Additivity of group properties

Benson [15] has created and developed a general method of calculation of the values of thermochemical and kinetic parameters based on a systematic use of the additivity of group properties on the one hand and the activated complex theory on the other. Other methods for estimating a priori kinetic parameters have recourse to structural analogies or semi-empirical correlations. 

The study of the molar volumes of the normal hydrocarbons provided the earliest example of the additivity of group properties (Kopp 1855). The experimentally determined heats of formation for the same homologous series of molecules, CH3(CH2)mCH3, also obey a group additivity scheme (Franklin 1949 Prosen 1946 Benson 1968 Pittam and Pilcher 1972). It is possible to fit the experimental heats of formation for this series, beginning with m = 0, with the expression,... 

This method consists of a first phase using the additivity of group properties. The values of S and obtained during this first phase are then improved by different... 

If S is a single atom or a group of atoms with the bonds attached to the same atom (such as a CHi group), then we have the additivity of bond properties, liie first-order approximation, as given by Eq. (3). 

Values based on rule of group additivity of thermochemical properties, using an assumed value, Hf0, for O—(6)2 group of 19 2 kcal., and further assuming that in the molecular series H—OnH, DH°(H—OnH) = 90 2kcal. for n > 2. 

Alternatively, for many classes of compounds the heats of formation can be estimated through additivity of bond properties or group additivity rules [32], Let s take a simple example using the additivity of bond properties to estimate the heat of formation of some species A. Suppose we know (1) the heat of formation of a related compound ABR, where B is the atom to which A is bonded and R is the rest of the molecule, (2) the heat of formation of BR, and (3) that for a series of other molecules in which a A-B bond occurs the A-B bond-dissociation-energy is nearly constant, and we assign it the value B.D.E.(A-B) J. Now consider the endothermic reaction... 

The framework of interactive design is entirely built on the premise of additivity of group contributions for the estimation of physical properties. Let us look at some typical illustrations. Table XV shows the estimation of normal boiling points T, and normal melting points T , using Joback s group contribution techniques (Joback and Reid, 1987), along with the... 

The invariance of the first-order density matrix with respect to unitary transformations ensures the invariance of all one-electron properties, like electrostatic potentials. Thus the transformation to localized orbitals does not alter the value of the potential at any point r of the space, but permits a chemically meaningful partition of this quantity. In fact, the lone pair , bond and core localized orbitals resulting from the Boys transformation are particularly suitable for our attempt a) to give a rational basis to the additivity rules for group contributions, and b) to find some criteria by which to measure the degree of conservation of group properties. 

In Equation 1.3, Z denotes summation. The summation over structural terms only has to be included for certain properties where the assumption of the strict additivity of group contributions results in large errors because the environment of a given group also plays an important role in the contribution of the group to that particular property. For example, structural terms must be used in calculating the Yg of certain types of polymers [3],... 

Covalent modification-. The additions of groups to proteins or deletions from proteins, usually causing a change in the protein properties. 

On the other hand, it is at the limit of near-perfect transferability of group properties as exhibited by the alkanes that one can detrmine whether or not a proposed theory meets the requirements of experiment, for at this limit one may experimentally determine to high precision the properties of atoms in molecules via their additive contributions. By demonstrating that the atoms defined by quantum mechanics account for and recover the experimentally measured properties of atoms in molecules, one establishes that the atoms of theory are the atoms of chemistry. There is no test of theory other than the demonstration that it predicts what can be measured. 

In fact, there is a hierarchy in calculating molecular properties by additivity of atomic, bond, or group properties, as was pointed out some time ago by Benson [1, 2]. The larger the substructures that have to be considered, the larger the number of inaements that can be derived and the higher the accuracy in the values obtained for a molecular property. 

The development of group additivity methods is very similar to the development of a QSPR method. Group additivity methods can be useful for properties that are additive by nature, such as the molecular volume. For most properties, QSPR is superior to group additivity techniques. 

Due to the noncrystalline, nonequilibrium nature of polymers, a statistical mechanical description is rigorously most correct. Thus, simply hnding a minimum-energy conformation and computing properties is not generally suf-hcient. It is usually necessary to compute ensemble averages, even of molecular properties. The additional work needed on the part of both the researcher to set up the simulation and the computer to run the simulation must be considered. When possible, it is advisable to use group additivity or analytic estimation methods. 

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