Valence angle deformation

The fact that molecular mechanics is a well-developed tool for organic molecules, whereas coordination compounds have in the past been modeled less frequently, is partly related to the difficulty in reliably modeling the angles at transition metal centers. In organic compounds sp3, sp2 and sp hybrids lead to relatively stiff angles of 109.5°, 120° and 180°, respectively, which are conveniently mod- 

There are rather trivial solutions to the former problem[58]. Fortunately, the electronic influence exerted by the metal ion is most often a relatively small effect which can be added as a minor perturbation to the ligand dictated geometry. As discussed in the Introduction (Fig. 1.1) this emerges from experimental structural and spectroscopic data1651.  

There are a number of ways to model the geometry of transition metal centers. One promising treatment is based on the addition of a ligand field term to the strain energy function (Eq. 3.15)[69,771. 

In this approach the metal-ligand interaction is modeled with a metal-ligand bonding interaction term, ML, approximated by a Morse function, a cellular ligand field stabilization energy term, (which is responsible for the coordination 

A number of functions with multiple minima have been proposed for modeling the valence angles around metals. The molecular mechanics program DREIDING, based on a generic force field, uses a harmonic cosine function (Eq. 3.16)[83]. 

3 However, that molecular mechanics of inorganic and coordination compounds is a quickly growing field is shown in some recent review articles116,24 1. 

4 Modeling of specific electronic effects due to the partly filled d-orbitals is discussed in Chapter 11. 

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- 

5) For simplicity, the discussion here is restricted to a-bonding. Some aspects of 7 bonding, including modeling of organometallic com- 

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The activation of the macromolecules as a consequence of valence angle deformation by mechanical action. 

In some cases (such as torsional barrier terms) it is possible to do this definitively, while in others (such as valence angle deformation force constants and ideal distances and angles) it is not. However, useful starting points for the empirical refinement can be derived from experiment. 

More accurate force constants for a number of transition metal complexes with ammine ligands have been derived by normal-coordinate analyses of infrared spectra[130, 31l The fundamental difference between spectroscopic and molecular mechanics force constants (see Section 3.4) leads to the expectation that some empirical adjustment of the force constants may be necessary even when these force constants have been derived by full normal-coordinate analyses of the infrared data. This is even more important for force constants associated with valence angle deformation (see below). It is unusual for bond-length deformation terms to be altered substantially from the spectroscopically derived values. 

An alternative approach to modeling the L-M-L angles is to set the force constants to zero and include nonbonded 1,3-interactions between the ligand atoms. In most force fields, 1,3-interactions are not explicitly included for any atoms, instead they are taken up in the force constants for the valence angle terms. This is an approximation because the 1,3-interactions are most often repulsive and thus the function used to calculate the strain energy arising from valence angle deformation should be asymmetric. It was shown that the nonbonded 1,3-interactions around the metal atom are in many cases a major determinant of the coordination... 

For a number of linear polymers, values of E for single crystals have been determined. This has been performed by direct measurements or by calculation from molecular dimensions and force constants for bond stretching and valence angle deformation (Treloar, 1960 Frensdorff, 1964 Sakurada and co-workers, 1962, 1970 Frank, 1970). 

PCA has been successfully applied to the mapping of valence angle deformations at metals and other atomic centres. For example, Murray-Rust [65] has studied the deformations from ideal symmetry in PO4 tetrahedra, whilst Auf der Heyde and Burgi [7, 8, 9] have used PCA to study the Berry [66] pseudorotational interconversion of trigonal bipyramidal and square planar five-coordinate metal centres. The use of symmetry-adapted deformation coordinates (see Chapter 2) is now well established for this kind of work, and the chemical interpretation of results is covered in detail in Chapter 5. In our final example [67], we examine deformations at three-coordinate copper centres to show how a PCA based on the L-Cu-L valence angles leads naturally to an interpretation in terms of the relevant symmetry-adapted angular deformation coordinates. This is an example of the analogy between normal coordinate analysis and PCA, as noted by Murray-Rust [65]. 

A mathematical method has been described for determining, from independent variables that include the contribution of valence-angle deformation, the potential barrier for conformational inversion in j8-D-glucopyranose. The energy required for the conversion of a chair form to a boat form was calculated to be 13.5 kcal.mole , and the energy required for the reverse process, 6.5 kcal.mole . Ex-... 

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