Bond perturbation values

Figure 2 Orientational dependence of SCF and correlation components to interaction energy in the water dimer as a function of deviation of H-bond from linearity. A refers to second-order Mpller-Plesset correlation contribution, corrected by the counterpoise method Eji p is a shorthand notation for the perturbation value of Edisp -...

In addition, optimized and normalized S values (field-inductive a bond perturbation) and P values (resonance n bond perturbation orthogonal to S) have been defined and used in QSAR studies [307]. The factorization of a values into different field and resonance contributions is reviewed in ref [306]. 

Also, additional powers of y arise from the long-range nature of the perturbation for small values of y. For example, consider the diagram that has a field point connected to each of two root points by a bond. The value of this diagram is... 

The single-bond covalent radius of C can be taken as half the interatomic distance in diamond, i.e. r(C) = 77.2pm. The corresponding values for doubly-bonded and triply-bonded carbon atoms are usually taken to be 66.7 and 60.3 pm respectively though variations occur, depending on details of the bonding and the nature of the attached atom (see also p. 292). Despite these smaller perturbations the underlying trend is clear the covalent radius of the carbon atom becomes smaller the lower the coordination number and the higher the formal bond order. 

As can be seen from Table I, the C-C bond distance as described by LDF is closer to experiment than the corresponding HF value obtained with a 6-3IG basis. Including correlation via second and third order Moller-Plesset perturbation theory and via Cl leads to very close agreement with experiment. The C-H bond length is significantly overestimated in the LDF calculations by almost 2%. The HCH bond angle is reasonably well described and lies close to all the HF and post-HF calculations. Still, all the theoretical values are too small by more than one degree compared with experiment the deviation from experiment is particularly pronounced for the semi-empirical MNDO calculation. 

The bond E-state indices add a perturbation of the BI value under the influence of all other bonds in the molecule ... 

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