Polyatomic molecules, dipole moment

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. 

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. 

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. 

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. 

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

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... 

Polar Molecule a molecule where the centers of positive and negative charge differ, creating a permanent dipole moment Polarizability ability of an electron cloud in a neutral atom to be distorted Polarized Light light in which the electromagnetic wave vibrates in only one plane Polyatomic Ion an ion consisting of more than one atom... 

In general, a polyatomic. molecule has a dipole moment when the centroid of positive charges, due to atomic nuclei, is displaced with respect to the centroid of negative charges due to the elections... 

The factor in (6.67) that multiplies the integral (6.73) contains the derivatives of the dipole-moment components with respect to the normal coordinate Qk, evaluated at the equilibrium configuration. We conclude that a radiative infrared transition in which the vibrational quantum number of the A th normal mode changes by one is forbidden unless the Acth mode has a change in dipole moment associated with it. The value of the equilibrium dipole moment de is irrelevant for infrared transitions of a polyatomic molecule. 

Theoretical calculation of a is not as straightforward as for, say, the dipole moment to find o one must include the applied electric field in the molecular Hamiltonian and calculate the resulting change in the molecular dipole moment. Theoretical values of the components of a have been calculated for several diatomic and small polyatomic molecules using a Hartree-Fock approach the calculated values are reasonably accurate. See Schaefer, pp. 243-250, for details.)... 

We now consider the electric-dipole selection rules for radiative transitions between energy levels of the same electronic state of a polyatomic molecule. The electric-dipole transition moment is (4.91), which becomes... 

Analysis of the rotational fine structure of IR bands yields the moments of inertia 7°, 7°, and 7 . From these, the molecular structure can be fitted. (It may be necessary to assign spectra of isotopically substituted species in order to have sufficient data for a structural determination.) Such structures are subject to the usual errors due to zero-point vibrations. Values of moments of inertia determined from IR work are less accurate than those obtained from microwave work. However, the pure-rotation spectra of many polyatomic molecules cannot be observed because the molecules have no permanent electric dipole moment in contrast, all polyatomic molecules have IR-active vibration-rotation bands, from which the rotational constants and structure can be determined. For example, the structure of the nonpolar molecule ethylene, CH2=CH2, was determined from IR study of the normal species and of CD2=CD2 to be8... 

---