Flag graphs and their applications in mathematical chemistry for benzenoids

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.     

Analytical solution of non-linear enzyme reaction equations arising in mathematical chemistry

The boundary value problem in basic enzyme reactions is formulated and approximate expressions for substrate and substrate-enzyme complex are presented. He’s Homotopy Perturbation method is used to give approximate and analytical solutions of non-linear reaction equations containing a non-linear term related to enzymatic reaction. The pertinent analytical solutions for the substrate, enzyme- substrate complex and free enzyme are discussed in terms of dimensionless parameters σ, ρ and e{\varepsilon} . The obtained concentration results are compared with the numerical solution acquired using Matlab program. They are found to be in satisfactory agreement.     

Scalar nonlinearities in physics and chemistry

Scalar nonlinearities are operators of the form N(u) = 〈Au, u〉Bu, where A, B are linear operators, and 〈·,·〉 is the inner product in a Hilbert space ??. This paper reviews applications of scalar nonlinearities. We show that operators of the form N(u) are found in equations that describe phenomena of classical mechanics, open systems of quantum mechanics, and chemical physics.     

Linking chemistry with physics: arguments and counterarguments

The many-faced relationship between chemistry and physics is one of the most discussed topics in the philosophy of chemistry. In his recent book Reducing Chemistry to Physics. Limits, Models, Consequences, Hinne Hettema (Reducing chemistry to physics. Limits, models, consequences, Rijksuniversiteit Groningen, Groningen, 2012) conceives this relationship as a reduction link, and devotes his work to defend this position on the basis of a “naturalized” concept of reduction. In the present paper I critically review three kinds of issues stemming from Hettema’s argumentation: philosophical, scientific and methodological.     

Theoretical studies in the chemistry and physics of heterocycles

LCAO-SCF calculations with four different sets of parameters are given for the -electron structure of pyrrole. The aim was mainly to discuss whether such a kind of calculations could account for the molecular properties, or the system ought to be explicitly included. The effects of different values for the integrals were discussed by comparing final results, concerning both the ground state and the excited states. A good agreement with experimental data was obtained. The usual limited configuration mixing on our SCF results, leading to a poor agreement for the energies as well as to a lack of qualitative sequence of intensities, does not allow a clear interpretation of the U.V. spectrum.

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Zusammenfassung Einige LCAO-SCF-Rechnungen werden für Pyrrol mit verschiedenen ParametersÄtzen durchgeführt, um zu klÄren, ob die Betrachtung der -Elektronen allein eine befriedigende Beschreibung der molekularen Eigenschaften erlaubt oder auch die -Elektronen explizit betrachtet werden müssen. Der Einflu\ verschiedener Integralwerte auf die Endergebnisse wird für den Grundzustand und die angeregten ZustÄnde diskutiert. Die übereinstimmung mit den experimentellen Ergebnissen ist gut. Die gewöhnliche begrenzte Konfigurationswechsel-wirkung gibt keine klare Interpretation der UV-Banden, weil für die berechneten Energien und IntensitÄten die übereinstimmung mit den experimentellen Werten nicht so gut ist.

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Résumé La méthode LCAO-SCF-MO est appliquée a l'étude de la structure électronique du pyrrole en utilisant quatre séries différentes de parametres. On discute en quelle mesure cette sorte de calculs peut expliquer les propriétés moleculaires, ou bien s'il faut tenir compte du systeme . Notre attention est particulierement dévouée à l'effect du choix de différentes valeurs des intégrales sur les résultats des calculs, à l'égard des propriétés soit de l'état fondamental comme des états excités. On obtient un très bon accord avec les données expérimentales. On conclue enfin qu'une intéraction de configuration limitée ne porte pas à une interpretation sûre du spectre U.V., ni pour les énergies d'excitation ni pour la séquence des intensités.

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We should like to thank Prof. G. del Re — Istituto di Fisica Teorica, Universitá di Napoli — for advice and discussions.This work was supported by a fund. of Consiglio nazionale delle Ricerche — Roma.     

Nested wreath groups and their applications to phylogeny in biology and Cayley trees in chemistry and physics

Nested wreath product groups arise from looped or recursive structures that contain repeated copies of the same structure one within the other. Phylogeny trees in biology, Cayley trees, Bethe lattices, NMR graphs of non-rigid molecules, ammoniated ammonium ions are all examples of structures that exhibit such nested wreath product automorphism groups. We show that the conjugacy classes, irreducible representations and character tables of these nested group structures can be generated using multinomial generating functions cast in terms of matrix types that can be simplified into generalized cycle type polynomials. The nested wreath product groups rapidly increase in orders, for example, a simple wreath product group \(\hbox {S}_{7}[\hbox {S}_{7}]\) consists of \((7!)^{8}\) or \(4.1633\times 10^{23}\) operations, 481,890 conjugacy classes, spanning a 481,891 \(\times \) 481,891 character table that would occupy 232,217,972 pages. We have obtained powerful recursive relations for the conjugacy classes, character tables and the orders of various conjugacy cases of any nested wreath product \(\{[\hbox {S}_{\mathrm{n}}]\}^{\mathrm{m}}\) or \(\hbox {S}_{\mathrm{n}}[\hbox {S}_{\mathrm{n}}[\hbox {S}_{\mathrm{n}}{\ldots }.[\hbox {S}_{\mathrm{n}}]]{\ldots }.]\) with order \(\left( {n!}\right) ^{a_m},\,\hbox {a}_{\mathrm{m}}=(\hbox {n}^{\mathrm{m}}-1)/(\hbox {n}-1)\). We have obtained the character tables of phylogenetic trees of any order, character tables of Cayley trees of degrees 3 and 4 and for Cayley trees of larger degrees, we have derived exact analytical expressions for the conjugacy classes and IRs for up to \(\{[\hbox {S}_{7}]\}^{\mathrm{m}}\) with order \((7!)^{137257}\) for \(\hbox {m}=7\). Applications to colorings of phylogenic trees in biology are considered.     

Mesoporous hybrid thin films: the physics and chemistry beneath

Mesoporous films containing organic or biological functions within an organised array of cavities are produced by combining sol-gel, self-assembly of supramolecular templates and surface chemistry. This paper reviews the essential physics and chemical concepts behind the synthesis of these complex multifunctional materials.     

Applications of caterpillar trees in chemistry and physics

The relations of caterpillar trees (which are also known as Gutman trees and benzenoid trees) to other mathematical objects such as polyhex graphs, Clar graphs, king polyominos, rook boards and Young diagrams are discussed. Potential uses of such trees in data reduction, computational graph theory, and in the ordering of graphs are considered. Combinatorial and physical properties of benzenoid hydrocarbons can be studied via related caterpillars. It thus becomes possible to study the properties of large graphs such as benzenoid (i.e. polyhex) graphs in terms of much smaller tree graphs. Generation of the cyclic structures of wreath and generalized wreath product groups through the use of caterpillar trees is illustrated.     

Highlights in chemistry and physics of polymer stabilization

Deactivation of free radicals, hydroperoxides and harmful solar radiation are the principal mechanisms increasing stability of commodity and engineering polymers. The stabilization process is accompanied by transformations of individual additives. New compounds influence specifically the integral protecting mechanism. Products contributing to the stability are most beneficial. Mechanistic data are used for optimisation of the inherent chemical efficiency and physical persistence and for explanation of deactivation of stabilizers.     

Concepts of convergence in mathematical chemistry

Some concepts of convergence used in mathematical chemistry are briefly reviewed: number convergence, uniform and non-uniform function convergence, convergence in norm and binary product, operator convergence, computer convergence, etc. Some properties of the abstract Hilbert space and some of its realizations in mathematical chemistry are discussed. Finally, it is pointed out that the scattering wave functions of importance in the theory of chemical reactions are limit points of theL ²Hilbert space — not in the norm, but in the sense of a non-uniform point-by-point convergence, which is of essential value in practical applications.     

The chemistry and physics of molecular surfaces

Configuration interaction calculations are carried out to study the potential energy surface for the system Ar-Ar ₂ ⁺ . An all-electron as well as a pseudopotential treatment is employed. It is found that in the perpendicular Ar approach the Ar ₂ ⁺ partner remains essentially unchanged and the potential can be characterized by an electrostatic ion-induced dipole interaction. In the collinear mode of Ar approach the Ar ₂ ⁺ bond separation increases considerably, the charge is redistributed and the interaction can be characterized as chemical bonding. The minimum on the surface is found to be the linear symmetric molecule with bond lengths of 2.62 Å. The optimum structure in the perpendicular approach lies 0.13 eV above the minimum and is the T-shaped molecule in which the Ar is 3.65 Å away from the midpoint of the Ar ₂ ⁺ (r=2.46 Å) system; the best equilateral triangle structure has a bond length of 2.99 Å but is found to lie 0.64 eV above the Ar ₃ ⁺ minimum. The dissociation energy into Ar ₂ ⁺ + Ar is calculated to be 0.16 eV in reasonable agreement with experimental values of 0.21 eV. The potential curves for the four lowest states of Ar ₂ ⁺ are also treated.     

The physics and chemistry of solar cells

The physics of the photovoltaic effect is analyzed using the example of a frontwall solar cell. The effect results from the interplay of the emitter, in which minority cariers are generated via absorbed light an diffuse to the junction, and the junction, in which the essential voltage drop occurs. The interplay is established by the minority carrier density at the emitter-junction interface, acting as prominent boundary condition, and connecting current through the device with applied voltage.The chemistry of the interlayer between emitter and junction has essential influence on this boundary condition by determining interface recombination and space charge. Both of these determine band connection and performance of the device.A brief review of material properties in the light of the basic cell operation is given.