Polyatomic linear

Figure 1. Translation, rotation, and vibration of a diatomic molecule. Every molecule has three translational degrees of freedom corresponding to motion of the center of mass of the molecule in the three Cartesian directions (left side). Diatomic and linear molecules also have two rotational degrees of freedom, about rotational axes perpendicular to the bond (center). Non-linear molecules have three rotational degrees of freedom. Vibrations involve no net momentum or angular momentum, instead corresponding to distortions of the internal structure of the molecule (right side). Diatomic molecules have one vibration, polyatomic linear molecules have 3V-5 vibrations, and nonlinear molecules have 3V-6 vibrations. Equilibrium stable isotope fractionations are driven mainly by the effects of isotopic substitution on vibrational frequencies.

It may occur to the reader that it is always possible to bring the orbitals together in such a way that the overlap is positive. For example, in Fig. 5.8g, h if negative overlap is obtained, one need only invert one of the atoms to achieve positive overlap. This is true for diatomic molecules or even for polyatomic linear molecules. However, when we come to cyclic compounds, we no longer have the freedom arbitrarily to invert atoms to obtain proper overlap matches. One example will suffice to illustrate this. 

Suppose that the dissociation products are a polyatomic linear molecule and an atom (e.g., BrC C- + Br), and that the available energy is well above the vibrational energies of the BrC=C- fragment. Then the vibrational density of states must be included in the PED. If the upper Br atom spin-orbit state is ignored, the PED for a... 

Data for diatomic diamagnetic molecules are contained in subvolmne 11/29A, and polyatomic linear molecnles are dealt with in subvolume II/29B. Data on paramagnetic species will be contained in subvolmne II/29E. For a more systematic presentation of their physical properties we chose to order the paramagnetic species in a way which deviates from Hill s rules. 

FIGURE 14.3 A diatomic (or polyatomic linear) molecule has only two defined rotational motions, which are equivalent to each other. 

Linear molecules have / , the moment of inertia about the molecular axis, equal to zero and equal to f, which are the moments of inertia about two axes perpendicular to the molecular axis and to each other. Polyatomic linear molecules and diatomic molecules have identical rotational energy equations. However, pure infrared rotational spectra can only be observed for those molecules which possess a permanent dipole moment. In carbon dioxide and acetylene, for example, the permanent dipole moment is zero because of symmetry. 

A polyatomic linear molecule can have two types of vibrational-rotational bands. A parallel band results when the change in dipole moment is parallel to the molecular axis. A perpendicular band results when the dipole moment change is perpendicular to the molecular axis. 

Table 3.15 lists the character tables and selection rules for important point groups. Polyatomic linear molecules which belong to the and groups are a special case. There are an infinite number of rotations about the axis on which the nuclei lie which yield an equivalent configuration of the molecule. The determination of the selection rules is based on the application of a reduction formula which for nonlinear molecules involves a summa-... 

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