Strain-free bond lengths

The 6th, 7th, and 8th terms of expression (9) are sometimes neglected or is related to (24,25). The potential constants of UBFF s, including the reference parameters, often deviate markedly from the corresponding VFF-constants. Especially the reference bond lengths b may assume values which hardly agree with intuitive ideas about strain-free bond lengths. 

Bond type Stretching force constant, mdyn/A Strain-free bond length, A... 

Diamond is an important commodity as a gemstone and as an industrial material and there are several excellent monographs on the science and technology of this material [3-5]. Diamond is most frequently found in a cubic form in which each carbon atom is linked to fom other carbon atoms by sp ct bonds in a strain-free tetrahedral array. Fig. 2A. The crystal stmcture is zinc blende type and the C-C bond length is 154 pm. Diamond also exists in an hexagonal form (Lonsdaleite) with a wurtzite crystal structure and a C-C bond length of 152 pm. The crystal density of both types of diamond is 3.52 g-cm. ... 

Fig. 20. The variation in strain energy, V, for various conformations of [M(18-crown-6)]n+ complex, as a function of strain-free M-0 bond length. The M—O bond lengths of various metal ions are indicated on the M-0 bond length axis. The curves are for the planar D3d (+-+-+-), half-buckled (+-+--), and buckled (++-+ +-) conformers shown in Fig. 21, and for the complex of the open chain complex of pentaethylene glycol. The calculations were carried as described in the text, and in Refs. (4 and 60). Redrawn after Ref. (60). 

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. 

A. L. Mackay. Our open models are surprisingly strain-free, given that you have equal bond lengths and 120° connections. 

Finke [34,36] believes that the nearly strain-free 19-membered ring conformation places the dmbim base in a position to form a nearly ideal Co—N bond length, a conclusion consistent with our earlier suggestions based on synthetic and theoretical models [154], In particular, studies from the Finke laboratory on varying the axial base in a series of AdoCbi+ models suggest that optimal kinetics... 

This approach can be used to model non-bonded interactions in molecular mechanics instead of using empirical potentials. The rule of thumb, equation (6.6) predicts effective strain-free zero-order bond lengths. As no interaction is possible at separations larger than 2 x rc, the maximum d0(obs) for C- C is 3.70 A, and hence do = 3.70 — 0.28/4 cs 3.6A d0(C---H) 2.75 — 0.19/5 = 2.55A. The separation between non-bonded H atoms depends on the atom to which they are linked - the H ionization sphere is completely embedded within that of the larger atom. As a first approximation d0(H- H)= do(C- H) is assumed. 

---