Geometric mean combining rule

Geometric-mean combining rules for both 12 and a have also been proposed by Calvin and Reed who use a Mie ( , 6) potential and treat the repulsive index n as an additional parameter. For the unlike interaction the geometric mean is also used for n. They have also suggested similar rules for the three parameters in the exp-6 potential. Kong has proposed combination rules involving the elfective number of outer-shell electrons. 

Also frequently employed for organic force fields are geometric mean combining rules,4 as well as more sophisticated mixing schemesA° >i3i... 

In combination with the Dupre equation (equation (7.15)) and Young s equation (equation (7.7)), this geometric mean combining rule is the basis for different approaches to calculate the solid surface tension from contact angle data (see Section 2.4 below). 

Xi is a measure of the deviation of the mixture from the ideal geometric mean combination rule and r" is the number of lattice sites occupied by a fluid molecule. 

The application of combination rules is essential when the coefficients are determined by empirical methods. Consider, for example, only the most frequent atoms in bio-molecules, H,C,N,0,S,P. Without a combination rule we would need 21 instead of 6 empirical parameters, and since these are not independent by their nature, they cannot be uniquely defined by empirical methods. The common practice in potential energy calculations has been to use a geometric mean combination rule... 

There are a number of authors (Owens and Wendt, 1969 Kaelble, 1970 Hamilton, 1974 Andrade et aL, 1979 Janczuk et ai., 1990) who, probably for intuitive reasons, implicitly postulated the existence of only one general property of polar molecules (designated by superscript, P), and who preferred a geometric mean combining rule for the polar interfacial tension, analogous to that Tised for 7 " (Eq. 5.26) so that ... 

S.Eq.l 1.7.2 expresses what is referred to as the geometric mean combining rule, whose origin and limitations are discussed in Section 7.6.4. 4.The performance of these combining rules becomes poorer, as we should expect, with increasing dissimilarity between species i andy. It would indeed be naive to expect that pure component properties alone would suffice for the prediction of mixture properties, considering the difference between intra- and inter- Oike and unlike species) molecular forces. And this difference becomes, of course, more pronounced as the dissimilarity between the species increases. 

Typically, a geometric mean combining rule is used for the interaction parameter... 

---