Polyatomic molecules, dipole

If one of the components of this electronic transition moment is non-zero, the electronic transition is said to be allowed if all components are zero it is said to be forbidden. In the case of diatomic molecules, if the transition is forbidden it is usually not observed unless as a very weak band occurring by magnetic dipole or electric quadnipole interactions. In polyatomic molecules forbidden electronic transitions are still often observed, but they are usually weak in comparison with allowed transitions. 

When applied to linear polyatomic molecules, these same selection rules result if the vibration is of a symmetry (i.e., has k = 0). If, on the other hand, the transition is of n symmetry (i.e., has k = 1), so the transition dipole lies perpendicular to the molecule s axis, one obtains ... 

This is the same as Equation (5.14) for a diatomic or linear polyatomic molecule and, again, the transitions show an equal spacing of 2B. The requirement that the molecule must have a permanent dipole moment applies to symmetric rotors also. 

In the case of H2O it is easy to see from the form of the normal modes, shown in Figure 4.15, that all the vibrations Vj, V2 and V3 involve a change of dipole moment and are infrared active, that is w=l-0 transitions in each vibration are allowed. The transitions may be labelled Ig, 2q and 3q according to a useful, but not universal, convention for polyatomic molecules in which N, refers to a transition with lower and upper state vibrational quantum numbers v" and v, respectively, in vibration N. 

Polar molecule A molecule in which there is a separation of charge and hence positive and negative poles, 183-185 dipole force, 237 orientation, 183 Polarimeter, 600 Polarity, 184-185 Pollutants, 6 Polyamide, 615-616 Polyatomic ion, 36,39 Polyatomic molecules, 654 Polyester A large molecule made up of ester units, 614-615 Polyethylene, 611-612... 

A polyatomic molecule may be nonpolar even if its bonds are polar. For example, the two fi+C—Ofi dipole moments in carbon dioxide, a linear molecule, point in opposite directions, and so they cancel each other (25) and C02 is a nonpolar... 

As we have seen by comparing C02 and H20, the shape of a polyatomic molecule affects whether or not it is polar. The same is true of more complicated molecules. For instance, the atoms and bonds are the same in c/s-dichloroethene (28) and frans-dichloroethene (29) but, in the latter, the C—Cl bonds point in opposite directions and the dipoles (which point along the C—Cl bonds) cancel. Thus, whereas c/s-dichloroethene is polar, traws-dichloroethene is nonpolar. Because dipole momenrs are directional, we can treat each bond dipole moment as a vector. The molecule as a whole will be nonpolar if the vector sum of the dipole moments of the bonds is zero. 

A diatomic molecule is polar if its bond is polar. A polyatomic molecule is polar if it has polar bonds arranged in space in such a way that the dipole moments associated with the bonds do not cancel. 

Applequist J, Carl JR, Fung K-K (1972) Atom dipole interaction model for molecular polarizability. Application to polyatomic molecules and determination of atom polarizabilities. J Am Chem Soc... 

We discuss bond lengths in the next section, but we defer the discussion of bond angles to Chapters 4 and 5, where we discuss all aspects of molecular geometry. In later sections of this chapter we discuss bond strength in terms of bond enthalpies and force constants, the determination of approximate values for these properties in polyatomic molecules, and the determination and analysis of dipole moments. 

The dipole moment, //, for a diatomic molecule (the situation for polyatomic molecules that have several bonds is more complex) can be expressed as... 

This type of spectra is given by diatomic molecules with permanent dipole moments, i.e. in heteronuclear diatomic molecules and polyatomic molecules with and without permanent dipole moment. 

Some polyatomic molecules like C02 CS2 or SnCl4 which do not possess a permanent dipole, but develop a fluctuating dipole due to certain modes of vibrations also respond to infrared region of electro magnetic radiation. 

Infrared intensities (IR) in polyatomic molecules can be calculated in the same way as in diatomic or triatomic molecules. One introduces a bond dipole operator tj with matrix elements given by Eq. (2.62), which we now rewrite as... 

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

For a diatomic molecule such as HCl, or the bond polarity is also the molecule s polarity. For polyatomic molecules, such as the examples that follow, molecular polarity depends on the polarity of all of the bonds and the angles at which the dipoles come together. Thus, molecular dipole—or just dipole—is a term used to describe the charge separation for the entire molecule. 

Molecular dynamic studies used in the interpretation of experiments, such as collision processes, require reliable potential energy surfaces (PES) of polyatomic molecules. Ab initio calculations are often not able to provide such PES, at least not for the whole range of nuclear configurations. On the other hand, these surfaces can be constructed to sufficiently good accuracy with semi-empirical models built from carefully chosen diatomic quantities. The electric dipole polarizability tensor is one of the crucial parameters for the construction of such potential energy curves (PEC) or surfaces [23-25]. The dependence of static dipole properties on the internuclear distance in diatomic molecules can be predicted from semi-empirical models [25,26]. However, the results of ab initio calculations for selected values of the internuclear distance are still needed in order to test and justify the reliability of the models. Actually, this work was initiated by F. Pirani, who pointed out the need for ab initio curves of the static dipole polarizability of diatomic molecules for a wide range of internuclear distances. 

This chapter assesses the performance of quantum chemical models with regard to the calculation of dipole moments. Several different classes of molecules, including diatomic and small polyatomic molecules, hydrocarbons, molecules with heteroatoms andhypervalent molecules are considered. The chapter concludes with assessment of the ability of quantum chemical models to calculate what are often subtle differences in dipole moments for different conformers. 

Table 10-1 Mean Absolute Errors in Dipole Moments for Diatomic and Small Polyatomic Molecules...

All density functional models exhibit similar behavior with regard to dipole moments in diatomic and small polyatomic molecules. Figures 10-6 (EDFl) and 10-8 (B3LYP) show clearly that, except for highly polar (ionic) molecules, limiting (6-311+G basis set) dipole moments are usually (but not always) larger than experimental values. 

Dipole moments for hydrocarbons are small (typically less than 1 debye), and provide a good test of different models to reproduce subtle effects. A small selection of data is provided in Table 10-2, for the same models used previously for diatomic and small polyatomic molecules. ... 

Table AlO-l Dipole Moments in Diatomic and Small Polyatomic Molecules. Hartree-Fock Models... 

Dipole moments in diatomic and small polyatomic molecules... 

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