Electronegativity bond length corrections

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. 

A number of empirical methods exist for the adjustment of covalent bond lengths for ionic effects.34,35 These are based primarily on formulas that involve the sum of the covalent radii corrected by a factor that is dependent on the electronegativity difference between the atoms. In many instances, quite good agreement is obtained between the predicted and experimental values, as shown by the listing in Table I. 

Now, suppose we wish to study the series Y—F, Y—Cl, Y-Br and Y—I. Here, we have to replace the X atom by hydrogen of appropriate artificial electronegativity but we must also pick an appropriate bond length so that the variation of the orbital energies along the series Y—F, Y—Cl, etc., is correctly reproduced. 

Structural parameters. Variations of bond lengths and bond angles in the Cl—N2—C3—N4—C5 moiety as a result of the aforementioned lpN-0c n overlap were introduced into MM2 by deriving conformationally dependent correction terms for r° and 6°. This treatment circumvented the electronegativity correction to bond lengths implemented in MM2-87 (Sections II.B.l and n.C.l). 

For example, the average value of the Si—C bond length found in the methylsilanes (Table 7-6) is 1.87 A. The sum of the single-bond radii of carbon and silicon is 1.94 A, which is 0.07 A larger. If this value is corrected for the 0.7 difference in electronegativity by the Schomaker-Stevenson term it becomes 1.88 A, in much better agreement with experiment. 

The observed bond lengths for bonds between unlike atotns (not of the first row) agree with those calculated from the average for bonds between like atoms, with the electronegativity correction. For example, the values 2.20 A for P—P and 1.98 A for Cl—Cl lead, with the electronegativity correction —0.054 A, to 2.036 A for P—Cl, in agreement with the experimental value 2.043 0.003 A for PC1S. We conclude that these bonds have about the same amount of doublebond character as those between like atoms. 

The pure single-bond distances (second column) are calculated from the boron radius 0.80 A and the halogen radii given in Section 9-4 (with 0.72 A for fluorine), with the electronegativity correction (Sec. 7-2). The corrections for double-bond character are made in the usual way (Sec. 7-5). The fifth and sixth columns give the observed bond lengths for BF BCU, BBr and the gas molecules BF, BC1, and BBr, respectively. 

Table 11 gives standard covalent radii for most of the elements of the periodic table. Most of these have been calculated from the best data available in the literature using the considerations of paragraphs 1 -3 above. Thus when radii or the appropriate multiplicity and hybridization are added and corrected for difference in electronegativity by the Stevenson and Schomaker relationship, the observed bond length will be obtained. For example, the O-F bond in OF would have the value 0.745 + 0.709 — 0.910.5) = 1.409 A. The experimental value is 1.41 A. 

Several force fields apply various modifiers and additional terms to address specific problems with the reduced set of standard terms. Allinger s electronegativity effect corrects the problem with substituents reducing the preferred bond lengths [24]. Adaptation of bond orders in conjugated systems is done by a simplified QM interpolation scheme [25-27], and cross terms can be used to, e.g., correct for the elongation of bonds when angles are compressed as shown in Eq. (12) [23]. 

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