Energy levels homonuclear diatomic

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

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. 

The molecular orbital energy-level diagrams of heteronuclear diatomic molecules are much harder to predict qualitatitvely and we have to calculate each one explicitly because the atomic orbitals contribute differently to each one. Figure 3.35 shows the calculated scheme typically found for CO and NO. We can use this diagram to state the electron configuration by using the same procedure as for homonuclear diatomic molecules. 

Construct and interpret a molecular orbital energy-level diagram for a homonuclear diatomic species (Sections 3.9 and 3.10). 

To describe the band structure of metals, we use the approach employed above to describe the bonding in molecules. First, we consider a chain of two atoms. The result is the same as that obtained for a homonuclear diatomic molecule we find two energy levels, the lower one bonding and the upper one antibonding. Upon adding additional atoms, we obtain an additional energy level per added electron, until a continuous band arises (Fig. 6.9). To describe the electron band of a metal in a... 

Proceeding in the spirit above it seems reasonable to inquire why s is equal to the number of equivalent rotations, rather than to the total number of symmetry operations for the molecule of interest. Rotational partition functions of the diatomic molecule were discussed immediately above. It was pointed out that symmetry requirements mandate that homonuclear diatomics occupy rotational states with either even or odd values of the rotational quantum number J depending on the nuclear spin quantum number I. Heteronuclear diatomics populate both even and odd J states. Similar behaviors are expected for polyatomic molecules but the analysis of polyatomic rotational wave functions is far more complex than it is for diatomics. Moreover the spacing between polyatomic rotational energy levels is small compared to kT and classical analysis is appropriate. These factors appreciated there is little motivation to study the quantum rules applying to individual rotational states of polyatomic molecules. 

Fig. 3.2 The bonding and antibonding states for (a) the homonuclear and (b) the heteronuclear diatomic molecule. The shift in the energy levels due to overlap repulsion has not been shown.

For homonuclear diatomic molecules the atomic energy-level mismatch vanishes so that aj = 0 and ac = 1. Hence, the change in the electronic... 

For a homonuclear diatomic molecule, the bond is purely covalent (a, = 0, ac = 1) whereas fora heteronudear diatomic molecule the bond shows mixed covalent-ionic character (a 0, ac 0). In the limit as the separation between the atomic energy levels on the two atoms becomes very large the bond becomes purely ionic (at = 1, ac = 0). 

The rotational energy levels for a homonuclear diatomic molecule follow Eq. 8.16, but the allowed possibilities for j are different. (The rules for a symmetric linear molecule with more than two atoms are even more complicated, and beyond the scope of this discussion.) If both nuclei of the atoms in a homonuclear diatomic have an odd number of nuclear particles (protons plus neutrons), the nuclei are termed fermions if the nuclei have an even number of nuclear particles, they are called bosons. For a homonuclear diatomic molecule composed of fermions (e.g., H— H or 35C1—35C1), only even-j rotational states are allowed. (This is due to the Pauli exclusion principle.) A homonuclear diatomic molecule composed of bosons (e.g., 2D—2D or 14N—14N) can only have odd- j rotational levels. 

Figure 2-12 Energy diagrams for a homonuclear diatomic molecule. Note that the differences in the energy levels of the atoms are larger than the energy differences between the molecular orbitals. Diagram (a) is appropriate for no interaction between 2s and 2p levels, and diagram (b) is appropriate for substantial interaction between 2s and 2p levels. Refer to pp. 36-38.

A molecule can only absorb infrared radiation if the vibration changes the dipole moment. Homonuclear diatomic molecules (such as N2) have no dipole moment no matter how much the atoms are separated, so they have no infrared spectra, just as they had no microwave spectra. They still have rotational and vibrational energy levels it is just that absorption of one infrared or microwave photon will not excite transitions between those levels. Heteronuclear diatomics (such as CO or HC1) absorb infrared radiation. All polyatomic molecules (three or more atoms) also absorb infrared radiation, because there are always some vibrations which create a dipole moment. For example, the bending modes of carbon dioxide make the molecule nonlinear and create a dipole moment, hence CO2 can absorb infrared radiation. 

For homonuclear diatomics, there are two energy level schemes, as shown in Fig. 3.3.2. 

Fig Molecular orbital energy level diagram for diatomic homonuclear molecules such as 02, F2, etc. 

For molecules, the spectroscopic nomenclature for molecular energy levels and their vibronic and rotational sublevels is messy and very specialized. Already for homonuclear or heteronuclear diatomic molecules a new quantum number shows up, which quantifies the angular momentum along the internuclear axis, but the reader need not be burdened with the associated nomenclature. 

Figure 9 Molecular orbital energy level diagram for homonuclear diatomics (a) without s-p mixing, (b) with s-p mixing...

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