Diatomic molecules symmetry orbitals

Two atomic orbitals on different nuclei must have the same symmetry around the bond axis to form a good bonding LCAOMO. In a diatomic molecule, two orbitals with different symmetry cannot form an eigenfunction of the appropriate symmetry operators. We will assume the same behavior in a polyatomic molecule. 

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... 

Let us first briefly review the construction of molecular orbitals in simple diatomic molecules, AB, using the linear combination of atomic orbitals (LCAO) scheme. The end product for the first long row of the periodic table is the well-known diagram in Fig. 6-1. We focus on two broad principles that are exploited in the construction of this diagram one has to do with symmetry and overlap, the other concerns energies. 

Usually the electronic structure of diatomic molecules is discussed in terms of the canonical molecular orbitals. In the case of homonuclear diatomics formed from atoms of the second period, these are the symmetry orbitals 1 og, 1 ou, 2ag,... 

The electronic states of a diatomic molecule such as H2 are approximately equal to linear combinations of atomic orbitals. For example, the groimd state is approximately proportional to the sum of Is orbitals from the two atoms IsA + Isb- An excited state is approximately proportional to the difference IsA — Isb- Although these LCAO (Linear Combination of Atomic Orbitals) wave functions are not quantitatively correct representations of the true wave functions, their shape, and hence their symmetry, is correct. 

This chapter consists of the application of the symmetry concepts of Chapter 2 to the construction of molecular orbitals for a range of diatomic molecules. The principles of molecular orbital theory are developed in the discussion of the bonding of the simplest molecular species, the one-electron dihydrogen molecule-ion, H2+, and the simplest molecule, the two-electron dihydrogen molecule. Valence bond theory is introduced and compared with molecular orbital theory. The photo-electron spectrum of the dihydrogen molecule is described and interpreted. 

The symmetry concepts of Chapter 2 and those of molecular orbital theory were applied to the construction of molecular orbitals for a range of diatomic molecules. 

Polyatomic molecules. The same term classifications hold for linear polyatomic molecules as for diatomic molecules. We now consider nonlinear polyatomics. With spin-orbit interaction neglected, the total electronic spin angular momentum operator 5 commutes with //el, and polyatomic-molecule terms are classified according to the multiplicity 25+1. For nonlinear molecules, the electronic orbital angular momentum operators do not commute with HeV The symmetry operators Or, Os,. .. (corresponding to the molecular symmetry operations R, 5,. ..) commute... 

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. 

To construct an orbital energy diagram for a diatomic molecule in which the two nuclei are different, we must remember that orbitals with the same symmetry repel each other. As shown earlier, this re-. pulsion is dependent on the energy difference between the molecular orbitals and on the size of the interaction. For diatomic molecules in which the two nuclei are not far from each other in the periodic table, the diagram will be approximately as shown in Figure 2-19. 

In diatomic molecules, or more generally in localized two-center bonds, orbitals of two atoms that may be combined to form an MO are those that have the same symmetry about the axis between the two atomic centers in the bond. This rule does not extend to constructing MOs that extend over three or more atoms more complicated rules would be necessary. 

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