Bent triatomic molecules bonding

In particular, ifz = r3j and z2 = r32 (in which case det[c] 3 = 1), the volume element for a bent triatomic molecule in bond-angle coordinates is obtained as... 

Figure 7.3 Nodal patterns and qualitative energies of MOs in linear and bent triatomic molecules according to Walsh [4]. The lowest three MOs, composed of 1s AOs on the constituent atoms (Fig. 7.2), participate little in the chemical bonding and are excluded. Horizontal coordinate is the bending angle 6. Orbital occupancies are shown for linear CO (0 = 180°) and for bent NO2 (0 = 134°). Irreducible representations are given for the MOs in and C v point groups at left and right, respectively.

The most common bent triatomic molecule that you encounter daily is H2O. Like SO2, H2O belongs to the C2V point group and possesses three modes of vibration, all of which are IR and Raman active. These are illustrated in Fig. 3.13a which shows a calculated IR spectrum of gaseous H2O. (An experimental spectrum would also show rotational fine structure.) In contrast, the IR spectrum of liquid water shown in Fig. 3.13b is broad and the two absorptions around 3700 cm are not resolved. The broadening arises from the presence of hydrogen bonding between water molecules (see Section 10.6). In addition, the vibrational wavenumbers in the liquid and gas phase spectra are shifted with respect to one another. 

A triatomic molecule A—B—C is modeled as three spheres connected by two springs and in addition, the bond angle 9 between A—B and B—C has an equilibrium value of 00- For instance, water has an equilibrium bond angle of 104.5°, so that if it is bent to another value the molecular energy is increased according to the quadratic equation... 

Figure 9.4. Walsh diagram showing correlation of orhitals between bent and hnear triatomic molecules, and suggesting variation in orbital energy with bond angle.

Fig. 4.12 The normalized eigenvalues, , of the triatomic molecule AH2 as a function of the bond angle, 2/3, for the particular choice of normalized atomic energy level mismatch, 5 = 1. The symmetries of the eigenfunctions are also shown for the bent and linear configurations.

Fig. 8.3 Emergence of antisymmetric dipole component da in addition to symmetric component ds in a bent BAB triatomic molecule as a result of an asymmetric stretching vibration, assuming that the dipole is a vectorial sum of bond dipoles, which are proportional -.jo bond lengths.

Table 5. Bond Distances for Bent MX2 Triatomic Molecules (in A)a,b...

Diatomic molecules containing atoms of different elements (for example, HCl, CO, and NO) have dipole moments and are called polar molecules. Diatomic molecules containing atoms of the same element (for example, H2, O2, and F2) are examples of nonpolar molecules because they do not have dipole moments. For a molecule made up of three or more atoms both the polarity of the bonds and the molecular geometry determine whether there is a dipole moment. Even if polar bonds are present, the molecule will not necessarily have a dipole moment. Carbon dioxide (CO2), for example, is a triatomic molecule, so its geometry is either linear or bent ... 

Can Lewis structures provide us with information regarding the actual spatial arrangements of atoms within molecules To explore this question, let us invent a triatomic molecule and call it XY2, in which X is the central atom with bonds to each Y atom. Each bond is polar since the joined atoms have different electronegativities. Therefore each bond contributes to the overall dipole moment of the molecule. Consider two possibilities for the molecular shape, linear and bent ... 

This simple MO pictnre for ozone can also be employed to describe the bonding in other bent triatomic molecnles of second-row elements, such as NO2. Example 4.7 applies molecular orbital theory to CO2, a linear second-row triatomic molecule. 

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