Isomeric diamondoids with the same number \(n\) of adamantane units (or cells), which share the same molecular formula \(\text{ C}_\mathrm{Q}(\text{ CH})_\mathrm{T}(\text{ CH}_{2})_\mathrm{S}\), can be divided into valence isomers by partitioning the number \(C \) of their carbon atoms according to whether they are Quaternary, Tertiary, or Secondary: \(C =Q +T +S\). Each [\(n\)]diamondoid has a dualist (or inner dual) with \(n\) vertices (situated at centers of adamantane units), and edges connecting vertices of adjacent adamantane units sharing a chair-shaped hexagon of carbon atoms. Such a dualist is characterized by a quadruplet of indices (denoted as p, s, t, q for primary, secondary, tertiary, or quaternary) specifying again the connectivity of each vertex by assimilating it with a virtual carbon atom. The diamond lattice is self-dual. Dualists help in classifying diamondoids as catamantanes with acyclic dualists, perimantanes with dualists having chair-shaped six-membered rings, or coronamantanes with dualists having only higher-membered rings. In turn, catamantanes can be either regular when they have formulas \(\text{ C}_{4n+6}\text{ H}_{4n+12}\), or irregular when the numbers of carbon and hydrogen atoms are lower than the above values for the given numbers \(n\) of adamantane units. Regular catamantanes can have branched or non-branched dualists and they are isomeric when having the same \(n\). Partitioned formulas reflect the branching patterns, encoded in their dualists. Partition formulas and codes are presented for all possible diamondoids with up to 7 adamantane units. A remarkable symmetry is observed for the table of partition periodic table of regular catamantanes with up to 7 adamantane units. Isomeric irregular catamantanes with six or more adamantane units may be valence-isomeric (or homomeric, sharing both the molecular and the partitioned formulas), or heteromeric when they have different partitioned formulas.

The dualist of an [n]diamondoid consists of vertices situated in the centers of each of the n adamantane units, and of edges connecting vertices corresponding to units sharing a chair-shaped hexagon of carbon atoms. Since the polycyclic structure of diamondoids is rather complex, so is their nomenclature. For specifying chemical constitution or isomerism of all diamondoids the Balaban-Schleyer graph-theoretical approach based on dualists has been generally adopted. However, when one needs to indicate the location of C and H atoms or of a substituent in a diamondoid or the stereochemical relationships between substituents, only the IUPAC polycycle nomenclature (von Baeyer nomenclature) provides the unique solution. This is so since each IUPAC name is associated with a unique atom numbering scheme. Diamondoids are classified into catamantanes (which can be regular or irregular), perimantanes, and coronamantanes. Regular catamantanes have molecular formulas C4n+6H4n+12. Among regular catamantanes, the rigid blade-shaped zigzag catamantanes (so called because their dualists consist of a zigzag line with a code of alternating digits 1 and 2) exhibit a simple pattern in their von Baeyer nomenclature. Their carbon atoms form a main ring with 4n + 4 atoms, and the remaining atoms form two 1-carbon bridges. All zigzag [n]catamantanes with n > 2 have quaternary carbon atoms, and the first bridgehead in the main ring is such an atom. Their partitioned formula is Cn−2(CH)2n+4(CH2)n+4. As a function of their parity, IUPAC names based on the von Baeyer approach have been devised for all zigzag catamantanes, allowing the unique location for every C and H atom. The dualist of such a zigzag catamantane defines a plane bisecting the molecule, and the stereochemical features of hydrogens attached to secondary carbon atoms can be specified relatively to that plane.

Isomeric diamond hydrocarbons (diamondoids or polymantanes) with the same number n of adamantane units share the same molecular formula CQ(CH)T(CH2)S and can be divided into valence isomers (denoted as Q–T–S) by partitioning the number C = Q + T + S of their carbon atoms according to whether they are quaternary, tertiary, or secondary. Vertices of dualists are the centers of adamantane units, and dualist edges connect vertices of adjacent adamantane units (sharing a chair-shaped hexagon). Dualists of diamondoids are hydrogen-depleted skeletons of staggered alkane or cycloalkane rotamers. Diamondoids with acyclic dualists can be classified as catamantanes, those having dualists with chair-shaped six-membered rings as perimantanes, and those having dualists with higher-membered rings that are not perimeters of hexagon-aggregates as coronamantanes. Diamondoids with n adamantane units may be classified into regular catamantanes when the molecular formula is C4n+6H4n+12, and irregular polymantanes (catamantanes or perimantanes) when the number of carbon atoms is lower than 4n + 6. The derivation is presented of formula-periodic tables of regular and irregular diamondoids that allow a better understanding of the shapes and properties of these hydrocarbons for which many applications are predicted.

Flag graphs have been used in the past for describing maps on closed surfaces. In this paper we use them for the first time in mathematical chemistry for describing benzenoids and some other similar structures. Examples include catacondensed and pericondensed benzenoids. Several theorems are included. Symmetries of benzenoid systems, flag graphs, and symmetry type graphs are briefly discussed.

After a brief history of the aromaticity concept, the use of Clar sextet circles is reviewed for explaining various aspects of planar aromatic systems (benzenoids, heterocycles) and of tridimensional carbon aggregates. When folding a graphene sheet for obtaining nanotubes, nanotori, or nanocones, the congruence of Clar sextet circles allows the classification of all such aggregates into two classes (congruent or incongruent) with marked differences in properties; this is in agreement with the well-known condition h − k ≡ 0 (mod 3), equivalent to congruence, in terms of the chiral vectors h and k for graphene sheets.

Molecular insights into cationic lipid assemblies are relatively hard to reveal due to intrinsic mobility of the structural elements, hydration of the polar head and counterion, etc. Using X-ray diffraction of 4,6-dimethyl-2-tetradecyl-1-(2-tetradecanoyloxyethyl)pyridinium hexafluorophosphate (1) single crystals we succeeded in visualizing the molecular assembly of this amphiphile, in particular its U-shape structure and the impact of various structural parameters, including the counterion. The two alkyl chains lie parallel in orthogonal planes, and that the pyridinium cationic rings appear closely to the hexafluorophosphate anions. The whole assembly has therefore nonpolar zones alternating with polar cationic–anionic channel-zones. The relevance of this molecular and crystal structure to the gene transfection ability of this cationic lipid is also discussed.

Starting from 4-chloro-3,5-dinitrobenzoic acid 1, compounds 2–10 (N-alkoxy-3,5-dinitro-4-aminobenzoic acid esters where alkoxy stands for methoxy, carboxymethoxy, triphenylmethoxy, or corresponding amides) have been obtained, from which compounds 3–5 and 7–10 are new, and for the known compounds 2 and 6 the synthetic procedure has been improved. The new derivatives have been characterized by appropriate means (IR, UV–Vis, 1H- and 13C-NMR, fluorescence) and their properties were studied. Thus, depending on their structure, the compounds have acid properties, fluorescence and complexing properties with alkaline cations.

Some of the semiregular (Archimedean) polyhedra (1–13 in Table 1) afford on truncation polyhedra that contain vertices where the sum of planar degrees for the faces which meet at those vertices is equal to (for 17, 18, and 23 in Table 3) or higher than 360° (21, 22, 24–26 in Table 3). Therefore such polyhedra are nonconvex.

Eric Clar’s qualitative ideas for benzenoids are described in application to various novel nanostructures: graphene, edges in graphene, carbon nanotubes, carbon nanocones, and carbon nanotori. The specially singled out most highly aromatic species with Clar structures consisting entirely of aromatic sextets are proposed to be termed “claromatic”. Several such claromatic nanostructures are identified as manifesting special properties. A molecular structural “(h,k)” characterization for benzo/grapheneic nanostructures is shown to link up neatly with Clar’s ideas.

The missing values for the solid angles of the two snub semiregular polyhedra have been calculated, and integrated into the whole series of Platonic and Archimedean polyhedra. This is the only criterion which so far gives an unambiguous answer (without any degeneracy leading to posets) on how to order these polyhedra according to their increasing complexity.

The newly introduced signature of benzenoids (a sequence of six real numbers si with i = 6−1) shows the composition of the π-electron partition by indicating the number of times all rings of the benzenoid are assigned 6, 5, 4, 3, 2, or 1 π-electrons. It allows the introduction of a new ordering criterion for such polycyclic aromatic hydrocarbons by summing some of the terms in the signature. There is an almost perfect linear correlation between sums s6 + s5 and s4 + s3 for isomeric cata- or peri-fused benzenoids, so that one can sort such isomers according to ascending s6 + s5 or to descending s4 + s3 sums (the resulting ordering does not differ much and agrees with that based on increasing numbers of Clar sextets and of Kekulé structures). Branched cata-condensed benzenoids have higher s6 + s5 sums than isomeric nonbranched systems. For nonisomeric peri-condensed benzenoids, both sums increase with increasing numbers of benzenoid rings and decrease with the number of internal carbon atoms. Other partial sums that have been explored are s6 + s5 + s3 and s6 + s2 + s1, and the last one appears to be more generally applicable as a parameter for the complexity of benzenoids and for ordering isomeric benzenoids.

The absorption and emission spectra in cyclohexane and methanol of the title phenoxathiinyl-phenyloxazole derivatives are presented and discussed. Comparing to the unsubstituted diphenyloxazole (PPO), the experimental results show a bathochromic shift of the emission band, a significant dependence of the maximum on the solvent polarity and a drastic decrease of the fluorescence quantum yield. Semiempirical MO calculations (AM1) in both the ground and excited states support the experimental findings. A charge transfer from the phenoxathiin fragment to the oxazole ring is predicted in the excited state explaining the solvatochromism of the compounds. The values for the singlet–triplet gap, 3500–5000 cm−1 point to an enhanced probability of intersystem crossing (ISC) non-radiative deactivation processes, in agreement with the low fluorescence quantum yields.

Absorption and emission properties of some phenoxy derivatives of diphenyloxazole (PPO) are presented and discussed. The photophysical properties reflect a dependence on the substituted 2 or 5 position of the oxazole ring. The experimental data were correlated with molecular parameters such as molecular flexibility, electronic structure and the singlet–triplet gap. The substitution with heteroatomic-bridged phenyls maintains the same frontier orbitals (m, m + 1) as in the parent compound, but introduces a new molecular orbital, m − 1, located on the terminal phenyl. The presence of the so-called band B in the absorption spectra of some diaryloxazoles was attributed to the m − 1 → m + 1 transition participating to the second excited state wave function. The other main component of this state, the m → m + 2 transition, was found to have a forbidden character, explaining the lack or the low intensity of band B. The decrease of the fluorescence quantum yield subsequent to substitution of PPO with phenoxy fragments was found to be due to the enhanced molecular flexibility comparing to PPO. The differences between the 2- or 5-substituted derivatives were rationalized in terms of a smaller S1–T2 gap for the former, thus increasing the rate of the overall nonradiative intersystem crossing processes.

For all Kekuléan perifusenes with 4, 5, and 6 benzenoid rings the partitions of π-electrons in each ring have been calculated. Trends in the partitions are discussed in connection with Clar's structures. Partition values are useful for discerning similarity/dissimilarity among benzenoids independently of visual overlapping of formulas and for comparing local features of benzenoids such as bay or cove regions.

We consider a graphical representation of proteins as an alternative to the usual representation of proteins as a sequence listing the natural amino acids. The approach is based on a graphical representation of triplets of DNA in which the interior of a square or the interior of a tetrahedron is used to accommodate 64 sites for the 64 codons. By associating a zigzag curve and various matrices with a protein, just as was the case with graphical representation of DNA, one can construct selected invariants to serve as protein descriptors. The approach is illustrated on the A-chain of human insulin.

After a brief history of the aromaticity concept, the use of Clar sextet circles is reviewed for explaining various aspects of planar aromatic systems (benzenoids, heterocycles) and of tridimensional carbon aggregates. When folding a graphene sheet for obtaining nanotubes, nanotori, or nanocones, the congruence of Clar sextet circles allows the classification of all such aggregates into two classes (congruent or incongruent) with marked differences in properties; this is in agreement with the well-known condition h − k ≡ 0 (mod 3), equivalent to congruence, in terms of the chiral vectors h and k for graphene sheets.