Molecular orbitals in diatomic molecules

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. 

As to the first, we note the interaction of the s orbital of atom A with the s orbital of B, the with the and the, pair of A with the p y pair of B. In principle, of course, we could have considered the possibility of an interaction between, say, the s orbital on A with a p orbital on B as shown in Fig. 6-2. The sketch shows that net overlap between these orbitals is zero and so no bonding or antibonding molecular orbitals are formed in this way. Now the labels s and p here 

We shall shortly draw on both of these symmetry and energy aspects of Fig. 6-1 in the construction of molecular orbitals for the octahedron. First, however, let us extend the picture to molecules with more than two atoms. 

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Wallis, R. F., and Hulburt, H. M., J. Chem. Phys. 22, 1774, "Approximation of molecular orbitals in diatomic molecules by diatomic orbitals."... 

In Chapters 4 and 6 we have distinguished between a molecular orbitals and 7T molecular orbitals in diatomic molecules on the basis of the symmetry of the m.o.s with respect to rotation around the intemuclear axis whereas a a orbital has cylindrical symmetry, a tt orbital changes sign upon a rotation of 180°. In Chapters 7 and 8 we have extended the notion of a orbitals to polyatomic molecules by referring to the local symmetry with respect to each X-Y intemuclear axis. We will now study systems of tt m.o.s in polyatomic species. 

The se the orie s are inevitablj based upem analyse s of the interactions and transformations of molecular orbitals, and consequently the accurate construction and re presentation of molecular orbitals has become essential, furthermore, although the forms of molecular orbitals in diatomics and of delocalized tt orbitals in conjugated systems are familiar, a general, non-computational method for determining the qualitative nature of or and t orbitals in arbitrary molecules has been lacking. 

The molecular orbital theory of polyatomic molecules follows the same principles as those outlined for diatomic molecules, but the molecular orbitals spread over all the atoms in the molecule. An electron pair in a bonding orbital helps to bind together the whole molecule, not just an individual pair of atoms. The energies of molecular orbitals in polyatomic molecules can be studied experimentally by using ultraviolet and visible spectroscopy (see Major Technique 2, following this chapter). 

To conclude this section. Example compares three diatomic molecules. Section 10-1 explores molecular orbitals in triatomic molecules. 

The actual energies of molecular orbitals for diatomic molecules are intermediate between the extremes of this diagram, approximately in the region set off by the vertical lines. Toward the right within this region, closer to the separated atoms, the energy sequence is the normal one of O2 and F2 further to the left, the order of molecular orbitals is that of B2, C2 and N2, with a-g(2p) above TT (2p). 

The system of energy levels for the molecular orbitals of diatomic molecules is often represented schematically as in Fig. 23.23, in which the energy levels of the two separated... 

In order to examine the workings of electronegativity perturbation, we will need to examine the orbitals of a molecule where the atoms arc not all identical and where each atom carries more than one atomic orbital. An important feature which results is that of orbital hybridization, namely the mixing of different atomic orbitals on the siinie center. In this chapter we will examine the nature of such hybridization, construct the molecular orbitals of diatomic molecules from different viewpoints, and describe the essence of electronegativity perturbations. 

Figure 3.6 shows the LCAO method for generating molecular orbitals of diatomic molecules such as H2. In real molecules, the atomic orbitals of elemental carbon are not really transformed into the molecular orbitals found in methane (CH4). Figure 3.6 represents a mathematical model that mixes atomic orbitals to predict molecular orbitals. Molecular orbitals exist in real molecules and the LCAO model attempts to use known atomic orbitals for atoms to predict the orbitals in the molecule. Molecular orbitals and atomic orbitals are very different in shape and energy, so it is not surprising that the model used for diatomic hydrogen fails for molecules containing other than s-orbitals. 

As in diatomics (Section 4.3), the molecular orbitals in polyatomic molecules may be expressed as linear combinations of atomic orbitals (AOs) centered on the nuclei. A minimal basis set of AOs contains all of the AOs that are occupied in the separated atoms [1, 2]. In the bent ozone molecule, for example, the separated O atoms have the ground state configuration (ls) (2s) (2p). The minimal basis set for ground-state O3 therefore consists of the Is, 2s, and three 2p orbitals centered on each of the oxygen nuclei (Fig. 7.1). The orientations selected for the 2p AOs in the basis set are of course arbitrary (aside from the constraint that basis AOs centered on any nucleus must be linearly independ-... 

Figure 14.68 Bonding molecular orbitals for diatomic molecules, Xj, of elements in the second period of the periodic table... 

In Section 10.8, we shall see the need to include d orbitals in the description of bonding between d-metal ions, such as Fe +, and proteins, such as hemoglobin. To get a sense of how molecular orbitals can be built from d orbitals, show how they can contribute to the formation of a and n orbitals in diatomic molecules. 

In this chapter the necessary theory to understand these two approaches is outlined. Orbital symmetry is introduced by consideration of atomic orbitals and their interaction to form molecular orbitals. The construction of correlation diagrams is illustrated for the formation of molecular orbitals of diatomic molecules. 

To obtain the MO structure of the diatomic molecules of the elements in the second period, we fill the available molecular orbitals in order of increasing energy. The results are... 

The ground-state electron configurations of diatomic molecules are deduced by forming molecular orbitals from all the valence-sbell atomic orbitals of the two atoms and adding the valence electrons to the molecular orbitals in order of increasing energy, in accord ivith the building-up principle. 

The basic principles dealing with the molecular orbital description of the bonding in diatomic molecules have been presented in the previous section. However, somewhat different considerations are involved when second-row elements are involved in the bonding because of the differences between s and p orbitals. When the orbitals being combined are p orbitals, the lobes can combine in such a way that the overlap is symmetric around the intemuclear axis. Overlap in this way gives rise to a a bond. This type of overlap involves p orbitals for which the overlap is essentially "end on" as shown in Figure 3.5. For reasons that will become clear later, it will be assumed that the pz orbital is the one used in this type of combination. 

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,... 

Heteroboranes, structure prediction for. 802-807 Heterocatenation. 741-742 Heterocyclic inorganic ring systems, 775-780 Heterogeneous catalysts, 705 Heteronuclear diatomic molecules. molecular orbitals in, 167-175... 

Homogeneous catalysts, 705 Homonuclear diatomic molecules. molecular orbitals in, 160-166... 

Molecular orbitals in heteronudear diatomic molecules. 167-175 in homonudear diatomic molecules, 160-166 of metallocenes. 670-673 in octahedral complexes, 414-418... 

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