Tetrahedral valence molecular orbitals

Fig. 2.6-1. Calculated valence molecular orbitals of tetrahedral P4 (isodensity surface drawn at a cut off of 0.05 a.u.). Only one representation of the similar degenerate MOs is given.

A quantitative consideration on the origin of the EFG should be based on reliable results from molecular orbital or DPT calculations, as pointed out in detail in Chap. 5. For a qualitative discussion, however, it will suffice to use the easy-to-handle one-electron approximation of the crystal field model. In this framework, it is easy to realize that in nickel(II) complexes of Oh and symmetry and in tetragonally distorted octahedral nickel(II) complexes, no valence electron contribution to the EFG should be expected (cf. Fig. 7.7 and Table 4.2). A temperature-dependent valence electron contribution is to be expected in distorted tetrahedral nickel(n) complexes for tetragonal distortion, e.g., Fzz = (4/7)e(r )3 for com-... 

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... 

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". 

Tetrahedral complexes arc favored by steric requirements, either simple electrostatic repulsions of charged ligands or van dcr Wauls repulsions of large ones. A valence bond (VB) point oT view ascribes tetrahedral structures to p% hybridization From a crystal field (CF) or molecular orbital (MO) viewpoint we have seer that, in general, tetrahedral structures are not stabilized by large LFSE. Tetrahedral complexes are thus favored by large ligands like Cl-. Br. and 1 and small metal ions of three types ... 

The transition metal ions possess a very stable set of d orbitals, and it is likely that d orbitals are involved in bonding in all transition metal complexes, regardless of structure. The common structures that use d valence orbitals for forming a bonding molecular orbitals are square-planar, tetrahedral, and octahedral. Examples of these structures are given in Figure 8-1. 

The electronic structure of tetrahedral oxyanions and their derivatives has been extensively studied by many authors during the past decades. The earlier attempts were summarized by Prins [1]. Since the work of Walsh [2] and that of Wolfsberg and Helmholz [3] several semi-empirical theoretical studies have been published [4-7]. Later ab initio [8-10] and scattered wave calculations [11] have been also reported. Among the experimental investigations, Prins mentioned the electron spin resonance measurements of radicals formed by ejection or addition of an electron from or to certain oxyanions, obtaining information on just those molecular orbitals which contained unpaired electrons. [12] X-ray absorption and emission studies provided usefial information on a limited number of molecular orbitals in the valence band [13-19]... 

The permanganate anion MnC)4 has a tetrahedral geometry with a Td point group symmetry, Fig. 1. At each oxygen atom, we have a core like 2s orbital as well as two 2-pn and one 2pffvalance orbitals. The total number of valence electrons is 32 of which 8 are in core type 2s levels and the remaining 24 in molecular orbitals spanned by 2pn, 2pa and 3d. We show in Fig. 2 the levels represented by orbitals made up of 2pn, 2pa and 3d. 

The description of such molecules as He2+, 02 and NO is more satisfactory by the molecular orbital method than by the Heitler-London since in the latter an additional concept, that of the three electron bond, must be introduced in order to explain the molecule and its properties. The conception of directional valency is perhaps more easily conceived by the method of localized pairs, but as already pointed out, the molecular orbital treatment of delocalized electrons also leads to the tetrahedral model of methane. 

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