# Some dimension problems in molecular databases

@article{Mezey2009SomeDP, title={Some dimension problems in molecular databases}, author={P. Mezey}, journal={Journal of Mathematical Chemistry}, year={2009}, volume={45}, pages={1-6} }

Molecular databases obtained either by combinatorial chemistry tools or by more traditional methods are usually organized according to a set of molecular properties. A database may be regarded as a multidimensional collection of points within a space spanned by the various molecular properties of interest, the property space. Some properties are likely to be more important than others, those considered important form the essential dimensions of the molecular database. How many properties are… Expand

#### 14 Citations

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#### References

SHOWING 1-10 OF 13 REFERENCES

The degree of similarity of three-dimensional bodies: Application to molecular shape analysis

- Mathematics
- 1991

Similarity of shape features of three-dimensional bodies is of importance in many fields. Computational methods that are suitable to provide numerical measures for such similarities are expected to… Expand

QUANTUM CHEMICAL SHAPE : NEW DENSITY DOMAIN RELATIONS FOR THE TOPOLOGY OF MOLECULAR BODIES, FUNCTIONAL GROUPS, AND CHEMICAL BONDING

- Chemistry
- 1994

A density domain (DD) is the formal body enclosed by a molecular isodensity contour (MIDCO) surface. Individual nuclear neighborhoods and various formal molecular fragments can be regarded as fuzzy… Expand

Functional Groups in Quantum Chemistry

- Chemistry
- 1996

Publisher Summary A chemical functional group is a collection of nuclei and the associated electron density, which occur with a similar nuclear arrangement and a similar local electron density cloud… Expand

A Functional Group Database: A Charge Density – DARC Approach

- Chemistry
- 1998

The principle of the DARC approach of hierarchical organization is applied to a molecular electron density representation of functional groups, designed to represent some of the large-scale features… Expand

Dimension Concepts and Reduced Dimensions in Toxicological QShAR Databases as Tools for Data Quality Assessment

- Computer Science
- 2001

Some of the tools for effective dimension reduction and dimension expansion are reviewed in the context of database quality control and conditions for database compatibility are presented. Expand

Relations among functional groups within a stoichiometry: A nuclear configuration space approach

- Physics
- 1992

A general scheme is proposed for the study of the interrelations and transformations of flexible functional groups within the configuration space M of all possible chemical species of a fixed overall… Expand

Local Electron Densities and Functional Groups in Quantum Chemistry

- Chemistry
- 1999

The connections between the quantum chemical concept of local electron densities and the traditional concept of functional groups of organic chemistry are explored. The Density Domain criterion of… Expand

Quantum chemistry of macromolecular shape

- Chemistry
- 1997

Some of the new developments in the quantum-chemical study of macromolecular shapes are reviewed, with special emphasis on the additive fuzzy electron density fragmentation methods and on the… Expand

Computational Aspects of Combinatorial Quantum Chemistry

- Physics
- 2001

The Additive Fuzzy Density Fragmentation (AFDF) principle and the Adjustable Density Matrix Assembler (ADMA) methods are proposed for a combinatorial construction of electron density representations… Expand

Shape in Chemistry: An Introduction to Molecular Shape and Topology

- Mathematics
- 1993

The intuitive concept of molecular shape the quantum chemical concept of molecular shape applied topology - the mathematics of the essential quantitative shape - activity relations in drug design and… Expand