Molecular quantum self-similarity measure

Based on the molecular quantum similarity measmes. Molecular Quantum Self-Similarity Measures (MQS-SM) were proposed as molecular descriptors where each molecule is compared with itself and all the others, and appropriate Hermitian operators 2 are associated to each molecular property [Ponec et al, 1999]. 

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 ... 

When A equals B, the similarity measure of Eq. [14] is called the molecular quantum self-similarity measure, which corresponds to the square of the Euclidean norm of the density function. In other words. 

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... 

Amat, L., Besalu, E. and Carbo-Dorca, R. (2001) Identification of active molecular sites using quantum-self-similarity measures. J. Chem. Inf. Comput. Sci., 41, 978-991. 

Molecular Basis of LEER. Modeling of the Electronic Substituent Effect Using Fragment Quantum Self-Similarity Measures. 

The Use of Ab Initio Quantum Molecular Self-Similarity Measures to Analyze Electron Charge Density Distributions. 

The methods applied in recent years by various groups to construct QSAR models for ART and analogues include docking calculations to heme [104, 105], CoMFA [106-109] and hologram QSAR [108] as well as the hypothetical active-site lattice (HASL) approach [107], self-organizing maps of the molecular electrostatic potential [110], quantum-similarity measures [111] and topological molecular connectivity descriptors [112]. 

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