Pi Components Research Articles

The Origin of Aromaticity: Important Role of the Sigma Framework in Benzene

The physical nature of aromaticity is addressed at a high ab initio level. It is conclusively shown that the extrinsic aromatic stabilization energy of benzene E(ease)B, estimated relative to its linear polyene counterpart(s), is very well-reproduced at the Hartree-Fock (HF) level. This is a consequence of the fact that the contributions arising from the zero-point vibrational energy (ZPVE) and electron correlation are rather small. More specifically, they yield together 2.0 kcalmol(-1) to the destabilization of benzene. A careful scrutiny of the HF energies by virial theorem shows further that the kinetic energies of the sigma and pi electrons E(T)HF(sigma) and E(T)HF(pi) are strictly additive in the gauge linear zig-zag polyenes, which also holds for their sum Et(T)HF This finding has the important corollary that E(ease)B is little dependent on the choice of the homodesmic reactions involving zig-zag polyenes. A detailed physical analysis of the sigma- and pi-electron contributions to extrinsic aromaticity requires explicit introduction of the potential energy terms Vne, Vee, and Vnn, which signify Coulomb interactions between the electrons and the nuclei. The Vee term involves repulsive interaction Vee(sigmapi) between the sigma and pi electrons, which cannot be unequivocally resolved into sigma and pi contributions. The same holds for the Vnn energy, which implicitly depends on the electron density distribution via the Born-Oppenheimer (BO) potential energy surface. Several possibilities for partitioning Vee(sigmapi) and Vnn terms into sigma and pi components are examined. It is argued that the stockholder principle is the most realistic, which strongly indicates that E(ease)B is a result of favorable sigma-framework interactions. In contrast, the pi-electron framework prefers the open-chain linear polyenes.

A time-dependent wave packet study of the vibronic and spin-orbit interactions in the dynamics of Cl((2)P)+H(2)-->HCl(X (1)Sigma(g) (+))+H((2)S) reaction.

We investigate the vibronic and spin-orbit (SO) coupling effects in the state-selected dynamics of the title reaction with the aid of a time-dependent wave packet approach. The ab initio potential energy surfaces of Capecchi and Werner [Science 296, 715 (2002)] have been employed for this purpose. Collinear approach of the Cl((2)P) atom to the H(2) molecule splits the degeneracy of the (2)P state and gives rise to (2)Sigma and (2)Pi electronic states. These two surfaces form a conical intersection at this geometry. These states transform as 1 (2)A('), 1 (2)A("), and 2 (2)A('), respectively, at the nonlinear configurations of the nuclei. In addition, the SO interaction due to Cl atom further splits these states into (2)Sigma(1/2), (2)Pi(3/2), and (2)Pi(1/2) components at the linear geometry. The ground-state reagent Cl((2)P(3/2))+H(2) correlates with (2)Sigma(1/2) and (2)Pi(3/2), where as the SO excited reagent Cl(*)((2)P(1/2))+H(2) correlates with (2)Pi(1/2) at the linear geometry. In order to elucidate the impact of the vibronic and SO coupling effects on the initial state-selected reactivity of these electronic states we carry out quantum scattering calculations based on a flux operator formalism and a time-dependent wave packet approach. In this work, total reaction probabilities and the time dependence of electronic population of the system by initiating the reaction on each of the above electronic states are presented. The role of conical intersection alone on the reaction dynamics is investigated with a coupled two-state model and for the total angular momentum J=0 (neglecting the electronic orbital angular momentum) both in a diabatic as well as in the adiabatic electronic representation. The SO interaction is then included and the dynamics is studied with a coupled three-state model comprising six diabatic surfaces for the total angular momentum J=0.5 neglecting the Coriolis Coupling terms of the Hamiltonian. Companion calculations are carried out for the uncoupled adiabatic and diabatic surfaces in order to explicitly reveal the impact of two different surface coupling mechanisms in the dynamics of this prototypical reaction.

Nickel-catalyzed reductive cyclizations and couplings.

For over 50 years, nickel catalysis has been applied in cycloaddition processes. Nickel-catalyzed reductive couplings and cyclizations, however, have only recently attracted a high level of interest. This group of new reactions allows a broad range of multicomponent couplings involving two or more pi components with a main-group or transition-metal reagent. These processes allow the assembly of important organic substructures from widely available reaction components. Multiple contiguous stereocenters, polycyclic ring systems, and novel arrays of complex functionality may often be prepared from simple, achiral, acyclic precursors. With three or more reactive functional groups participating in the catalytic processes, many mechanistic questions abound, including the precise timing of bond constructions and the nature of reactive intermediates. This Review is thus aimed at providing a critical evaluation of recent progress in this rapidly developing field.

Sigma-pi separation of the electron localization function and aromaticity.

The electron localization function (ELF) has been separated in its sigma and pi components. The topological analysis of the new ELFsigma and ELFpi functions has been used to quantify the concept of resonance. The highest bifurcation values of these functions describe in a correct way the aromaticity of classical ring molecules and some new aromatic compounds as B6CO6, Al4(2-), and N5-. In the case of Al4(2-), an important sigma delocalization contribution has been found, which is in agreement with previous interpretation.

Features of the electron density in magnesium diboride: reconstruction from X-ray diffraction data and comparison with TB-LMTO and FPLO calculations.

Features of the electron density in MgB(2) reconstructed from room-temperature single-crystal X-ray diffraction intensities using a multipole model are considered. Topological analysis of the total electron density has been applied to characterize the atomic interactions in magnesium diboride. The shared-type B-B interaction in the B-atom layer reveals that both sigma and pi components of the bonding are strong. A closed-shell-type weak B-B pi interaction along the c axis of the unit cell has also been found. The Mg-B closed-shell interaction exhibits a bond path that is significantly curved towards the vertical Mg-atom chain ([110] direction). The latter two facts reflect two sorts of bonding interactions along the [001] direction. Integration of the electron density over the zero-flux atomic basins reveals a charge transfer of approximately 1.4 (1) electrons from the Mg atoms to the B-atom network. The calculated electric-field gradients at nuclear positions are in good agreement with experimental NMR values. The anharmonic displacement of the B atoms is also discussed. Calculations of the electron density by tight-binding linear muffin-tin orbital (TB-LMTO) and full-potential non-orthogonal local orbital (FPLO) methods confirm the results of the reconstruction from X-ray diffraction; for example, a charge transfer of 1.5 and 1.6 electrons, respectively, was found.

Towards an understanding of the bonding in polyoxometalates through bond order and bond energy analysis.

The molecular and electronic structures of transition metal complexes, [MOCl5]n- (n = 2 for M = V,Nb,Ta and n = 1 for Mo,W) and mixed-metal polyoxometalates, [M'M5O19]3-V,Nb,Ta, M = Mo,W) containing a single terminal oxo group on each metal, and of complexes of the uranyl ion [UO2]2+, [UO2(H2O)5]2+ and [UO2Cl4]2-, have been calculated using density functional methods. The calculated structures of the complexes are in good agreement with available experimental parameters. For the mixed-metal hexametalates, for which no crystallographic data is available, the calculations predict a small tetragonal compression of the clusters with only minor structural changes compared to the parent molybdate and tungstate. The metal oxygen bonding in these anions has been probed using Mayer-Mulliken, bond energy and atoms in molecule analyses (AIM). These methods provide a consistent description of the bonding in polyoxometalates. The terminal bonds between transition metal or uranium and oxygen atoms have large sigma and pi components with the pi contributions exceeding the sigma bonding. The transition metals utilize their d orbitals almost exclusively to bond to oxygen whilst uranium uses both its 5f and 6d orbitals. Oxygen atom charges increase and covalency indexes decrease with coordination number, with a marked separation of these terms according to the oxygen atom type. The total valency and AIM energies of the oxygen atoms are predicted to be almost constant for all types of oxygen site. The constancy of the bonding power of the oxygen atoms appears to be an important factor in determining the gross structures and details of the bonding in polyoxometalates. The Mayer Mulliken approach provides direct characterization of the bonding power of atoms and the extent of the interaction between pairs of atoms that is consistent with the results of the considerably more computationally demanding bond energy and AIM approaches.

Dynamical calculation of crystal truncation rods for surfaces and interfaces using a Cartesian coordinate transformation technique.

A dynamical calculation scheme that employs Cartesian coordinates with a z axis normal to the crystal surface to define polarization unit vectors and wavefields is applied to interpret the intensity distribution of crystal truncation rods for surfaces and interfaces. A comparison between this calculation scheme and the asymptotic iteration approach using the conventional presentation of the polarization components of the wavefields, with the sigma and pi components perpendicular to the wavevectors, is presented. It is found that the use of Cartesian coordinate systems can provide correct boundary conditions in determining the wavefield amplitudes, thus leading to a rigorous and general calculation scheme for dynamical diffraction from surfaces and interfaces.

尿素加ポリアクリルアミドゲル等電点電気泳動法による軽種馬のPiフェノタイピング

Isoelectric focusing (IEF) using polyacrylamide gel containing urea (Urea-PAG) was used for the characterization of equine protease inhibitor (Pi) types in light breed horses to solve the following problems in conventional IEF and two-dimensional (2-D) electrophoresis: typing complexity due to high heterogeneity of Pi system and overlapping of Pi and esterase (Es) components on IEF, operational complexity and time-consumption on 2-D. The Urea-PAG IEF method had high resolution capacity, clearly distinguishing at least 10 types frequently observed in light breed horses. Es components were not detected on Urea-PAG. There was little complexity of Pi typing as shown by these results, and thus the typing procedure is simpler and more rapid than conventional IEF and 2-D. The present method should thus prove quite adequate for exact classification of Pi system in light breed horses.

Purification of human recombinant superoxide dismutase by isoelectric focusing in a multicompartment electrolyzer with zwitterionic membranes.

Human recombinant superoxide dismutase (SOD), purified to homogeneity, is resolved by both conventional isoelectric focusing and immobilized pH gradients into three bands, with isoelectric points (pIs) in the pH range 4.8 to 5.1, the pI 4.80 form representing the minor component. Due to the fact that this enzyme is expressed in E. coli, N-terminal acetylation or glycosylation should be ruled out. When purified by small-scale preparative isoelectric focusing in immobilized pH gradient gels, it was found that, upon subsequent analysis, the pI 5.07 form would band in the same position, but the intermediate pI 4.92 band would split into the upper (pI 5.07) and the lower (pI 4.80) species, in nearly the same amounts, whereas the lowest pI component would always generate both the intermediate and upper forms. Enzymatic essays pointed out that these three isoforms had nearly the same specific activity, slightly higher than that of the starting material. Metal analysis indicated that all three forms contained the same metal/protein ratio, approaching the value Cu2Zn2-SOD, as reported in the literature. Circular dichroism spectra of the pI 4.80 and 5.07 forms showed the same profile in the 190-240 nm range, but marked differences in the 250-350 nm region. Treatment with EDTA produces 1-2 additional, slightly higher pI isoforms, whereas treatment with KCN generates a number of higher pI components, reaching pI values as high as pH 7, with nearly complete disappearance of the three major SOD isoforms. It is concluded that these three isoforms could represent interconvertible species, the highest pI component representing the most stable conformer.

Shifts of isoelectric points between cellular and secreted antibodies as revealed by isoelectric focusing and immobilized pH gradients

Charge microheterogeneity of monoclonal antibodies, as revealed by isoelectric focusing in carrier ampholytes, has been known for a long time. Here we demonstrate, in the case of monoclonals against the gp-41 of the HIV-1 virus, that this heterogeneity is already present within the cell sap of hybridoma cells during antibody synthesis. When the monoclonals are secreted extracellularly, the same isoelectric point (pI) spectrum is maintained, but there is marked redistribution of the relative isoform abundance towards the lower pI components. This suggests in vivo processing of such forms, possibly via glycosylation or deamidation. The secreted antibodies are also analyzed by immobilized pH gradients (IPG), where they demonstrate an even more extensive heterogeneity, due to the marked increment in resolving power. Single bands are purified by preparative IPGs in a multicompartment electrolyzer and are shown to be stable with time. Thus, artefactual heterogeneity produced by the focusing technique is completely excluded and cellular processing is clearly established.

Non-relativistic spectrum of the q2q2 system in large harmonic oscillator bases

The non-relativistic S-wave spectrum of the q2q2 system composed of u and d quarks is investigated in harmonic oscillator bases including all the configurations up to Nh(cross) omega oscillator excitation energy with N<or=6 using a two-body interaction deduced from Bhaduri's potential. The lowest 2+ states are found near the rho rho threshold and, in the same mass region, certain 0+ states are characterised by very small pi pi components. These findings are consistent with bag model results and reinforce the multiquark interpretation of 0+ and 2+ resonances observed in pn annihilations and gamma gamma reactions.

Comparative study of the proteinase inhibitor pattern in serum and cerebrospinal fluid

After concentration the α 1-proteinase inhibitors (Pi) of cerebrospinal fluid (CSF) were separated by isoelectric focusing. The relative amounts of the different Pi components in the CSF were compared with those in the serum of the same donor. The Pi components were identified by crossed isoelectric focusing. Most of the serum Pi components could be detected in the CSF but their relative proportions in serum and CSF differed considerably. The typical serum Pi patterns observed for different phenotypes were not reflected in the CSF. In cases when CSF protein levels were abnormally high alterations of the CSF Pi pattern were observed, i.e. the proportions of at least some of the Pi components approached those in serum. It is concluded that CSF Pi components originate from the serum and that a highly selective blood-CSF barrier function results in a considerable alteration of the concentration pattern. It has been shown by crossed isoelectric focusing technique that at least two proteins acting as Pi in serum do not exert antiproteolytic activity in CSF. Consequently, in CSF these Pi components may have been chemically modified, resulting in an alteration of the acceptor sites but not of the isoelectric point of the inhibitor molecule.

On linear failure rates : Anthony A. Salvia. IEEE Trans. Reliab.R-27, (2) 145 (June 1978)

Let Y1,…, Yn be independent identically distributed random variables with distribution function F(x, θ), θ = (θ′1, θ′2), where θi (i = 1, 2) is a vector of pi components, p = p1 + p2 and for ∀θ∈I, an open interval in Rp, F(x, θ) is continuous. In the present paper the author shows that the asymptotic distribution of modified Cramér-Smirnov statistic under Hn: θ1 = θ10 + n−1/2γ, θ2 unspecified, where γ is a given vector independent of n, is the distribution of a sum of weighted noncentral χ12 variables whose weights are eigenvalues of a covariance function of a Gaussian process and noncentrality parameters are Fourier coefficients of the mean function of the Gaussian process. Further, the author exploits the special form of the covariance function by using perturbation theory to obtain the noncentrality parameters and the weights. The technique is applicable to other goodness-of-fit statistics such as U2 [G. S. Watson, Biometrika 48 (1961), 109–114].

The slow ERG potentials in hereditary retinal dystrophy of albino and pigmented rats

The slow ERG potentials of different sites of generation—PI, PII-related and Slow PIII—were studied at different ages in normal and mutant rats reared in a dark environment. The manifestations of these potentials in the normal rat were similar to the adult rabbit although their amplitudes in comparison to the b-wave were lower. They were peculiarly dependent on age and were highest during the fifth week of age. In the adult, normal pigmented rats, early PI components slightly exceeded Slow PIII but Slow PIII dominated in the records from adult albinos. In the mutant albino or pigmented rats, all slow ERG components were evident at the age of 21 days except the late positive transient of PI. The negative transient of PI disappeared after 26 days but a slow c-wave survived beyond 5 weeks. The iodate-isolated Slow PIII was better preserved than any PI component but it also was sluggish in response to the cessation of illumination. Responses to azide and thiocyanate were well preserved in 4-month-old mutants. The preservation of PI was generally better at any age for the pigmented than the albino mutants. An interpretation of the findings, based upon previous analyses in the rabbit—Slow PIII originating in the distal Müller cell process, PI generated by the pigment epithelium—leads to the conclusions (a) that the electrical properties of the pigment epithelium are not primarily affected in the dystrophic rat and (b) that the accumulation of debris impedes the chemical communication between still functioning photoreceptors and pigment epithelium as well as distal Müller cell processes.

PSO-based optimization of PI regulator and VA loading of a SRF-based multi-converter DVR

This paper deals with a design of optimal parameters of PI regulator in voltage control loop. The design aims to minimize voltampere (VA) loading of synchronous reference frame (SRF) based multi converter-DVR in parallel feeder distribution systems. To improve the power quality by using power conditioner with multi converters in each feeder distribution system under different load considerations, a dynamic model of synchronous-reference- frame (SRF) has been adopted. It is desirable to have optimization of PI components and generate the reference compensate voltages for series active filters (SAF) of MC-DVR. Therefore, series active filters help to inject optimal voltages at optimal angle in such a way that a minimum VA loading of MCDVR is possible. The optimal value PI components and optimal series injected angle of series active power filters are computed using particle swarm optimization (PSO) technique and the results are verified with genetic algorithm (GA). The simulation results show that the proposed PSO technique causes minimum error and minimum VA loading angle by optimally choosing parameters of PI and minimum VA angle as compared to GA technique.Keywords: Active power filter (APF), synchronous reference frame (SRF), Genetic algorithm (GA), Particle Swarm Optimization (PSO) and multi converter dynamic voltage restorer (MC-DVR).

Studies of the circular dichroism of bisdiamine complexes of cobalt(III).

Circular dichroism spectra are reported for cis-bis-diamine d 6 metal complexes with C 4v symmetry, of the type cis-[Co(en) 2(NH 3)(X)] n+. An empirical molecular orbital treatment is used to predict and assign the circular dichroism transitions associated with the d→ d absorption bands. The theory is extended to the trans-bisdiamine and cis-bisdiamine metal complexes with D 4hand C 2 symmetry, respectively. The band splittings of the d→ d transitions of the trans-bisdiamine complexes are twice those of the cis-bisdiamine complexes with C 4v symmetry. Linear relationships are found experimentally between the frequencies of the circular dichroism components of the visible absorption bands and δΔ, the empirical molecular orbital parameter, which has sigma and pi components, and is the digonal perturbation due to the ligands.