Strain-free distance

Table 2.4. Strain-free distances r0 for the metal-ligand bonding interaction.00...

The fact that the computed Co-N distance for D3o63-[Co(sar)]3+ is smaller than that preferred by the metal-free ligand indicates that the Co-N bonds are elongated in this compound (the fact that the computed and observed values for Co-N are larger than the strain-free distance r0, used in our force field (1.905 A) is irrelevant since force field parameters are not necessarily physically meaningful, see Sections 3.5, 9.2 and 10.2). 

O-M-O bond angles required. One can relate bite sizes (distances between the donor atoms) of strain-free chelate rings of different sizes to the dimensions of the chair form of the cyclohexane ring (39), which has the minimum steric strain possible for a cycloalkane. The bite size of strain-free four- and six-membered chelate rings both correspond to... 

Like many other chemical concepts the concept of strain is only semi-quantitative and lacks precise definition. Molecules are considered strained if they contain internal coordinates (interatomic distances (bond lengths, distances between non-bonded atoms), bond angles, torsion angles) which deviate from values regarded as normal and strain-free . For instance, the normal bond angle at the tetra-coordinated carbon atom is close to the tetrahedral value of 109.47°. In the course of force field calculations these normal values are defined more satisfactorily, though in a somewhat different way, as force field parameters. 

Early attempts to establish the existence or otherwise of a geometric factor were based upon the assumption that the surfaces of metal particles consisted of extensive arrays of atoms arranged in well-defined low index planes the optimum metal—metal distances for the strain-free adsorption of the reactant hydrocarbon were calculated [84,157]. As noted in Sect. 4.2 (p. 50) such an approach led to the conclusion that only certain crystal planes should be active in alkene and alkyne hydrogenation... 

By assuming atomic radii to be specified by ionization radii, r0, the diatomic curves could, in principle, be used to calculate the dissociation energy of any covalent bond, irrespective of bond order, only from its interatomic distance. This promise is largely fulfilled, but the calculated energies are proportionately too low in virtually all cases. The obvious reason for this is that the calculation makes no allowance for steric interactions that occur in molecular environments. Because of this effect the (experimentally measured) interatomic distances used in the calculation do not refer to the strain-free situation modelled by ionization radii. 

Under an applied voltage the stress-free filaments in a bent bimorph will be in two planes, one above and one below the central plane and at equal distances a from it. The centre plane is strain free because the stresses on opposite sides of the joining layer are equal and opposed to one another. The steps in the argument are illustrated in Fig. 6.29 and the stress system is similar to that set up in a heated bimetallic strip, as analysed by S. Timoshenko [20]. 

Molecular mechanics calculations have been used to describe low- 471-473] and high-order metal-metal bonds[473,474]. These will be discussed here although many relevant examples are classical rather than organometallic coordination compounds. The force constant for Rh-Rh single bonds has been determined from the vibrational frequency of the metal-metal bond and the strain-free value was fitted using a conventional force field for the ligand systems and a series of experimentally determined structures (Fig. 14.6). The Rh-Rh bond distances cover a range of ca. 0.25 A, and the experimentally observed trends are reasonably well reproduced by the calculations (Table 14.2). 

In the original force fields, AlUnger and ofhers used Hooke s-law harmonic potentials for a diagonal force field (Eq. 4). If /o, 6t, and are the strain-free bond distances, angles, and torsion angles and fen and are the relevant force constants, then the potential function for the molecule is given by... 

For an efficient screening, MOE database search starts with prefiltering steps including the discard of conformers that do not match feature types and interfeature distances of the pharmacophore model. After this fast filtering of database molecules, the fitting between the model features and the chemical functions of the conformer starts. For this purpose, MOE performs a rigid body superimposition between conformer and model features. In other words, only translational and strain-free rotational movement is allowed for model fitting. Similar to DS CATALYST, only conformers of database molecules are retrieved that fall within the tolerance radii of a user-specified number of pharmacophore model features [20]. 

Table 3.4 Strain-free bond distances r for the metal-ligand bonding interaction."...

Figure 17.14 shows the relationship of the distance between atoms and the force between them and an approximation, which is fairly true, is that the straight line portion of the curve is 1% strain on either side of the neutral or strain free position. It was the work of... 

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