Eigenvalues hydrogen bonds

Fig. 12. Variation of the positive curvature, A3 at bond CP, with hydrogen contact distance, d(H - -O). The data points obtained from a number of charge density investigations reported in the literature and were fitted using exponential equations. Circles and dashed line joint X-ray and neutron, filled squares and solid line X-ray data only. Among the three eigenvalues, A3 was found to be giving the best representation for hydrogen bonds having closed-shell interactions (reproduced with permission from Espinosa et al. [65]).

Molecular descriptors are usually classified into several classes by a mixed taxonomy based on different points of view. For example, descriptors are often distinguished by their physico-chemical meaning such as - electronic descriptors, - steric descriptors, lipophilicity descriptors, -> hydrogen-bonding descriptors, - shape descriptors, charge descriptors, - electric polarization descriptors, - reactivity descriptors, moreover, on the basis of the specific mathematical tool used for the calculation of the molecular descriptors, - autocorrelation descriptors, -> eigenvalue-based descriptors, -> determinant-based descriptors, - Wiener-type indices, - Schultz-type indices can be distinguished. 

Here g>h(<2) is equal to the X—H stretching mode when the hydrogen bonding is still not switched. This allows the calculation of the eigenvalues [66]... 

The BCUT descriptors are the lowest and highest eigenvalues of a connectivity matrix of a molecule in which the diagonal elements for each atom are assigned properties such as atomic charges, atomic polarizability, or atomic hydrogen bond parameters, respectively. 

In general, we have four different eigenvalues A. A particularly simple case occurs when Wab = bb = 0, but Waa 0 and Wp 0. For instance, there is hydrogen bonding ( AA < 0) and nonadditivity (lVp<0) of the hydrogen bonding, but other interactions are negligible. In this case, the secular equation is... 

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