Quantum similarity measure

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... 

Having established the most important concepts for MQS, the next step is to actually compute the numerical values associated with the quantum similarity measures. Electron densities can naturally be obtained from many quantum chemical methods such as DFT, Hartree-Fock, configuration interaction, and many more, even from experiment. 

Amat, L. and Carbo-Dorca, R. (1999) Fitted electronic density functions from H to Rn for use in quantum similarity measures cis-diamminedichloroplatinum(II) complex as an application example. 

R. Modeling antimalarial activity application of kinetic energy density quantum similarity measures as descriptors in QSAR./. Chem. Inf. Comput. Sci. 2000, 40, 1400—1407. 

This section also includes at the end an analysis of the electron spin spin contact integrals, a well known and simple relativistic correction term, which are also studied in this paper due to their close relationship with Quantum Similarity Measures [66c]. The form of sudi integrals corresponds to some kind of many function, many center overlap. 

These results permit one to see that the same will occur when the integral of an arbitrary number of CETO products centered at arbitrary sites (Aj) is to be evaluated. Any permutation of the functions in the product will leave the integral invariant and WO-CEITO transformation rules as well as overlap integral evaluation will be sufficient to obtain this kind of integrals. These characteristics, which are also present when using GTO functions, may appear interesting when dealing with Quantum Similarity measures [66b,d]. 

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. 

Carb6, R. and Calabuig, B. (1992d). Quantum Similarity Measures, Molecular Cloud Description, and Structure-Properties Relationships. J.Chem.Inf.Comput.Sci.,32,600-606. 

Lobato, M., Amat, L., Besalil, E. and Carbd-Dorca, R. (1997). Structure-Activity Relationships of a Steroid Family Using Quantum Similarity Measures and Topological Quantum Similarity Indexes. Quant.Struct.-Act.Relat., 16,465-472. 

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. 

Mezey P (1999) The holographic electron density theorem and quantum similarity measures. Mol Phys 96(2) 169-178... 

Quantum Self-Similarity Measures quantum similarity quantum similarity = quantum similarity Quantum Similarity Indices quantum similarity Quantum Similarity Measures quantum similarity representation molecular descriptors rigidity —> flexibility indices... 

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]. 

Gallegos Sahner, A. and Girones, X. (2005) Topological quantum similarity measures applications in QSAR. /. Mol Struct. (Theochem), 727, 97-106. 

The n th order Quantum Similarity Measure between two quantum systems A and B with respect to an operator fV, can be defined as an integral of the following kind ... 

In previous papers [1,2] the authors have worked out the theoretical foundation of Quantum Similarity (QS). In this paper, several practical results will be listed. All of them came from some of the Quantum Similarity Measures (QSM) defined previously and are particular cases of the general QSM definition obtained in reference [1]. 

Quantum Similarity Measure has been outlined and several related Quantum Similarity Indices have been defined in Section 5. 

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