Understanding High‐Resolution Spectra of Nonrigid Molecules Using Group Theory

Abstract

Permutation-inversion group theory has developed to become an important tool in the high-resolution spectroscopy of nonrigid molecules. This large class of molecules is very intriguing to study. Small molecules such as ammonia or Na(3) are known to be nonrigid. With increasing size, however, several large-amplitude motions are possible in a molecule, and can even interact with each other. The high-resolution spectra of nonrigid molecules are known to be quite complicated and very rich in information. Details about the molecule and its internal dynamics can be extracted, such as the molecular structure, the character of the chemical bonds, and the barrier heights to internal rotation and their dependence on the chemical bonds. However, due to the nonrigidity of the molecule and the complexity of such spectra, their analysis is usually quite challenging. Theoretical methods are needed for their prediction and analysis. This Review concentrates on permutation-inversion group theory and its usefulness for the analysis of high-resolution spectra of nonrigid molecules, which is examined in more detail using different examples. In a separate section, a special aspect of molecular symmetry is discussed: the breakdown of symmetry principles. Special emphasis is placed on the breakdown of space inversion symmetry (parity violation) in chiral molecules and its possible implications in high-resolution spectroscopy.

Increased thermal stabilization of polymer photovoltaic cells with oligomeric PCBM

“…This suggest that the ATRAP attack has occurred at a 1,4-phenylene position on the C 60 sphere which retains the same symmetry as the starting material. 38,39 ATRAP cis attacks are inhibited by steric effects to the benefit of the equatorial and the trans positions. Given the known mechanism, 26 the perfect match in the absorption spectra is thus an indication of the ATRAP substitution on PCBM occurring at a symmetrical 1,4-phenylene trans position.…”

Quantitative symmetry and chirality—A fast computational algorithm for large structures: Proteins, macromolecules, nanotubes, and unit cells

“…Another area of chemistry where symmetry and chirality are central is classical crystallography 6–14, 88–93. Inversion symmetry (usually termed centrosymmetricity in crystallography88–90) and mirror symmetry are important for understanding physical properties of crystals such as piezoelectricity, optical nonlinearity, ferroelectricity and more 91–93.…”

“…Yet, contrary to common belief, perfect symmetry is very rare—nature commonly settles for systems with at least small deviations from exact symmetry 16–22. This is true from the macroscopic level15–22 (faces and other animal patterns, trees, and skeletal constructs), to the microscopic level15–18 (diatoms and viruses), to large biomolecules9–22 (ferritin), and down to the smallest ones9–20 (vibrating methane). Unlike other physical properties, which can take on many different numerical values, often lying on a continuous spectrum, symmetry has been treated as a binary qualitative property, namely as a dichotomy: a system can either be symmetric or not.…”

“…Symmetry is a fundamental descriptive tool of nature,1–20 which points to connections and similarities between different parts of a system. One can use these connections to reduce the computational complexity of problems, to simplify the description of the system and to learn about the physics and chemistry of the system.…”

“…This idea is expressed by Noether's theorem, which states that every symmetry of the system is directly connected to some conservation law 5. Some well‐known examples include the conservation of momentum with respect to translational symmetry,6–8 the spectroscopic selection rules dictated by molecular symmetry,9–14 the use of symmetry considerations to suggest the existence of fundamental particles and forces,6–8 and the use of symmetry in evolutionary biology 15–18…”