Atomic and Group Volumes

The study of the molar volumes of hydrocarbons by Kopp in 1855 provided the earliest example of the addivitity of group properties. Table 5 and 6 list the molecular volume and the contribution of each atom and functional group to this volume as determined by both the 0.002 and 0.001 au envelope of the charge density for a number of hydrocarbons obtained from 6-31G /6-31G calculations. Table 5 also lists the fraction of the total electronic charge of the atom contained within the stated envelope .  

The atomic volume of carbon is another property like its population iV(C), whose value increases with increasing s character, the values of r(C) in ethane, ethylene and acetylene being 65, 92 and 121 au, respectively, paralleling the trend in N C) values which at this basis set in the same order as 5.76, 5.92 and 6.12e. On the basis of these results one anticipates that the atomic volume of carbon will also exhibit an increase with increasing geometric strain, as this also causes an increase in the s character of the carbon atom. 

In the normal and branched alkanes the general behaviour, as noted above, is for the volume of a carbon atom to decrease as its stability and electron population increase. This behaviour is what is observed for atomic volumes of the free atoms across a short row of the periodic table, from an alkali metal to an inert gas. In the strained hydrocarbons, on the other hand, just the opposite behaviour is observed, with the volume increasing along with an increase in population and stability of the carbon. 

This study of the properties of atoms in molecules shows that a carbon atom subjected to geometrical strain, an unsaturated carbon atom and an sp carbon in a carbocation exhibit similar properties with respect to changes in their atomic populations, energies 

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The importance of high density as a feature of potential fuel systems that seek to maximize net volumetric heat of combustion is well documented. The prediction of the crystal density of an unknown compound typically has been approached through the use of volume additivity procedures [29-32]. Here, the crystal-molecular volume ycm) is calculated by summing appropriate crystal-atomic or group volumes Vca Vcm = ca) and the corresponding crystal density is ob-... 

Much of our theoretical knowledge of distances between atoms in molecules, bond angles, diameters of atoms, and even volumes of functional groups has been confirmed and refined by X-ray crystallographic methods, especially diffraction.3... 

Tables 12.4 and 12.5 give a summary of average contributions to the molecular volume and surface, and to the (PE) at 7 A cutoff, for the most common atoms and groups. From these tables, total molecular volumes and surfaces can be obtained, and (PE) - and hence the sublimation energy - can be estimated, since (PE)7a s 0.85 Ai/s- Sublimation heats estimated from this correlation are too low for molecules with polar groups, having strong electrostatic interactions in the crystal or forming C-H...OorC-H...N hydrogen bonds (see 12.4.2.2).

Traditional methods to estimate solid-phase density from molecular structure are primarily based on a simple summation of appropriate atomic or group volumes. The basic disadvantage of these group or volume additivity procedures is that they disregard crystal-packing efficiency and molecular conformation. Thus, conformational isomras, or even different compounds with the same functional group composition, wiU aU be calculated to have the same density. To solve this problem, Ammon and coworkers have developed a scheme to estimate molecular densities by predicting possible crystal... 

Atomic and group properties in the alkanes TABLE 6. Molar volumes of molecules and functional groups... 

Here, e is the additive atomic and group contribution for the energy of vaporization of the solvent and V( is the additive atomic and group contribution for the molar volume of the solvent. 

Polar interactions, which result from dispersion forces (van der Waals interactions) are best described by molar refractiv-ity MR, which is a refractive index-corrected molar volume. Thus, it has also been used to describe steric features of substituents. Like log P, MR is an additive constitutive molecular property which can be calculated from atom and group contributions. " ... 

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