Mathematical studies of Kekulé structures

The perfect matching vector and forcing and the Kekulé-vector of cata-benzenoids are defined. Two theorems are given which set the sufficient and necessary conditions for HKZ-vector (Harary et al. J Math Chem 6:295, 1991) and Kekulé-vector in cata-benzenoids. Additional two theorems are obtained which give sharp bounds for the modules of HKZ- and Kekulé vectors. Dedicated to Professor Tadeusz Marek Krygowski on the happy occasion of his 70th birthday.     

Some Comments on the Matter Wave-light Wave Hypothesis

From the de Broglie matter wave hypothesis and Planck’s energy quantization law, and assuming conservation of energy in the absorption of a photon and its consequent conversion to kinetic energy of motion by a material particle initially at rest, one can deduce a simple mathematical relationship between the wavelength λ (or frequency ν), of the photon absorbed by the particle at rest, and the resulting de Broglie matter wave length, λ_D, of the particle with kinetic energy of motion of mv²/2. The relationship so deduced, λ_D∝√λ, suggests that visible wavelengths of light, from about 4000 ?, in the violet, to beyond about 7000 ?, in the red, on absorption by an electron at rest, lead to material electron wavelengths, λ_D, of the order of the size of the electron transfer proteins seen in the photosynthetic reaction centers of photosynthesizing organisms, at about a size of 50–100 ?. In addition to understanding the mechanism of photosynthesis as a material wave mediated phenomenon, further areas of importance of the relations pointed out in this paper are in the design of experiments to gain a deeper understanding of the basic tenets of wave mechanics, and in the use of tunable lasers to probe various properties of material waves, and to precisely control their properties for applications including lithography.     

Pentaazadienido-Komplexe von Zink,Cadmium und Quecksilber Die Kristallstruktur von [Cd(EtOC6H4-N5-C6H4OEt)2(py)2] und [Hg(tol-N5-tol)2(py)]

Pentaazadienido Complexes of Zinc, Cadmium, and Mercury. The Crystal Structure of [Cd(EtOC₆H₄-N₅-C₆H₄OEt)₂(py)₂] and [Hg(tol-N₅-tol)₂(py)] The pentaazadienido complexes [M(EtOC₆H₄N₅C₆H₄OEt)₂] (M = Zn ( 1 ), Cd ( 2 )) are formed by the reaction of [M(NH₃)₄]²⁺ with [EtOC₆H₄N₅C₆H₄OEt]^? in aqueous ammonia. 2 crystallizes from pyridine as [Cd(EtOC₆H₄N₅C₆H₄OEt)₂py₂] ( 3 ) with the triclinic space group P1 and a = 937.2(2); b = 1422.7(2); c = 2085.5(2) pm; α = 75.28(1)°; β = 94.74(1)°; γ = 99.75(1)°; Z = 2. The central Cd²⁺ ion of 3 exhibits an octahedral coordination by two pyridine ligands in cis arrangement and two (N1, N3)-²⁺ chelating pentaazadienide ions. The reaction of [HgI₄]² with the 1,5-di(tolyl)pentaazadienide anion in aqueous ammonia affords [Hg(p-tol-N₅-tol)₂] ( 4 ), which crystallizes from pyridine in form of [Hg(tol-N₅-tol)₂py] ( 5 ) with the space group P1 and a = 1176.2(4); b = 1203.1(3); c = 1295.6(5) pm; α = 100.77(3)°; β = 110.08(3)°; γ = 94.29(2)°; Z = 2. In 5 the Hg²⁺ cation is threefold coordinated by two monodentate (N3)-η¹ pentaazadienid anions and one pyridine ligand. Within the N₅ chains of the pentaazadienid anions of 3 and 5 localized N? N double bonds are found in the positions N1? N2 and N4? N5 with distances between 125 and 129 pm.     

Terminally Dimetallated N,N′‐Dimethylpiperazines with Doubly Spirocyclic Structures

Dilithiated N,N′‐dimethyl‐piperazine, LiCH₂N(CH₂CH₂)₂ NCH₂Li ( 2 ) was prepared by transmetallation of N,N′‐bis(trimethylstannylmethyl)‐piperazine ( 1 ) with ⁿBuLi and was isolated as a highly pyrophoric yellowish powder in high yield. Compound 2 was characterized by elemental analysis and was reacted as difunctional aminomethylating reagent with dialkyl‐earth metal chlorides, R₂MCl (M = Al, Ga; R = Me, ^tBu) which resulted in the formation of spirocyclic adducts of N,N′‐bis(dialkylmetallamethyl)‐piperazine and unreacted dialkylmetal chlorides, [(Me₂AlCl)Me₂AlCH₂N(CH₂CH₂)₂NCH₂AlMe₂(ClAlMe₂)] ( 3 ) and [(^tBu₂GaCl)^tBu₂GaCH₂N(CH₂CH₂)₂NCH₂Ga^tBu₂(ClGa^tBu₂)] ( 4 ) with five‐membered rings. Compounds 1 , 3 and 4 were identified by NMR‐spectroscopy (¹H, ¹³C, ¹¹⁹Sn for 1 , ²⁷Al for 3 ), mass spectra (EI, for 1 ) and by crystal structure determinations.     

Fast folding and comparison of RNA secondary structures

Summary Computer codes for computation and comparison of RNA secondary structures, the Vienna RNA package, are presented, that are based on dynamic programming algorithms and aim at predictions of structures with minimum free energies as well as at computations of the equilibrium partition functions and base pairing probabilities.An efficient heuristic for the inverse folding problem of RNA is introduced. In addition we present compact and efficient programs for the comparison of RNA secondary structures based on tree editing and alignment.All computer codes are written in ANSI C. They include implementations of modified algorithms on parallel computers with distributed memory. Performance analysis carried out on an Intel Hypercube shows that parallel computing becomes gradually more and more efficient the longer the sequences are.

---

Schnelle Faltung und Vergleich von Sekundärstrukturen von RNA

Zusammenfassung Die im Vienna RNA package enthaltenen Computer Programme für die Berechnung und den Vergleich von RNA Sekundärstrukturen werden präsentiert. Ihren Kern bilden Algorithmen zur Vorhersage von Strukturen minimaler Energie sowie zur Berechnung von Zustandssumme und Basenpaarungswahrscheinlichkeiten mittels dynamischer Programmierung.Ein effizienter heuristischer Algorithmus für das inverse Faltungsproblem wird vorgestellt. Darüberhinaus präsentieren wir kompakte und effiziente Programme zum Vergleich von RNA Sekundärstrukturen durch Baum-Editierung und Alignierung.Alle Programme sind in ANSI C geschrieben, darunter auch eine Implementation des Faltungs-algorithmus für Parallelrechner mit verteiltem Speicher. Wie Tests auf einem Intel Hypercube zeigen, wird das Parallelrechnen umso effizienter je länger die Sequenzen sind.

     

Dynamik linearer Molekülanionen in den Hydrogensulfiden von Natrium,Kalium und Rubidium: Differential-Scanning-Kalorimetrie,Röntgen- und Neutronenbeugung

Dynamical Behaviour of Linear Molecular Anions in the Hydrogensulfides of Sodium, Potassium and Rubidium: Differential Scanning Calorimetry, X-ray and Neutron Diffraction Hydrogensulfides of the alkali metals M ? Na, K, Rb were prepared in autoclaves by the reaction of the corresponding metals with H₂S and D₂S, respectively, in the temperature range from 50°C to 150°C. Differential scanning calorimetry, X-ray and neutron diffraction methods reveal that both, the HS^?-and DS^?-compounds occur in three crystalline modifications with HT ? high-, MT ? medium- and LT ? low-temperature form: The temperatures and enthalpies for the changes of modifications of the H- and D-compounds are given and the atomic arrangements revealed mainly by neutron diffraction data are discussed, in relation to, for example, size of cations.     

Photochemical synthesis of a palladium dichloromethyl complex, {(hexyl)HC(N-methyl-imidazol-2-yl)2}Pd(CHCl2)Cl.: X-ray molecular structures of {(hexyl)HC(N-methylimidazolyl-2-yl)2}Pd(X)Cl, X=Cl, and CHCl2

The reaction of (hexyl)HC(mim)₂ (1, mim=N-methyl-imidazol-2-yl) with (cod)PdMeCl in C₆H₆ yields {(hexyl)HC(mim)₂}Pd(Me)Cl (3). The photochemical reaction of 3 with CH₂Cl₂ at 23 °C in ambient room light yields {(hexyl)HC(mim)₂}Pd(CHCl₂)Cl (4). It is proposed that this reaction proceeds by homolytic scission of the PdMe bond of 3.     

Neue neutrale und kationische Mono‐Aziridin‐Komplexe des Typs [CpMn(CO)2Az], [CpCr(NO)2Az]+ und [(Ph3P)(CO)4ReAz]+ über CO‐, Hydrid‐ und Chlorid‐Abspaltungsreaktionen

Novel Neutral and Cationic Mono‐Aziridine Complexes of the Type [CpMn(CO)₂Az], [CpCr(NO)₂Az]⁺, and [(Ph₃P)(CO)₄ReAz]⁺ via CO‐, Hydride‐, and Chloride‐Elimination Reactions The monoaziridine complexes 1 — 5 are obtained by three differently induced substitution reactions. The photolytically induced CO substitution reaction of [CpMn(CO)₃] with 2, 2‐dimethylaziridine leads to the neutral N‐coordinate aziridine complex [Cp(CO)₂Mn{$\overline{N(H)CMe₂C}$ H₂}] ( 1 ). The protonation of [(Ph₃P)(CO)₄ReH] with CF₃SO₃H and consecutive treatment with 2, 2‐dimethylaziridine or 2‐ethylaziridine gives the salt‐like aziridine complexes [(Ph₃P)(CO)₄Re{$\overline{N(H)CMe₂C}$ H₂}](CF₃SO₃) ( 2 ) or [(Ph₃P)(CO)₄Re{ H₂}](CF₃SO₃) ( 3 ) by hydride elimination reactions. The like‐wise salt‐like complexes [Cp(NO)₂Cr{$\overline{N(H)CMe₂C}$ H₂}](BF₄) ( 4 ) and [Cp(NO)₂Cr{ H₂}](CF₃SO₃) ( 5 ) are synthesized from [CpCr(NO)₂Cl] by chloride elimination with AgX (X = BF₄, CF₃SO₃) in the presence of 2, 2‐dimethylaziridine or 2‐ethylaziridine, respectively. As a result of X‐ray structure analyses, the metal atoms are trigonal pyramidally ( 1, 4, 5 ) or octahedrally ( 2, 3 , cis‐position) configurated; the intact three‐membered rings coordinate through the distorted tetrahedrally configurated N atoms. All compounds 1‐5 are stable with respect to the directed thermal alkene elimination to give the corresponding nitrene complexes; the IR, ¹H‐ and ¹³C{¹H}‐NMR, and MS spectra are reported and discussed.     

SinH/SinH-(n=3～8)的结构和电子亲合能的研究

选用四种不同的密度泛函理论方法(B3LYP，B3P86，BLYP，BP86)，在全电子的双ξ加极化加弥散函数基组(DZP )下，对SinH／SinH^-(n=3～8)体系进行研究，获得它们的基态结构和电子亲合能。预测Si3H／Si3H^-,Si4H／Si4H^-,Si5H／Si5H^-,Si6H／Si6H^-，Si7H／Si7H^-和Si8H／Si8H^-的基态结构分别为C2v(^2B2)／C2v(1^A1)氢桥结构，Cs(^2A’)／C(^1A’)，C2v(^2B2)／C2v(^1A1)，C2v(^2B2或^2B1)／C4v(^1A1)，C5v(^2A1)／C5v(^1A1)和C5(^2A‘‘)／C3v(^1A1)。在电子亲合能方面，B3LYP方法预测的电子亲合能是最可靠的，预测Si3H，Si4H，Si5H，Si6H，Si7H和Si8H的电子亲合能分别为2．56，2．59，2．84，2．86，3．19和3．14eV。     

Characterization of the monovalent ion position and hydrogen-bond network in guanine quartets by DFT calculations of NMR parameters

Conformational stability of G-quartets found in telomeric DNA quadruplex structures requires the coordination of monovalent ions. Here, an extensive Hartree-Fock and density functional theory analysis of the energetically favored position of Li+, Na+, and K+ ions is presented. The calculations show that at quartet-quartet distances observed in DNA quadruplex structures (3.3 A), the Li+ and Na+ ions favor positions of 0.55 and 0.95 A outside the plane of the G-quartet, respectively. The larger K+ ion prefers a central position between successive G-quartets. The energy barrier separating the minima in the quartet-ion-quartet model are much smaller for the Li+ and Na+ ions compared with the K+ ion; this suggests that K+ ions will not move as freely through the central channel of the DNA quadruplex. Spin-spin coupling constants and isotropic chemical shifts in G-quartets extracted from crystal structures of K+- and Na+-coordinated DNA quadruplexes were calculated with B3LYP/6-311G(d). The results show that the sizes of the trans-hydrogen-bond couplings are influenced primarily by the hydrogen bond geometry and only slightly by the presence of the ion. The calculations show that the R(N2N7) distance of the N2-H2...N7 hydrogen bond is characterized by strong correlations to both the chemical shifts of the donor group atoms and the (h2)J(N2N7) couplings. In contrast, weaker correlations between the (h3)J(N1C6') couplings and single geometric factors related to the N1-H1...O6=C6 hydrogen bond are observed. As such, deriving geometric information on the hydrogen bond through the use of trans-hydrogen-bond couplings and chemical shifts is more complex for the N1-H1...O6=C6 hydrogen bond than for the N2-H2...N7 moiety. The computed trans-hydrogen-bond couplings are shown to correlate with the experimentally determined couplings. However, the experimental values do not show such strong geometric dependencies.