Molecular orbitals in methane

Figure 6. Representations for the bonding molecular orbitals in methane.

Such a transformation can be used for relocalizing a given set of delocalized molecular orbitals in conformity with the chemical formula. For instance, the occupied orbitals of methane can be transformed into orbitals very close to simple two-center MO s constructed from tetrahedral sp3 hybrid orbitals and Is hydrogen orbitals 24,25,26) a. unitary transformation can hardly modify the wave function, except for an immaterial phase factor therefore, it leads to a description which is as valid as that in terms of the canonical delocalized Hartree-Fock orbitals. Of course, the localization obtained in this way is not perfect, but it is usually much better than is often believed. In the case of methane, the best localized orbitals are uniquely determined by symmetry 27> for less symmetric molecules one needs a criterion for best localization 28 29>, a problem on which we shall not insist here. A careful inspection reveals that there are three classes of compounds ... 

The H-C-H bond angle in methane is 109.5°. The H-O-H bond angle of water is close to this number but the H-S-H bond angle of H2S is near 90°. What does this tell us about the bonding in water and H2S Draw a diagram of the molecular orbitals in H2S. 

This orientation of the molecule reveals that methane possesses three twofold symmetry axes, one each along the x, y, and z axes. Because of this molecular symmetry, the proper molecular orbitals of methane must possess symmetry with respect to these same axes. There are two possibilities the orbital may be unchanged by 180° rotation about the axis (symmetric), or it may be transformed into an orbital of identical shape but opposite sign by the symmetry operation (antisymmetric). The carbon 2s-orbital is symmetric with respect to each axis, but the three 2p-orbitals are each antisymmetric to two of the axes and symmetric with respect to one. The combinations which give rise to molecular orbitals that meet these symmetry requirements are shown in Fig. 1.11. 

An alternative but equivalent model for describing benzene (and other resonance-stabilized structures) is molecular orbital theory. We have already seen how this theory can explain the formation of molecular structures such as methane, ethene and others. In localized molecules like ethene, C2H4, two unhybridized p orbitals overlap to form a Jt molecular orbital in which a pair of electrons is shared between tbe nuclei of two carbon atoms. In molecular orbital theory, resonance-stabilized structures are described in terms of delocalized Jt orbitals where the Jt electron clouds extend over three or more atoms. 

Figure A11.1 The radial functions used with s-type basis functions for C atoms in the 6-31C basis set. a) The six primitive Caussians (dashed lines) are shown scaled by their contraction coefficients (dp in equation Al 1.2). Their sum gives the contracted function (solid bold line) used for the core region, b) The three primitive Caussians (dashed lines) scaled by the contraction coefficients and the contracted function (solid bold line) used for the valence region, c) Example use of all three basis functions to form the C(2s) atomic orbital in the 2a, molecular orbital of methane. The three basis functions are shown as dashed lines scaled by the SCF coefficients given in the formula. The resulting summed radial function is shown as the bold solid line.

Hence we have two molecular orbitals, one along the line of centres, the other as two sausage-like clouds, called the n orbital or n bond (and the two electrons in it, the n electrons). The double bond is shorter than a single C—C bond because of the double overlap but the n electron cloud is easily attacked by other atoms, hence the reactivity of ethene compared with methane or ethane. 

Fig. 1.18. Molecular orbital energy diagram for methane. Energies are in atomic units. ...

For a molecule as simple as Fl2, it is hard to see much difference between the valence bond and molecular orbital methods. The most important differences appear- in molecules with more than two atoms. In those cases, the valence bond method continues to view a molecule as a collection of bonds between connected atoms. The molecular- orbital method, however, leads to a picture in which the sane electron can be associated with many, or even all, of the atoms in a molecule. We ll have more to say about the similarities and differences in valence bond and molecular- orbital theory as we continue to develop their principles, beginning with the simplest alkanes methane, ethane, and propane. 

We are now ready to account for the bonding in methane. In the promoted, hybridized atom each of the electrons in the four sp3 hybrid orbitals can pair with an electron in a hydrogen ls-orbital. Their overlapping orbitals form four o-bonds that point toward the corners of a tetrahedron (Fig. 3.14). The valence-bond description is now consistent with experimental data on molecular geometry. 

The development of molecular orbital theory (MO theory) in the late 1920s overcame these difficulties. It explains why the electron pair is so important for bond formation and predicts that oxygen is paramagnetic. It accommodates electron-deficient compounds such as the boranes just as naturally as it deals with methane and water. Furthermore, molecular orbital theory can be extended to account for the structures and properties of metals and semiconductors. It can also be used to account for the electronic spectra of molecules, which arise when an electron makes a transition from an occupied molecular orbital to a vacant molecular orbital. 

Having seen the development of the molecular orbital diagram for AB2 and AB3 molecules, we will now consider tetrahedral molecules such as CH4, SiH4, or SiF4. In this symmetry, the valence shell s orbital on the central atom transforms as A, whereas the px, py, and pz orbitals transform as T2 (see Table 5.5). For methane, the combination of hydrogen orbitals that transforms as A1 is... 

Both the Si and Ti excited states arise from the promotion of an electron from the n molecular orbital to the Jt molecular orbital. They are referred to as (njji ) and 3(n,tt ) states, respectively. The S2 and T2 states arise from the promotion of an electron from the n molecular orbital to the Jt molecular orbital and are referred to as 1(n,nx ) and 3(jt,Jt ) states, respectively. The state diagram for methanal is shown in Figure 1.11. With regard to the different spin states in molecules, the following ideas are important ... 

Now we can consider the bonding in methane. Using orbital overlap as in the hydrogen molecule as a model, each sp orbital of carbon can now overlap with a 1 orbital of a hydrogen atom, generating a bonding molecular orbital, i.e. a ct bond. Four such... 

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