Related Experiment Video
Updated: Aug 9, 2026

Iterative Optimization of DNA Duplexes for Crystallization of SeqA-DNA Complexes
Published on: November 1, 2012
Algebraic determination of generating functions for coordination sequences in crystal structures
1Instituto de Química, Universidade Federal do Rio de Janeiro, A-632, Cidade Universitária, 21945-970 Ilha do Fundão, Rio de Janeiro, Brazil. jgeon@iq.ufrj.br
Abstract:
Given a connected crystalline structure, the set of paths and cycles of the quotient graph of its bond net is embedded into a commutative ring structure. Multiplication combines walks to build up geodesics of the net whereas addition stands symbolically for enumerating a collection of walks. Topological criteria are used to define zero divisors which enable the development of an algebraic generator into a combination of geodesics that are in a one-to-one correspondence with the vertices of the net. A ring mapping gives the generating function of the coordination sequence in the net.
Related Concept Videos
Coordination Compounds and Nomenclature
Coordination Number and Geometry
Valence Bond Theory
Crystal Field Theory - Octahedral Complexes
To explain the observed behavior of transition metal complexes (such as colors), a model involving electrostatic interactions between the electrons from the ligands and the electrons in the unhybridized d orbitals of the central metal atom has been developed. This electrostatic model is crystal field theory (CFT). It helps to understand, interpret, and predict the colors, magnetic behavior, and some structures of coordination compounds of transition metals.
CFT focuses on...
Crystal Field Theory - Tetrahedral and Square Planar Complexes
Crystal field theory (CFT) is applicable to molecules in geometries other than octahedral. In octahedral complexes, the lobes of the dx2−y2 and dz2 orbitals point directly at the ligands. For tetrahedral complexes, the d orbitals remain in place, but with only four ligands located between the axes. None of the orbitals points directly at the tetrahedral ligands. However, the dx2−y2 and dz2 orbitals (along the Cartesian axes) overlap with the ligands less than the dxy,...
Determination of Crystal Structures

