Molecular alignment, MQSM

Figure 5 clearly shows a dependence of the overlap MQSM on the mutual position of both molecules in space. Molecular alignment thus has important influence on the MQSM. One of the applications of molecular quantum similarity is the possibility to quantitatively express the similarity and especially to compare and order the degree of similarity over pairs of... 

From a mathematical point of view, we can propose maximization of the MQSM as a function of a set of molecular alignment parameters in such a way as to obtain a superposition procedure with a general scope. Several algorithms aimed directly at maximizing the MQSM have been published. The first example is the MaxiSim algorithm developed by Constans et al. A second one is the quantum similarity superposition algorithm (QSSA) by Bultinck et al. An algorithm developed by Stefanov and Cioslowski is similar to the MaxiSim and QSSA ideas, and it will therefore not be described explicitly because it invokes similar points of view. 

Finally, it is worth mentioning that alignment-free methods for evaluating molecular similarity have been tested [45]. Recently, the question about the necessary positive definite nature the MQSM matrices must possess has been put forward and a building up algorithm for a set of molecular structures has been described [53]. 

Another matter is the consistency of the molecular quantum similarity matrix Z. The MQSM produced by a specific alignment technique for a given molecular pair of the set of molecules that construct Z should not be contradictory with the computed MQSM for the other pairs of molecules. To illustrate this point, consider the Euclidean distance, as defined by the square root of Eq. [13] ... 

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