Methane point group

Fig. 3.4. Symmetry elements of methane (point group, T. TABLE 3.2...

This is the point group to which all regular tetrahedral molecules, such as methane (Figure 4.12a), silane (SiFl4) and nickel tetracarbonyl (Ni(CO)4), belong. 

The methane molecule is a very important molecule in organic chemistry, the geometry around the tetravalent carbon atom being basic to the understanding of the structure, isomerism and optical activity of a very large number of compounds. It is a tetrahedral molecule belonging to the tetrahedral point group, Td. 

Type 4. More than one axis higher than twofold point groups I d, /, , /, (also Th, T, 0,1). Methane (Td), cubane (Oh, Figure 1.1), dodecahedrane (//, Figure 1.1), and buckminsterfullerene, Cat (E, Chapter 11). The symbol Kh denotes the point group of the sphere. 

A symmetry analysis of the basis orbitals for methane (T point group) identifies the representations for the central... 

For methane, the vectors point at the comers of a tetrahedron or at alternate corners of a cube. Using the point group, we can use these four vectors as the basis of a reducible representation. As usual, the character for each vector is 1 if it remains unchanged by the symmetry operation, and 0 if it changes position in any other way (reversing direction is not an option for hybrids). The reducible representation for these four vectors is then r = Aj + T. ... 

We consider first groups lacking a C axis. A molecule with no elements of symmetry (other than the identity E) belongs to the point group C. The identity element is equivalent to Ci, a rotation by In/l radians or 360°. Very few small molecules are this unsymmetrical—one example is the trisubstituted methane ... 

Methane BDE, 76, 113 geometry of, 32 orbital energies, 26 point group of, 6 reaction with methyl radical, 149 total energy, 29... 

As a straightforward example we can calculate the ( ieff)H of any hydrogen atom of methane. The axis system is most conveniently oriented through the carbon atom along the three S4 axes of improper rotation that characterise the point group symmetry of this Td molecule. In this axis system each hydrogen atom is equidistant from each axis, r, and the rotational inertia about each axis is equivalent, 1= 4/mh Then... 

In case methane molecule is distorted to (a) point group due to bond lengthening and (b) to C2v point group due to scissor action of molecular vibration. More d-orbitals would become available for bonding. 

To take a concrete example, any MO calculation of the electronic structure of the ethene (ethylene) molecule wiU generate two lowest MOs (almost degenerate) which are just the in-phase and out-of-phase linear combinations of the basis functions used to describe the Is shells of the carbon atoms. The fact that they occur as molecular orbitals rather than remaining actually unchanged as atomic orbitals is simply an artifact of the symmetry of ethene the MOs are computed as symmetric or antisymmetric with respect to the operations of the point group which in this case includes reflection in a plane perpendicular to the C—C axis. If a calculation is carried through on the isoelectronic methanal (formaldehyde) molecule the oxygen Is AO and the carbon Is AO survive the calculation almost unscathed as the lowest MOs . 

A tetrahedral AX molecule, for example, methane, CH, has the point group of the regular tetrahedron, T. Gradual substitution of the X ligands by B ligands leads to less symmetrical tetrahedral configurations (Figure 3-19a), until complete substitution is accomplished. 

Methane. The AOs for a minimal-basis-set SCF calculation of CH4 are the carbon Is, 2s, 2p 2py, and 2p AOs and a Is AO on each hydrogen atom. The point group of CH4 is S rf. Group theory (see Cotton or Schonland) gives the possible symmetry... 

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