Homonuclear diatomic molecules atomic / -orbital combinations

There exists no uniformity as regards the relation between localized orbitals and canonical orbitals. For example, if one considers an atom with two electrons in a (Is) atomic orbital and two electrons in a (2s) atomic orbital, then one finds that the localized atomic orbitals are rather close to the canonical atomic orbitals, which indicates that the canonical orbitals themselves are already highly, though not maximally, localized.18) (In this case, localization essentially diminishes the (Is) character of the (2s) orbital.) The opposite situation is found, on the other hand, if one considers the two inner shells in a homonuclear diatomic molecule. Here, the canonical orbitals are the molecular orbitals (lo ) and (1 ou), i.e. the bonding and the antibonding combinations of the (Is) orbitals from the two atoms, which are completely delocalized. In contrast, the localization procedure yields two localized orbitals which are essentially the inner shell orbital on the first atom and that on the second atom.19 It is thus apparent that the canonical orbitals may be identical with the localized orbitals, that they may be close to the localized orbitals, that they may be identical with the completely delocalized orbitals, or that they may be intermediate in character. 

Up to now we have only considered combining two atoms of the same element to form homonuclear diatomic molecules. Now we shall consider what happens when the two atoms are different. First of all, how do the atomic orbitals of different elements differ They have the same sorts of orbitals Is, 2s, 2p, etc. and these orbitals will be the same shapes but the orbitals will have different energies. For... 

There are three mutually perpendicular 2p orbitals in each atom. When the six p orbitals in two atoms combine, the two orbitals that interact end to end form a a and a a MO, and the two pairs of orbitals that interact side to side form two -IT MOs of the same energy and two tt MOs of the same energy. Combining these orientations with the energy order gives the expected MO diagram for the /7-block Period 2 homonuclear diatomic molecules (Figure 11.19A). 

Let us consider an element in the first short Period having 2s and 2p orbitals in its valence shell. When two such atoms are combined into a homonuclear diatomic molecule, the two sets of atomic orbitals may combine into various MO s. Before we can specify the electronic structures of the diatomic molecules of these elements, we must know the relative energies of these MO s. 

The MO approximation puts the electrons of a molecule in molecular orbitals, which extend over the whole molecule. As an approximation to the molecular orbitals, we usually use linear combinations of atomic orbitals. The VB method puts the electrons of a molecule in atomic orbitals and constructs the molecular wave function by allowing for exchange of the valence electron pairs between the atomic orbitals of the bonding atoms. We compared the two methods for H2. We now consider other homonuclear diatomic molecules. 

The atomic orbitals should have comparable energies. Thus in-the formation of homonuclear diatomic molecule, the Is orbital of one atom does not combine with 2s or 2p orbital of another atom of the same element. Similarly, 2s orbital will not combine with 2p orbitals. However, in heterodiatomic molecules this may not be true. 

Let us first recall the simple case of a homonuclear diatomic molecule B-B, each atom B with one atomic orbital of energy a and with a coupling matrix element p and overlap S. The molecular orbital energies, corresponding to bonding and antibonding combinations = (p (p )l / 2 2S), are ... 

When two atoms containing s and p valence orbitals are combined into a homonuclear diatomic molecule a set of molecular orbitals with shapes and symmetry properties as those already described arises. The relative energies of... 

Homonuclear diatomic molecules (molecules made up of two atoms of the same kind) formed from second-period elements have between 2 and 16 valence electrons. To explain bonding in these molecules, we must consider the next set of higher energy molecular orbitals, which can be approximated by linear combinations of the valence atomic orbitals of the period 2 elements. 

Sketch the bonding and antibonding molecular orbitals that result from linear combinations of the 2p atomic orbitals in a homonuclear diatomic molecule. (The Ip, orbitals are those whose lobes are oriented along the bonding axis.)... 

To begin orrr discussion, we consider H2, the simplest homonuclear diatomic molecule. According to valence borrd theory, an H2 molecule forms when two H atoms are close enough for their Is atomic orbitals to overlap. According to molecular orbital theory, two H atoms come together to form H2 when their Is atomic orbitals combine to ve molecular orbit s. Figure 9.11 shows the Is... 

In the linear combinahons of atomic orbitals used to describe diatomic systems, we find energehc preference for those combinations that have the fewest nodal planes between the atomic centers. A nodal plane between nuclei implies diminished electron density between the nuclei, a feature we associate with antibonding. Let us analyze several S5unmetry-adapted linear combinations of atomic orbitals of a homonuclear diatomic molecule starting with combinahons of s orbitals. 

In the case of ethylene the a framework is formed by the carbon sp -orbitals and the rr-bond is formed by the sideways overlap of the remaining two p-orbitals. The two 7r-orbitals have the same symmetry as the ir 2p and 7T 2p orbitals of a homonuclear diatomic molecule (Fig. 1.6), and the sequence of energy levels of these two orbitals is the same (Fig. 1.7). We need to know how such information may be deduced for ethylene and larger conjugated hydrocarbons. In most cases the information required does not provide a searching test of a molecular orbital approximation. Indeed for 7r-orbitals the information can usually be provided by the simple Huckel (1931) molecular orbital method (HMO) which uses the linear combination of atomic orbitals (LCAO), or even by the free electron model (FEM). These methods and the results they give are outlined in the remainder of this chapter. 

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