Bensons Method

A natural extension of the bond energy approach is to account for interactions close to the chemical bond in question (which certainly affect the stability, and hence the thermodynamic properties). Based on this concept, a number of group contribution methods have been developed over the years, and many of these methods have been reviewed in Ref. 171. Benson s second-order group contribution method, probably the most successful and widely embraced method, was developed some 30 years ago as an improvement to bond energy (or bond contribution) methods for the prediction of thermochemical properties.167 This improvement was accomplished by accounting for  

It is important to note that Benson s method may require the use of correction terms for molecules having rings, cis/trans or ortho/para isomers, 1,5-repulsions, or gauche interactions. The user is referred to Benson s book162 for a complete description of the method. Some pertinent notation used in this method is as follows  

CO 2 Carbonyl group (aldehydes, ketones, esters, carboxylic acids) 

Nb 0 Aromatic nitrogen (pyridine, pyrazine, and pyrimidine, but not pyridazine) 

As an example of the group contribution concept, consider the Benson methylene groups shown below, where C represents a tetrahedral carbon, and Cb represents an aromatic carbon, Cd represents a doubly bonded carbon. Each of these values was determined from experimental thermodynamic data. Note that the contribution of the C-(H)2(X)(Y) group to the enthalpy of formation is different in each bonded environment. 

BENSON S thermochemical kinetics takes the transition-state theory as a starting point for the calculation of a rate constant. It will be shown that this theory introduces two properties, the standard entropy and the standard enthalpy of activation AjS and AjH , which are the thermodynamic properties of the reaction  

The calculation of AjS and, in certain cases, of AjH is based upon two main principles. 

How do we proceed The calculation of heats of formation has a long history and was quite successful in limited areas long before molecular mechanics was developed. Thus, we will initially follow a historical path in this discussion. Brief, clear earlier reviews include those written by Wiberg and by Fan.  

if one adds up these numbers for many (but not all) hydrocarbon molecules, one can get acceptable values for heats of formation. And indeed, if one looks at a series of ketones, for example, using a similar scheme one can calculate correctly many (but not all) of their heats of formation. So it would seem that we are on the right path, but we are not there yet. 

note that this compound exists in cis and Irans forms and that the latter is much more highly strained. (It may not be evident from the structures shown, but while the internal and external C-C-C bond angles at the bridgehead carbon are lOb-O and 115.4°, respectively, in the cis isomer, those in the Irans are 102.3° and 125.8°.) If we use two cyclopentane increments, we can calculate approximately correctly the heat of formation for the cis isomer, where the total strain is approximately the same as that of two cyclopentanes. But the trans isomer is much more strained than that (about 6kcal/mol more), due to very distorted bond angles, and the calculated heat of formation value would be very wrong. 

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The Benson group contribution method, and more recent methodologies, allow the computation of heat of hydrogenation reactions, even for large molecules (note that Benson method gives the reaction enthalpy assuming each species to be a perfect gas ). Software and database (e.g., NIST) are also available. 

Color Reaction Based on the Formation of Nitrosophenols (Pearl-Benson Method)... 

The procedure for the Pearl-Benson method is described in detail in Chapter 2.2.4. This method has been used primarily to detect and estimate quantitatively... 

Of the methods for determining lignin in solution based on a specific chemical reaction, that involving nitrosation, the so-called Pearl-Benson method, has found the widest application. In this procedure, reaction of the phenolic units in lignin with acidified sodium nitrite leads to the formation of a nitrosophenol which, upon addition of alkali, is tautomerized to an intensely colored quinone mono-oxime. The absorbance of the latter structure is measured at 430 nm and related to lignin concentration by calibration with a standard lignin. The procedure described below is essentially that developed by Barnes et al. (1963), who modified the original Pearl-Benson method (Pearl and Benson 1940) to improve its sensitivity. 

Although developed originally and used principally for the determination of lignosulfonates in sea water, the applicability of the Pearl-Benson method has been widened to include the determination of not only lignosulfonates but of other lignins as well in fresh water. In its present form the sensitivity of the method is such that, in the absence of any extraneous absorbance, lignosulfonate concentrations as low as 0.2 to 0.5 ppm can be determined (Goldschmid 1971). 

The principal drawback of the method is its lack of specificity for phenols having the characteristic lignin structure. Thus, other phenolic impurities in water (e.g., tannins) would most likely be nitrosated under the conditions specified in the procedure and thereby contribute the absorbance reading. In addition, certain nitrogen-containing and inorganic substances commonly found in fresh- and sea water are also known to react with nitrous acid (Felicetta and McCarthy (1963). However, in comparison to other colorimetric and to UV spectrophotometric procedures, the Pearl-Benson method has been found to be less affected by interfering impurities (Jurkiewicz 1977). 

The group contribution parameters can be taken from Table 3.1. A more sophisticated method has been proposed by Domalski and Hearing (21, 22(. As well, the Benson method is widely used and further developed with industrial support [23, 24],... 

If one looks at a molecule such as heptane, for example, one can add all of the appropriate increments and calculate the heat of formation with acceptable accuracy by the method previously described. But there are a few things that are really not proper about that kind of calculation. Heptane in the gas phase at 25°C (where heats of formation are defined) is actually a complicated mixture (a Boltzmann distribution) of a great many conformations, most of which have different enthalpies and entropies. Additionally, each of these conformations is also a Boltzmann distribution over the possible translational, vibrational, and rotational states. The Benson method works adequately for many cases like this because these statistical mechanical terms can be lumped into the increments and averaged out, and they are not explicitly considered. By adjusting the values of the parameters in Eq. (11.1) or (11.2), much of the resulting error of neglecting the statistical mechanics can be canceled out, or at least minimized, in simple cases. But we would like for this scheme to work for more complex cases too. As the system becomes more complicated, errors tend to cancel out less well. So let us go back and approach this problem in a more proper way. 

This difference between the hypothetical point on the potential surface and the real molecule can be well described by statistical mechanics. With respect to heats of formation, the ways for calculating them (by quantum mechanical methods or by molecular mechanical methods) require either the explicit inclusion of statistical mechanics (the details of this procedure have been spelled out in fulf and will be outlined in the following) or else an implicit inclusion by lumping the statistical effects into the bond energies and hoping for the best, as in the Benson method. 

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