Group additivity

Group additivity schemes are based on the idea that molecular properties are the aggregate of contributions from identifiable groups, such as -CH3. 

To predict AhydH298(ethene), we shall also need Af//298(ethene) which can be estimated as the sum of two =CH2 contributions taken from the table of alkene group contributions, Table 3.3. In Table 3.3, carbon atoms designated with a subscripted d are double bonded carbons, so =CH2 is given as Cd(H)2. The predicted Af//29g(ethene) is 2(6.27) = 12.54 kcal mol 1 which leads to the predicted Ahyd//298(ethene) 

In a like way, we can obtain a group enthalpy parameter for the -CH2- group in propane. The equation 

So far we have assumed that we know all Af H29i (w-alkane) values necessary to obtain group or bond parameters. Once having generated a sufficient number of parameters from a small but reliable database, we can, in principle, calculate any desired A H29g. Given the nearly 20 million molecules that have been characterized over the history of 

On the other hand, the last two entries in Table 3.2 hint at the weakness of empirical methods. They show that the environment of a group may lead to many parameters other than simple group energies when we are talking about a molecule of, say, biochemical or medical complexity. For every new group and every new environmental factor characterized, one or more new parameters must be determined, perhaps causing the parameter base to grow beyond reasonable bounds. Of course, any environmental factor that is real but is not included in the parameter set, causes an error in the calculated thermochemical properties. 

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When group additivity is valid, S consists of a group with the bonds of X and Y attached to two adjacent atoms as in Eq (4),... 

Group additivity methods must be derived as a consistent set. It is not correct to combine fragments from different group additivity techniques, even for the same property. This additivity approximation essentially ignores effects due to the location of one functional group relative to another. Some of these methods have a series of corrections for various classes of compounds to correct for this. Other methods use some sort of topological description. 

It is important to realize that many important processes, such as retention times in a given chromatographic column, are not just a simple aspect of a molecule. These are actually statistical averages of all possible interactions of that molecule and another. These sorts of processes can only be modeled on a molecular level by obtaining many results and then using a statistical distribution of those results. In some cases, group additivities or QSPR methods may be substituted. 

Surface tension is usually predicted using group additivity methods for neat liquids. It is much more difficult to predict the surface tension of a mixture, especially when surfactants are involved. Very large molecular dynamics or Monte Carlo simulations can also be used. Often, it is easier to measure surface tension in the laboratory than to compute it. 

Completely ah initio predictions can be more accurate than any experimental result currently available. This is only true of properties that depend on the behavior of isolated molecules. Colligative properties, which are due to the interaction between molecules, can be computed more reliably with methods based on thermodynamics, statistical mechanics, structure-activity relationships, or completely empirical group additivity methods. 

Empirical methods, such as group additivity, cannot be expected to be any more accurate than the uncertainty in the experimental data used to parameterize them. They can be much less accurate if the functional form is poorly chosen or if predicting properties for compounds significantly different from those in the training set. 

An example of using one predicted property to predict another is predicting the adsorption of chemicals in soil. This is usually done by first predicting an octanol water partition coelficient and then using an equation that relates this to soil adsorption. This type of property-property relationship is most reliable for monofunctional compounds. Structure-property relationships, and to a lesser extent group additivity methods, are more reliable for multifunctional compounds than this type of relationship. 

The primary problem with explicit solvent calculations is the significant amount of computer resources necessary. This may also require a significant amount of work for the researcher. One solution to this problem is to model the molecule of interest with quantum mechanics and the solvent with molecular mechanics as described in the previous chapter. Other ways to make the computational resource requirements tractable are to derive an analytic equation for the property of interest, use a group additivity method, or model the solvent as a continuum. 

A similar technique is to derive a group additivity method. In this method, a contribution for each functional group must be determined. The contributions for the functional groups composing the molecule are then added. This is usually done from computations on a whole list of molecules using a htting technique, similar to that employed in QSPR. 

Analytic equations or group additivity techniques when applicable. 

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. 

The simplest empirical calculations use a group additivity method. These calculations can be performed very quickly on small desktop computers. They are most accurate for a small organic molecule with common functional groups. The prediction is only as good as the aspects of molecular structure being par-... 

Another technique employs a database search. The calculation starts with a molecular structure and searches a database of known spectra to find those with the most similar molecular structure. The known spectra are then used to derive parameters for inclusion in a group additivity calculation. This can be a fairly sophisticated technique incorporating weight factors to account for how closely the known molecule conforms to typical values for the component functional groups. The use of a large database of compounds can make this a very accurate technique. It also ensures that liquid, rather than gas-phase, spectra are being predicted. 

Other techniques that work well on small computers are based on the molecules topology or indices from graph theory. These fields of mathematics classify and quantify systems of interconnected points, which correspond well to atoms and bonds between them. Indices can be defined to quantify whether the system is linear or has many cyclic groups or cross links. Properties can be empirically fitted to these indices. Topological and group theory indices are also combined with group additivity techniques or used as QSPR descriptors. 

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. 

The van der Waals volume of a molecule is the volume actually occupied by the atoms. It is reliably computed with a group additivity technique. Connectivity indices can also be used. 

The solubility parameter is not calculated directly. It is calculated as the square root of the cohesive energy density. There are a number of group additivity techniques for computing cohesive energy. None of these techniques is best for all polymers. 

Computed optical properties tend not to be extremely accurate for polymers. The optical absorption spectra (UV/VIS) must be computed from semiempiri-cal or ah initio calculations. Vibrational spectra (IR) can be computed with some molecular mechanics or orbital-based methods. The refractive index is most often calculated from a group additivity technique, with a correction for density. 

The molar sound velocity can be predicted with group additivity techniques. It, in turn, may be used to predict the mechanical properties due to high-frequency deformations. 

Rubbery materials are usually lightly cross-linked. Their properties depend on the mean distance between cross links and chain rigidity. Cross linking can be quantified by the use of functions derived from graph theory, such as the Rao or molar Hartmann functions. These can be incorporated into both group additivity and QSPR equations. 

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