|
Internet Electronic Journal of Molecular Design - IEJMD, ISSN 1538-6414, CODEN IEJMAT
| ABSTRACT - Internet Electron. J. Mol. Des. March 2002, Volume 1, Number 3, 142-156 |
The Block-Polynomials and Block-Spectra of Dendrimers
Vladimir R. Rosenfeld and Mircea V. Diudea
Internet Electron. J. Mol. Des. 2002, 1, 142-156
|
Abstract:
Dendrimers represent a novel class of hyperbranched
supramolecular structures that promoted novel fundamental
and applicative research. Applications of dendrimers include
simulation of enzymatic reactions, artificial vaccines, gene
carriers and homogeneous catalysis. The polynomial description
of molecular structures is one of the most essential and elegant
procedure of encoding topological properties and providing
valuable descriptors, such as polynomial roots and coefficients.
From the mathematical point of view, dendrimers represent a
generalized recursive class of graphs. The block construction of
dendrimers is simulated with block polynomials, which allow the
study of their roots, i.e., their spectrum of eigenvalues. The study
of the block polynomial behavior envisaged the transmittance of
hereditary spectral properties along a recursive series of
dendrimers. A novel description of supramolecular dendritic
molecules is given. The obtained results can be used to design
molecular structures with tailored electronic and photonic properties.
|