Molecular bonding profiles

We present a refinement of recently proposed characterization of molecules based on a sequence of powers of interatomic separations referred to as molecular profiles. The molecular profiles and closely related shape profiles were based on the averaging contributions arising from different powers of interatomic distances for atoms in a molecule or atoms at the molecular periphery, respectively. Consequently, molecular models in which atoms have the same set of coordinates but different bonding patterns will result in identical molecular profiles. In this article we outline a refinement of molecular profiles in which the bonding pattern in a molecule is fully acknowledged. This is accomplished by adding ghost sites along chemical bonds. The distance-based invariants of the augmented matrix reflect the bonding pattern of a structure giving different molecular profiles for molecules having the same atomic coordinates but different bondings. The procedure is general and applies to two-dimensional and three-dimensional molecular skeletons. Equally, the approach can be applied to van der Waals-type molecular surfaces and molecular contours of equal electron densities in order to obtain characterization of more realistic molecular models.Dedicated to a leading graph theorist, Professor R. C. Read, for sharing his mathematical talents on chemical structures.     

Chemical applications of topology and group theory. 26. The sextuple diamond-square-diamond rearrangement of the icosahedron through a cuboctahedron intermediate

The details of the symmetry factoring of the graphs corresponding to the icosahedron and the cuboctahedron are presented. Such symmetry factoring procedures use the sequence of two-foldC ₂ and threefoldC ₃ elementsC ₂ xC ₂ x CZ x C3 to give disconnected graphs having eigenvalue spectra similar to those of the original polyhedra but with components having only one and two vertices. In addition, the same symmetry factoring sequence is used to determine the eigenvalue spectrum of an intermediate in the sextuple diamond-square process for conversion of the icosahedron to the cuboctahedron.This paper is dedicated to Professor Frank Harary in recognition of his pioneering work in areas of graph theory closely related to chemical problems. For part 25 of this series, see ref. [1].     

Precise Molecular Fission and Fusion: Quantitative Self‐Assembly and Chemistry of a Metallo‐Cuboctahedron

Inspiration for molecular design and construction can be derived from mathematically based structures. In the quest for new materials, the adaptation of new building blocks can lead to unexpected results. Towards these ends, the quantitative single‐step self‐assembly of a shape‐persistent, Archimedean‐based building block, which generates the largest molecular sphere (a cuboctahedron) that has been unequivocally characterized by synchrotron X‐ray analysis, is described. The unique properties of this new construct give rise to a dilution‐based transformation into two identical spheres (octahedra) each possessing one half of the molecular weight of the parent structure; concentration of this octahedron reconstitutes the original cuboctahedron. These chemical phenomena are reminiscent of biological fission and fusion processes. The large 6 nm cage structure was further analyzed by 1D and 2D NMR spectroscopy, mass spectrometry, and collision cross‐section analysis. New routes to molecular encapsulation can be envisioned.     

Correlation of product ion profiles with molecular structures of androgenic and anabolic steroids in ESI MS/MS

Androgenic and anabolic steroids (AASs) are a class of chemical substances closely related to testosterone in molecular structure. They can be abused to enhance performances in human and equine athletes, and are banned by the sports authorities. To assist with method development for doping analyses of AASs, investigations were conducted to correlate their product ion profiles with the molecular structures. Although very similar in chemical structure, AASs generated noticeably different product ion profiles from collision‐induced dissociation (CID). On the basis of both outlines of the product ion profiles and molecular structures, AASs studied were classified into six subclasses. In each subclass, the product ion profiles were identical or similar. However, the product ion profiles in one subclass were remarkably different from those in another. The classification reveals that the position and number of double bond(s) in conjugation with the 3‐carbonyl group in the molecular structure of an AAS have significant effects on product ion profile. The presence or absence of the 19‐methyl group in an AAS also has a remarkable influence on its product ion profile. A substitution in the A‐, B‐ or D‐ring of an AAS may cause a shift in mass value of the product ions. The correlation of product ion profiles with molecular structures of AASs has the implication that each AAS can be characterized by a combination of its [M + H]⁺ ion and product ion profile and as a result be identified with specificity. The classified product ion pattern may be useful in the identification of unknown AASs. Copyright © 2010 John Wiley & Sons, Ltd.     

Frustration effects in antiferromagnetic molecules: The cuboctahedron

Frustration of magnetic systems which is caused by competing interactions is the driving force of several unusual phenomena such as plateaus and jumps of the magnetization curve as well as of unusual energy spectra with for instance many singlet levels below the first triplet state. The antiferromagnetic cuboctahedron can serve as a paradigmatic example of certain frustrated antiferromagnets. In addition it has the advantage that its complete energy spectrum can be obtained up to individual spin quantum numbers of s = 3/2 (16 777 216 states).     

Hydrogen storage inside a toroidal carbon nanostructure C120: Density functional theory computer simulation

Ab initio density functional calculations were performed for a toroidal carbon C₁₂₀ nanostructure. Hydrogen molecules, n = 1–15, were added inside the nanotorus and for each one of these systems a geometry optimization was obtained. The cohesive energy shows that these structures are energetically stable. For example, the binding energies are ?34.95 and ?36.19 Hartrees and the interatomic distances H? H are 0.753 and 0.772 Å for 1 and 14 molecules, respectively. Considering only molecular hydrogen, we have always seen so far weak physisorption into the C₁₂₀ nanotorus. There is no chemisorption until the number oh hydrogen molecules are increased to 14. In this case, four hydrogen atoms are chemisorbed. With 15 molecules, there are 10 hydrogen atoms chemisorbed just at the inner nanotorus surface forming 10 H? C bondings with bond length close to that in methane. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem 110:2495–2508, 2010     

蒙特卡洛模拟退火与距离限制相结合的方法——在多肽溶液构象分析中的应用

Distance geometry and molecular dynamics are currently employed in determining molecular structures with interatomic distances from NMR NOESY experiment. Because of the flexibility of peptide, distances obtained from NMR are usually not sufficient to confine its structure. Both distance geometry and molecular dynamics will bias in the conformational space at this circumstance. Constraint Monte Carlo simulated annealing was established to solve this problem. Distance constraints were included into the ECEPP/2 force field by introducing a harmonic energy term. Conformational analysis of a pentapeptide with eight interatomic distances from NMR was carried out as a test. By comparison of the 100 conformers obtained from constraint simulated annealing and the 100 conformers from distance geometry calculation, it was found that constraint simulated annealing can cover the outcomes of distance geometry and at the same time give more con-formers fitting to the experimental data. The result shows that constraint Monte-Carlo simulated annealing is more valid in constructing peptide structures from NMR distances than currently employed methods when no sufficient distances from NMR are available.     

Structure of hydrogenated silicon clusters. Small clusters

The ground state structures of silicon hydride clusters Si_nH_m containing up to 12 silicon atoms are obtained by numerical modeling. The cluster geometry is optimized for a wide set of initial structures using the MINDO/3 approximation for Monte Carlo simulation of interatomic interactions. The energy of the cluster depending on the content of hydrogen is studied, and it is shown that the Si-H and Si-Si bond energies depend little on the cluster size.     

Maximum filling principle and sublattice characteristics for the atoms of period 3 elements

The most important characteristics of the Voronoi-Dirichlet polyhedra (VDP) of A atoms (A = Na, Mg, Al, Si, P, S, Cl, or Ar) were determined. The sublattices contain chemically identical A atoms in the crystal structures of 232006 inorganic, coordination, and organoelement compounds. The VDP of A atoms have most often 14 faces, the Fedorov cuboctahedron being the most abundant VDP type. The effect of the nature of the A atoms on the characteristic A-A interatomic distances in the homoatomic sublattices of the crystal structures was considered.     

Geometric and electronic similarities between transition structures for electrocyclizations and sigmatropic hydrogen shifts

This paper reports new theoretical evidence that supports previous proposals concerning the similarity between transition structures for electrocyclizations and sigmatropic hydrogen shifts. This evidence was obtained using two recently proposed methodologies, namely the so-called generalized population analysis and the formalism of molecular quantum similarity indices. Analysis of multicenter bond indices shows that the transition structures for cationic [1,n] hydrogen shifts do indeed have three-center indices that are similar to those of other three-center carbocations. In addition, the close resemblance of the electronic structures of electrocyclic and sigmatropic transition structures that differ by only a proton is supported by the values of their quantum molecular similarity indices.     

Double icosahedron‐based motif of Nin (n = 20−30)

A genetic algorithm (GA) coupled with a tight‐binding (TB) interatomic potential was used to search for the low‐energy structures of the medium‐sized Ni_n (n = 20?30) clusters. The low‐energy candidate structures from the GA/TB search were further optimized by using the density functional theory calculations with the Perdew, Burke, and Ernzerhof exchange‐correlation energy functional. The obtained lowest‐energy structures of the medium‐sized Ni_n (n = 20?30) clusters are shown to exhibit double icosahedron‐based motif. The properties of the nickel clusters including binding energies, second differences in energy, and especially magnetic properties have also been studied. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

The electronic structure of small lithium clusters

Ab initio molecular orbital calculations using the STO-6G and STO6-21G basis sets have been performed for the cluster series Li _n ⁺ , Li _n , and Li _n ^– (wheren=2–7). Thirty-two optimized structures are discussed and reported, many of which (especially for the anionic structures) have not yet been considered. The calculations suggest that for all three species the optimum geometries are planar. Of the two levels of theories that were investigated, STO-6G//STO-6G and STO6-21G//STO-6G, the latter hybrid theory was found to be less reliable. In particular, for the anionic structures these calculations should provide a platform from which more sophisticated, i.e., configuration interaction, geometry optimization can be performed.     

Structural Classification and General Principles for the Design of Spherical Molecular Hosts

Cryptands, carcerands, polyoxometalates, and molecular capsules are cagelike hosts that complex guests through encapsulation. Following the discovery of a nanometer scale supramolecular shell-like spheroid, these and other shell-like hosts were structurally classified. Their frameworks may be catalogued according to principles of solid geometry. This has led to the identification of hosts that have not yet been synthesized or discovered (such as the cuboctahedron shown; X=O, S) and should lead to the design of additional container assemblies.     

Structure and analysis of atomic vibrations in clusters of Cu n (n ≤ 20)

The binding energy, equilibrium geometry, and vibration frequencies of free clusters Cu _n (2 ≤ n ≤ 20) are calculated using the potentials of interatomic interactions found using the tight-binding approximation. The nonmonotonic dependence of the clusters’ minimum vibration frequency on their sizes and the extreme values for the number of atoms in a cluster n = 4, 6, 13, and 19 is demonstrated. It is noted that this result agrees with the theoretical and experimental data on stable structures of small and medium metallic clusters.     

Low-Bias Conductance Mechanism of Diarylethene Isomers:a First-Principle Study

The structure-property relationship of diarylethene (DAE)-derivative molecular isomers, which involve ring-closed and ring-open forms, is investigated by employing the non-equilibrium Green's function formalism combined with density functional theory. Molecular junctions are formed by the isomers connecting to Au(111) electrodes through flanked pyridine groups. The difference in electronic structures caused by different geometry structures for the two isomers, particularly the interatomic alternative single bond and double bond of the ring-closed molecule, contributes to the vastly different low-bias conductance values. The lowest unoccupied molecular orbital (LUMO) of the isomers is the main channel for electron transport. In addition, more electrons transferred to the ring-closed molecular junction in the equilibrium condition, thereby decreasing the LUMO energy to near the Fermi energy, which may contribute to a larger conductance value at the Fermi level. Our findings are helpful for understanding the mechanism of low-bias conductance and are conducive to the design of high-performance molecular switching based on diarylethene or diarylethene-derivative molecules.     

Analysis of commercial dyes by capillary column supercritical fluid chromatography

High resolution separations of selected commercial azo, aniline, and anthraquinone dyes by capillary column supercritical fluid chromatography (SFC) are demonstrated. Supercritical n-pentane was used as a mobile phase and provided efficient separations of multi-functional, polar disperse dyes with molecular weights up to approximately 700 daltons.     

Morphology and microphase separation of star copolymers

Star copolymers have attracted significant interest due to their different characteristics compared with diblock copolymers, including higher critical micelle concentration, lower viscosity, unique spatial shape, or morphologies. Development of synthetic skills such as anionic polymerization and controlled radical polymerization have made it possible to make diverse architectures of polymers. Depending on the molecular architecture of the copolymer, numerous morphologies are possible, for instance, Archimedean tiling patterns and cylindrical microdomains at symmetric volume fraction for miktoarm star copolymers as well as asymmetric lamellar microdomains for star‐shaped copolymers, which have not been reported for linear block copolymers. In this review, we focus on morphologies and microphase separations of miktoarm (A_mB_n and ABC miktoarm) star copolymers and star‐shaped [(A‐b‐B)_n] copolymers with nonlinear architecture. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 1–21     

Perturbation theory with an approximate perturbation: The effect of charge overlap on interatomic interactions

The evaluation of interatomic interactions at large separations (R) typically involves neglecting electron exchange, treating the Coulomb interaction between atoms as a perturbation, neglecting third- and higher-order energy contributions, and approximating the Coulomb interaction by a short expansion in spherical harmonics and, usually, powers of R^?1. This last approximation, using an approximate perturbing Hamiltonian to evaluate a second-order perturbed energy, is examined here; error bounds and a simple correction are introduced. Three illustrative applications to the H? H⁺ interaction are given: the error incurred by truncating the spherical-harmonic expansion is bounded, the R^?1 expansion is corrected for the overlap of the “atomic” charge distributions, and the R^?1 expansion is analyzed to see why it works as well as it does.     

Relative spatial profiles of barium ion and atom in the argon inductively coupled plasma as obtained by laser excited fluorescence

Relative ionic and atomic fluorescence profiles for barium have been obtained in an argon inductively coupled plasma by exciting different transitions with a nitrogen-laser pumped tunable dye laser and measuring the resulting fluorescence pulses with a boxcar averager. Spatially resolved profiles are directly obtained without the need of an Abel inversion procedure, with a volume resolution of approximately 0.2 mm³. The profiles are given along the excitation axis as well as along the observation axis, for different heights above the coil and different input powers. At low heights, the ion profile resembles a hollow pencil with a typical double-peaked, asymmetric distribution, while the atom profile seems to be complementary to the ion profile. Some scatter from water is also evident at low heights.     

Symmetry simplifications of space types in configuration interaction induced by orbital degeneracy

Symmetry simplifications are introduced in configuration interaction (CI ) by reducing the number of symmetry-allowed space types if there is degeneracy in some of the molecular orbitals by constructing the unique space types. A new symmetry group which we call the configuration symmetry group is defined and is shown to be expressible as a generalized wreath product group. Generating functions are derived for enumerating the equivalence classes of space types. A double coset method is expounded which constructs the representatives of all equivalence classes of space types using the cycle index of generalized wreath product and the double cosets of label subgroup with generalized wreath product in the symmetric group S_n, if n is twice the number of occupied and virtual orbitals. Method is illustrated with CI using the localized orbitals of polyenes, CI in benzene, and atomic CI for several reference states.