H and C NMR assignments of the three dicyclopenta-fused pyrene congeners

Complete ¹H and ¹³C NMR assignments of the (di-)cyclopenta-fused pyrene congeners, cyclopenta[cd]- (2), dicyclopenta[cd,fg]- (3), dicyclopenta[cd,jk]- (4) and dicyclopenta[cd,mn]pyrene (5), respectively, are achieved using two-dimensional (2D) NMR spectroscopy. The experimental ¹³C chemical shift assignments are compared with computed ab initio CTOCD-PZ2/6-31G^∗∗13C chemical shifts; a satisfactory agreement is found. Substituent-induced chemical shifts in the pyrene core induced by annelation of cyclopenta moieties are discussed. Effects of dicyclopenta topology on electronic structure are illustrated for 3-5.     

Counterexamples to a proposed algorithm for Fries structures of benzenoids

The Fries number of a benzenoid is the maximum number of benzenoid hexagons over all of its Kekulé structures (perfect matchings), and a Fries canonical structure is a perfect matching that realises this maximum. A recently published algorithm claims to determine Fries canonical structures of benzenoids via iterated Hadamard products based on the adjacency matrix (Ciesielski et?al. in Symmetry 2:1390–1400, 2010). This algorithm is re-examined here. Convergence is typically rapid and often yields a single candidate perfect matching, but the algorithm can give an exponential number of choices, of which only a small number are canonical. More worryingly, the algorithm is found to give incorrect results for the Fries number for some benzenoids with as few as seven hexagonal faces. We give a combinatorial reformulation of the algorithm in terms of linear combinations of perfect matchings (with weights at each stage proportional to the products of weights of the edges included in a matching). In all the cases we have examined, the algorithm converges to a maximum-weight matching (or combination of maximum-weight matchings), and where the algorithm fails, either no best Fries matching is of maximum weight, or a best Fries matching is of maximum weight but a sub-optimal matching of the same weight is chosen.     

Commensurate and incommensurate hydrogen bonds. An exercise in crystal engineering.

Ureas characteristically form one-dimensional hydrogen-bonded alpha-networks with a repeat distance of about 4.60 A. Oxamides form similar alpha-networks with a longer 5.05 A repeat distance. The urea of glycine and the oxamide of glycine were each cocrystallized with a series of four bipyridines, including two urea derivatives and two oxamide derivatives. This series of eight cocrystals was studied by X-ray diffraction in order to see what would happen when molecules that would normally form alpha-networks with incommensurate distances were forced into the same crystal. The two all-urea crystals and the two all-oxamide crystals contained the expected alpha-networks with repeat distances in accordance with normal urea or oxamide values. Four of the crystals were mixed, containing both oxamide and urea molecules. Three consisted of two-dimensional beta-networks with alternating parallel urea and oxamide subnetworks. The repeat distances averaged 4.87 A, a value close to the value expected for oxamides, but shorter than any previously observed examples. In the fourth mixed crystal, the urea alpha-network formed with a normal urea repeat distance, but the oxamide network did not form, the oxamide adopting an unusual molecular conformation that maximizes intramolecular hydrogen bonds instead.     

Semiempirical molecular orbital techniques applied to silicon dioxide: MINDO/3

We present a discussion of MINDO/3, a semiempirical molecular orbital program, which we have applied to clusters of atoms used to represent silicon dioxide. We have obtained MINDO/3 parameters for the Si-O interaction and have calculated a variety of observables for both molecules and solid-state clusters, for both open- and closed-shell systems. With some exceptions, we find very good agreement with other calculations and with experiment. In particular, our results for both E′₁ and E′₄ defects support existing models which feature asymmetric atomic relaxations.     

Acoustic Analysis of the Interaction of Choral Arrangements, Musical Selection, and Microphone Location

Acoustic differences were evaluated among three choral arrangements and two choral textures recorded at three microphone locations. A choir was recorded when singing two musical selections of different choral texture, one homophonic and one polyphonic. Both musical selections were sung in three choral arrangements: block sectional, sectional-in-columns, and mixed. Microphones were placed at the level of the choristers, the conductor, and the audience. The recordings at each location were analyzed using long-term average spectrum (LTAS). The LTAS from the mixed arrangement exhibited more signal amplitude than the other arrangements in the range of 1000-3500Hz. When considering the musical selections, the chorus produced more signal amplitude in the region of 1800-2200Hz for the homophonic selection. In addition, the LTAS produced by the choir for the homophonic selection varied across the microphone locations. As for the microphone location, the LTAS of the signal detected directly in front of the chorus had a greater slope than the other two locations. Thus, the acoustic signal near the choristers differed from the signals near the conductor and in the audience. Conductors may be using acoustic information from the region of the second and third formants when they decide how to arrange a choir for a particular musical selection.     

On 2-designs

Denote by M_v the set of integers b for which there exists a 2-design (linear space) with v points and b lines. M_v is determined as accurately as possible. On one hand, it is shown for v > v₀ that M_v contains the interval [v + p + 1, v + p + q ? 1]. On the other hand for v of the form p² + p + 1 it is shown that the interval [v + 1, v + p ? 1] is disjoint from M_v; and if v > v₀ and p is of the form q² + q, then an additional interval [v + p + 1, v + p + q ? 1] is disjoint from M_v.