Diatomic molecule, orbitals properties

For the orbital parts of the electronic wave functions of two electronic states the selection rules depend entirely on symmetry properties. [In fact, the electronic selection rules can also be obtained, from symmetry arguments only, for diatomic molecules and atoms, using the (or and Kf point groups, respectively but it is more... 

The simplest diatomic molecule consists of two nuclei and a single electron. That species, H2+, has properties some of which are well known. For example, in H2+ the internuclear distance is 104 pm and the bond energy is 268kJ/mol. Proceeding as illustrated in the previous section, the wave function for the bonding molecular orbital can be written as... 

As can be seen from its ground-state molecular orbital diagram in Figure 4.11, dioxygen has a paramagnetic ground state. It is the only stable homonuclear diatomic molecule with this property. 

Up to now we have been discussing the local properties of the exchange-correlation potential as a function of the spatial coordinate r. However there are also important proi rtira of the exchange-correlation potential as a function of the particle number. In fact there are close connections between the properties as a function of the particle number and the local properties of the exchange-correlation potential. For instance the bumps in the exchange-correlation potential are closely related to the discontinuity properties of the potential as a function of the orbital occupation number [38]. For heteronuclear diatomic molecules for example there are also similar connections between the bond midpoint shape of the potential and the behavior of the potential as a function of the number of electrons transferred from one atomic fragment to another when... 

The concepts which we need for understanding the structural trends within covalently bonded solids are most easily introduced by first considering the much simpler system of diatomic molecules. They are well described within the molecular orbital (MO) framework that is based on the overlapping of atomic wave functions. This picture, therefore, makes direct contact with the properties of the individual free atoms which we discussed in the previous chapter, in particular the atomic energy levels and angular character of the valence orbitals. We will see that ubiquitous quantum mechanical concepts such as the covalent bond, overlap repulsion, hybrid orbitals, and the relative degree of covalency versus ionicity all arise naturally from solutions of the one-electron Schrodinger equation for diatomic molecules such as H2, N2, and LiH. 

In general, it is advantageous to use the symmetry elements of a molecule in dealing with the molecular orbitals. For example, consider the symmetry properties of a homonuclear diatomic molecule... 

The symmetry operations E, C, and av (reflection in a plane that contains the axis A-B) are present. All molecules that possess these symmetry properties have the point-group symmetry Coov The orbitals are characterized by symbols similar to those used for a homonuclear diatomic molecule, such as a, n, etc. The character table for CMV is given in Table 2-2. 

One of the interesting successes of the molecular orbital approach to bonding in diatomic molecules is the fact that molecules such as 02 and B2 are correctly predicted to be paramagnetic, but the valence bond structures for these molecules are unsatisfactory. Properties for many diatomic species are shown in Table 2.5. 

Carbon monoxide. Carbon monoxide is one of the most commonly used probe molecules in the study of the chemical properties of metal surfaces. CO represents a step in the direction of complexity compared to atomic adsorbates and diatomic molecules. On one hand, the bonding involves molecular orbitals and it is sensitive to the detailed electronic structure of the metal surface. This allows one to use the CO bonding properties as a probe of changes in surface electronic structure. Yet at the same time, in many cases CO retains aspects of the simplicity that atomic adsorbates have. 

The Hg atom has a 6s closed electronic shell. It is isoelec-tronic with helium, and is therefore van der Waals bound in the diatomic molecule and in small clusters. For intermediate sized clusters the bands derived from the atomic 6s and 6p orbitals broaden as indicated in fig. 1, but a finite gap A remains until the full 6s band overlaps with the empty 6p band, giving bulk Hg its metallic character. This change in chemical binding has a strong influence, not only on the physical properties of mercury clusters, but also on the properties of expanded Hg, and on Hg layers on solid and liquid surfaces. For a rigid cluster the electronic states are discreet and not continuous as in fig. 1. Also the term band for a bundle of electronic states will be used repeatedly in this paper, although incipient band might be better. As the clusters discussed here are relatively hot, possibly liquid, any discreet structure will be broadened into some form of structured band . 

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