Energy levels diatomic molecule

MO energy-level diagram for diatomic molecules (energy increases vertically). Note that there are two n2p and two orbitals,... 

To compare the relative populations of vibrational levels, the intensities of vibrational transitions out of these levels are compared. Figure B2.3.10 displays typical potential energy curves of the ground and an excited electronic state of a diatomic molecule. The intensity of a (v, v ) vibrational transition can be written as... 

Diatomic molecules have only one vibrational mode, but VER mechanisms are paradoxically quite complex (see examples C3.5.6.1 and C3.5.6.2). Consequently there is an enonnous variability in VER lifetimes, which may range from 56 s (liquid N2 [18]) to 1 ps (e.g. XeF in Ar [25]), and a high level of sensitivity to environment. A remarkable feature of simpler systems is spontaneous concentration and localization of vibrational energy due to anhannonicity. Collisional up-pumping processes such as... 

The rotational motion of a linear polyatomic molecule can be treated as an extension of the diatomic molecule case. One obtains the Yj m (0,(1)) as rotational wavefunctions and, within the approximation in which the centrifugal potential is approximated at the equilibrium geometry of the molecule (Re), the energy levels are ... 

The same expression applies also to any linear polyatomic molecule but, because / is likely to be larger than for a diatomic molecule, the energy levels of Figure 1.12 tend to be more closely spaced. 

We have seen in Section 1.3.6 how the vibrational energy levels of a diatomic molecule, treated in the harmonic oscillator approximation, are given by... 

Just as the electrical behaviour of a real diatomic molecule is not accurately harmonic, neither is its mechanical behaviour. The potential function, vibrational energy levels and wave functions shown in Figure f.i3 were derived by assuming that vibrational motion obeys Hooke s law, as expressed by Equation (1.63), but this assumption is reasonable only... 

Figure 6.4 Potential energy curve and energy levels for a diatomic molecule behaving as an anharmonic oscillator compared with those for a harmonic oscillator (dashed curve)...

As for diatomic molecules, there are stacks of rotational energy levels associated with all vibrational levels of a polyatomic molecule. The resulting term values S are given by the sum of the rotational and vibrational term values... 

In a diatomic molecule one of the main effects of mechanical anharmonicity, the only type that concerns us in detail, is to cause the vibrational energy levels to close up smoothly with increasing v, as shown in Figure 6.4. The separation of the levels becomes zero at the limit of dissociation. 

Figure 7.14 Molecular orbital energy level diagram for first-row homonuclear diatomic molecules. The 2p, 2py, 2p atomic orbitals are degenerate in an atom and have been separated for convenience. (In O2 and F2 the order of

We have seen in Section 6.1.3.2 that, for diatomic molecules, vibrational energy levels, other than those with v = 1, in the ground electronic state are very often obtained not from... 

The name dissociation energy is given to the work required to break up a diatomic molecule which is in its lowest rotation-vibrational state, and to leave the two particles (either atoms or ions) at rest in a vacuum. This quantity, which will be denoted by D , corresponds to the length of the arrow in Fig. 7 or Fig. 8a, where the length is the vertical distance between the lowest level of the molecule and the horizontal line which... 

Quantum mechanics predicts that a diatomic molecule has a set of rotational energy levels ej given by... 

Equation (4.18) applies only to a diatomic or linear polyatomic molecule. Similar kinds of rotational energy levels are present in more complicated molecules. We will describe the various kinds in more detail in Chapter 10. 

Vibrational Energy Levels A diatomic molecule has a single set of vibrational energy levels resulting from the vibration of the two atoms around the center of mass of the molecule. A vibrating molecule is usually approximated by a harmonic oscillatord for which... 

This procedure assumes that the translational, rotational, vibrational, and electronic energy levels are independent. This is not completely so. In the instance of diatomic molecules, we will see how to correct for the interaction. For more complicated molecules we will ignore the correction since it is usually a small effect. 

With the advent of modern high-speed computers, this is not difficult to do for diatomic molecules, and it is the procedure followed when energy level information is available to perform the summation. Similar procedures have been followed for some nonlinear molecules, although as we have noted earlier, Table 10.4 gives reliable values for these molecules under most circumstances. References can be found in the literature to formulas and tables for calculating corrections for selected nonlinear molecules.12... 

The rotational energy levels of (a) a heavy diatomic molecule and (b) a light diatomic molecule. Note that the energy levels are closer together for the heavy diatomic molecule. Microwaves arc absorbed when transitions take place between neighboring energy levels. 

FIGURE 3.31 Atypical molecular orbital energy-level diagram for the homonuclear diatomic molecules Li2 through N2. Each box represents one molecular orbital and can accommodate up to two electrons. 

FIGURE 3.33 A typical d molecular orbital energy-level diagram for a heteronuclear diatomic molecule AB the relative contributions of the atomic orbitals to the molecular orbitals are represented by the relative sizes of the spheres and the horizontal position of the boxes. In this case, A is the more electronegative of the two elements. 

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