Diatomic and linear polyatomic molecules

This Schrodinger equation relates to the rotation of diatomic and linear polyatomic molecules. It also arises when treating the angular motions of electrons in any spherically symmetric potential... 

Although in a classical system v ( can take any value, in a quantum mechanical system it can take only certain values, and we shall now see what these are for diatomic and linear polyatomic molecules. 

Rotational Raman spectra of diatomic and linear polyatomic molecules... 

The molecular electronic wave functions ipe] are classified using the operators that commute with Hei. For diatomic (and linear polyatomic) molecules, the operator Lz for the component of the total electronic orbital angular momentum along the internuclear axis commutes with Hel (although L2 does not commute with tfel). The Lz eigenvalues are MLh,... 

For diatomic (and linear polyatomic) molecules, the basis set usually consists of several STOs centered on each atom. Thus the MOs are expressed as LCAOs—linear combinations of atomic orbitals. In a mini- ia/-basis-set calculation, only inner-shell and valence-shell STOs are used. Thus a minimal basis calculation of HF would use as basis functions l.sH, 1 F, 2jf, 2/ ctf, 2p7TF, 2pTTF, where 2poF is a fluorine 2p AO along the internuclear (z) axis (i.e., a 2pz AO), and the 2pir and 2pir AOs are... 

Line Intensities for Diatomic and Linear Polyatomic Molecules... 

For diatomic and linear polyatomic molecules where the angular momentum of the molecule arises from end-over-end rotation about its centre of gravity, it can be readily demonstrated that the rotational spectral line frequency neglecting centrifugal stretching, is given approximately by... 

The probabilities of absorption by structures larger than an atom are determined in essentially the same way. For diatomic and linear polyatomic molecules the orbital momentum selection rule becomes AA = 0, 1, where A is the symbol for molecular total orbital angular momentum. For systems with appropriate symmetry, the rules are g m, -I- <-> H-, —. For non-linear polyatomic molecules... 

For diatomic and linear polyatomic molecules, rotational motion is restricted to an axis perpendicular to the molecular longitudinal axis. A corresponding diagram is shown in... 

Transitions between rotational states lead to emission or absorption in the microwave region. For diatomic and linear polyatomic molecules with permanent dipole moments, the selection rule is... 

Raman spectroscopy involves inelastic scattering of light instead of absorption or emission. The selection mles for Raman transitions are different from those of absorption and emission spectroscopy, so that many transitions that are forbidden in absorption and emission occur in Raman scattering. Raman scattering requires that the motion modulate the polarizability of the molecule. For rotational Raman transitions in diatomic and linear polyatomic molecules... 

It should be emphasized that the and coefficients in Eq. (8.17) are evaluated for the case of a polyatomic non-linear molecule, linearly polarized incident light and rectangular experimental setup as shown in Fig. 8.1. Alternative sets of coefficients are to be used for experiments with unpolarized (natural) exciting light and different experimental geometries. These are summarized in Table 8.1. The polarizability terms for 27 most commonly employed scattering geomeUies [252] are presented. Different coefficients are used in the case of diatomic and linear polyatomic molecules as well [253]... 

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