Hodgkins-Richards index

Besides the Carbo index another index that has been used in the field of QSM is the Hodgkin-Richards index, which uses an arithmetic mean instead of the geometric... 

In the Carbo index, the denominator is the geometric mean of the self-similarities. Naturally, we could also think about using the arithmetic mean, which gives rise to the Hodgkin-Richards index " " " originally developed for comparisons of electrostatic potentials ... 

In all three of these approaches, the similarity indices should be maximized. Both the Carbo index and the Hodgkin-Richards index were used by Boon et al. % whereas in the applications of AIM, the Cioslowski similarity measure was For the atom-centered approach, we can use all... 

As has been pointed out numerous times, if vA = kvb => SCar(vA,vB) = 1, for all K. This prompted Hodgkin and Richards (49) to define a slightly modified form of the similarity, usually called the Hodgkin similarity index, that does not suffer from this problem, namely,... 

As discussed in the previous section for vectors, if F and Fg differ only by a constant, that is, if F = K Fg, then SCar(F ,Fg) = 1 regardless of the specific form of the functions. While this is not a likely occurrence in practical applications, Hodgkin and Richards (49) nonetheless defined a slightly altered similarity measure, usually referred to as the Hodgkin similarity index, which is not affected by this problem and is given by... 

There are many different types of similarity indexes, including the association coefficients (e.g., Tanimoto coefficient [27], Jaccard coefficient [38], Hodgkin-Richards coefficient [39,40]), the correlation coefficients or cosinelike indexes, and the distance coefficients or dissimilarity indexes (e.g., Hamming distance) [26],... 

With respect to the Carbo index, it is less sensitive to the shape of the property distribution but more sensitive to its magnitude [Hodgkin and Wchards, 1987 Richards and Hodgkin, 1988]. It is defined as ... 

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