Home
This Title All WIREs
WIREs RSS Feed
How to cite this WIREs title:
WIREs Comput Mol Sci
Impact Factor: 16.778

Communications on quantum similarity (4): collective distances computed by means of similarity matrices, as generators of intrinsic ordering among quantum multimolecular polyhedra

Full article on Wiley Online Library:   HTML PDF

Can't access this content? Tell your librarian.

This study generalizes the notion of distance via defining an axiomatic collective distance, between arbitrary vector sets. A first part discusses conceptual tools, which can be later useful for general mathematical practice or as computational quantum similarity indices. After preliminary definitions, two elements, which can be associated with arbitrary sets of a vector space, are described: the centroid and the variance vectors. The Minkowski norm of the variance vector is shown to comply with the axioms of a collective distance. The role of the Gram matrix, associated with a vector set, is linked to the definition of numerical variance. Several simple application examples involving linear algebra and N‐dimensional geometry are given. In a second part, all previous definitions are applied to quantum multimolecular polyhedra (QMP), where a set of molecular quantum mechanical density functions act as vertices. The numerical Minkowski norm of the variance vector in any QMP could be considered as a superposition of molecular contributions, corresponding to a new set of quantum similarity indices, which can generate intrinsic ordering among QMP vertices. In this way, the role of quantum similarity matrix elements is evidenced. Application to collections of molecular structures is analyzed as an illustrative practical exercise. The connection of the QMP framework with classical and quantum quantitative structure–properties relation (QSPR) becomes evident with the aid of numerical examples computed over several molecular sets acting as QMP. WIREs Comput Mol Sci 2015, 5:380–404. doi: 10.1002/wcms.1223 This article is categorized under: Structure and Mechanism > Molecular Structures Computer and Information Science > Chemoinformatics Computer and Information Science > Computer Algorithms and Programming
Linear plot of the least squares result obtained for chlorobenzenes fish toxicity as a function of quantum multimolecular polyhedron (QMP) variance indices.
[ Normal View | Magnified View ]
Last N = 10 benzenesulfonamides set plot of biological activity versus quantum multimolecular polyhedron (QMP) variance indices.
[ Normal View | Magnified View ]
First N = 19 benzenesulfonamides set plot of biological activity versus quantum multimolecular polyhedron (QMP) variance indices.
[ Normal View | Magnified View ]
Whole N = 29 benzenesulfonamides set plot of biological activity versus quantum multimolecular polyhedron (QMP) variance indices.
[ Normal View | Magnified View ]
Cramer steroids TeBG biological activity versus quantum multimolecular polyhedron (QMP) variance indices.
[ Normal View | Magnified View ]
Cramer steroids CBG biological activity versus quantum multimolecular polyhedron (QMP) variance indices.
[ Normal View | Magnified View ]

Browse by Topic

Computer and Information Science > Chemoinformatics
Computer and Information Science > Computer Algorithms and Programming
Structure and Mechanism > Molecular Structures

Access to this WIREs title is by subscription only.

Recommend to Your
Librarian Now!

The latest WIREs articles in your inbox

Sign Up for Article Alerts