Symmetry is a fascinating structural property of matter. Many molecular systems tend to create symmetric structures. While the common view of symmetry is dichotomous – a molecule is considered either symmetric or not - numerous experimental and theoretical measurements show that approximate symmetry is much more common. One may ask then how far from symmetry is a given molecular structure or "what is the symmetry content of a molecule". The continuous symmetry measures (CSM) developed by Avnir and coworkers answer these questions by quantifying the level of symmetry of a given structure and provide a new terminology for symmetry analysis. Our group study various phenomenon that involve approximate symmetry using the CSM methodology in combination with computational chemistry tools. A short overview of the current projects follows.
Molecules are flexible structures, thefore their chirality level can change by e.g., conformational flexibility, thermal fluctuations, solvent effects, modes of crystallization and many other processes. A dichotomic yes/no description of chirality is insufficient to describe the molecular structure in such cases. A more realistic view of chirality is based on measuring the chirality content of a given molecular structure on a normalized continuous scale that allows comparison of different structures. Using the continuous chirality measure (CCM) we investigate the abundance of chirality of organic molecules and drugs that are generally considered achiral.
Aspirin conformers in the gas phase. All are chiral.
Glycine, the smallest amino acids, is commonly considered achiral. However, when chirality measures are added to the Ramachandran plot of glycine, new structural properties emerge showing that it is practically always conformationally chiral within the protein.
oontinuous chirality measure of each amino acid residue in proteins emerges as a powerful tool for structural analysis when added to Ramachandran plots. A chiral Ramachandran plot of Gly is presented here with a color scale (light areas – highly chiral, dark areas – achiral), revealing the richness of its conformational chirality in various secondary structures.
Image credit: Huan Wang, Ilana Broitman, Inbal Tuvi-Arad.
Developing Improved Algorithms for Symmetry Analysis
Our group focus on improving the Continous Symmetry Measure algorithms in terms of accuracy and efficiency, making it useful to study the symmetry of macromolecules and proteins, bulk systems and much more. In addition we are developing a host of supporting tools to calculate the CSM for huge databases of molecular coordinates taken from a variety of sources such as the Cambridge Crystallographic Database, Gaussian log files, molecular dynamics results and more.
Helicene with 43 phenyl rings.
Near-Symmetry and Temperature
Symmetric molecules may lose their symmetry as the temperature rises. In the gas phase and in the absence of intermolecular interactions, thermal fluctuations constantly distort molecules from their equilibrium geometries. In fact, the probability of finding a molecule with perfect symmetry at a given temperature is most probably negligible, even if the ground state geometry is perfectly symmetric. Our research focuses on statistical analysis of the temperature effect on the geometry, in relatation to entropy and reactivity.
Dynamics of the cyclopentadienyl anion.
Chirality versus temperature for the cyclopentadienyl anion.
Symmetry in Pericyclic Reactions
The Woodward-Hoffmann rules teach us that orbital symmetry is conserved in concerted pericyclic reactions. As a consequence, reactions occur readily when there is a matching between orbital symmetry characteristics of reactants and products, but with difficulty otherwise. However, many reactions produce the correct product anticipated by the Woodward-Hoffmann rules, without following a strict concerted mechanism. Our study focuses on the role of symmetry in these reactions in relation to substitution, solvent and tunneling effects.
The Internet offers unprecedented opportunities for chemical education. The availability of huge chemical databases, of three-dimensional and dynamic graphics together with the computational power and the communicational features of the web, provide foundations for exciting new ways to teach learn and visualize complicated chemical phenomena.
Learning with Video
The technology of live video streaming (LVS) enables audio and video broadcasting through the internet directly into users' personal computers. When applied to education, students can view and interact, in real time, with their instructors and classmates during a live session. Following the session students can access the archive of recorded lessons. By allowing students to attend class remotely, LVS expands classroom walls and time frame. These features make it particularly attractive for distance education. The ability of students to access the class sessions archive provide them with full control over their learning pace with the confidence that they did not miss anything regardless of their participation in the live sessions. Our study focuses on LVS viewing strategies of undergraduate chemistry students. Our goal is to identify key aspects in the courses' materials that require special attention, assess the effectiveness of the video sessions, and learn how to improve them for future use.