Hamiltonian circuits,Hamiltonian paths and branching graphs of benzenoid systems

A benzenoid systemH is a finite connected subgraph of the infinite hexagonal lattice with out cut bonds and non-hexagonal interior faces. The branching graphG ofH consists of all vertices ofH of degree 3 and bonds among them. In this paper, the following results are obtained:

1. A necessary condition for a benzenoid system to have a Hamiltonian circuit.
2. A necessary and sufficient condition for a benzenoid system to have a Hamiltonian path.
3. A characterization of connected subgraphs of the infinite hexagonal lattice which are branching graphs of benzenoid systems.
4. A proof that if a disconnected subgraph G of the infinite hexagonal lattice given along with the positions of its vertices is the branching graph of a benzenoid system H, then H is unique.

     

Dynamics of the photoinduced desorption of nitric oxide molecules from the surface of pure and modified platinum

The distribution of NO molecules desorbed from a Pt(111) surface due to valence electron excitation over rotational energy levels N(J) is analyzed using a simple impulse-induced model. A linear dependence is found between lnN(J) and (E_r)^1/2, where E_r is the rotational energy of the desorbed molecules. The lifetime of the excited state and the critical time of residence in the excited state estimated using this dependence are found to be close to one another (~10^?15 s). The frequency and amplitude of the tilting vibrations of the adsorbed molecules in the excited state are estimated.     

A Quantum Chemical Study of C<Subscript>60</Subscript>Cl<Subscript>30</Subscript>, C<Subscript>60</Subscript>(OH)<Subscript>30</Subscript> Molecules and Fe@C<Subscript>60</Subscript>(OH)<Subscript>30</Subscript> Endocomplex

(U)PBE0/cc-pVDZ method is used to study the structure of C₆₀Cl₃₀, C₆₀(OH)₃₀ molecules and Fe@C₆₀(OH)₃₀ endocomplex. The triplet state of the endocomplex is shown to be the lowest in energy among its four states corresponding to different spin multiplicities and positions of Fe nucleus within the fullerene cavity. This state is characterized by bonding between the iron atom and one of two benzenoid cycles of the carbon cage, six internuclear Fe–C distances (208 pm), and 1s²2s²2p⁶3s²3p⁶3d^7.24s^0.14p^0.3 electron configuration of iron with spin population of 2.36.     

A mechanophysical phase transition provides a dramatic example of colour polymorphism: the tribochromism of a substituted tri(methylene)tetrahydrofuran-2-one

Background

Derivatives of fulgides have been shown to have interesting photochromic properties. We have synthesised a number of such derivatives and have found, in some cases, that crystals can be made to change colour on crushing, a phenomenon we have termed “tribochromism”. We have studied a number of derivatives by X-ray crystallography, to see if the colour is linked to molecular structure or crystal packing, or both, and our structural results have been supported by calculation of molecular and lattice energies.

Results

A number of 5-dicyanomethylene-4-diphenylmethylene-3-disubstitutedmethylene-tetrahydrofuran-2-one compounds have been prepared and structurally characterised. The compounds are obtained as yellow or dark red crystals, or, in one case, both. In two cases where yellow crystals were obtained, we found that crushing the crystals gave a deep red powder. Structure determinations, including those of the one compound which gave both coloured forms, depending on crystallisation conditions, showed that the yellow crystals contained molecules in which the structure comprised a folded conformation at the diphenylmethylene site, whilst the red crystals contained molecules in a twisted conformation at this site. Lattice energy and molecular conformation energies were calculated for all molecules, and showed that the conformational energy of the molecule in structure IIIa (yellow) is marginally higher, and the conformation thus less stable, than that of the molecule in structure IIIb (red). However, the van der Waals energy for crystal structure IIIa, is slightly stronger than that of structure IIIb – which may be viewed as a hint of a metastable packing preference for IIIa, overcome by the contribution of a more stabilising Coulomb energy to the overall more favourable lattice energy of structure IIIb.

Conclusions

Our studies have shown that the crystal colour is correlated with one of two molecular conformations which are different in energy, but that the less stable conformation can be stabilised by its host crystal lattice.

Open image in new window

Graphical abstract Graphical representation of the structural and colour change in the tribochromic compound (III).

     

Inelastic deformation of glassy polyaryleneetherketone: Energy accumulation and deformation mechanism

The plastic deformation of glassy non-annealed polyaryleneetherketone (PAEK) was investigated via deformation calorimetry and thermally stimulated recovery of residual strain. Polymer samples were deformed at room temperature under uniaxial compression up to ε_def =–(40?50)% at a rate of 0.04 min^?1. It was found that PAEK behaves in the deformation process similarly to many other glassy polymers: It stores internal energy excess at loading and contains two types of different inelastic strain carriers, namely the delayed elastic (ε_de) and plastic (ε_pl) strain carriers. The maximum level of the accumulated energy in PAEK reaches ≈ 8.3 J/g, which is close to those for glassy polystyrene and polycarbonate. Nearly all the deformation energy stored in PAEK is carried by the delayed-elastic strain. The carriers of plastic strain carry no extra energy or a very small amount of it. The inelastic deformation of glassy PAEK proceeds in two stages. The carriers of ε_de are nucleated at the first stage of the deformation process, and the carriers of ε_pl are nucleated at the second stage. It was shown that, during glassy-polymer loading, the molecular level structures carrying ε_pl never appear by themselves, but appear only as a result of spontaneous reorganization of ε_de. In other words, the plastic deformation appears in PAEK owing to the two-step process. This situation is typical for all glassy polymers.     

Analyzing the efficiency of proton transfer to carbon in Kirby’s enzyme model—a computational approach

A mechanistic study using ab initio and DFT calculation methods on the intramolecular ring-closing of enol ethers 1Z, 1E, and 2 (Kirby’s enzyme models for aldolase and isomerase) has revealed that proton transfer is the rate determining step and involves two stages: re-organization of the global minimum structure (having the lowest enthalpic energy and a relatively long distance between the two reactive centers, r) to a more organized ground state conformation (having the smallest r distance among all the conformations), and a second stage by which the proton is transferred from the organized state to the corresponding transition state. The energy needed for the first stage to occur is dependent on the rotation barrier for the proton to be in proximity to the CC double bond carbon (proximity effects), whereas, that needed for the second step is largely affected by the strain energies of the reactant and the corresponding product. In addition, it was found that the oxocarbocation intermediate involved in the proton transfer is unstable and undergoes ring-closing to the corresponding product with zero activation energy. Further, the calculated DFT effective molarities (EM) for 1Z, 1E, and 2 were found to correlate strongly with experimental EM values.     

Linkage position influences of anthracene and tricyanovinyl groups on the opto-electrical and photovoltaic properties of anthracene-based organic small molecules

Anthracene-based small molecules incorporating an electron accepting tricyanovinyl (TCV) group was prepared to investigate the linkage position influences of the anthracene and TCV groups on the opto-electrical and photovoltaic properties of the molecules. The maximum absorptions of the anthracene-based molecules incorporating the TCV group at the phenyl group of the triphenylamine unit (TCV-TpaA_9,10T, TCV-TpaTA_9,10T, and TCV-TpaA_2,6T) or at the thiophene unit (TpaA_9,10T-TCV, TpaTA_9,10T-TCV, and TpaA_2,6T-TCV) were found to be dependent on the linkage position of the anthracene unit. The HOMO energy levels of the molecules containing TCV group at the phenyl group of the triphenylamine unit were deeper than those of the molecules containing TCV group at the thiophene unit. The solution processed small molecule organic solar cells (SMOSCs) prepared with the structure of ITO/PEDOT:PSS/TCV-TpaA_9,10T or TCV-TpaA_2,6T or TpaA_2,6T-TCV:PC₇₁BM (2:1 wt %)/LiF/Al exhibited a maximum energy conversion efficiency of 1.04%, 1.67%, and 1.95%, respectively, under AM 1.5 irradiation (100 mW cm⁻²).     

Tensile yield of isotactic polypropylene in terms of a lamellar‐cluster model

In this study, the structural factors controlling the yield in isotactic polypropylene materials were theoretically investigated. To describe the yielding behavior of spherulitic polypropylenes, we introduced a new structural unit, lamellar clusters, which are several stacked lamellae bound by tie molecules. It was shown that tie molecules between adjacent lamellar clusters produce a concentrated load acting on the cluster surface, leading to the bending deformation of the lamellar clusters. The yielding behavior can be explained if one assumes that the disintegration of the lamellar clusters occurs when the elastic‐strain energy stored by the bending deformation reaches a critical value. By applying the fracture theory of composites to a system consisting of lamellar clusters and tie molecules, we found the yield stress σ_y to be proportional to , in which E_Y is the Young's modulus and U_y is the yield energy. The proportional coefficient between σ_y and depends only on the cluster size and tie‐molecule density, so this proportionality is expected to be true for other spherulitic semicrystalline polymers such as polyethylenes, being independent of temperature and tensile rate. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 1037–1044, 2000     

Monoethanolamine: Cluster Structure Motives

Structures and energy characteristics of clusters composed of monoethanolamine molecules are analyzed using the results of quantum chemical calculations carried out at the density functional level (DFT-B3LYP/6-31G(d,p)) and in the second order of the Møller—Plesset perturbation theory (MP2/6-31G(d, p)). Similar structural motives of hydrogen-bond networks are found in clusters that correspond to the gas-phase aggregation of initially independent molecules and the detachment of thermally distorted crystal lattice fragments. The energies of different hydrogen bonds are compared, and structural motives atypical of crystalline monoethanolamine are found. The studied clusters are shown to be prototypes of the inherent structural fragments of liquid monoethanolamine.     

Synthesis,Spectroscopic and Computational Studies of CT Complexes of Amino Acids with Iodine as σ Acceptor

Understanding the charge transfer process between bioactive molecules and inorganic or organic molecules is significant as this interaction can be used to interpret bioactive molecule–receptor interactions. A comprehensive spectrophotometric study has been performed to explore the complexation chemistry of the amino acids, tyrosine, lysine and arginine, with iodine as σ acceptor. The molecular structure, spectroscopic characteristics and the interactive modes have been deduced from UV–Vis and IR spectra. The binding ratio of complexation has been determined to be 1:1 for iodine with the amino acids. The association constant (K), extinction coefficient (ε _max), ionization potential (IP), energy of the charge transfer complex (E _CT), resonance energy (R _N ), dissociation energy (W) and standard Gibbs energy (ΔG°) have been computed. An in silico study has been carried out using GAMESS computations to understand the structural features. Highest occupied molecular orbital and lowest unoccupied molecular orbital calculations helped us in characterizing the chemical reactivity and kinetic stability of the molecules. A good consistency between experimental and computational results has been found.     

Kekuléan benzenoids

A Kekulé structure for a benzenoid or a fullerene $\Gamma $ is a set of edges $K$ such that each vertex of $\Gamma $ is incident with exactly one edge in $K$ , i.e. a perfect matching. All fullerenes admit a Kekulé structure; however, this is not true for benzenoids. In this paper, we develop methods for deciding whether or not a given benzenoid admits a Kekulé structure by constructing Kekulé structures that have a high density of benzene rings. The benzene rings of the Kekulé structure $K$ are the faces in $\Gamma $ that have exactly three edges in $K$ . The Fries number of $\Gamma $ is the maximum number of benzene rings over all possible Kekulé structures for $\Gamma $ and the set of benzene rings giving the Fries number is called a Fries set. The Clar number is the maximum number of independent benzene rings over all possible Kekulé structures for $\Gamma $ and the set of benzene rings giving the Clar number is called a Clar set. Our method of constructing Kekulé structures for benzenoids generally gives good estimates for the Clar and Fries numbers, often the exact values.     

A new theoretical approach to the empirical resonance energies of the aromatic hydrocarbons

In the framework of the Hückel MO approximation, the differences in total binding energy between a given molecule and the corresponding distorted Kekulé-type structure are calculated for a variety of benzenoid hydrocarbons. The total binding energy is assumed to be given by the sum of the -electron and -electron binding energies. It is shown that there is a good linear relationship between the calculated differences in total binding energy and the -electron delocalization energies (DE) as obtained by using the simple Hückel MO method. This provides a physical basis for the use of the -electron DE as a theoretical index to the empirical resonance energy (RE). Further, by examining the changes in -electron binding energy between a given molecule and the corresponding distorted Kekulé-type structure, it is concluded that in benzenoid hydrocarbons the main contributor to the RE is not the -electron DE but the compressional energy of bonds.     

On the Distribution of π-Electrons into Rings of Conjugated Hydrocarbons Containing a Linear Polyacene Fragment

Summary. A method for assessing the -electron contents (EC) of rings of benzenoid hydrocarbons, based on the examination of their Kekulé structures, was recently put forward by Balaban and Randi. We now show that all hexagons belonging to a linear polyacene fragment of a conjugated hydrocarbon (not necessarily benzenoid) have mutually equal EC-values.     

On the Distribution of π-Electrons into Rings of Conjugated Hydrocarbons Containing a Linear Polyacene Fragment

A method for assessing the -electron contents (EC) of rings of benzenoid hydrocarbons, based on the examination of their Kekulé structures, was recently put forward by Balaban and Randi. We now show that all hexagons belonging to a linear polyacene fragment of a conjugated hydrocarbon (not necessarily benzenoid) have mutually equal EC-values.     

Equivalence of the deformed Rosen–Morse potential energy model and Tietz potential energy model

By applying the dissociation energy and the equilibrium bond length for a diatomic molecule as explicit parameters, we generate an improved expression for the deformed Rosen–Morse potential energy model. It is found that the deformed Rosen–Morse potential model and the well-known Tietz potential model are the same empirical potential function for diatomic molecules. With the help of the energy spectrum expression of the deformed Rosen–Morse potential model, we obtain exact closed-form expressions of diatomic anharmonicity constants $\omega _e x_e $ ω e x e and $\omega _e y_e $ ω e y e .     

Phasenumwandlungserscheinungen in Lecithin/Wasser-Systemen

1. By means of differential-scanning-calorimetry the phase transition temperatures and -enthalpies were determined and evaluated for the three following lecithin/water systems: 1,2-dimyristoyl-lecithin/water; 1,2-dipalmitoyl-lecithin/water; 1,2-distearoyllecithin/water.
2. The preparation of the lecithin/water mixtures was made by adsorption of water from the gaseous phase. The adsorption isotherms were evaluated by the BET equation.
3. Four phase transitions were found for the monohydrates of the lecithins. The parameters depend systematically on the length of the alkyl residues.
4. In the heterogeneous two phase region the main-transition and the pre-transition occurred. The thermodynamical parameters of both transitions depend on the alkyl chain length.
5. Whole the results refer to the conclusion that the lecithin head group hydration is a stepwise process. The hydration of the first shell is finished if 5 to 6 molecules water per molecule lecithin are present, while the second hydration shell is complete when about 13 water molecules are adsorbed

     

Characteristics of the hydrogen bond and the structure of Н-complexes of <Emphasis Type="Italic">p</Emphasis>-n-propyloxybenzoic acid and <Emphasis Type="Italic">p</Emphasis>-n-propyloxy-<Emphasis Type="Italic">p</Emphasis>′-cyanobiphenyl

The conformational properties of p-n-propyloxybenzoic acid and p-n-propyloxy-p′-cyanobiphenyl molecules, which can exhibit liquid crystalline properties in the formation of Н-complexes, are studied (DFT/B3LYP)/cc-pVTZ method). It is found that a molecule of p-n-propyloxybenzoic acid has 16 conformers that can be divided into four groups with respect to relative energies (0 kcal/mol, 1.6 kcal/mol, 6.5 kcal/mol, and 8.1 kcal/mol), and a molecule of p-n-propyloxy-p′-cyanobiphenyl has six conformers with relative energies of 0 kcal/mol (two conformers, φ(С_Ph–O–C–C)=180°) and 1.6 kcal/mol (four conformers, φ(С_Ph–O–C–C)=64.4°). In all conformers of the 3-AOCB molecule, phenyl rings are turned at 35° relative to each other. A conformation with the planar arrangement of two rings has a higher energy by 1.5 kcal/mol. Barriers to the internal rotation of different groups are determined and it is established that the structural nonrigidity of the molecules is mainly due to the possible rotation of the–C₂Н₅ moiety about the C–C bond. It is shown that with increasing temperature the vibrational amplitudes of the OC₃H₇ substituent, which enhance the probabilities of transitions between the conformers, become appreciably larger. It is found that p-n-propyloxybenzoic acid and p-n-propyloxy-p′-cyanobiphenyl can form Н-complexes with the medium hydrogen bond. Two types of the structural organization of Н-complexes are considered: linear and angular. The similarity of energies of Н-complexes with different structures (NBO analysis) can be the reason for the occurrence of two liquid crystalline subphases of p-n-propyloxybenzoic acid and p-n-propyloxy-p′-cyanobiphenyl system.     

Enhancing the Production of <Emphasis Type="SmallCaps">d</Emphasis>-Mannitol by an Artificial Mutant of <Emphasis Type="Italic">Penicillium</Emphasis> sp. T2-M10

d-Mannitol belongs to a linear polyol with six-carbon and has indispensable usage in medicine and industry. In order to obtain more efficient d-mannitol producer, this study has screened out a stable mutant Penicillium sp. T2-M10 that was isolated from the initial d-mannitol-produced strain Penicillium sp.T2-8 via UV irradiation as well as nitrosoguanidine (NTG) induction. The mutant had a considerable enhancement in yield of d-mannitol based on optimizing fermentation. The production condition was optimized as the PDB medium with 24 g/L glucose for 9 days. The results showed that the production of d-mannitol from the mutant strain T2-M10 increased 125% in contrast with the parental strain. Meanwhile, the fact that d-mannitol is the main product in the mutant simplified the process of purification. Our finding revealed the potential value of the mutant strain Penicillium sp. T2-M10 to be a d-mannitol-producing strain.     

Extended solvent-contact model approach to blind SAMPL5 prediction challenge for the distribution coefficients of drug-like molecules

The performance of the extended solvent-contact model has been addressed in the SAMPL5 blind prediction challenge for distribution coefficient (LogD) of drug-like molecules with respect to the cyclohexane/water partitioning system. All the atomic parameters defined for 41 atom types in the solvation free energy function were optimized by operating a standard genetic algorithm with respect to water and cyclohexane solvents. In the parameterizations for cyclohexane, the experimental solvation free energy (ΔG _sol ) data of 15 molecules for 1-octanol were combined with those of 77 molecules for cyclohexane to construct a training set because ΔG _sol values of the former were unavailable for cyclohexane in publicly accessible databases. Using this hybrid training set, we established the LogD prediction model with the correlation coefficient (R), average error (AE), and root mean square error (RMSE) of 0.55, 1.53, and 3.03, respectively, for the comparison of experimental and computational results for 53 SAMPL5 molecules. The modest accuracy in LogD prediction could be attributed to the incomplete optimization of atomic solvation parameters for cyclohexane. With respect to 31 SAMPL5 molecules containing the atom types for which experimental reference data for ΔG _sol were available for both water and cyclohexane, the accuracy in LogD prediction increased remarkably with the R, AE, and RMSE values of 0.82, 0.89, and 1.60, respectively. This significant enhancement in performance stemmed from the better optimization of atomic solvation parameters by limiting the element of training set to the molecules with experimental ΔG _sol data for cyclohexane. Due to the simplicity in model building and to low computational cost for parameterizations, the extended solvent-contact model is anticipated to serve as a valuable computational tool for LogD prediction upon the enrichment of experimental ΔG _sol data for organic solvents.     

Density functional theory studies of conformational stabilities and rotational barriers of 2- and 3-thiophenecarboxaldehydes

The molecular structures, conformational stabilities, and infrared vibrational wavenumbers of 2-thiophenecarboxaldehyde and 3-thiophenecarboxaldehyde are computed using Becke-3–Lee–Yang–Parr (B3LYP) with the 6-311++G** basis set. From the computations, cis-2-thiophenecarboxaldehyde is found to be more stable than the transfer conformer with an energy difference of 1.22 kcal/mol, while trans-3-thiophenecarboxaldehyde is found to be more stable than the cis conformer by 0.89 kcal/mol. The computed dipole moments, structural parameters, relative stabilities of the conformers and infrared vibrational wavenumbers of the two molecules coherently support the experimental data in the literature. The normal vibrational wavenumbers are characterized in terms of the potential energy distribution using the VEDA4 program. The effect of solvents on the conformational stability of the molecules in nine different solvents is investigated using the polarizable continuum model.