Concurrent Symmetries: The Interplay Between Local and Global Molecular Symmetries

Abstract

We analyze in this article the degree to which different groups of atoms retain local symmetries when assembled in a molecule. This study is carried out by applying continuous symmetry measures to several families of mixed sandwiches, a variety of piano-stool molecules, and several organic groups. An analysis of the local symmetry of the electron density shows that, sandwiched between two regions of different symmetry that correspond to the ligand sets, its symmetry is cylindrical at the central metal atom.

Stereochemistry of 2,6‐Diaminoadamantane Salts: Transannular Interactions

“…Higher values can be qualitatively interpreted as an absence of the corresponding symmetry element." [25] Each of the four (2RS,6RS)-3A and (2RS,6RS)-3B diammonium ions in the crystal structure also exhibit pseudo-C 2 symmetry, such that one ion is closer to ideality than the other. Genuine The hydrogen-bonding arrangements in the crystal structure of 3 are worthy of comment.…”

Effects of Temperature on the Shape and Symmetry of Molecules and Solids

“…In our case, the differencei nm asses between Ba nd Ci s not so much relevant,b ut the rigidity of the different molecules is quite different. If we considert he frequency of the totally symmetric breathing mode for the inner cluster as an average measuref or the rigidity of the structure (w % 51,39,38,30,and 27 THz for C 4 H 4 ,B 6 H 6 2À ,C 8 H 8 ,B 12 H 12 2À ,a nd C 20 H 20 , respectively) we will find that the average displacement will be lowest for the most rigid tetrahedrane molecule and largest for dodecahedrane. It is also noticeable that, in general,h ydrocarbonsa re more rigid than the boranes, for instancet he smaller B 6 H 6 2À has practically the same frequency for the breathing mode than C 8 H 8 .I fw ec onsider also the radii of the clusters (r = 0.92, 1.20, 1.36, 1.66. and 2.17 ,a nd C 20 H 20 ,r espectively) as am easure of their size, the ratio between the size of the average displacement calculated using Equation (2) and the radius of the cluster gives us the clue to understandt he trendsf ound for the symmetry loss as the temperature is raised.…”

“…CMSs have also been used to describe geometrical changes along reaction paths, particularly for enantiomerization processes . An interesting application of CSMs, closely related to the type of work described here is the analysis of environmental effects on molecular symmetry, with a special emphasis on the coexistence of apparently contradictory symmetries in a same system …”

Analyzing the electronic structure of molecules using continuous symmetry measures

“…Geometric CSMs and CShMs have been successfully applied to a variety of stereochemical problems such as the description of the coordination environement, chirality, and reactivity of chemical compounds . The usefulness of these measures is especially evident when they are applied in conjunction with a statistical analysis to a large set of structural data obtained from a search in databases such as the Cambridge Structural Database .…”