Natural bond length

Another type of correction, which is related to cross terms, is the modification of parameters based on atoms not directly involved in the interaction described by the parameter. Carbon-carbon bond lengths, for example, become shorter if there are electronegative atoms present at either end. Such electronegativity effects may be modelled by adding a correction to the natural bond length based on the atoms which are attached to the A-B bond. 

The natural bond length varies between 1.503 A and 1.337 A for bond orders between 0 and 1, these are the values for pure single and double bonds between two sp -carbons. Similarly the force constant varies between the values used for isolated single and double bonds. The rotational barrier for an isolated double bond is 60kcal/mol, since there are four torsional contributions for a double bond. 

Most of the data for these parameterization studies came from ah initio calculations although other sources were also used, in particular, to validate the resulting force field. Thus a set of small model molecules with different conformations of the R—N—C—N—R moiety was calculated at various levels of theory and the results used to derive torsional parameters, hydrogen bond parameters and conformationally dependent correction terms for natural bond lengths and angles, as described below ... 

Outer C—N bonds. Outer C—N bonds in the R—N—C—N—R moiety are known22,26 to inversely depend on the adjacent inner bond lengths probably due to a hybridization effect. Natural bond lengths for those bonds were determined according to ... 

It has been known for a long time that amines which have a hydrogen on a carbon attached to the nitrogen so that the C—H bond is antiperiplanar to the lone pair, show abnormally low stretching frequencies for those C—H bonds. In order to reproduce this (Bohlmann) effect MM3 corrects the natural bond lengths and force constants of such C—H bonds by31 ... 

Natural bond length and stretching force constants... 

Ihe natural bond length varies between 1.503 A and 1.337 A for bond orders between 0 comparing experimental heats of formation, the zero point of the energy scale must be... 

Here is the force constant, lo is the natural bond length, and / is the actual bond length. 

Suppose we first consider benzene, and decide how we might deal with it in a force-field calculation. Can we find a natural bond length and a force constant for bond stretching, which would presumably be somewhere in between those for a carbon- carbon single bond and a carbon- carbon double bond, and which will adequately reproduce the structure of benzene The answer is that we can, and simple benzene derivatives can then be dealt with using these parameters by the methods previously discussed. We only need to call the benzene bond a special kind of carbon-carbon bond with its own parameters. 

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