Molecular volume and surface

Intrinsic molecular volume, or the volume of the envelope of atomic spheres, can easily be calculated. Let N be the number of atoms in a molecule, with nuclear positions Xj reckoned in some reference frame, say the inertial reference frame. Let Ri be the atomic intermolecular non-bonding radius of atom i, briefly called henceforth the atomic radius. Let nj be the distance between the nuclei of two atoms joined by a chemical bond. Whenever ry is smaller than the sum of atomic radii, the sphere of atom i cuts into the sphere of atom j a spherical cap of height /ly. Molecular volume, Vm, can be calculated [8,10] by computing the total volume of the atomic spheres and subtracting the volumes of the intersecting caps  

This method runs into difficulties with highly branched or strained bond connectivities because several spherical caps may overlap and the cap volumes may be subtracted more than once. For example, the volume is underestimated by some 10% for cyclopropane ring systems. Alternatively, Vm can be calculated more accurately [10] by subdividing a parallelepiped box that contains the whole molecule into a very large number of small cubes, and counting the number of those elementary cubes that are inside at least one atomic sphere (Ain). If V° is the volume of the cube (typically, 10 A ), one gets 

The dimensions of the sides of the parallelepiped are conveniently taken as the difference between extreme atomic points along the inertial axes plus the largest atomic radius. An analytical calculation of molecular volume is also possible [12], although differences between the various methods of calculation usually do not exceed a few percent for non-strained molecules. 

The density of a condensed phase is mainly determined by the weight of the nuclei, which take only a small fraction of space, and thus depends only marginally on space occupation. A molecular self-density. Dm, can be defined as the ratio of molecular mass to molecular volume [13]  

As seen in Fig. 1.3, crystal density correlates very strictly with molecular self-density, so that a high density in a crystalline material depends primarily on the heavy elements contained in the molecule, and only to a minor extent on efficient space occupation. 

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Geometric Examination. The polymer chemist needs to examine the various characteristics of the molecule in the molecular workspace. Bond lengths, bond angles and torsional angles can be measured for the current structure and compared to accepted values. In addition, other geometric properties can be computed like overall dimension, moments of inertia, molecular volume and surface area. 

Many groups have discussed the correlation between solubility and molecular properties [14-19], and the octanol/water partition coefficient, the molecular volume and surface area, the boiling point and charge distribution in the molecules are well-documented molecular descriptors that correlate strongly with experimental solubility. 

All current activity coefficient estimation models are by necessity semi-empirical in nature, because too little is known about solution theory for outright estimation. Chemical modeling is not readily available and is not far enough developed to make this type of calculation. The constants required by these models must be estimated using either experimental data (e.g. an infinite dilution activity coefficient or a molar volume) or group contributions derived from experimental data (e.g. interaction constants, molecular volumes and surface areas). 

Galvez, (. (2003) Prediction of molecular volume and surface of alkanes by molecular topology. /. Chem. Inf. Comput. Sci, 43, 1231-1239. 

Geometric/Biophysical Rotation axes, molecular volume and surface area... 

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).

Aqueous Solubility of Polychlorinated Biphenyls Related to Molecular Structure This paper contains solubility data for 44 PCB congeners and outlines correlations with molecular volume and surface area. Several values are listed and referenced for most congeners. 

Water Solubilities of Polynuclear Aromatic and Heteroaromatic Compounds Water solubilities of polynuclear aromatic and heteroaromatic (oxygen, sulfur, and nitrogen) hydrocarbons have been compiled and evaluated and correlated with molecular volume, and surface area. 

Values for molecular volume and surface area used here were computed using the radii set and the numerical procedure described earlier [1], More recently. 

Table 1.3 Group increments to molecular volume and surface. All dangling bonds are to non-hydrogen atoms...

A somewhat more appropriate and physically acceptable definition of molecular volume and surface can be derived from the spatial extension of the electron density. The electron density p(x,y,z) can nowadays be easily calculated on a three-dimensional... 

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