Atomic increments

For any molecule, additivity of atomic properties requires as many variables as there are different atom types contained in the molecule. For example, for acetic add, C2H+O2, three different atomic increments are needed, one each for a carbon, a hydrogen, and an oxygen atom. 

From van der Waals volumes calculated from atomic increments [57],... 

Torrens F (2004) Effect of type, size, and deformation on the polarizability of carbon nanotubes from atomic increments. Nanotechnology 15 S259-264. 

On the other hand, the volume contribution of structural groups already contains inbuilt information on the influence of the atomic surroundings. As a consequence the Van der Waals volume of the structural units can approximately be calculated as the sum of the Van der Waals volumes of the composing structural groups. Bondi (1964,1968) was the first to calculate the contributions of about 60 structural groups to Vw. Later Slonimskii et al. (1970) and Askadskii (1987) calculated about 100 values of atomic increments in different surroundings. Since the two approaches used the same method of calculation, and nearly equal basic data on the atomic radii, the calculated values for the structural units are approximately equal. In Table 4.2 also the group increments of Vw are shown, next to those of M. By means of these data the Van der Waals volumes of the Structural Units are easily calculated. 

The latter free energy can be represented as a surface integral over the solvent accessible surface of the molecule on the basis of a local free energy surface density (FESD) p. This surface density function is represented in terms of a three-dimensional scalar field which is comprised of a sum of atomic increment functions to describe lipophilicity in the molecular environment.The empirical model parameters are obtained by a least squares procedure with experimental log P values as reference data. It is found that the procedure works not only for the prediction of unknown partition coefficients but also for the localization and quantification of the contribution of arbitrary fragments to this quantity. In addition, the... 

The lack of agreement between the experimental bond distances and the Schomaker-Stevenson estimates indicates that the additivity principle based on atomic increments is not very appropriate for a wide range of compounds. Shorter bond distances than the estimated ones are usually regarded as an indication of higher bond order. However, this approach fails to explain the elongation of the bond distances above the estimated... 

Table 12.4. Average Atomic Increments for Molecular Surface, S, Molecular Volume, V, and Packing Energy at 7 A Cutoff (for the central atom in each entry lines represent dangling bonds to other carbon atoms)...

For a general compound the molar volume can be estimated from the atomic increments following Le Bas (Table 9.10)... 

Is 586 A . This can be compared with the value of 543 a calculated for enkephalin by the method of atomic Increments (Edwards, 1970), which gives an estimate of the minimum molecular volume by summing the Van der Waals radii of the constitutent atoms. The close correspondence between the calculated molecular volume and that o bta1ned from our experimental data suggests that enkephalin Is monomeric In aqueous solution at concentrations of 2-50 mg/ml, and 5-60 C. 

Aromatic rings provide the circuits in which circular electric currents can be induced by external magnetic field, hence magnetic susceptibiUty Xm of aromatic molecules is (i) highly anisotropic and (ii) higher than the sum of atomic increments Xa, its exhaltation provides one of the quantitative measures of aromaticity [41] ... 

The resort to graphical representation of the empirical correlations shows the difficulties of the analytical description, due to the multiplicity of factors influencing the electronic structure of crystals. The task can be simplified, making use of the additive character of Eg. Hooge [308, 309] expressed the band gaps of binary compounds as the sums of atomic increments, the increment of each element being constant and depending only on its EN,... 

Experimental refractions of elements of Groups 14-17 are close to the additive values of atomic increments derived by Eisenlohr [131, 132], Vogel et al. [133, 134]... 

Reid et al. [ 1 ] present values for Va for the most common atoms. Some atom increments are given in Table A6.3. Alternative equations to Equation A6.2 are presented by Wild and Charpentier [3]. The viscosity of the solvent is an important parameter in Equations A6.2 and A6.3. The viscosity can easily be determined experimentally, and experimental values are always preferred to theoretical correlations. The viscosity is strongly influenced by temperature. The temperature dependence can often be accounted for with simple empirical correlations of the type... 

Fig. 8.9. UNI lattice energies for 308 crystal structures (from the SMALL database, no hydrogen bonds) as a function of the overall molecular polarizability computed by sums of approximate atomic increments.

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