Broken Symmetry Group in the Octahedral [Me(urea)6]2+, 3+ Cation With Chelate Hydrogen Bonds

Models of abstract and real systems based on broken symmetry group

“…If one of the pre-requisites for the group is not fulfilled, then the group is broken and turns to be some other algebraic structure. For example, the rejection of the necessity to have an "inverse element" (from the axioms of symmetry) leads to the formation of a set structure, which is called a semigroup [14]. The following table 5 of substitutions in two-line matrices is a simple example of a semigroup.…”

Structure Transformations in Broken Symmetry Groups—Abstraction and Visualization

“…In our research, the first case of the broken symmetry group (BSG) finding and new properties showing up was the structure of the complex octahedral cation [Me(urea) 6 ] 2+,3+ (reference code "WOKNIT" in the database [12] with chelate hydrogen bonds [10,13]. Previously, the overview article [14] reported a crystalo-chemical research of possible combinations of directed H-bonds in different structures of complex compounds with carbamide.…”

“…Previously, the overview article [14] reported a crystalo-chemical research of possible combinations of directed H-bonds in different structures of complex compounds with carbamide. The description of the symmetry of complex cation [13] with double hydrogen bond required the "defect" substitutes entry to be in the form of two-rowed matrices as follows: ( 012345 223550 ), or, briefly, with the use of the "coding" (lower row):…”