Variational calculation of vibrational energies of triatomic molecules using SCF optimized modes

A self-consistent field optimization of the vibrational coordinates for nonlinear triatomic molecules is presented. The optimal coordinates are obtained by making a three-dimensional rotational transformation of the normal modes and determining the rotation angles as those for which the SCF energy is stationary. The utility of the optimized coordinates in full variational calculations of vibrational energies is studied for the molecules of H₂O, O₃, H₂D⁺, H₂T⁺, and D₂T⁺. For H₂O and O₃, the optimization procedure leads to the local mode representation. It is shown that the use of the optimal coordinates in variational calculations allows a large reduction of the dimension of the Hamiltonian matrix to be diagonalized in order to reach convergence.     

"One-pot" methylation of N-Nosyl-alpha-amino acid methyl esters with diazomethane and their coupling to prepare N-methyl dipeptides

N-Nosyl-alpha-amino acid methyl esters are methylated quantitatively with diazomethane. After proper deprotection of the amino function by treatment with the reagent system mercaptoacetic acid/sodium methoxide, the obtained N-methyl amino acid methyl esters are coupled with N-Fmoc amino acid chlorides to afford the corresponding dipeptides. The obtained products do not show any detectable extent of racemization by (1)H NMR and HPLC.     

Variable selection in discriminant analysis based on the location model for mixed variables

Non-parametric smoothing of the location model is a potential basis for discriminating between groups of objects using mixtures of continuous and categorical variables simultaneously. However, it may lead to unreliable estimates of parameters when too many variables are involved. This paper proposes a method for performing variable selection on the basis of distance between groups as measured by smoothed Kullback–Leibler divergence. Searching strategies using forward, backward and stepwise selections are outlined, and corresponding stopping rules derived from asymptotic distributional results are proposed. Results from a Monte Carlo study demonstrate the feasibility of the method. Examples on real data show that the method is generally competitive with, and sometimes is better than, other existing classification methods.     

Reaction of 4,5-diamino-1,6-dihydropyrimidin-6-ones with two equivalents of chalcones

The reaction of 4,5-diamino-1,6-dihydropyrimidin-6-ones 1 with two equivalents of the chalcones 2 leads in an acidic medium to the formation of the 2,3,6,7-tetrahydro-1H-pyrimido[4,5-b][1,4]diazepin-6-one derivatives 3a-d . The structure elucidation of the products is based on nmr measurements and an X-ray diffraction.     

Competitive binding exchange between alkali metal ions (K+, Rb+, and Cs+) and Na+ ions bound to the dimeric quadruplex [d(G4T4G4)]2: a 23Na and 1H NMR study

A comparative study of the competitive cation exchange between the alkali metal ions K⁺, Rb⁺, and Cs⁺ and the Na⁺ ions bound to the dimeric quadruplex [d(G₄T₄G₄)]₂ was performed in aqueous solution by a combined use of the ²³Na and ¹H NMR spectroscopy. The titration data confirm the different binding affinities of these ions for the G‐quadruplex and, in particular, major differences in the behavior of Cs⁺ as compared to the other ions were found. Accordingly, Cs⁺ competes with Na⁺ only for the binding sites at the quadruplex surface (primarily phosphate groups), while K⁺ and Rb⁺ are also able to replace sodium ions located inside the quadruplex. Furthermore, the ¹H NMR results relative to the CsCl titration evidence a close approach of Cs⁺ ions to the phosphate groups in the narrow groove of [d(G₄T₄G₄)]₂. Based on a three‐site exchange model, the ²³Na NMR relaxation data lead to an estimate of the relative binding affinity of Cs⁺ versus Na⁺ for the quadruplex surface of 0.5 at 298 K. Comparing this value to those reported in the literature for the surface of the G‐quadruplex formed by 5′‐guanosinemonophosphate and for the surface of double‐helical DNA suggests that topology factors may have an important influence on the cation affinity for the phosphate groups on DNA. Copyright © 2009 John Wiley & Sons, Ltd.     

Unexpected transformation of quinones to spirolactones and to naturally occurring naphthalenic compounds

In the last few years, natural quinones of the lapachol group have been used as starting points for the preparation of several bioactive heterocyclic compounds. Herein, we announce that lapachones, derivatives of lapachol, under certain conditions in the presence of inorganic reagents give unexpected products, spirolactones and naphthalenic derivatives, nordihydrolapachenone and tetrahydrotectol, both naturally occurring compounds. Nordihydrolapachenone was identified by X-ray analysis. Lapachol itself can also be converted to tetrahydrotectol.     

Synthesis and structural analysis of 5‐cyanodihydropyrazolo[3,4‐b]pyridines

Several new 3‐aryl‐5‐cyanopyrazolo[3,4‐b]pyridines were easily prepared from 3‐amino‐5‐arylpyrazoles and α‐cyanochalcones. Structural analysis using NMR solution studies revealed the 2H‐tautomers as the preferred tautomer in solution (DMSO‐d₆). X‐ray diffraction confirmed the 2H‐tautomers as the unique tau‐tomer species in the crystalline state as well. Geometry optimization of 1H and 2H‐tautomers at semi‐empirical levels (AM1, MINDO/3) were performed, indicating that in all cases the 2H‐tautomers are more stable than the corresponding 1H‐tautomers.     

The Painlevé Property for Quasihomogenous Systems and a Many-Body Problem in the Plane

We investigate a many-body problem in the plane introduced by Calogero and intensively studied by Calogero, Françoise and Sommacal. An ad hoc complexification transforms the many-body problem to a system of second order autonomous complex equations depending on some complex constants that describe the two-body interactions. We investigate the sets of two-body interaction constants that make the complexified equation have the Painlevé Property, this is, its solutions are given by single-valued meromorphic functions. In this case the original system has only periodic isochronous solutions. We exhibit a family of settings where the system displays this property and show that it is not present in the three- and four-body problems that do not fall within our class. For this, we introduce a necessary condition for the presence of the Painlevé Property in some quasihomogenous systems.     

Totally Permutable Products of Finite Groups Satisfying SC or PST

Finite groups G=AB factorized by two subgroups A and B such that every subgroup of A permutes with every subgroup of B are studied in this paper. The behaviour of such products with respect to the class of finite groups in which Sylow-permutability is transitive is analyzed.     

Dimensional crossover in alternating spin chains

The effect of antiferromagnetic interchain coupling in alternating spin chains is studied by means of spin wave (SW) theory and density matrix renormalization group (DMRG). Two limiting cases are investigated, the two-leg ladder and its two-dimensional (2D) generalization. For the 2D case, SW approximation predicts a smooth-dimensional crossover keeping the ground state ordered, whereas in the ladder case the DMRG results show a gapped ground state for any J>0. Furthermore, the behavior of the correlation functions closely resemble the uniform spin- ladder. However, for small J, the gap behaves quadratically as Δ0.6J². Similarly to uniform spin chains, it is conjectured an analogous spin gap behavior for an arbitrary number of mixed spin chains.