The concept of bond order: Part II

Abstract

We recently suggested [l] a method for the computation of bond orders from ab initio molecular wavefunctions, based on the Dean and Richards charge-partition technique [ 21. A calibration for carbon-carbon bonds was obtained by calculating the charge per unit volume in spheres in the internuclear regions of ethane, ethylene and acetylene (where the carbon-carbon distance was a diameter), This is illustrated in Fig. l(a). While the excellent linear correlation with formal bond order is pleasing, it does not however prove the validity of the method since there is no independent verification that the intercept on the charge axis corresponds with a zero bond order. With this in mind we have performed calculations on the molecular fragments CH3, CH,? and CH, having the same geometries as in the reference molecules (Fig. 2). Wavefunctions were obtained using the Gaussian 70 program [ 31 with an STO-3G basis set [4], allowing the maximum multiplicity in each case (i.e. 2, 3 and 4 respectively). Charges were then calculated, by the Dean and Richards method [ 51, in analogous spheres to those used for the cahbration calculations. The results are presented in Table 1 and Fig. l(b). By analogy with the simple picture of bond formation between two atoms, we hoped that twice the value of the charge per unit volume (i.e. the sum for two identical fragments without interaction) would correspond to a zero bond order, the bond strength being due to the extra internuclear localisation resulting from the interaction between fragments. Remarkably, for the methyl fragments, this value does indeed correspond quite closely to the “zero-bond order” charge of the calibration. For the ethylenic and acetylenic fragments a progressively greater charge is observed. This is hardly surprising since one could not expect a diatomic analogy to apply to compounds having unsaturation. However a further point of interest is that the progression of fragment charge again produces an excellent straight line. We believe that this confirmation of the significance of the zero of our bond order scale lends further support to the method, and indicates the viability of its use in the study of molecular properties.