D-orbital directionality

A number of approaches for the computation of cavity shapes, sizes and elasticities have been reported and discussed in detail and controversially, and the methods, applications and interpretations have been reviewed extensively.91016"19,228 230,236 238 These also include models which appreciate chelate ring sizes12,17,239,240 and the directionality of the metal d-orbitals and the ligand lone pairs (misdirected valences).14,19,197,241... 

The directionality in the bonding between a d-block metal ion and attached groups such as ammonia or chloride can now be understood in terms of the directional quality of the d orbitals. In 1929, Bethe described the crystal field theory (CFT) model to account for the spectroscopic properties of transition metal ions in crystals. Later, in the 1950s, this theory formed the basis of a widely used bonding model for molecular transition metal compounds. The CFT ionic bonding model has since been superseded by ligand field theory (LFT) and the molecular orbital (MO) theory, which make allowance for covalency in the bonding to the metal ion. However, CFT is still widely used as it provides a simple conceptual model which explains many of the properties of transition metal ions. 

Comba P, Hambley TW, Strohle M. The directionality of d-orbitals and molecular-mechanics calculations of octahedral transition metal compounds. Helv Chim Acta 1995 78 2042-2047. 

In molecules such as H2O, the composition of the four hybrid orbitals (two bonding and two lone pairs) on the O atom will be slightly different In such cases, the actual percent composition of each hybrid orbital will be dictated by the molecule s geometry. For sp" hybridized orbitals (n= I -3), the relationship between the bond angle (0) and the decimal percent s-character (S) is given by Equation (10.8). For hybrids that also contain some d-orbital character, the relationship between the bond angle and directionality of the hybrid orbitals is somewhat more complex and is not discussed in this textbook. 

The directionality of an orbital in space is associated with a third set of quantum numbers called magnetic. For the p orbitals the magnetic quantum numbers are — 1,0, and 1, each representing one of the three different orthogonal directions in space (see the three 2p orbitals in Figure 1.1). The 2s and 2p orbitals make up the valence shell for carbon. Later in this chapter, we will examine metals, which contain d orbitals. The magnetic quantum numbers for rf orbitals are -2, -1,0,1, and 2. 

Among atomic orbitals, s orbitals are spherical and have no directionality. Other orbitals are nonspherical, so, in addition to having shape, every orbital points in some direction. Like energy and orbital shape, orbital direction is quantized. Unlike footballs, p, d, and f orbitals have restricted numbers of possible orientations. The magnetic quantum number (fflj) indexes these restrictions. 

One may speculate about the causes of strong chemisorption of some ions and the weak chemisorption of others. The four metals, with strongly chemisorbed ions on GaAs, (Ru, Pb, Ir, Rh) have several stable oxidation states and thus radii, some of which approach those of the lattice components. The orbitals of these metals and ions also have substantial mixed sp ( 60%) and d( 40%) character, which makes varying orbital hybridizations and thus a range of orbitals of different directionality possible.41 In some cases, orbitals binding at two or more surface sites can be envisaged. 

With regard to the formation of ionic compounds, it is not too relevant whether the 8p or 7d shell is occupied in the neutral atom, as studied in extenso by Mann and Wdber (50). Instead, the significant question for more ionic compounds is whether in the ions, after all outer s, p and d electrons are removed, some g or f electrons will be in frontier orbitals or whether they might be easily excited to an outer electron shell so that they can be removed as well. Prince and Waber (103) showed that even in the divalent state of element 126 one g electron has changed to an / electronic state. However, the 8s electrons are not the first to be removed. Thus, the divalent ions will be expected to act as soft Lewis acids and possibly form covalent complex ions readily. Crystal or ligand fields influence the nature of the hybridization. Details such as directionality of bonds... 

SCHEME 9.R.1 Atomic orbitals in the valence shell of a transition metal the labels s, p, and d happen to denote the shape of the orbital (spherical, polar, and dipolar, respectively), while the subscripts (such as x, y, and z) indicate the orbital s directionality in the space around the nucleus. 

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