Methane , molecular orbitals

Fig. 1.14. Combinations of atomic orbitals leading to the methane molecular orbitals.

This particular calculation used as a basis set the I5-, 2s-, and three 2p-orbitals of carbon and the l5-orbitals of the four hydrogens. The lowest molecular orbital is principally Is in character. A significant feature of this and other MO calculations on methane is that unlike a picture involving localized bonds derived from 5p -hybrid carbon orbitals, there are not four equivalent orbitals. We can obtain an understanding of this feature of the MO picture by a qualitative analysis of the origin of the methane molecular orbitals. For simplicity, we will consider the orbitals to be derived from the carbon 2s-, 2p -, 2py-, and 2p -orbitals and ignore the carbon Is-orbital. The most convenient frame of reference for the tetrahedral methane molecule is described by a cube with hydrogen atoms at alternate corners and the carbon atom, centered in the cube, as shown below ... 

Methane—Molecular Orbitals or Discrete Single Bonds with sp Hybrids ... 

The Hydrogen Atom 811 Methane—Molecular Orbitals or Discrete Single Bonds with sp Hybrids 827 Koopmans Theorem—A Connection Between Ab Initio Calculations and Experiment 828 A Matrix Approach to Setting Up the LCAO Method 832 Through-Bond Coupling and Spin Preferences 861 Cy clobu tadiene at the Two-Electron Level of Theory 862... 

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. ...

Fig. 1.20. Atomic orbital combinations giving rise to bonding molecular orbitals for methane.

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. 

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. 

FIGURE 3.37 The molecular orbital energy-level diagram for methane and the occupation of the orbitals by the eight valence electrons of the atoms. 

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... 

Figure 1.9 Molecular orbital diagram for methanal, showing the n —> tt and n —> n transitions. The boundary surfaces of the n, n and Jt molecular orbitals...

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 ... 

Fig. 4. Molecular orbitals showing the hybridization of s and p orbitals, (a) Acetylene (C2H2, sp hybridization) (b) ethylene (C2H4, sp hybridization), and (c) methane (CH4, sp hybridization).

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... 

Herzberg (Nobel prize for Chemistry, 1971) commented on the two distinct photoionizations from methane that this observation illustrates the rather drastic nature of the approximation made in the valence bond treatment of CH4, in which the 2s and 2p electrons of the carbon atom are considered as degenerate and where this degeneracy is used to form tetrahedral orbitals representing mixtures of 2s and 2p atomic orbitals. The molecular orbital treatment does not have this difficulty". 

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