三梯级和四梯级圆筒和Mbius分子的拓扑特性研究

Walba等以其卓越的工作,合成了三-THYME(C_(42)H_(72)O_(18))和四-THYME(C_(56)H_(96)O_(24))圆筒及其Mbius扭曲环带分子,被誉为拓扑学进入有机化学领域的奇迹,成为迄今为止拓扑立体化学研究的重要内容,但从拓扑学的观点探索分子图拓扑结构特性尚缺乏深入研究,本文作者考虑到一般性,曾将扭曲数T为偶数(0,2,4)的定义为Hckel型,扭曲数     

Effects of complex formation on vibrational circular dichroism spectra

The determination of absolute configurations of chiral compounds using VCD is performed by comparing measured vibrational circular dichroism (VCD) spectra with calculated spectra. The process is based on two facts: the two enantiomers have rotational strengths of opposite sign, and the absolute configuration of the molecule used in the calculation is known. However, calculations on isolated molecules very often predict VCD intensities of very different magnitude or even different signs compared to the spectra measured in solution. Therefore, we have carefully analyzed what type of changes are induced by complexation of a solvent molecule to a solute. In the theoretical example of benzoyl-benzoic acid (in a particular chiral conformation) hydrogen bonded to the achiral NH3, we distinguish six cases, ranging from no or very small changes in the rotational strengths of solute modes (case A) to changes of sign of rotational strengths (case B), changes in magnitude (case C), nonzero rotational strengths for modes of the achiral solvent ("transfer of chirality", case D), large frequency shifts accompanied by giant enhancements of the IR and VCD intensities of modes involved in hydrogen bonding (case E), and emergence of new peaks (case F). In this work, all of these situations will be discussed and their origin will be elucidated. On the basis of our analysis, we advocate that codes for VCD rotational strength calculation should output for each mode i the angle xi(i) between the electric and magnetic transition dipole moments because only "robust modes" with xi far from 90 degrees should be used for the determination of the absolute configuration.     

Enumerating the total colorings of a polyhedron and application to polyhedral links

In this paper we consider the enumeration problem of a particular three-dimensional molecular or chemical compound system which has a polyhedral frame where the vertices, edges and faces represent ‘units’ such as atoms, bonds, ligands, polymers, or other objects of chemical interests. In this system, chirality is also taken into account. This enumeration problem is mathematically modeled as the ‘total coloring’ enumeration problem of a polyhedron: i.e., the number of ways to color all the vertices, edges and faces of the polyhedron by using three or more corresponding color sets, in which some colors may be chiral. We establish a general formula for this enumeration problem by extending the fundamental version of Pólya’s enumeration theorem. In particular, we apply this technique to the enumeration problem of polyhedral links which have received special attention from biochemists, mathematical chemists and mathematicians over the past two decades.     

The architecture of polyhedral links and their HOMFLY polynomials

A general approach is proposed to elucidate the topological characteristics of molecules with the shape of polyhedral links. For an arbitrary polyhedral graph, four classes of polyhedral links can be obtained by applying the operation of ‘X-tangle covering’ to the related reduced sets. The relationships between the W-polynomial of a polyhedral graph and the HOMFLY polynomial of each kind of polyhedral links are established. These relationships not only simplify the computation but also provide a method of constructing a general formula for the HOMFLY polynomial of polyhedral links.     

Information theoretical study of chirality: enantiomers with one and two asymmetric centra

In this work, the Kullback-Leibler information deficiency is probed as a chirality measure. It is argued that the information deficiency, calculated using the shape functions of the R and S enantiomers, considering one as reference for the other, gives an information theory based expression useful for quantifying chirality. The measure is evaluated for five chiral halomethanes possessing one asymmetric carbon atom with hydrogen, fluorine, chlorine, bromine, and iodine as substituents. To demonstrate the general applicability, a study of two halogen-substituted ethanes possessing two asymmetric carbon atoms has been included as well. The basic expression of the sum of the local information deficiency over all atoms can be decomposed into separate summations over coinciding and noncoinciding atoms, or into a global and a mixing entropy term, or into a local entropy contribution for each atom individually based on the Hirshfeld partitioning. Avnir's continuous chirality measure (CCM) has been computed and confronted with the information deficiency. Finally, the relationship between chirality and optical rotation is used to study the proposed measure. The results illustrate Mezey's holographic electron density theorem with an intuitively appealing division of the strength of propagation of the atomic chirality from an asymmetric carbon atom throughout the molecule. The local information deficiency of the carbon atom is proposed as a measure of chirality; more precisely, the difference in information between the R and the S enantiomer turns out to be a quantitative measure of the chirality of the system. It may be evaluated as the arithmetic mean of the different alignments, or considering only the alignment resulting in the highest similarity value, or using the QSSA alignment.     

Topological analysis of some special graphs. III. Regular polyhedra

A regular polyhedron is isomorphic to a cluster on which every face has same number of bonds and every atom has an equal number of coordinating atoms. A general strategy for generating the eigenvectors and the eigenvalues of regular polyhedra is given. Net sign analyses are also performed on the eigenvectors of regular polyhedra. The results provide us a quick way to grasp the topological feature of the electronic structure of clusters having interesting topology.     

Topological analysis of some special graphs: III. Regular polyhedra

A regular polyhedron is isomorphic to a cluster on which every face has same number of bonds and every atom has an equal number of coordinating atoms. A general strategy for generating the eigenvectors and the eigenvalues of regular polyhedra is given. Not sign analyses are also performed on the eigenvectors of regular polyhedra. The results provide us a quick way to grasp the topological feature of the electronic structure of clusters having interesting topology.     

The truncation of a cage graph

The modern nanotechnology applies various cage molecules having a polyhedral shape. Topologically, a polyhedron is represented by its map. Since such a map is a plane graph, one may apply various graph-theoretical methods also for studying polyhedra. Of similar use are molecular (multi)tori. The surface of a multitorus is locally plane and allows one to apply much the same mathematical methods. This text is an introduction into the spectral theory of truncated cage graphs and truncated multitori. It anticipates further extensions.     

Chiral molecular nanosilicas

Molecular nanoparticles including polyoxometalates, proteins, fullerenes and polyhedral oligosiloxane (POSS) are nanosized objects with atomic precision, among which POSS derivatives are the smallest nanosilicas. Incorporation of molecular nanoparticles into chiral aggregates either by chiral matrices or self-assembly allows for the transfer of supramolecular chirality, yet the construction of intrinsic chirality with atomic precision in discrete molecules remains a great challenge. In this work, we present a molecular folding strategy to construct giant POSS molecules with inherent chirality. Ferrocenyl diamino acids are conjugated by two or four POSS segments. Hydrogen bonding-driven folding of diamino acid arms into parallel β-sheets facilitates the chirality transfer from amino acids to ferrocene and POSS respectively, disregarding the flexible alkyl spacers. Single crystal X-ray structures, density functional theory (DFT) calculations, circular dichroism and vibrational circular dichroism spectroscopy clearly verify the preferential formation of one enantiomer containing chiral molecular nanosilicas. The chiral orientation and chiroptical properties of POSS show pronounced dependence on the substituents of α-amino acids, affording an alternative way to control the folding behavior and POSS chirality in addition to the absolute configuration of amino acids. Through the kinetic nanoprecipitation protocol, one-dimensional aggregation enables chirality transfer from the molecular scale to the micrometer scale, self-assembling into helices in accordance with the packing propensity of POSS in a crystal phase. This work, by illustrating the construction of chiral molecular nanosilicas, paves a new way to obtain discrete chiral molecular nanoparticles for potential chiroptical applications.

A molecular folding strategy is developed to construct ferrocenyl diamino acid conjugated polyhedral oligosiloxane molecules. Hydrogen bonding-driven folding facilitates the chirality transfer from the molecular scale to the micrometer scale.     

Constrained and unconstrained chirality functions. A new method, going from discrete to continuous space, to find the best overlap between enantiomer atoms

This paper provides two different functions for quantifying geometric chirality. Both are based on Euclidean distances between enantiomer atoms and the best associated RMS, but, depending on the function, atoms are paired without or with constraint. In the first, the best match between the enantiomer atoms is sought by means of a completely new method in which one enantiomer is fitted onto a spline approximation of the other. This method reestablishes the continuity between similarity and dissimilarity, broken in discrete space by atom-per-atom shape recognition treatments. In the second, each enantiomer atom is paired with its mirror image and only the mirror location is optimized. Congruity-based chirality measures are grouped into two classes according to whether the discrimination function between the chiral object and the reference object takes some constraint into account (second class) or does not (first class). In this paper, our constrained or unconstrained chirality function is compared with the continuous chirality measure (second class). It is inferred that only chirality scales of the same class can be correlated.     

On the equivalence of conformational and enantiomeric changes of atomic configuration for vibrational circular dichroism signs

We study systematically the vibrational circular dichroism (VCD) spectra of the conformers of a simple chiral molecule, with one chiral carbon and an "achiral" alkyl substituent of varying length. The vibrational modes can be divided into a group involving the chiral center and its direct neighbors and the modes of the achiral substituent. Conformational changes that consist of rotations around the bond from the next-nearest neighbor to the following carbon, and bond rotations further in the chain, do not affect the modes around the chiral center. However, conformational changes within the chiral fragment have dramatic effects, often reversing the sign of the rotational strength. The equivalence of the effect of enantiomeric change of the atomic configuration and conformational change on the VCD sign (rotational strength) is studied. It is explained as an effect of atomic characteristics, such as the nuclear amplitudes in some vibrational modes as well as the atomic polar and axial tensors, being to a high degree determined by the local topology of the atomic configuration. They reflect the local physics of the electron motions that generate the chemical bonds rather than the overall shape of the molecule.     

Stereoanalysis of fullerenes with a chiral molecular framework

Stereoanalysis of three fullerene molecules with a chiral molecular framework C₃₂, C₇₆, and C₇₈ and achiral fullerene C₆₀ molecule was carried out. Comparative quantitative analysis of the degree of chirality showed topology to be the major factor governing the chirality of fullerenes. A procedure for determining the relative contribution of topological chirality to the total chirality of the molecule is proposed. Structural fragments responsible for chirality are found. The title fullerenes are assigned to the corresponding subclasses of homochirality. A classification system of isomeric fullerenes is proposed.     

The quantitative measurement of rotational motion of the subfragment-1 region of myosin by saturation transfer epr spectroscopy.

According to current models of muscle contraction (Huxley, H. E., Science 164: 1356-1366 [1969]), motion of flexible myosin crossbridges is essential to the contractile cycle. Using a spin-label analog of iodoacetamide bound to the subfragment No. 1 (S1) region of myosin, we have obtained rotational correlation times (tau 2) for this region of the molecule with the ultimate goal of making quantitative measurements of the motion of the crossbridges under conditions comparable to those in living, contracting muscle. We used the newly developed technique of saturation transfer electron paramagnetic resonance spectroscopy (Hyde, J.S., and Thomas, D.D., Ann. N.Y. Acad Sci. 22:680-692 [1973]), which is uniquely sensitive to rotational motion in the range of 10(-7)-10(-3) sec. Our results indicate that the spin label is rigidly bound to S1 (tau 2 for isolated S1 is 2 X 10(-7) sec) and that the motion of the label reflects the motion of the S1 region of myosin. the value of tau 2 for the S1 segment of myosin is less than twice that for isolated S1, while the molecular weights differ by a factor of 4, indicating flexibility of myosin in agreement with the conclusions of Mendelson et al. (Biochemistry 12:2250-2255 [1973]). Adding F-actin increses tau 2 in either myosin or isolated S1 by a factor of mearly 103, indicating rigid immobilization of S1 by actin. Formation of myosin filaments (at an ionic strength of 0.15 or less) increses tau 2 by a factor of 10-30, depending on the ionic strength, indicating a decrease of the rotational mobility of S1 in these agregates. The remaining motion is at least a factor of 10 faster than would be expected for the filament itself, suggesting motion of the S1 region independent of the filament backbone but slower than in a single molecule. F-actin has a strong immobilizing effect on labeled S1 in myosin filaments (in 0.137 M KC1), but the immobilization is less complete than that observed when F-actin is added to labeled myosin monomers (in 0.5 M KC1). A spin-label analog of maleimide, attached to the SH-2 thiol groups of S1, is immobilized to a much lesser extent by F-actin than is the label on SH-1 groups. The maleimide label also was attached directly to F-actin and was sufficiently immobilized to suggest rigid binding to actin.     

A novel approach to the use of graph theory in structure–activity relationship studies. Application to the qualitative evaluation of mutagenicity in a series of nonfused ring aromatic compounds

In this article we describe a novel approach to the application of graph theory in structure–activity relationship studies. An information–theoretical topological index for the vertices of a molecular graph has been used for the qualitative evaluation of the mutagenic activity of a series of nonfused ring aromatic compounds. The use of a vertex index contrasts with the conventional approach of using a topological index for the entire molecule. The idea is to identify regions, or substructures in the molecules (molecular graphs) which may be used to determine certain biological activity of chemical compounds. The results obtained in this paper indicate that the present approach is capable of classifying the mutagenic activity of the compounds under consideration and may find useful application in structure–activity relationship studies of diverse bioactive compounds.     

Chemical signed graph theory

Chemical signed graph theory is presented. Each topological orbital of an N-vertex molecular graph is represented by a vertex-signed graph (VSG ) that is generated by assigning a sign, either plus or minus, to the vertices without solving the secular matrix equation. The bonding capacity of each VSG is represented by its corresponding edge-signed graph (ESG ) and is quantified by the net sign of the ESG . The resulting 2^N–1 configurations of VSG s can be divided into several groups according to the net signs of the corresponding ESG s. Summation of an appropriate set of degenerate VSG s is found to yield the conventional, canonical molecular orbitals. The distribution of the number of VSG s with respect to the net sign is found to be binomial, which can be related to bond percolation in statistical physics. © 1994 John Wiley & Sons, Inc.