Piperazine Functionalization of C70 for Incorporation into Supramolecular Assemblies

The photochemical reaction of piperazine with C₇₀ produces a mono‐adduct (N(CH₂CH₂)₂NC₇₀) in high yield (67 %) along with three bis‐adducts. These piperazine adducts can combine with various Lewis acids to form crystalline supramolecular aggregates suitable for X‐ray diffraction. The structure of the mono‐adduct was determined from examination of the adduct I₂N(CH₂CH₂)₂NI₂C₇₀ that was formed by reaction of N(CH₂CH₂)₂NC₇₀ with I₂. Crystals of polymeric {Rh₂(O₂CCF₃)₄N(CH₂CH₂)₂NC₇₀}_n?nC₆H₆ that formed from reaction of the mono‐adduct with Rh₂(O₂CCF₃)₄ contain a sinusoidal strand of alternating molecules of N(CH₂CH₂)₂NC₇₀ and Rh₂(O₂CCF₃)₄ connected through Rh?N bonds. Silver nitrate reacts with N(CH₂CH₂)₂NC₇₀ to form black crystals of {(Ag(NO₃))₄(N(CH₂CH₂)₂NC₇₀)₄}_n?7nCH₂Cl₂ that contain parallel, nearly linear chains of alternating (N(CH₂CH₂)₂NC₇₀ molecules and silver ions. Four of these {Ag(NO₃)N(CH₂CH₂)₂NC₇₀}_n chains adopt a structure that resembles a columnar micelle with the ionic silver nitrate portion in the center and the nearly non‐polar C₇₀ cages encircling that core. Of the three bis‐adducts, one was definitively identified through crystallization in the presence of I₂ as ¹²{N(CH₂CH₂)₂N}₂C₇₀ with addends on opposite poles of the C₇₀ cage and a structure with C_2v symmetry. In ¹²{I₂N(CH₂CH₂)₂N}₂C₇₀, individual ¹²{I₂N(CH₂CH₂)₂N}₂C₇₀ units are further connected by secondary I2???N2 interactions to form chains that occur in layers within the crystal. Halogen bond formation between a Lewis base such as a tertiary amine and I₂ is suggested as a method to produce ordered crystals with complex supramolecular structures from substances that are otherwise difficult to crystallize.     

Toward the classification of biangular harmonic frames

Equiangular tight frames (ETFs) and biangular tight frames (BTFs) – sets of unit vectors with basis-like properties whose pairwise absolute inner products admit exactly one or two values, respectively – are useful for many applications. A well-understood class of ETFs are those which manifest as harmonic frames – vector sets defined in terms of the characters of finite abelian groups – because they are characterized by combinatorial objects called difference sets.This work is dedicated to the study of the underlying combinatorial structures of harmonic BTFs. We show that if a harmonic frame is generated by a divisible difference set, a partial difference set or by a special structure with certain Gauss summing properties – all three of which are generalizations of difference sets that fall under the umbrella term “bidifference set” – then it is either a BTF or an ETF. However, we also show that the relationship between harmonic BTFs and bidifference sets is not as straightforward as the correspondence between harmonic ETFs and difference sets, as there are examples of bidifference sets that do not generate harmonic BTFs. In addition, we study another class of combinatorial structures, the nested divisible difference sets, which yields an example of a harmonic BTF that is not generated by a bidifference set.     

Cooperative and diminutive interplay between the sodium bonding with hydrogen and dihydrogen bondings in ternary complexes of NaC3N with HMgH and HCN (HNC)

Ternary complexes of NaC₃N with HMgH and HCN (HNC) are connected by sodium, hydrogen and dihydrogen bonds. Molecular geometries and interaction energies of dyads and triads are investigated at the MøllerPlesset perturbation theory of the second order/aug-cc-pVDZ computational level. Particular attention is paid to parameters, such as cooperative energies and many-body interaction energies. Triads with the HMgH molecule located at the end of the chain show an energetic cooperativity ranging between ?2.13 and ?10.53 kJ mol^?1. When the HMgH molecule is located in the middle, the obtained cluster is diminutive with an energetic effect with values 4.39 and 6.77 kJ mol^?1. The electronic properties of the complexes are analysed using parameters derived from the atoms in molecules methodology. Based on the energy decomposition analysis, it can be seen that the stabilities of the complexes are predicted to be attributable mainly to electrostatic effects.