Tetrahedral structure of methane

The theory of stereochemistry by van t and Le Bel (1874) is based on similar considerations to those of Kekuld, which led to the assumption that in methane the bonds from carbon to the hydrogen atoms form the tetrahedron angle. 

We illustrate the considerations by a well-known simple example. If the stmcture of the dichloromethane would be as that the chlorine atoms are placed in the comers of a square and the carbon atom is placed in the center of the square, then two isomers of dichloromethane would be possible. The situation is shown in Fig. 15.4. 

On the other hand, the fact that there exists only one isomer can be explained with the assumption of a tetrahedral structure of the methane stmcture. 

---

The axes of the sp orbitals point toward the corners of a tetrahedron Therefore sp hybridization of carbon is consistent with the tetrahedral structure of methane Each C—H bond is a ct bond m which a half filled Is orbital of hydrogen over laps with a half filled sp orbital of carbon along a line drawn between them... 

At this stage, it looks as though electron promotion should result in two different types of bonds in methane, one bond from the overlap of a hydrogen ls-orbital and a carbon 2s-orbital, and three more bonds from the overlap of hydrogen Is-orbitals with each of the three carbon 2/ -orbitals. The overlap with the 2p-orbitals should result in three cr-bonds at 90° to one another. However, this arrangement is inconsistent with the known tetrahedral structure of methane with four equivalent bonds. 

Figure 1.2 The tetrahedral structure of methane. Bonding electrons in methane principally occupy the space within the wire mesh.

Like ammonia, the structure is similar to the tetrahedral structure of methane. The two lone pairs repel each other in order to be as far apart as possible. The squeezing of the hydrogens in water is even greater than that in ammonia. The H-O-H bond angle in water is 104.5°. 

The tetrahedral structure of methane has been verified by electron diffraction (Fig. 2.1c), which shows beyond question the arrangement of atoms in such siihple molecules. Later on, we shall examine some of the evidence that led chemists to accept this tetrahedral structure long before quantum mechanics or electron diffraction was known. 

Analysis of this type of expression shows that LC is just another one-electron function with w = 0 or 1, directed at a special angle, that depends on the coefficients a, b and c. An infinite number of such linear combinations is possible, each defining another one-electron eigenfunction directed at one of an infinite number of angles, measured with respect to the original laboratory coordinate system. The important conclusion is that each linear combination corresponds to a new choice of axes. Selection of the polar axis along any Z always leaves Px and Py undefined as separate entities. In particular, there is no hope ever to simulate the tetrahedral structure of methane in terms of a linear combination of carbon electron eigenfunctions. That requires four linear combinations, each with a different polar axis, which is physically impossible. 

For example, the four C — H bonds of methane (CH4) are oriented toward the corners of a regular tetrahedron, with the carbon in the center and an approximately 109° angle between each C — H bond, as was originally postulated by J. H. van t Hoff and L. A. Le Bel in 1874. Figure 1.4 shows the tetrahedral structure of methane. 

The tetrahedral structure of methane, CH4, is given below on the left. Place individual bond dipole moments on the diagram. What value would you assign to the net molecular dipole moment The symmetric and asymmetric stretching vibrations of methane are indicated on the different orientation of methane... 

---