Ideal valence angle

The energy associated with distortion of valence angles is calculated in a similar way but it is important to note that ideal valence angles are entered into MOMEC in radians. For example, for an aliphatic C-C-C group the ideal angle is 109.4° which is inserted as 1.911 and the force constant is 0.45 mdyn A rad-2. Thus, the energy associated with distortion of such an angle to 115° is calculated as ... 

C16H2207 l,5-Anhydro-2,3,4-tri-0-benzoylxylitol (ATBXYL10)114 PI Z = 2 Dx = 1.32 R = 0.053 for 3,536 intensities. The crystal structure contains centrosymmetrically related d and l enantiomers. The pyranoid conformation is an almost ideal (d) [1C4(l)]i withQ = 60 pm, 0=1°, with normal bond-lengths and valence-angles. The benzoyl groups are equatorial, with their planes approximately normal to the mean plane of the pyranoid ring. 

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. 

Ideal (or equilibrium) bond lengths, valence angles, etc., are the distances and angles that give a zero strain energy with respect to that parameter (see force field). 

A quadratic function defines a symmetric parabola and therefore cannot exactly reproduce the true relationship between the distortion of a bond length or valence angle and the energy needed to effect that distortion. However, a central assumption in the application of simple molecular mechanics models is that distortions from ideal values are small and in such cases it is only necessary that the potential energy function be realistic in the region of the ideal value. This is shown in Fig. 17.8.1, where a quadratic curve is compared to a Morse potential that is believed to more accurately reflect the relationship between bond length distortion and energy cost. 

Using the Lewis formula as a guide, determine the arrangement of the bonded atoms (the molecular geometry) about the central atom, as well as the location of the unshared valence electron pairs on that atom (parts B of Sections 8-5 through 8-12 Tables 8-3 and 8-4). This description includes ideal bond angles. 

Studies of this type are frequently performed to investigate configurational variations, e.g. at metal centres. The obvious initial parameters are the relevant valence angles L-M-L, where L represents a ligating atom. Such studies may then be broken down chemically according to the nature of L. However, it is often more informative to study the deviations of observed coordination geometries from some idealized symmetric form [7, 8, 9], as described in Chapter 2. This requires use of symmetry-adapted deformation coordinates which can readily be calculated, using the CSD System, for instance, as simple linear combinations of standard internal coordinates. 

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]. 

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