Molecular bond length deformation

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. 

Dynamic processes such as conformational interconversion or bond length deformation associated with changes in electronic or oxidation states have energy barriers associated with them. It is sometimes possible to obtain measures of these barriers, either directly or indirectly, but there are no experimental methods for determining the mechanisms by which these changes occur. Also, if the barriers are low it can be almost impossible to obtain experimental measures of them. Molecular mechanics calculations can be used to obtain theoretically based estimates of the barriers, irrespective of their height, and can also give mechanistic information. 

By molecular mechanics we mean a method by which we calculate the total energy of a molecule in a particular geometry with reference to a hypothetical molecule with no bond-angle or bond-length deformations, no torsional strain and no steric repulsion and with a given number of single and multiple bonds. The energy difference is obtained as the sum of six components ... 

Thus, the theoretical modulus of elasticity depends on the two force constants for the bond length deformation and bond angle expansion, as well as on bond length, bond angle, and molecular cross-sectional area. Thus, polymers with about the same cross-sectional area can have very different moduli of elasticity (Table 11-3). 

An unstrained olefinic double bond in the ground state is described by six atoms lying in a plane with bond angles near 120° and bond lengths of about 134.0 pm. Two classes of deformations can be distinguished in nonplanar or out-of-plane (oop) distortions, substituents move perpendicular to the molecular plane, whereas planarity is maintained with the planar or in-plane (ip) distortions of substituents. For a systematic approach, these static distortions can be derived from the normal vibrations of ethylene. 

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