Vibrational states diatomics

For example, for the collinear reaction A+BC this would be the probability that if initially the diatom BC is in a vibrational state then after the reaction a diatom AB is fonned (in any product vibrational state). In... 

By using this approach, it is possible to calculate vibrational state-selected cross-sections from minimal END trajectories obtained with a classical description of the nuclei. We have studied vibrationally excited H2(v) molecules produced in collisions with 30-eV protons [42,43]. The relevant experiments were performed by Toennies et al. [46] with comparisons to theoretical studies using the trajectory surface hopping model [11,47] fTSHM). This system has also stimulated a quantum mechanical study [48] using diatomics-in-molecule (DIM) surfaces [49] and invoicing the infinite-onler sudden approximation (lOSA). 

As is the case for diatomic molecules, rotational fine structure of electronic spectra of polyatomic molecules is very similar, in principle, to that of their infrared vibrational spectra. For linear, symmetric rotor, spherical rotor and asymmetric rotor molecules the selection mles are the same as those discussed in Sections 6.2.4.1 to 6.2.4.4. The major difference, in practice, is that, as for diatomics, there is likely to be a much larger change of geometry, and therefore of rotational constants, from one electronic state to another than from one vibrational state to another. 

The name dissociation energy is given to the work required to break up a diatomic molecule which is in its lowest rotation-vibrational state, and to leave the two particles (either atoms or ions) at rest in a vacuum. This quantity, which will be denoted by D , corresponds to the length of the arrow in Fig. 7 or Fig. 8a, where the length is the vertical distance between the lowest level of the molecule and the horizontal line which... 

In Eq. (5.2), the function i iv(r) 2/r = P(r)/r is an example of a so-called radial distribution (RD) function, in the form in which it is obtained from gas-electron diffraction, in this case for a particular vibrational state of a diatomic molecule. It is seen that the molecular intensity curve is the Fourier transform of Pf. The reverse, by inversion, the RD function is the Fourier transformation of the molecular intensities ... 

The following figure shows energy levels for two different vibrational states of a diatomic molecule. (Fig. 14.2)... 

Table 12.1 Dipole moments, polarizabilities, and isotope effects for some diatomic and simple polyatomic molecules (ground vibrational state values)...

The methods described above are all based on the Born-Oppenheimer approximation. Therefore, they can be used to calculate polarizabilities of diatomic molecules for a given internuclear distance R. However, if one is interested in values of the polarizability tensors, and C", for a particular vibrational state /i )), one has to average the polarizability radial functions a(R) and C(R) with the vibrational wavefunction i.e., one has to... 

Lithium and fluorine form a diatomic molecule that has a large dipole moment in the gas phase it has been measured to be 6.3248 D in the ground vibrational state. The equilibrium intemuclear distance is 1.564 A, and, therefore, the apparent... 

For a molecule in a given electronic and vibrational state, it is convenient to define the permanent dipole operator d = (i/r // i/r), where v/) is a product of the electronic and vibrational states. This vector operator depends on the angles that specify the orientation of the molecule with respect to the external field axis. For diatomic molecules, d is directed along the intermolecular axis. The Stark shifts of the molecule in a DC electric field can (almost always) be found by treating the molecule as a rigid rotor and diagonalizing the matrix of the operator... 

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... 

We have already mentioned (expressions 30—33) the widely used LEPS surface for atom-diatom reactions. This may be regarded as purely empirical or semi-empirical in any modification in which some integrals are evaluated. Another system for which fairly elaborate potential functions have been used is for non-reactive atom-diatom scattering. The experiment for which the potential is designed is the change of rotational or vibrational state of a diatomic molecule by collision with a third atom, and also the quasi bound states, which may be observed spectroscopically, of van der Waals molecules such as Ar—H2 (133). 

The Montroll-Shuler equation can also predict how fast a molecule which is created in a highly excited vibrational state will decay to the equilibrium state. This is of interest in connection with chemiluminescence phenomena. In certain cases one finds experimentally that this relaxation is much faster than what one would expect from the master equation of Montroll and Shuler and improved versions of this equation. One possible mechanism for this fast relaxation is that although most of the collisions in which the diatomic molecule participates are between the diatomic molecule and an inert gas atom, there will also be some collisions between diatomic molecules. In the latter case we have the situation where two diatomic molecules in quantum state n collide producing, with fairly high probability, molecules in quantum states n I and n + 1, respectively. The number of such collisions is, of course quite small compared to the number of collisions of the first kind, but since they are so extremely efficient they may still be of importance. This mechanism, we believe, was first suggested in connection with chemiluminescence by Norrish in a Faraday Society discussion.5 The equations describing this relaxation had, however, been discussed several years earlier by Shuler6 and Osipov.7... 

Fig. VII-2.—Some vibrational energy levels for an idealised diatomic molecule. The electronic energy curve has been approximated by a parabola, corresponding to a Qooke s-law interaction between the two atoms. The firat five vibrational states are represented. They are separated by the energy difference hv. The lowest vibrational state, with v 0, has the zero-point vibrational energy...

Consider a one-dimensional harmonic oscillator with vibrational frequency 5x 1013 sec-1 and mass 1 x 10-23 g. (These are typical values for a diatomic molecule.) Find the average lifetime of the t>=l vibrational state. 

Ordinarily M will be in its ground electronic and vibrational state. The lines in the photoelectron spectrum will thus be due to M+ being produced in different electronic and vibrational states. The photoelectron spectrum consists of a number of bands each band corresponds to removal of an electron from a different MO of M and production of a different electronic state of M +. For diatomics and for polyatomics that are not too large, vibrational structure is resolved. The strongest vibrational line in a band is given by the vertical transition from M to M + for example, the 0 = 0—>3... 

Exercise 28-4 Explain qualitatively how temperature could have an effect on the appearance of the absorption spectrum of a diatomic molecule A—B with energy levels such as are shown in Figure 28-1, knowing that most molecules usually are in their lowest vibrational state at room temperature. 

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