Molecular quantum similarity measures

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... 

By different mathematical transformations. Molecular Quantum Similarity Indices (MQSI) are derived from molecular quantum similarity measures. They are divided into two main classes C-class indices, referred to as correlation-like indices ranging from 0 (maximum dissimilarity) to 1 (maximum similarity), and D-class indices, referred to as distance-like indices ranging from 0 (maximum similarity) to infinity (maximum dissimilarity). C-class indices can be transformed into D-class indices d, by the following ... 

Amat, L., Robert, D., Besalh, E. and Carbo-Dorca, R. (1998). Molecular Quantum Similarity Measures Tuned 3D QSAR An Antitumoral Family Vahdation Study. J.ChemJnfCom-put.Sci., 38, 624-631. 

Carbo, R. and Calabuig, B. (1992a). Molecular Quantum Similarity Measures and N-Dimen-sional Representation of Quantum Objects. I. Theoretical Foundations. Int.JQuant.Chem., 42, 1681-1693. 

Robert, D. and Carb6-Dorca, R. (1998a). A Formal Comparison Between Molecular Quantum Similarity Measures and Indices. J.Chem.Inf.Comput.Sci., 38, 469 75. 

By different mathematical transformations. Molecular Quantum Similarity Indices (MQSI) are derived from molecular quantum similarity measures. They are divided into two main classes C-class indices, referred to as correlation-like indices ranging from 0 (maximum... 

Based on the molecular quantum similarity measures. Molecular Quantum Self-Similarity Measures (MQS-SM) were proposed as molecular descriptors calculated by comparing each molecule with itself and all the others, and using appropriate Hermitian operators D associated to each molecular property [Ponec, Amat et al., 1999]. 

Molecular quantum similarity measures tuned 3D QSAR an antitumoral family validation study./. Chem. Inf. Comput. Sci., 38, 624—631. 

Molecular quantum similarity measures, like any of the off-diagonal elements of the SM, ZAB, involving the QSM between quantum objects A and B, can be easily transformed into a number lying within the interval [0 1], just by using the simple rule ... 

Molecular quantum similarity measures, as formulated in integral (1), are dependent on the relative position of both studied molecules in space. Consequently, a procedure capable of arranging the molecular coordinates needs to be established. Two methodologies have been implemented to deal with this question the maximal similarity rule (MSR) [71], which considers that the optimal orientation corresponds to the one that maximizes the value of integral (1) and the topo-geometrical superposition algorithm... 

Robert D, Amat L, Carbo-Dorca R. Three-dimensional quantitative structure-activity relationships from tuned molecular quantum similarity measures prediction of the corticosteroid-binding globulin binding affinity for a steroid family. J Chem Inf Comput Sci 1999 39 333-344. 

Amat L, Carbo-Dorca R, Ponec R. Molecular quantum similarity measures as an alternative to log P values in QSAR studies. J Comput Chem 1998 19 1575-1583. 

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 ... 

Until now, we have only used the Dirac delta function to yield molecular quantum similarity measures. The key equations in this regard are... 

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... 

As a final note, on several occasions, alignment-free methods have been used to quantify molecular similarity in the field of molecular quantum similarity, these methods have not yet fovmd extensive application. One method to obtain molecular quantum similarity measures without the need for molecular alignment was published by Boon et al. They use statistical techniques, more specifically, the autocorrelation function. This technique offers an interesting alternative method for similarity studies by removing completely the important obstacle of molecular alignment. 

Until now the molecular quantum similarity measure has primarily been the integral measure Zab- The direct comparison of two values Zab and Zcd does not directly yield an idea of the degree of similarity. Consequently, a numerical transformation must be established, which allows the comparison of the similarity degree between different pairs of molecules. 

A firm theoretical basis has been estabHshed for molecular quantum similarity, and many computational tools have been developed that allow for the evaluation and quantification of molecular quantum similarity measures among sets of molecules or atoms. Molecular quantum similarity is also the basis of quantum QSAR, another active field of research. 

Density Molecular Quantum Similarity Measures A General Connection Between Theoretical Calculations and Experimental Results. 

Molecular Quantum Similarity Measures as Descriptors for Quantum QSAR. 

Comparison Between Molecular Quantum Similarity Measures and Indices. 

QSAR from Tuned Molecular Quantum Similarity Measures Prediction of the CBG Binding Affinity for a Steroid Eamily. 

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