Molecular rotation diatomic molecules

The direct dissociation of diatomic molecules is the most well studied process in gas-surface dynamics, the one for which the combination of surface science and molecular beam teclmiques allied to the computation of total energies and detailed and painstaking solution of the molecular dynamics has been most successful. The result is a substantial body of knowledge concerning the importance of the various degrees of freedom (e.g. molecular rotation) to the reaction dynamics, the details of which are contained in a number of review articles [2, 36, 37, 38, 39, 40 and 41]. 

Molecular rotation has two competing influences on the dissociation of diatomics [, and ]. A molecule will only be able to dissociate if its bond is oriented correctly with respect to the plane of the surface. If the bond is parallel to the plane, then dissociation will take place, whereas if the molecule is end-on to the surface, dissociation requires one atom to be ejected into the gas phase. In most cases, this reverse Eley-RideaF process is energetically very... 

The molecular constants o , B, Xe, D, and ae for any diatomic molecule may be determined with great accuracy from an analysis of the molecule s vibrational and rotational spectra." Thus, it is not necessary in practice to solve the electronic Schrodinger equation (10.28b) to obtain the ground-state energy o(R). 

It was shown in the previous chapter that the Schr dinger equation for molecular rotation depends on the type of rotator, as defined in Section 9.2.2. For linear molecules and, hence, diatomics, the energy is given by Eq. (9-40),... 

Iachello, F., and Levine, R. D. (1982), Algebraic Approach to Molecular Rotation-Vibration Spectra. I. Diatomic Molecules, 7. Chem. Phys. 77, 3046. 

The Section on Molecular Rotation and Vibration provides an introduction to how vibrational and rotational energy levels and wavefunctions are expressed for diatomic, linear polyatomic, and non-linear polyatomic molecules whose electronic energies are described by a single potential energy surface. Rotations of "rigid" molecules and harmonic vibrations of uncoupled normal modes constitute the starting point of such treatments. 

Van der Waals molecules of heavier homonuclear diatomics have also been studied, using similar techniques to the ones mentioned above. However, the numbers of bound states generally are much greater for such systems, and the band structures are richer and therefore harder to resolve. Detailed work has shown that for the more massive diatomics molecular rotation is more or less hindered and the level structures are much more complex than the ones seen in the H2-X systems. Rather uncertain band contour analyses are used in those cases but a few reasonably well resolved band spectra of van der Waals molecules are known [49, 267]. 

Consider the molecular rotational partition function for the CO molecule, a linear diatomic molecule. The moment of inertia of CO is / = 1.4498 x 10-46 kg-m2, and its rotational symmetry number is a = 1. Thus, evaluating Eq. 8.65 at T = 300 K, we find the rotational partition function to be... 

The selection rule (4.138) differs from previously discussed selection rules in that it holds well for nonradiative transitions, as well as for radiative transitions. In deriving (4.138), we made no reference to the operator d, beyond the statement that it did not involve the nuclear spin coordinates. For any time-dependent perturbation that does not involve nuclear spin, the selection rule (4.138) will hold. Thus molecular collisions will not cause nonradiative transitions between symmetric and antisymmetric rotational levels of a homonuclear diatomic molecule. If we somehow start with all the molecules in symmetric levels, the collisions will not populate the antisymmetric levels. 

Next we consider planar molecules. The electronic wave function is expressed with respect to molecule-fixed axes, which we can take to be the abc principal axes of inertia. To achieve inversion of all particles with respect to space-fixed axes, we first rotate all the electrons and nuclei by 180° about the c axis (which is perpendicular to the molecular plane) we then reflect all the electrons in the molecular ab plane. The net effect of these two transformations is the desired space-fixed inversion of all particles. (Compare the corresponding discussion for diatomic molecules in Section 4.7.) The first step rotates the electrons and nuclei together and therefore has no effect on the molecule-fixed coordinates of either the electrons or the nuclei. (The abc axes rotate with the nuclei.) Thus the first step has no effect on tpel. The second step is a reflection of electronic spatial coordinates in the molecular plane this is a symmetry plane and the corresponding operator Oa has the possible eigenvalues +1 and — 1 (since its square is the unit operator). The electronic wave functions of a planar molecule can thus be classified as having... 

The shape of the vibration-rotation bands in infrared absorption and Raman scattering experiments on diatomic molecules dissolved in a host fluid have been used to determine2,15 the autocorrelation functions unit vector pointing along the molecular axis and P2(x) is the Legendre polynomial of index 2. These correlation functions measure the rate of rotational reorientation of the molecule in the host fluid. The observed temperature- and density-dependence of these functions yields a great deal of information about reorientation in solids, liquids, and gases. These correlation functions have been successfully evaluated on the basis of molecular models.15... 

Consider the unit vector u(t) pointing in the direction of the molecular axis of a diatomic molecule at time t. The angle that this vector makes with u(0) is denoted by 0(0- According to Debye63 the rotational diffusion coefficient, DR, is... 

The photochemist may find it necessary to pay attention to the rotational terms of diatomic molecules in a few instances, especially when he uses ortho-para hydrogen conversion and also when he uses spectral analysis to identify molecular species. On the other hand only very rarely does he use light sufficiently monochromatic to excite a system of molecules to one and only one rotational level. We will, however, describe one such experiment and indicate the conclusions which may be drawn therefrom. 

The rotational relaxation of polyatomic spherical top molecules can be treated approximately on the classical rough sphere model. This has been done for homo-molecular collisions by Wang Chang and Uhlenbeck101. They find a simple expression resembling that obtained by Brout for diatomic molecules... 

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