Molecular quantum similarity measures MQSM

Two objects are similar and have similar properties to the extent that they have similar distributions of charge in real space. Thus chemical similarity should be defined and determined using the atoms of QTAIM whose properties are directly determined by their spatial charge distributions [32]. Current measures of molecular similarity are couched in terms of Carbo s molecular quantum similarity measure (MQSM) [33-35], a procedure that requires maximization of the spatial integration of the overlap of the density distributions of two molecules the similarity of which is to be determined, and where the product of the density distributions can be weighted by some operator [36]. The MQSM method has several difficulties associated with its implementation [31] ... 

Introducing the notion of a molecular quantum similarity measure (MQSM) ZAB as... 

Finally, three further studies on QSAR of artemisininoids applying a variety of quantum-chemical and conventional molecular descriptors [105], molecular quantum-similarity measures (MQSM, [111]) and topological descriptors based on molecular connectivity [112] have led to models of quite satisfactory statistical performance. However, apart from showing the applicability of the respective QSAR approaches to this type of compounds both studies offer comparatively little new information with respect to structure-activity relationships. 

It is called a molecular quantum similarity measure (MQSM), and it corresponds to the similarity integral between molecules A and B. In the first integral in Eq. [13], a so-called molecular quantum self-similarity measure (MQSSM) is obtained ... 

Once an operator has been chosen for the calculation of the MQSM for a set of N molecules, one can calculate all MQSMs between every two molecules, which gives rise to the whole N x N array of MQSM. This symmetrical matrix is called the molecular quantum similarity measure matrix (MQSMM), denoted Z. 

If we consider the molecular quantum similarity measures in, e.g., Eq. [21], we should be aware of the important fact that the MQSM depends... 

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