Polyatomic molecules orbital hybridization

Klessinger, M. (1965) Self-consistent group calculations on polyatomic molecules. II. Hybridization and optimum orbitals in water. /. Chem. Phys., 43, S117-S119. 

Hybrid orbitals may be considered as perfectioned AOs, adopted in the calculation of localized MOs in polyatomic molecules, with the LCAO method (cf. section 1.17.1). In the case of hybrid orbitals sp, the four linear combinations of s and p orbitals (Tbi, Tc2, Te, Te ) that lead to tetrahedral symmetry are... 

Just as in the non-linear polyatomic-molecule case, the atomic orbitals which constitute a given molecular orbital must have the same symmetry as that of the molecular orbital. This means that o,%, and 8 molecular orbitals are formed, via LCAO-MO, from m=0, m= 1, and m= 2 atomic orbitals, respectively. In the diatomic N2 molecule, for example, the core orbitals are of o symmetry as are the molecular orbitals formed from the 2s and 2pz atomic orbitals (or their hybrids) on each Nitrogen atom. The molecular orbitals fonned from the atomic 2p i =(2px- i 2py) and the 2p+j =(2px + i 2py ) orbitals are of Jt symmetry and have m = -1 and +1. 

In this section, we first discuss the bonding in two linear triatomic molecules BeH2 with only a bonds and C02 with both a and n bonds. Then we go on to treat other polyatomic molecules with the hybridization theory. Next we discuss the derivation of a self-consistent set of covalent radii for the atoms. Finally, we study the bonding and reactivity of conjugated polyenes by applying Hiickel molecular orbital theory. 

If we prefer to describe the bonding of a polyatomic molecule using localized two-center, two-electron (2c-2e) bonds, we can turn to the hybridization theory, which is an integral part of the valence bond method. In this model, for AX systems, we linearly combine the atomic orbitals on atom A in such a way that the resultant combinations (called hybrid orbitals) point toward the X atoms. For our BeH2 molecule in hand, two equivalent, colinear hybrid orbitals are constructed from the 2s and 2pz orbitals on Be, which can overlap with the two Is hydrogen orbitals to form two Be-H single bonds. (The 2p and 2py... 

Analyze the hybrid orbitals used in bonding in polyatomic molecules and ions... 

Covalent bonds in polyatomic molecules and ions are formed by the overlap of hybrid orbitals, or of hybrid orbitals with unhybridized ones. Therefore, the hybridization bonding scheme is still within the framework of valence bond theory electrons in a molecule are assumed to occupy hybrid orbitals of the individual atoms. 

So far we have discussed chemical bonding only in terms of electron pairs. However, the properties of a molecule cannot always be explained accurately by a single structure. A case in point is the O3 molecule, discussed in Section 9.8. There we overcame the dilemma by introducing the concept of resonance. In this section we will tackle the problem in another way—by applying the molecular orbital approach. As in Section 9.8, we will use the benzene molecule and the carbonate ion as examples. Note that in discussing the bonding of polyatomic molecules or ions, it is convenient to determine fust the hybridization state of the atoms present (a valence bond approach), followed by the formation of appropriate molecular orbitals. 

In the previous section, we emphasized that hybridization of some or all of the valence atomic orbitals of the central atom in an XY species provided a scheme for describing the X—Y f7-bonding. In, for example, the formation of sp, sp and sp d hybrid orbitals, some p or d atomic orbitals remain unhybridized and, if appropriate, may participate in the formation of TT-bonds. In this section we use the examples of C2H4, HCN and BF3 to illustrate how multiple bonds in polyatomic molecules are treated within VB theory. Before considering the bonding in any molecule, the ground state electronic configurations of the atoms involved should be noted. 

Despite its successes, the application of valence bond theory to the bonding in polyatomic molecules leads to conceptual difficulties. The method dictates that bonds are localized and, as a consequence, sets of resonance structures and bonding pictures involving hybridization schemes become rather tedious to establish, even for relatively small molecules (e.g. see Figure 4.10c). We therefore turn our attention to molecular orbital (MO) theory. 

Two theories go hand in hand in a discussion of covalent bonding. The valence shell electron pair repulsion (VSEPR) theory helps us to understand and predict the spatial arrangement of atoms in a polyatomic molecule or ion. It does not, however, explain hoav bonding occurs, ] ist where it occurs and where unshared pairs of valence shell electrons are directed. The valence bond (VB) theory describes how the bonding takes place, in terms of overlapping atomic orbitals. In this theory, the atomic orbitals discussed in Chapter 5 are often mixed, or hybridized, to form new orbitals with different spatial orientations. Used together, these two simple ideas enable us to understand the bonding, molecular shapes, and properties of a wide variety of polyatomic molecules and ions. 

MO theory is extensively used for those polyatomic molecules in which multiple bonding occurs. We have already considered how N02 is formulated in VB theory as a resonance hybrid (3-V). In MO theory it can be treated in the following way. We first assume that a set of a bonds is formed using four electrons and that several other electron pairs are non-bonding. Thus we write a framework of nuclei and a electrons (3-VII). There are still four electrons to be assigned and each of the three atoms has an empty pn orbital (one whose nodal plane coincides with the molecular plane). If we start with... 

SECTION 9.5 To extend the ideas of valence-bond theory to polyatomic molecules, we must envision mixing s, p, and sometimes d orbitals to form hybrid orbitals. The process of hybridization leads to hybrid atomic orbitals that have a large lobe directed to overlap with orbitals on another atom to make a bond. Hybrid orbitals can also accommodate nonbonding pairs. A particular mode of hybridization can be associated with each of three common electron-domain geometries (linear = sp trigonal planar = sp -, tetrahedral = sp ). 

Before going on to discuss the hybridization of d orbitals, let us specify what we need to know in order to apply hybridization to bonding in polyatomic molecules in general. In essence, hybridization simply extends Lewis theory and the VSEPR model. To assign a suitable state of hybridization to the central atom in a molecule, we must have some idea about the geometry of the molecule. The steps are as follows ... 

Valence Bond Theory for Polyatomic Molecules Requires the Use of Hybrid Orbitals 240... 

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