C76 fullerene chlorides and cage transformations. Structural and theoretical study

Chlorination of the D(2)-C(76) fullerene under various conditions is studied in detail. It is found that, in addition to the previously known C(76)Cl(18) and C(76)Cl(34), a number of intermediate chlorides are formed, with all molecules falling into two structural types. The first type is observed in the C(76)Cl(18)-C(76)Cl(28) range, whereas further chlorination provides the C(76)Cl(30)-C(76)Cl(34) compounds of the second type exhibiting a major change in the addition motif. We also present a detailed theoretical rationalization of the previously observed skeletal rearrangement in the D(2)-C(76) that affords the non-IPR (18917)C(76)Cl(24) compound.     

Facile Separation,Spectroscopic Identification,and Electrochemical Properties of Higher Trifluoromethylated Derivatives of [70]Fullerene

We survey the structure and electronic properties of the family of higher trifluoromethylated C₇₀(CF₃)_n molecules with n=14, 16, 18, and 20. Twenty‐two available compounds, of which thirteen are newly obtained and characterized, demonstrate the broad diversity of π‐system topologies, which enabled us to study the interplay between the CF₃ addition pattern and the electronic properties. UV/Vis spectroscopic and cyclic voltammetric studies demonstrate the importance of the exact addition pattern rather than the plain number of addends. Of particular interest is the skew pentagonal pyramid (SPP) addition pattern, which enables formation of closed‐shell cyclopentadienyl anions C₇₀(CF₃)_{n? 1} ^? through CF₃ detachment upon electron transfer. A detailed study of the process is presented for a SPP‐C₇₀(CF₃)₁₆ where potentiostatic electrolysis at the second reduction potential gives C₇₀(CF₃)₁₅^? oxidizable to a persistent C₇₀(CF₃)₁₅^· radical. Together with the literature data for the lower C₇₀(CF₃)_n compounds with n=2–12, the present results show good correlation between the experimental boundary level positions and the DFT predictions. The compounds turn out to be electron acceptor molecular semiconductors with experimental LUMO energies and HOMO–LUMO gaps within the ranges of ?4.3 to ?3.7 eV and 1.6 to 3.3 eV, respectively, depending on the shape of the conjugated fragments. The HOMO levels fall within the range of ?5.6 to ?6.9 eV and show linear correlation with the number of addends.     

THE MITRA‐WAN FORESTRY MODEL: A DISCRETE‐TIME OPTIMAL CONTROL PROBLEM

In this paper, we present some new properties of the Mitra‐Wan forestry model written as a discrete‐time optimal control problem. For this problem, the set of stationary states is characterized. For the optimal long‐run management, we consider the following optimality criteria: average optimality, good control policies, bias optimality, and overtaking optimality. We establish relationships between these criteria and show that the value of average optimal policies is constant and equals the value in the optimal stationary state.