Splitting of n-fold rotationally symmetric graphs

R. A. Davidson's rules for splitting an n-fold rotationally symmetric graph can be derived from a unitary transformation on the adjacency matrix. The McClelland and D'Amato rules are special cases with n = 2 and n = 3, respectively.     

Influence of the water molecule on cation-pi interaction: ab initio second order Møller-Plesset perturbation theory (MP2) calculations

The influence of introducing water molecules into a cation-pi complex on the interaction between the cation and the pi system was investigated using the MP2/6-311++G method to explore how a cation-pi complex changes in terms of both its geometry and its binding strength during the hydration. The calculation on the methylammonium-benzene complex showed that the cation-pi interaction is weakened by introducing H(2)O molecules into the system. For example, the optimized interaction distance between the cation and the benzene becomes longer and longer, the transferred charge between them becomes less and less, and the cation-pi binding strength becomes weaker and weaker as the water molecule is introduced one by one. Furthermore, the introduction of the third water molecule leads to a dramatic change in both the complex geometry and the binding energy, resulting in the destruction of the cation-pi interaction. The decomposition on the binding energy shows that the influence is mostly brought out through the electrostatic and induction interactions. This study also demonstrated that the basis set superposition error, thermal energy, and zero-point vibrational energy are significant and needed to be corrected for accurately predicting the binding strength in a hydrated cation-pi complex at the MP2/6-311++G level. Therefore, the results are helpful to better understand the role of water molecules in some biological processes involving cation-pi interactions.     

Optical Properties of Model Compounds of Polyaniline

The UV and visible spectra of six model compounds were studied. These compounds can be considered as models of polyaniline in the reduced, cation radical, partially oxidized and oxidized forms. After treatment of a mixture of equal molar quantities of the reduced form (DPPD) and the oxidized form (QDIM) with acid, the following reaction was observed: DPPD(I)+QDIM(III)+2H⁺=2DPPD⁺(II) After similar treatment of the partially oxidized form (V) with acid, the radical cation salt formed. The UV and visible spectra of polyaniline in the reduced form, oxidized form and conductive form are similar to the spectra of DPPD, QDIM and DPPD⁺ or radical cation salt of V respectively. We propose that the polyaniline synthesized by chemical oxidation of aniline consists of oxidized and reduced repeat units. Upon protonation a redox reaction (or electron rearrangement) occurs and forms delocalized radical cations (polarons) in the polymer chain which are highly conductive.