamental vibrations (normal modes). As an example. Figure 2.2 shows the various vibration modes feasible for a 3-atomic side group. Here, N >3 due to the polymer rest (not shown). 

Make a plot of Cy as a function of temperature for an ideal gas composed of diatomic molecules vibrating as a harmonic oscillator according to the energy level expression of E (kj mohi) = 23.0 (n + 1/2). 

The vibrational selection rule for the harmonic oscillator, Au = 1, applies to polyatomic molecules just as it did to diatomic molecules. Vibrational energy can, therefore, change in units of hcoi/ln. Transitions in which one of the three normal modes of energy changes by Au = - -1 (for example Ui = 0 1, U2 = U3 = 0 or 1 = 1) 2 = 3, i>3 = 2 3) result from absorption of a photon having one of three fundamental frequencies of the molecule. In the actual case, anharmonicities also allow transitions with Au, = 2, 3,... so that, for example, weak absorption also occurs at 2coi, 3(Ui, etc. and at coi + coj, 2vibrational transitions often play major roles in planetary spectroscopy. 

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