On the generalized approach to the structure count

A generalized approach to the structure count of n-radical-m-cation systems based on the properties of the acyclic polynomial is presented. The mathematical proof for the expression relating the structure count to the coefficients of the acyclic polynomial is given. The connection between the structure count of biradical structures and the number of Dewar structures is discussed and tested on some examples.     

Immanants and immanantal polynomials of chemical graphs

The much-studied determinant and characteristic polynomial and the less well-known permanent and permanental polynomial are special cases of a large class of objects, the immanants and immanantal polynomials. These have received some attention in the mathematical literature, but very little has appeared on their applications to chemical graphs. The present study focuses on these and also generalizes the acyclic or matching polynomial to an equally large class of acyclic immanantal polynomials, generalizes the Sachs theorem to immanantal polynomials, and sets forth relationships between the immanants and other graph properties, namely, Kekulé structure count, number of Hamiltonian cycles, Clar covering polynomial, and Hosoya sextet polynomial.     

A graphical evaluation of characteristic polynomials of huckel trees

Characteristic polynomials of acyclic carbon chains (Huckel trees) are treated in a systematic way. Formulas of coefficients (a_k) of the polynomial are obtained in terms of connectivities that were introduced for dealing with moments in a previous paper. Based on the meaning of a_k, a graph-theoretical analysis is given such that a_k can be expressed as a linear combination of binomial factors specified by a set of graphs containing ½k edges. The numerical relationship is disclosed between each binomial factor and its specified graph. This stimulates the proposal of a novel approach for evaluating ak by simply collecting the graph set of defnite edges. The approach is equally applicable for the evaluation of matching polynomials of cyclic systems and extendable to the investigation of general trees.     

Coulson function and Hosoya index: extension of the relationship to polycyclic graphs and to new types of matching polynomials

Gutman et al. [Chem. Phys. Lett. 355 (2002) 378–382] established a relationship between the Coulson function, , where \phi is the characteristic polynomial, and the Hosoya index Z, which is the sum over all k of the counts of all k-matchings. Like the original Coulson function, this relationship was postulated only for trees. The present study shows that the relationship can be extended to (poly)cyclic graphs by substituting the matching, or acyclic, polynomial for the characteristic polynomial. In addition, the relationship is extended to new types of matching polynomials that match cycles larger than edges (2-cyc1es). Finally, this presentation demonstrates a rigorous mathematical relationship between the graph adjacency matrices and the coefficients of these polynomials and describes computational algorithms for calculating them.     

Diastereoselective Synthesis of Open‐Chain Secondary Alkyllithium Compounds and Trapping Reactions with Electrophiles

A practical stereoselective iodide–lithium exchange was used in the first general preparation of functionalized stereodefined acyclic secondary nonstabilized lithium reagents from the corresponding secondary alkyl iodides. These lithium reagents react with various electrophiles including carbon electrophiles with high retention of configuration. Kinetic data on the configurational stability of these acyclic alkyllithium reagents are given. This methodology offers a new entry to chiral synthons for the stereoselective synthesis of open‐chain molecules.     

Exploration of the accessible chemical space of acyclic alkanes

Saturated acyclic alkanes show steric strain if they are highly branched and, in extreme cases, fall apart rapidly at room temperature. Consequently, attempts to count the number of isomeric forms for a given molecular formula that neglect this physical consideration will inevitably overestimate the size of the available chemical space. Here we derive iterative equations to enumerate the number of isomers (both structural and optical are considered separately) for the alkane series that take into account the inherent instability of certain carbon skeletons. These function by filtering out certain substructures from the graph representation of the molecule which have been found to be thermodynamically unstable. We use these relations to report new estimates of the size of physically accessible chemical space for acyclic alkanes and show that for large molecules there are more isomers that are structurally disallowed than there are allowed.     

The factorisation of chemical graphs and their polynomials: A systematic study of certain trees

Characteristic polynomials of the set of 284 trees which have 1 – 12 vertices of valency 1 – 3 have been examined for possible factors (divisors) using polynomial division. Twenty of these trees are prime in the sense that they contain no other trees in the set as factors. The remaining 264 trees can all be constructed from a subset of 5 trees and a at of 152 non-graphical polynomials. Some of these polynomials exhibit iso- or sub-spectral relationships with acyclic (matching) polynomials of certain cyclic structures. A few cyclic factors of trees are noted briefly. Twenty pairs and one triad of the trees examined are isospectral.     

Generalized Wheland polynomial for large graphs

We report the generalized Wheland polynomial for acyclic graphs depicting polyenes havingn = 10 carbon atoms. We consider the problem of deriving generalized Wheland polynomials for larger chains by recursion. The recursion Wh(n + l;x) =, Wh(n; x) + (1 –x)Wh(n – 1;x) allows one to find the next larger generalized Wheland polynomial for a chain having an even number of vertices by knowing generalized Wheland polynomials of chains having fewer vertices. The recursion, however, does not allow one to predict the generalized Wheland polynomial for a chain having an odd number of vertices from smaller chains! Here we report a procedure which allows one to derive the generalized Wheland polynomial for a chain having an odd number of vertices. This is achieved by combining the coefficients for rings having the same number of vertices. The generalized Wheland polynomials for odd rings are simply related to the generalized Wheland polynomials for smaller chains and can be derived from the information on smaller chains. This makes it possible to extend the recursion for generalized Wheland polynomials for arbitrarily largen.     

Characteristic polynomials of large graphs. On alternate form of characteristic polynomial [1]

A recursion exists between the absolute magnitudes of the coefficients of the characteristic polynomials of certain families of cyclic and acyclic graphs which makes their computation quite easy for very large graphs using a pencil-and-a-paper approach. Structural requirements are given for such families of graphs which are of interest to the problem of recognition defined in [1].     

The development for the synthesis of chiral acyclic nucleosides and their phosphonates

Acyclic nucleosides and their phosphonates possess significantly antiviral and cytostatic activities. For acyclic nucleosides and their phosphonates, the introduction of a chiral group to their side chain or the absolute configuration of the chiral atom could affect their biological activities obviously. Thus, the asymmetric synthesis of chiral acyclic nucleosides and their phosphonates has received continuous attention. The previous reports mainly focus on employing the chiral pool and chiral auxiliary methods for the synthesis of chiral acyclic nucleosides and their phosphonates. In contrast, the asymmetric catalysis methods for the synthesis of acyclic nucleosides and their phosphonates are still in the beginning. This digest paper will serve to highlight the significant progress that has been made in these areas.     

Graph theory of molecular orbitals beyond tight-binding approximation

The graph theory of molecular orbitals including second neighbor interactions (η) is considered here. Graphical methods of getting the characteristic polynomial for the π system of a conjugated molecule are given. It is shown that the characteristic polynomial can be factorized if there are symmetries in the molecule.     

无环鸟苷和鸟嘌呤的高效毛细管电泳测定

对无环鸟苷和鸟嘌呤的高效毛细管电泳分离测定条件进行了 详细研究，建立了以２－氨基－５－巯基－３，４－噻二唑为内标的快速、灵敏的ＨＰＣＥ定量分析方法。     

Recent applications of ring-closing metathesis in the synthesis of lactams and macrolactams

Lactams are an important class of compounds owing to their presence in numerous biologically active molecules of natural and unnatural nature. They are also highly versatile intermediates that can be elaborated into interesting compounds for potential use in organic and medicinal chemistry endeavors. In this feature article, the reader will be given a background to olefin metathesis followed by concise discussions (with selected examples) to report recent applications of ring-closing metathesis to form lactams and macrolactams from acyclic diene precursors, an area which continues to deposit attractive applications in the chemical literature en route or in the final step to the target molecules.     

Characterization of sixty alkenes in a cat-cracked gasoline naphtha by gas chromatography

Summary The alkene-rich petrol fraction from refinery fluid catalytic cracking (FCC) has been characterized by GC and GC-MS. Quantitative proportions and retention data of 52 acyclic and 11 cyclic C₅–C₇ alkenes are given. Relative retentions are reported for methylsilicone and aluminium oxide stationary phases as methylene units (MU). Applications of mass spectra, single-ion GC-MS monitoring and retention data for identifications are demonstrated.     

Stereocontrol at the steady state in radical cyclizations of acyclic dihalides

The first examples of manipulating stereocontrol solely by reaction topography in radical cyclizations starting from acyclic precursors are reported. The kinetic model for acyclic compound stereoselection is verified experimentally by conducting a series of radical cyclizations of 1,3-dihalo-2-(1-phenyl-3-butynyl)propanes with triphenyltin hydride and measuring the ratios of the products. Monohalide intermediates are observed for the first time, and evidence that bromide- and iodide-substituted radicals have different cyclization rate constants is provided.     

Opening of the ring of five-membered aromatic heterocycles under the influence of bases (review)

The review is devoted to a discussion of the various mechanisms of dehydration of five-membered aromatic heterocycles under the influence of bases; this reaction can be used in many cases for the synthesis of hard-to-obtain polyunsaturated acyclic compounds.Part of the material in this review was presented in a lecture given by S. Gronowitz at Moscow State University on May 31, 1976.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 4, pp. 435–451, April, 1978.     

Spin adaptation of antisymmetrized geminal product wave functions

A spin-free polynomial representation of antisymmetrized geminal products is presented for several cases. In particular, products of identical geminals, which possess different spin multiplicity, are considered. The cases of singlet geminals, singlet geminals with one or two triplet geminals coupled to the lowest possible spin multiplet, and triplet geminals coupled to an arbitrary multiplet are considered in detail, and explicit polynomial representation is given.     

Acyclic tautomers in crystalline carbohydrates: the keto forms of 1-deoxy-1-carboxymethylamino-D-2-pentuloses (pentulose-glycines)

NMR and X-ray diffraction studies on acyclic carbohydrate keto tautomers of N-(1-deoxy-d-erythro-2-pentulos-1-yl)- and N-(1-deoxy-d-threo-2-pentulos-1-yl)glycines (ribulose-glycine, 1 and xylulose-glycine, 2), are reported. In aqueous solutions, both 1 and 2 exist as a tautomeric mixture, with the beta-furanose as a major form, followed by the alpha-furanose and the acyclic keto tautomer. Both 1 and 2 crystallize as zwitterions in the acyclic keto form. Solid-state 13C NMR spectra reveal the existence of two crystallographically independent molecules in 2 but only one in crystalline 1. The structure of 2 was solved by X-ray diffraction; in the crystal, two conformational isomers, 2a and 2b in a 1:1 ratio, were identified. The conformers are packed in stacks of similar molecules, with a system of intermolecular hydrogen bonds involving all hydroxyl, ammonium, and carboxyl groups. The structural data indicate that the sugar portion of acyclic 2 adopts conformations similar to those proposed for the parent d-xylulose.     

Fluorescent cyclodextrins as chemosensors for the detection of cyclic and acyclic alcohols

Molecular sensing abilities and selectivities of a “turn-on” chemosensor, NBDamine-appended α-cyclodextrin (NC0αCD), were studied for cyclic alcohols and acyclic alcohols. This chemosensor is more sensitive to cyclic alcohols than acyclic alcohols, although its binding affinity is stronger for acyclic alcohols than cyclic alcohols.