Methane geometry

Two other examples will sufhce. Methane physisorbs on NaCl(lOO) and an early study showed that the symmetrical, IR-inactive v mode could now be observed [97]. In more recent work, polarized FTIR rehection spectroscopy was used to determine that on being adsorbed, the three-fold degeneracies of the vs and v modes were partially removed [98]. This hnding allowed consideration of possible adsorbate-adsorbent geometries one was that of a tripod with three of the methane hydrogens on the surface. The systems were at between 4 and 40 K so that the equilibrium pressure was very low, about 10 atm. 

The tetrahedral geometry of methane is often explained with the valence shell electron pair repulsion (VSEPR) model The VSEPR model rests on the idea that an electron pair either a bonded pair or an unshared pair associated with a particular atom will be as far away from the atom s other electron pairs as possible Thus a tetrahedral geomehy permits the four bonds of methane to be maximally separated and is charac terized by H—C—H angles of 109 5° a value referred to as the tetrahedral angle... 

The chemistry of propylene is characterized both by the double bond and by the aHyUc hydrogen atoms. Propylene is the smallest stable unsaturated hydrocarbon molecule that exhibits low order symmetry, ie, only reflection along the main plane. This loss of symmetry, which implies the possibiUty of different types of chemical reactions, is also responsible for the existence of the propylene dipole moment of 0.35 D. Carbon atoms 1 and 2 have trigonal planar geometry identical to that of ethylene. Generally, these carbons are not free to rotate, because of the double bond. Carbon atom 3 is tetrahedral, like methane, and is free to rotate. The hydrogen atoms attached to this carbon are aUyflc. 

Figure 4.9. Flame speed-distance relationship of methane-air fiames in adoubie piate geometry (2.5 X 2.5 m) as found by Moen et al. (1980b). Tube spirals (diameter H = 4 cm) were introduced between the plates (plate separation D). The pitch P (see Figure 4.8 for definition) was held constant. P = 3.8 cm. (a) H/D = 0.34 (b) HID = 0.25 (c) H/D = 0.13.

A tube 10 m long and 2.5 m inside diameter was used for experiments with methane (Moen et al. 1982) and propane (Hjertager et al. 1984). These often-cited experiments showed that very intense gas explosions were possible in this tube, which had an aspect ratio of only 4 but which contained internal obstructions. Pressures of up to 4.0 bar for methane and 13.9 bar for propane were reported. Obstruction parameters, for example, blockage ratio and pitch, were varied. As with cylindrical geometry, explosions became more severe with increasing obstacle density. 

We win run this job on methane at the Hartree-Fock level using the 6-31G(d) basis our molecule specification is the result of a geometry optimization using the B3LYP Density Functional Theory method with the same basis set. This combination is cited... 

Examine the structures of the two transition states (chlorine atom+methane and chlorine+methyI radical). For each, characterize the transition state as early (close to the geometry of the reactants) or as late (close to the geometry of the products) In Ught of the thermodynamics of the individual steps, are your results anticipated by the Hammond Postulate Explain. 

Table 7 shows the calculated properties of the molecules in this series. The molecular geometries were inferred from available data for H2S and dimethyl sulphone. Methane... 

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. 

Table 1 Coefficients for 7[ (a ) for third harmonic generation (THG), degenerate four wave mixing (DFWM), electric field induced second harmonic generation (ESHG), and Kerr effect in methane at the experimental geometry rcH = 2.052 a.u. A CCSD wavefunction and the t-aug-cc-pVDZ basis were used. (Results given in atomic units, the number in parentheses indicate powers of ten.)...

Table 4 Comparison of various ab initio results and experimental estimates for the dispersion coefficients of the electronic hyperpolarizabilities 7jj and 7 of methane. (All results in atomic units. Results for the dispersion coefficients refer to single point calculations at the equilibrium geometry. Where available, dispersion coefficients for the vibrational average are given in parentheses.)...

Methane is the simplest molecule with a tetrahedral shape, but many molecules contain atoms with tetrahedral geometry. Because tetrahedral geometry is so prevalent in chemistry, it is important to be able to visualize the shape of a tetrahedron. 

Tetrahedral molecular geometry, with 109.5° bond angles, minimizes repulsion among the bonding electron pairs of methane. ... 

Any hybrid orbital is named from the atomic valence orbitals from which It Is constmcted. To match the geometry of methane, we need four orbitals that point at the comers of a tetrahedron. We construct this set from one s orbital and three p orbitals, so the hybrids are called s p hybrid orbitais. Figure 10-8a shows the detailed shape of an s p hybrid orbital. For the sake of convenience and to keep our figures as uncluttered as possible, we use the stylized view of hybrid orbitals shown in Figure 10-8Z). In this representation, we omit the small backside lobe, and we slim down the orbital in order to show several orbitals around an atom. Figure 10-8c shows a stylized view of an s p hybridized atom. This part of the figure shows that all four s p hybrids have the same shape, but each points to a different comer of a regular tetrahedron. 

We generate hybrid orbitals on inner atoms whose bond angles are not readily reproduced using direct orbital overlap with standard atomic orbitals. Consequently, each of the electron group geometries described in Chapter 9 is associated with its own specific set of hybrid orbitals. Each type of hybrid orbital scheme shares the characteristics described in our discussion of methane ... 

Table 3 Geometry obtained for the methanal Si(n,n ) excited state. Distances in A, angles in degrees, energies in Hartrees, and barrier height in cm . ...

The hybridized orbital approach is a simplified way of predicting the geometry of a molecule by mixing the valence orbitals of its atoms. For example, methane (CH ) is composed of a carbon atom with an electron configuration of Is 2s 2p. The hydrogen atom has an electron configuration of Is. The geometry of the methane... 

Now let us return to our discussion of the conical intersection structure for the [2+2] photochemical cycloaddition of two ethylenes and photochemical di-Jt-methane rearrangement. They are both similar to the 4 orbital 4 electron model just discussed, except that we have p and p overlaps rather than Is orbital overlaps. In Figure 9.5 it is clear that the conical intersection geometry is associated with T = 0 in Eq. 9.2b. Thus (inspecting Figure 9.5) we can deduce that... 

Let us summarize briefly at this stage. We have seen that the point of degeneracy forms an extended hyperline which we have illnstrated in detail for a four electrons in four Is orbitals model. The geometries that lie on the hyperline are predictable for the 4 orbital 4 electron case using the VB bond energy (Eq. 9.1) and the London formula (Eq. 9.2). This concept can be nsed to provide nseful qualitative information in other problems. Thns we were able to rationalize the conical intersection geometry for a [2+2] photochemical cycloaddition and the di-Jt-methane rearrangement. 

Figure 1.10 The tetrahedral, trigonal pyramidal, and angular geometries of the methane, ammonia, and water molecules based on the tetrahedral arrangement of four electron pairs.

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