Hybrid orbitals Subject

Viewed from the standpoint of molecular orbital theory, as it has developed during the last decade or so3, the above simple pictures of the sulfur bonding in a dialkyl sulfide are somewhat naive but they serve to introduce the subject and act as a basis for discussing the bonding in sulfoxides and sulfones. It will be convenient to use the second of the two pictures as the basis for further discussion, i.e. that involving the use of 3sp3 hybridized orbitals on sulfur. 

The double bond in ethylene contains one a bond and one 7r bond. The a bond forms from the end-on overlap of two hybrid orbitals, and the 7i bond forms from the side-by-side overlap of two atomic p orbitals. Figure 10-21 shows the complete orbital picture of the bonding in ethylene. Ethylene is the simplest of a class of molecules, the alkenes, all of which contain CDC double bonds. The alkenes are the subject of our Box on page 404. 

Ozone, which has 18 valehce electrohs, exemplifies bent molecules. Another example is the hitrite ahioh, the subject of Extra Practice Exercise. The bohdihg of NO2 can be represented using s p hybrid orbitals for the inner nitrogen atom and one set of delocalized n orbitals. 

The orbitals containing the bonding electrons are hybrids formed by the addition of the wave functions of the s-, p-, d-, and f- types (the additions are subject to the normalization and orthogonalization conditions). Formation of the hybrid orbitals occurs in selected symmetric directions and causes the hybrids to extend like arms on the otherwise spherical atoms. These arms overlap with similar arms on other atoms. The greater the overlap, the stronger the bonds (Pauling, 1963). 

The foregoing discussion of valence is. of course, a simplified one. From ihe development of the quantum theory and its application to the structure of the atom, there has ensued a quantum theory of valence and of the structure of the molecule, discussed in this hook under Molecule. Topics thal are basically important to modem views of molecular structure include, in addition to those already indicated the Schroedinger wave equation the molecular orbital method (introduced in the article on Molecule) as well as directed valence bonds bond energies, hybrid orbitals, the effect of Van der Waals forces and electron-dcticiem molecules. Some of these subjects are clearly beyond the space available in this book and its scope of treatment. Even more so is their use in interpretation of molecular structure. [However, sec Crystal Field Theory and Ligand.)... 

The concept of hybridization of atomic orbitals was subsequently introduced, in an attempt to interpret the difference between the actual bond angle for the water molecule and the value of 90° considered in the previous model. This concept had already been introduced to interpret, for example, the tetrahedral geometry of the methane molecule. We shall come back to this subject later in the chapter, to conclude that, although it is possible to establish a correlation between molecular geometry and hybrid orbitals, it is not correct to take the latter as the basis of an explanation of the former. This distinction is very important in teaching. 

The classical explanation for the increased coordination or valency of sulphur is its use of atomic d orbitals in molecules to form more hybrid orbitals for bonding than can be formed from just s- and p-type orbitals10. The dominant thinking on this subject today11 is that d-type orbitals provide needed spatial flexibility12 for bonding molecular orbitals that are formed even without the d orbitals (in theoretical descriptions or calculations, for example). The d orbitals in hypervalent sulphur are needed for quantitative accuracy and have not been found to be required for the qualitative electronic structure description13. 

Without studying in detail the properties and shapes of various hybrid orbitals, we shall review the essential points. This subject is treated more completely in other works 7,8,9,11 which the interested reader is referred. 

It is recommended that the reader become familiar with the point-group symmetry tools developed in Appendix E before proceeding with this section. In particular, it is important to know how to label atomic orbitals as well as the various hybrids that can be formed from them according to the irreducible representations of the molecule s point group and how to construct symmetry adapted combinations of atomic, hybrid, and molecular orbitals using projection operator methods. If additional material on group theory is needed. Cotton s book on this subject is very good and provides many excellent chemical applications. 

Gas-Phase Spectroscopy. The 336-nm absorption band of triplet imidogen was first observed by Eder in 1892 and has been the subject of numerous subsequent studies. The singlet state of NH absorbs at 324 nm. The CASSCF (6,5)/ CASPT2 level of theory predicts transitions at 323 and 293 nm for singlet and triplet imidogen, respectively. In each spin state, an electron is promoted from the sp hybrid lone pair to a singly occupied 2p orbital as shown below for NH. 

A subtle but key difference in the methodologies is that the orbital containing the two electrons in the C-X bond is frozen in the LSCF method, optimized in the context of an X-H bond in the link atom method, and optimized subject only to the constraint that atom C s contribution be a particular sp hybrid in the GHO method. In the link atom and LSCF methods, the MM partial charge on atom C interacts with some or all of the quantum system in the GHO method, it is only used to set the population in the frozen orbitals. 

In the ground states of 22-electron molecules, two electrons are placed in a further orbital which is more localized on atom A than on atoms B. This orbital is built from a p, orbital of A in the 90° molecule and from a pure s orbital of A in the linear molecule. At intervening angles the orbital represents the second sp hybrid that can be formed from the s and p, orbitals of A. This second sp hybrid points in the —z direction and so restores symmetry to the electron cloud around A.. The bond electrons are now subject to repulsions from the electrons in the sp hybrids which tend to cause bending in opposite directions thus the molecule resumes a linear or nearly linear form. 

It is evident from a comparison of 5 and 4 that the reflection transforms >pi into i/j2. The reader should verify that the a reflection and the C2 rotation also transform symmetry correct. The result we have found will generally hold when molecular orbitals constructed by the LCAO method from hybrid atomic orbitals are subjected to symmetry operations. Each of those orbitals in the set of MO s that is not already symmetry correct will be transformed by a symmetry operation into another orbital of the set. 

The mode of 02 coordination was for some time a subject of controversy. It now seems settled that the ligand molecule is bonded via one O atom, with an Fe-O-O angle of c. 120°. This is consistent with the prediction of a rather crude VB description of the 02 molecule, which allocates two lone pairs to each atom the valence state of O is (sp2)2(sp2)2(sp2)1(p)1. This description is inconsistent with the observed paramagnetism of 02 (which can readily be explained in terms of MO theory). However, oxygenated haemoglobin Hb.402 is diamagnetic and we may fairly describe the Fe-0 bond in terms of a filled sp2 hybrid donor orbital from the O atom. 

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