Tetrahedral methane

SI Tetrahedral Methane, cyclohexane, methanol, carbon tetrachloride... 

Representations of tetrahedral methane (a) space-filling model (b) ball-and-stick model (c) ball-and-stick model, highlighting the tetrahedral faces (d) ball-and-stick drawing using wedge representations for the out-of-plane bonds. 

The same kind of sp3 hybridization that describes the bonds to carbon in the tetrahedral methane molecule also describes bonds to nitrogen in the trigonal pyramidal ammonia molecule, to oxygen in the bent water molecule, and to all other atoms that VSEPR theory predicts to have a tetrahedral arrangement of four charge clouds. 

In tetrahedral methane, the H-C-H bond angle is 109.5°. In planar methane, this angle would be 90° and bonding electrons would be closer together. Thus, repulsion between electrons in different bonds would be greater in planar methane than in tetrahedral methane. Consequently, planar methane would be less stable than tetrahedral methane. 

In the tetrahedral methane molecule (its parameters then correspond to subscript 0 in eqs. (3.132), (3.133)), we notice that the 57X57XE matrix further simplifies as s nm = 1 and, therefore, simple analytical expressions become possible. Also, we notice that the FA approximation is adequate here as, for example, even very large elongation of one C-H bond by 0.1 A leads to changes of the bond geminal amplitudes u, v, and w not exceeding 0.003. The same applies to the expectation values of the pseudospin (f) operators representing the one- and two-electron density matrix elements. 

Fig. 15.7. c-Type interactions between the unoccupied Is AO of a proton and the doubly occupied sp3 AO of a CH3 anion influence of the magnitude of the overlap on the stabilization of the transition states of two bond-forming reactions. Left, formation of tetrahedral methane right, formation of a fictitious stereoisomer—an unsymmetrical trigonal bipyramid. 

FIGURE 1.22 The sp hybrid orbitals are arranged in a tetrahedral fashion around carbon. Each orbital contains one electron and can form a bond with a hydrogen atom to give a tetrahedral methane molecule. Note Only the major lobe of each sp orbital is shown. As indicated in Figure 1.21, each orbital contains a smaller back lobe, which has been omitted for the sake of clarity.)... 

A molecular electric potential exists because some types of atoms in a molecule attract electrons better than others. For instance, it is well known that fluorine attracts electrons more than hydrogen in HF, resulting in a nonzero dipole moment for this molecule. In the linear molecule carbon dioxide, electronic charge migrates toward the oxygens giving the molecule a measurable quadrupole moment. Even tetrahedral methane has a measurable octupole moment due to charge separation in its C —H bonds its dipole and quadrupole moments are zero by symmetry. 

Representations of the three-dimensional structure of methane, CH4. (a) Tetrahedral methane structure, (b) Ball and stick model of tetrahedral methane, (c) Three-dimensional representation of structure (b). 

FIGURE 302. (a) Depictions of tetrahedral methane as well as the nonsuperimposahle mirror images (enantiomers) of lactic acid (from Pope, Journal of the Society of the Arts, 1901) (b) enantiomeric crystals of quartz, arising from its hidden helical structure. (From General Chemistry by Linus Pauling 1947 by Linus Pauling. Used with the permission of W.H. Freeman and Company.)... 

The same procedure can be applied to molecules of the type AH , where A is an element from the second or third row of the periodic table. In particular, starting from tetrahedral methane, CH4, the archetype of organic molecules, one can obtain the organic fragments pyramidal CH3(C3v), bent CH2(C2v), and CH(Coov), by removing one, two, or three atoms ofhydrogen (5-2). 

The modem chemist could not reasonably have expected either planar or pyramidal CH4 to be potentially isolable molecules, i.e. to be potential energy surface minima, and indeed as we have seen calculation indicates that they are not (and the inversion transition state for tetrahedral methane is not planar Chapter 1). Consider however the simple artifice of anchoring the basal bonds of pyramidal methane to a... 

Tetrahedral methane. The four faces of a tetrahedron are equilateral triangles, and the angle between any two lines drawn from the center to two corners is 109.5°. 

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