Bent triatomic molecules

Figure 9.24 shows part of the laser Stark spectrum of the bent triatomic molecule FNO obtained with a CO infrared laser operating at 1837.430 cm All the transitions shown are Stark components of the rotational line of the Ig vibrational transition, where Vj is the N-F stretching vibration. The rotational symbolism is that for a symmetric rotor (to which FNO approximates) for which q implies that AA = 0, P implies that A/ = — 1 and the numbers indicate that K" = 7 and J" = 8 (see Section 6.2.4.2). In an electric field each J level is split into (J + 1) components (see Section 5.2.3), each specified by its value of Mj. The selection mle when the radiation is polarized perpendicular to the field (as here) is AMj = 1. Eight of the resulting Stark components are shown. 

For bent triatomic molecules one can easily construct a local mode Hamiltonian whose eigenvalues reproduce the spectrum ... 

Figure 4.14 Local vibrational quantum numbers of bent triatomic molecules. Also shown are the relative displacements of the atoms in the different modes.

The normal-mode Hamiltonians for bent triatomic molecules... 

The local-to-normal transition is again characterized by the locality parameter of Eq. (4.75). Locality parameters of several bent triatomic molecules are shown in Table 4.6. 

Figure 4.19 Normal-mode vibrational quantum numbers for a bent triatomic molecule. Contrast the results for water, which is (cf. Table 4.6) near the local-mode limit with that for S02, which is near the normal-mode limit.

Calculations of vibrational spectra of bent triatomic molecules with second order Hamiltonians produce results with accuracies of the order of 1-5 cm-1. An example is shown in Table 4.9. These results should again be compared with those of a Dunham expansion with cubic terms [Eq. (0.1)]. An example of such an expansion for the bent S02 molecule is given in Table 0.1. Note that because the Hamiltonian (4.96) has fewer parameters, it establishes definite numerical relations between the many Dunham coefficients similar to the so-called x — K relations (Mills and Robiette, 1985). For example, to the lowest order in l/N one has for the symmetric XY2 case the energies E(vu v2, V3) given by... 

We have discussed up to now vibrational spectra of linear and bent triatomic molecules. We address here the problem of rotational spectra and rotation-vibration interactions.3 At the level of Hamiltonians discussed up to this point we only have two contributions to rotational energies, coming from the operators C(0(3]2)) and IC(0(412))I2. The eigenvalues of these operators are... 

Figure 9.3. Orbital geometry and nomenclature for a bent triatomic molecule. Solid contours indicate regions where the wave function is positive broken contours indicate regions where the wave function is negative.

Take, for example, the bent triatomic molecule B—A—B (say, HsO). Following Table 3-7.1, it is not linear, it does not have two or more Cn with n 3, it does have a Ct axis hut there are not n Ct axes perpendicular to this axis, it does possess two [Pg.48]

This expression has been analyzed for the dissociation of ICN. The initial thermal distribution corresponds to large j. A distribution peaked around j 25 was obtained, in good agreement with experimental data. The analysis has been generalized to describe the case of a bent triatomic molecule (53,5A). Moreover, these authors consider the scalar coupling which corresponds to indirect photodissociation. 

Morse, M.D. and Freed, K.F. (1980). Rotational distributions in photodissociation The bent triatomic molecule, Chem. Phys. Lett. 74, 49-55. 

Several examples will be considered to illustrate the classification of molecules into point groups. Consider, for instance, the bent triatomic molecule of type AB2(H20) shown in Fig. 1-21. Following the rules... 

Table 9 Dependence of spectroscopic constants on anharmonic force constants for bent triatomic molecules of C2B symmetry ...

Bent Triatomic Molecules.—Calculations have been reported for many bent triatomic molecules (see Table 4). The general force field contains 2re + 4/ + 6/3 + 9A parameters, the relation to the primary spectroscopic constants being shown in Table 9. The fact that these are asymmetric top molecules, for which otj, a , and a can all be determined (generally from the microwave spectrum for the heavier molecules), means that 9 a values are available from each isotopic species to determine the 6 cubic force constants, so that the cubic force field is generally well determined. For the quartic force field the situation is much less satisfactory the experimental data on the anharmonic constants xrs are generally incomplete, and are in any case insufficient to fix all the quartic constants without good isotopic data. 

Table 13 Anharmonic force fields of some bent triatomic molecules in curvilinear internal co-ordinates, up to cubic terms only ...

FIGURE 6.47 (a) Ball-and-stick model (bottom) and molecular orbitals for bent triatomic molecules. The central atom has three sp hybrid orbitals (not shown) that would lie In the plane of the molecule. From the three orbitals perpendicular to this plane, three 77 orbitals can be constructed. (b) Correlation diagram for the 77 orbitals. 

FIGURE 20.9 The three types of vibrational motion that are possible for a bent triatomic molecule. Arrows show the displacement of each atom during each type of vibration. 

The first example is quite simple, but serves to introduce the idea. The structure of water has already been discussed. You will recall that it is a bent triatomic molecule based on a tetrahedron, with the two lone pairs of the oxygen pointed towards the unoccupied comers of the tetrahedron. Given this structure, what is the shape of the closely related compound, hydrogen peroxide, H202 ... 

Sulphur-Nitrogen Compounds.—Linear Compounds. Results from ab initio Hartree-Fock calculations on the ground states of NSF and SSO have been reported.87 The photoelectron spectra of the bent, triatomic molecules NSF, SSO, 03, S02, and NSC1 were compared and experimental details of the photoelectron spectrum of SSO presented. Pyrolysis of the tetrathiatriazyl halide S4N3X at low pressures gives the corresponding thiazyl halide XSN where X = C1 or Br but not where X = I 88... 

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... 

TABLE 3 Force Fields of Symmetric Bent Triatomic Molecules in Terms of Coordinates 6rt/r, 6 r2/r, and 6a... 

In practice, inertia defects have been used successfully as a source of information on the harmonic force field only for bent triatomic molecules, particularly for 03, S02, Se02, OF2, and similar molecules.14-16 For bent triatomics the vibrational inertia defect may be written in... 

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