General classical theory of spinning particles in a meson field

An exact classical theory of the motion of a point dipole in a meson field is given which takes into account the effects of the reaction of the emitted meson field. The meson field is characterized by a constant $\chi =\mu /\hslash $ of the dimensions of a reciprocal length, $\mu $ being the meson mass, and as $\chi \rightarrow $ 0 the theory of this paper goes over continuously into the theory of the preceding paper for the motion of a spinning particle in a Maxwell field. The mass of the particle and the spin angular momentum are arbitrary mechanical constants. The field contributes a small finite addition to the mass, and a negative moment of inertia about an axis perpendicular to the spin axis. A cross-section (formula (88 a)) is given for the scattering of transversely polarized neutral mesons by the rotation of the spin of the neutron or proton which should be valid up to energies of 10$^{9}$ eV. For low energies E it agrees completely with the old quantum cross-section, having a dependence on energy proportional to p$^{4}$/E$^{2}$ (p being the meson momentum). At higher energies it deviates completely from the quantum cross-section, which it supersedes by taking into account the effects of radiation reaction on the rotation of the spin. The cross-section is a maximum at E $\sim $ 3$\cdot $5$\mu $, its value at this point being 3 $\times $ 10$^{-26}$ cm.$^{2}$, after which it decreases rapidly, becoming proportional to E$^{-2}$ at high energies. Thus the quantum theory of the interaction of neutrons with mesons goes wrong for E $\gtrsim $ 3$\mu $. The scattering of longitudinally polarized mesons is due to the translational but not the rotational motion of the dipole and is at least twenty thousand times smaller. With the assumption previously made by the present author that the heavy partilesc may exist in states of any integral charge, and in particular that protons of charge 2e and - e may occur in nature, the above results can be applied to charged mesons. Thus transversely polarised mesons should undergo a very big scattering and consequent absorption at energies near 3$\cdot $5$\mu $. Hence the energy spectrum of transversely polarized mesons should fall off rapidly for energies below about 3$\mu $. Scattering plays a relatively unimportant part in the absorption of longitudinally polarized mesons, and they are therefore much more penetrating. The theory does not lead to Heisenberg explosions and multiple processes.

Non-linear theory of a positive-column in a magnetic-field

A nonlinear theory of an intermediate pressure discharge column in a magnetic field is presented. Motion of the neutral gas is considered. The continuity and momentum transfer equations for charged particles and neutral particles are solved by numerical methods. The main result obtained is that the rotating velocities of ionic gas and neutral gas are approximately equal. Bohm's criterion and potential inversion in the presence of neutral gas motion are also discussed.

Theory of the positive column of a gas discharge

An attempt is made to provide a theoretical explanation of the effect of the positive column on the voltage-current characteristic of a glow or an arc discharge. Such theories have been developed before, and all are based on balancing the production and loss of charged particles and accounting for the energy supplied to the plasma by the applied electric field. Differences among the theories arise from the approximations and omissions made in selecting processes that affect the particle and energy balances. This work is primarily concerned with the deviation from the ambipolar description of the positive column caused by space charge, electron-ion volume recombination, and temperature inhomogeneities.

The presentation is divided into three parts, the first of which involved the derivation of the final macroscopic equations from kinetic theory. The final equations are obtained by taking the first three moments of the Boltzmann equation for each of the three species in the plasma. Although the method used and the equations obtained are not novel, the derivation is carried out in detail in order to appraise the validity of numerous approximations and to justify the use of data from other sources. The equations are applied to a molecular hydrogen discharge contained between parallel walls. The applied electric field is parallel to the walls, and the dependent variables—electron and ion flux to the walls, electron and ion densities, transverse electric field, and gas temperature—vary only in the direction perpendicular to the walls. The mathematical description is given by a sixth-order nonlinear two-point boundary value problem which contains the applied field as a parameter. The amount of neutral gas and its temperature at the walls are held fixed, and the relation between the applied field and the electron density at the center of the discharge is obtained in the process of solving the problem. This relation corresponds to that between current and voltage and is used to interpret the effect of space charge, recombination, and temperature inhomogeneities on the voltage-current characteristic of the discharge.

The complete solution of the equations is impractical both numerically and analytically, and in Part II the gas temperature is assumed uniform so as to focus on the combined effects of space charge and recombination. The terms representing these effects are treated as perturbations to equations that would otherwise describe the ambipolar situation. However, the term representing space charge is not negligible in a thin boundary layer or sheath near the walls, and consequently the perturbation problem is singular. Separate solutions must be obtained in the sheath and in the main region of the discharge, and the relation between the electron density and the applied field is not determined until these solutions are matched.

In Part III the electron and ion densities are assumed equal, and the complicated space-charge calculation is thereby replaced by the ambipolar description. Recombination and temperature inhomogeneities are both important at high values of the electron density. However, the formulation of the problem permits a comparison of the relative effects, and temperature inhomogeneities are shown to be important at lower values of the electron density than recombination. The equations are solved by a direct numerical integration and by treating the term representing temperature inhomogeneities as a perturbation.

The conclusions reached in the study are primarily concerned with the association of the relation between electron density and axial field with the voltage-current characteristic. It is known that the effect of space charge can account for the subnormal glow discharge and that the normal glow corresponds to a close approach to an ambipolar situation. The effect of temperature inhomogeneities helps explain the decreasing characteristic of the arc, and the effect of recombination is not expected to appear except at very high electron densities.

The vacuum Regge Trajectory in conventional field theory

The effect on the scattering amplitude of the existence of a pole in the angular momentum plane near J = 1 in the channel with the quantum numbers of the vacuum is calculated. This is then compared with a fourth order calculation of the scattering of neutral vector mesons from a fermion pair field in the limit of large momentum transfer. The presence of the third double spectral function in the perturbation amplitude complicates the identification of pole trajectory parameters, and the limitations of previous methods of treating this are discussed. A gauge invariant scheme for extracting the contribution of the vacuum trajectory is presented which gives agreement with unitarity predictions, but further calculations must be done to determine the position and slope of the trajectory at s = 0. The residual portion of the amplitude is compared with the Gribov singularity.

Fe−TPP Coordination Network with Metalloporphyrinic Neutral Radicals and Face-to-Face and Edge-to-Face π−π Stacking

Artículo científico Inorg. Chem. 2013, 52, 8074−8081

Ab initio calculations for the neutral and charged O vacancy in sapphire

The energetics, lattice relaxation, and the defect-induced states of st single O vacancy in alpha-Al2O3 are studied by means of supercell total-energy calculations using a first-principles method based on density-functional theory. The supercell model with 120 atoms in a hexagonal lattice is sufficiently large to give realistic results for an isolated single vacancy (square). Self-consistent calculations are performed for each assumed configuration of lattice relaxation involving the nearest-neighbor Al atoms and the next-nearest-neighbor O atoms of the vacancy site. Total-energy data thus accumulated are used to construct an energy hypersurface. A theoretical zero-temperature vacancy formation energy of 5.83 eV is obtained. Our results show a large relaxation of Al (O) atoms away from the vacancy site by about 16% (8%) of the original Al-square (O-square) distances. The relaxation of the neighboring Al atoms has a much weaker energy dependence than the O atoms. The O vacancy introduces a deep and doubly occupied defect level, or an F center in the gap, and three unoccupied defect levels near the conduction band edge, the positions of the latter are sensitive to the degree of relaxation. The defect state wave functions are found to be not so localized, but extend up to the boundary of the supercell. Defect-induced levels are also found in the valence-band region below the O 2s and the O 2p bands. Also investigated is the case of a singly occupied defect level (an F+ center). This is done by reducing both the total number of electrons in the supercell and the background positive charge by one electron in the self-consistent electronic structure calculations. The optical transitions between the occupied and excited states of the: F and F+ centers are also investigated and found to be anisotropic in agreement with optical data.

Electronic structures of 4d transition metal monoxides by density functional theory

Bond distances, dissociation energies, ionization potentials and electron affinities of 4d transition metal monoxides from YO to CdO and their positive and negative ions were studied by use of density functional methods B3LYP, BLYP, B3PW91, BPW91, B3P86, BP86, SVWN, MPW1PW91 and PBE1PBE. It was found that calculated properties are highly dependent on the functionals employed, especially for dissociation energy. For most neutral species, pure density functionals BLYP, BPW91 and BP86 have good performance in predicting dissociation energy than hybrid density functionals B3LYP, B3PW91 and B3P86. In addition, BLYP gives the largest bond distance compared with other density functional methods, while SVWN gives shortest bond distance, largest dissociation energy and electron affinity. For the ground state, the spin multiplicity of the charged species can be obtained by +/- 1 of their corresponding neutral species.

Electronic structures of 5d transition metal monoxides by density functional theory

Bond distances, vibrational frequencies, electron affinities, ionization potentials, and dissociation energies of the diatomic 5d transition metal (except La) monoxides and their positively and negatively charged ions were studied by use of density functional methods B3LYP, BLYP, B3PW91, BPW91, B3P86, BP86, MPW1PW91, PBE1PBE, and SVWN. Our calculation shows that for each individual species, the calculated properties are quite sensitive to the method used. Compared with hybrid density functional method B3PW91 (B3P86), pure density functional method BPW91 (BP86) gives longer bond distance (lower vibrational frequency) from HfO to PtO for neutral species, HfO+ to IrO+ for cationic species, and HfO- to AuO- for anionic species. While for B3LYP and BLYP, the trend was observed for cationic species from HfO+ to IrO+ and anionic species from HfO- to AuO- (except TaO-), but not for neutrals. Pure density function methods BLYP, BPW91, and BP86 give larger dissociation energy compared with hybrid density functional methods B3LYP, B3PW91, and B3P86. SVWN in most cases gives the smallest bond distance, while BLYP gives the largest value. MPW1PW91 and PBE1PBE show the same performance in predicting the spectroscopic constants.

In vitro study on the binding of neutral red to bovine serum albumin by molecular spectroscopy

In this paper, the binding of neutral red (NR) to bovine serum albumin (BSA) under physiological conditions has been studied by spectroscopy method including fluorescence, circular dichroism (CD) and Fourier transform infrared (FT-IR) spectroscopy. The Stern-Volmer fluorescence quenching constant (K-SV), binding constant (K-b) and the number of binding sites (It) were measured by fluorescence quenching method. Fluorescence experiments were also performed at different ionic strengths. It was found K-SV was ionic strength dependent, which indicated the electrostatic interactions were part of the binding forces. The distance r between donor (BSA) and acceptor (NR) was obtained according to Foster's non-radiative energy transfer theory. CD spectroscopy and FT-IR spectroscopy were used to investigate the structural information of BSA molecules on the binding of NR, and the results showed no change of BSA conformation in our experimental conditions.

GENERAL ALPHA-N INDEX AND ITS APPLICATION .2. THE CORRELATION BETWEEN THE GENERAL ALPHA-N INDEX AND PHYSICAL-PROPERTIES OF NEUTRAL PHOSPHORUS-COMPOUNDS

The relationship between the alpha-N index and physical properties of neutral phosphorus extractants is studied. Using the general alpha-N index which could describe extractants with minute difference in structure, the good correlation between it and various physical properties of the neutral phosphorus extractants (e.g., densities, refractive index, shift ratio of paper chromatography and IR frequencies of bond P = O) is obtained. The result indicates that general alpha-N index is a good topological index of organic compounds.

GENERAL ALPHA-N INDEX AND ITS APPLICATION .1. GENERAL ALPHA-N INDEX AND ITS APPLICATION IN THE EXTRACTION OF Y, CE, U, AND TH BY NEUTRAL PHOSPHORUS EXTRACTANCTS

The general a(N) index is established for molecules containing heteroatoms, rings, and multiple bonds. The general a(N) index is able to describe molecules with minute differences in structure and can also reveal the properties of molecules. This theory is successfully applied to the case of neutral phosphorus extractants. Both the molecular polarity and steric effect are characterized by the general a(N) index. The relationships between these properties and the distribution ratios for extracting Y, Ce, U, and Th are also shown by the general a(N) index.

Can density functional theory (DFT) be used as an aid to a deeper understanding of tandem mass spectrometric fragmentation pathways?

Prediction of tandem mass spectrometric (MS/MS) fragmentation for non-peptidic molecules based on structure is of immense interest to the mass spectrometrist. If a reliable approach to MS/MS prediction could be achieved its impact within the pharmaceutical industry could be immense. Many publications have stressed that the fragmentation of a molecular ion or protonated molecule is a complex process that depends on many parameters, making prediction difficult. Commercial prediction software relies on a collection of general heuristic rules of fragmentation, which involve cleaving every bond in the structure to produce a list of 'expected' masses which can be compared with the experimental data. These approaches do not take into account the thermodynamic or molecular orbital effects that impact on the molecule at the point of protonation which could influence the potential sites of bond cleavage based on the structural motif. A series of compounds have been studied by examining the experimentally derived high-resolution MS/MS data and comparing it with the in silico modelling of the neutral and protonated structures. The effect that protonation at specific sites can have on the bond lengths has also been determined. We have calculated the thermodynamically most stable protonated species and have observed how that information can help predict the cleavage site for that ion. The data have shown that this use of in silico techniques could be a possible way to predict MS/MS spectra. Copyright (C) 2009 John Wiley & Sons, Ltd.

Electronic structure of the nitrogen-vacancy center in diamond from first-principles theory

The nitrogen-vacancy (NV) center is a paramagnetic defect in diamond with applications as a qubit. Here, we investigate its electronic structure by using ab initio density functional theory for five different NV center models of two different cluster sizes. We describe the symmetry and energetics of the low-lying states and compare the optical frequencies obtained to experimental results. We compute the major transition of the negatively charged NV centers to within 25–100 meV accuracy and find that it is energetically favorable for substitutional nitrogens to donate an electron to NV0. The excited state of the major transition and the NV0 state with a neutral donor nitrogen are found to be close in energy.

A complete analytic theory for structure and dynamics of populations and communities spanning wide ranges in body size

The prediction and management of ecosystem responses to global environmental change would profit from a clearer understanding of the mechanisms determining the structure and dynamics of ecological communities. The analytic theory presented here develops a causally closed picture for the mechanisms controlling community and population size structure, in particular community size spectra, and their dynamic responses to perturbations, with emphasis on marine ecosystems. Important implications are summarised in non-technical form. These include the identification of three different responses of community size spectra to size-specific pressures (of which one is the classical trophic cascade), an explanation for the observed slow recovery of fish communities from exploitation, and clarification of the mechanism controlling predation mortality rates. The theory builds on a community model that describes trophic interactions among size-structured populations and explicitly represents the full life cycles of species. An approximate time-dependent analytic solution of the model is obtained by coarse graining over maturation body sizes to obtain a simple description of the model steady state, linearising near the steady state, and then eliminating intraspecific size structure by means of the quasi-neutral approximation. The result is a convolution equation for trophic interactions among species of different maturation body sizes, which is solved analytically using a novel technique based on a multiscale expansion.

Resonantly Enhanced Multi-Photon Ionization Spectrum of the Neutral Green Fluorescent Protein Chromophore

The photophysics of the green fluorescent protein is governed by the electronic structure of the chromophore at the heart of its β-barrel protein structure. We present the first two-color, resonance-enhanced, multiphoton ionization spectrum of the isolated neutral chromophore in vacuo with supporting electronic structure calculations. We find the absorption maximum to be 3.65 ± 0.05 eV (340 ± 5 nm), which is blue-shifted by 0.5 eV (55 nm) from the absorption maximum of the protein in its neutral form. Our results show that interactions between the chromophore and the protein have a significant influence on the electronic structure of the neutral chromophore during photoabsorption and provide a benchmark for the rational design of novel chromophores as fluorescent markers or photomanipulators.