Angular geometry

Thus far, we have only considered the angular geometry of complexes variations in bond lengths also pose challenges. For example, the gross inequality of bond lengths in [NiF ] and many copper(ii) and chromium(iii) complexes requires an explanation. Questions of this kind are also addressed in Chapter 7. 

The change from high- to low-spin configurations is necessarily discontinuous. A given complex is either on one side of the divide or the other. We conclude this section with a look at how the steric role of the d shell can affect angular geometries within a series of just high-spin, nominally tetrahedral nickel(ii) complexes. 

Keywords Lewis bases Dihalogens Halogen bond Angular geometry ... 

Attention will be paid to the systematic relationship of the geometries of B- XY to those of hydrogen-bonded complexes in the corresponding series B- HX, especially for angular geometries, which are dealt with in detail in Sects. 3.1, 3.2 and 3.3. Radial geometries are treated only in summary (Sect. 3.4) here, but a detailed analysis is available in [19]. 

The discussions of Sects. 3.1,3.2 and 3.3 are structured by reference to a set of rules that were proposed some years ago [103,104] for rationalising the angular geometries of hydrogen-bonded complexes of the type B- -HX, where X is a halogen atom. These rules are as follows ... 

The equilibrium angular geometry of a hydrogen-bonded complex B- HX... 

Angular Geometries of B- -CIF and B -HCI in Which B is a Mixed n-Pair/n-Pair Donor... 

The equilibrium angular geometry of a halogen-bonded complex B- XY can be predicted by assuming that the internuclear axis of a XY or X2 molecule bes ... 

The rules for predicting angular geometries of halogen-bonded complexes B- XY have recently received support from a wide ranging analysis of X-ray diffraction studies in the solid state by Laurence and co-workers [205]. This study not only confirms the validity of the rules in connection with complexes B- XY, where XY is Cl2, Br2, I2, IC1 and IBr, with many Lewis bases B but also reinforces the conclusion that halogen bonds Z- X - Y show a smaller propensity to be non-linear that do hydrogen bonds Z- H — X. 

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.

We see that it is a consequence of the Pauli principle and bond formation that the electrons in most molecules are found as pairs of opposite spin—both bonding pairs and nonbonding pairs. The Pauli principle therefore provides the quantum mechanical basis for Lewis s rule of two. It also provides an explanation for why the four pairs of electrons of an octet have a tetrahedral arrangement, as was first proposed by Lewis, and why therefore the water molecule has an angular geometry and the ammonia molecule a triangular pyramidal geometry. The Pauli principle therefore provides the physical basis for the VSEPR model. 

The polar interaction changes the geometry of the transition state of the reaction R02 + RH. Atoms C, H, O of the reaction center O H C of this reaction are in a straight line for the reaction of the peroxyl radical with a hydrocarbon. The reaction center O H C has an angular geometry in the reaction of the polar peroxyl radical with a polar molecule of the ketone. The interatomic distances rc H and i o n and angles peroxyl radical reactions with ketones calculated by the IPM method [79,80] are given in Table 8.15. 

The final cu-bonded formulas (3.213), (3.214), and (3.219)-(3.221) bear an obvious resemblance to the usual VSEPR representations of these hypervalent species. Indeed, each cu-bonded structure has the same number of formal bond pairs (bp) and lone pairs (lp) as the VSEPR representation. Furthermore, the predicted angular geometries of the two models are essentially identical, with the linear (or near-linear) cu-bonded ligands occupying axial positions in the SN2-like trigonal bipyramidal motif. 

However, the implications (HB-l)-(HB-5) of the cu-bonded model go far beyond those of the VSEPR model. The VSEPR model addresses only the angular geometry about the central atom, and provides no clear basis forjudging the length, strength,... 

Zr, Hf), group 6 (Cr, Mo, W), and group 10 (Ni, Pd, Pt). (Note that CrH6 was optimized with MoH -like angular geometry to prevent formation of the Cr(H2)3 dihydrogen complex.)... 

A very promising recent approach to modeling angular geometries, the VAL-BOND model[30], is based on Pauling s 1931 paper1311 that established the fundamental principles of directed covalent bonds formed by hybridization. The VALBOND force field, which uses conventional terms for bond stretching, torsions, improper tor-... 

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