Density Functional Theory Calculations on Rhodamine B and Pinacyanol Chloride. Optimized Ground State,Dipole Moment,Vertical Ionization Potential,Adiabatic Electron Affinity and Lowest Excited Triplet State

The ground state configuration of the gas phase cationic dyes pinacyanol chloride and rhodamine B are optimized with HF/6–311 + G(2d,2p) method and basis set. B3PW91/6–311 + G(2df,2p) functional and basis set is used to calculate the Mulliken atom charge distribution, total molecular energy, the dipole moment, the vertical ionization potential, the adiabatic electron affinity and the lowest excited triplet state, the last three as an energy difference between separately calculated open shell and ground states. The triplet and extra electron states are optimized to find the relaxation energy. In the ground state optimization of both dyes the chloride anion migrates to a position near the center of the chromophore. For rhodamine B the benzoidal group turns perpendicular to the chromophore plane. For both dyes, the LUMO is mostly of π character associated with the aromatic part of the molecule containing the chromophore. The highest occupied MOs consist of three almost degenerate eigenvectors involving the chloride anion coordinated with σ electrons in the molecular framework. The fourth highest MO is of π character. For both molecules in the gas phase ionization process the chloride anion loses the significant fraction of electric charge. In electron capture, the excess charge goes mainly on the dye cation.     

Radical Reactivity of the Biradical [⋅P(μ-NTer)2P⋅] and Isolation of a Persistent Phosphorus-Cantered Monoradical [⋅P(μ-NTer)2P-Et]

The activation of C−Br bonds in various bromoalkanes by the biradical [⋅P(μ-NTer)₂P⋅] ( 1 ) (Ter=2,6-bis-(2,4,6-trimethylphenyl)-phenyl) is reported, yielding trans-addition products of the type [Br−P(μ-NTer)₂P−R] ( 2 ), so-called 1,3-substituted cyclo-1,3-diphospha-2,4-diazanes. This addition reaction, which represents a new easy approach to asymmetrically substituted cyclo-1,3-diphospha-2,4-diazanes, was investigated mechanistically by different spectroscopic methods (NMR, EPR, IR, Raman); the results suggested a stepwise radical reaction mechanism, as evidenced by the in-situ detection of the phosphorus-centered monoradical [⋅P(μ-NTer)₂P-R].< To provide further evidence for the radical mechanism, [⋅P(μ-NTer)₂P-Et] ( 3Et ⋅) was synthesized directly by reduction of the bromoethane addition product [Br-P(μ-NTer)₂P-Et] ( 2 a ) with magnesium, resulting in the formation of the persistent phosphorus-centered monoradical [⋅P(μ-NTer)₂P-Et], which could be isolated and fully characterized, including single-crystal X-ray diffraction. Comparison of the EPR spectrum of the radical intermediate in the addition reaction with that of the synthesized new [⋅P(μ-NTer)₂P-Et] radical clearly proves the existence of radicals over the course of the reaction of biradical [⋅P(μ-NTer)₂P⋅] ( 1 ) with bromoethane. Extensive DFT and coupled cluster calculations corroborate the experimental data for a radical mechanism in the reaction of biradical [⋅P(μ-NTer)₂P⋅] with EtBr. In the field of hetero-cyclobutane-1,3-diyls, the demonstration of a stepwise radical reaction represents a new aspect and closes the gap between P-centered biradicals and P-centered monoradicals in terms of radical reactivity.     

Solid-Phase Synthesis of an Insect Pyrokinin Analog Incorporating an Imidazoline Ring as Isosteric Replacement of a trans Peptide Bond

A facile solid-phase synthetic method for incorporating the imidazoline ring motif, a surrogate for a trans peptide bond, into bioactive peptides is reported. The example described is the synthesis of an imidazoline peptidomimetic analog of an insect pyrokinin neuropeptide via a cyclization reaction of an iminium salt generated from the preceding amino acid and 2,4-diaminopropanoic acid (Dap).     

Nearest neighbor and hard sphere models in continuum percolation

Consider a Poisson process X in R ^d with density 1. We connect each point of X to its k nearest neighbors by undirected edges. The number k is the parameter in this model. We show that, for k = 1, no percolation occurs in any dimension, while, for k = 2, percolation occurs when the dimension is sufficiently large. We also show that if percolation occurs, then there is exactly one infinite cluster. Another percolation model is obtained by putting balls of radius zero around each point of X and let the radii grow linearly in time until they hit another ball. We show that this model exists and that there is no percolation in the limiting configuration. Finally we discuss some general properties of percolation models where balls placed at Poisson points are not allowed to overlap (but are allowed to be tangent). © 1996 John Wiley & Sons, Inc.     

Stereoretentive and regioselective selenium-catalyzed intermolecular propargylic C–H amination of alkynes

Herein we report an intermolecular propargylic C–H amination of alkynes. This reaction is operationally convenient and requires no transition metal catalysts or additives. Terminal, silyl, and internal alkynes bearing a wide range of functional groups can be aminated in high yields. The regioselectivity of amination for unsymmetrical internal alkynes is strongly influenced by substitution pattern (tertiary > secondary > primary) and by relatively remote heteroatomic substituents. We demonstrate that amination of alkynes bearing α-stereocenters occurs with retention of configuration at the newly-formed C–N bond. Competition experiments between alkynes, kinetic isotope effects, and DFT calculations are performed to confirm the mechanistic hypothesis that initial ene reaction of a selenium bis(imide) species is the rate- and product-determining step. This ene reaction has a transition state that results in substantial partial positive charge development at the carbon atom closer to the amination position. Inductive and/or hyperconjugative stabilization or destabilization of this positive charge explains the observed regioselectivities.

Selenium catalysis enables a general intermolecular propargylic C–H amination of alkynes. The concerted mechanism gives rise to high regioselectivity for the more electron-rich end of the alkyne and retention of the C–H propargylic stereocenter.     

Three-component Heck–Diels–Alder cascade processes involving alkylallenes, aryl iodides and dienophiles

A wide variety of aryl/heteroaryl iodides undergo an intermolecular Heck reaction with alkylallenes to furnish 1,3-dienes. These subsequently react in situ with various dienophiles to give Diels–Alder adducts. The chemistry has been extended to incorporate cyclisation-anion capture methodology and the stereochemistry of the products has been determined.     

A Fast Algorithm for Wave Propagation from a Plane or a Cylindrical Surface

The newly developed Taylor-Interpolation-FFT (TI-FFT) algorithm dramatically increases the computational speeds for millimeter wave propagation from a planar (cylindrical) surface onto a “quasi-planar” (“quasi-cylindrical”) surface. Two different scenarios are considered in this article: the planar TI-FFT is for the computation of the wave propagation from a plane onto a “quasi-planar” surface and the cylindrical TI-FFT is for the computation of wave propagation from a cylindrical surface onto a “quasi-cylindrical” surface. Due to the use of the FFT, the TI-FFT algorithm has a computational complexity of O(N ² log₂  N ²) for an N × N computational grid, instead of N ⁴ for the direct integration method. The TI-FFT algorithm has a low sampling rate according to the Nyquist sampling theorem. The algorithm has accuracy down to −80 dB and it works particularly well for narrow-band fields and “quasi-planar” (“quasi-cylindrical”) surfaces.     

On state restrained linear-quadratic control problems

A finite dimensional linear autonomous control process with subspace state restraint is considered from the controllability and minimum quadratic cost points of view. The problem of holding in a subspace on an infinite time interval with finite total control energy is also considered.