Stark mixing by ion-Rydberg atom (molecule) collisions

Classical molecular dynamics simulations are performed to cover Stark mixing transitions (nℓ→nℓ^′) in Rydberg atoms by collision with slow ions. Accuracy is tested by comparison with the exact analytical classical probabilities previously obtained when the ion–atom potential is taken as the long-range ion–dipole interaction. The results are provided not only for the ion–dipole interaction but also for the full electrostatic interaction. It is shown, by comparison, that the ion–dipole potential alone provides reliable probabilities. The method is highly accurate and is very amenable to ready inclusion of other processes competing with Stark mixing.     

Construction of Trigonometrically and Exponentially Fitted Runge–Kutta–Nyström Methods for the Numerical Solution of the Schrödinger Equation and Related Problems – a Method of 8th Algebraic Order

General conditions are presented for an m-stage Runge–Kutta–Nyström fitting to exponential and trigonometric functions. As an example an 8th order Runge–Kutta–Nyström method is constructed. Numerical results on the numerical solution of the Schrödinger equation and related problems indicate that the new method is more accurate than the classical one (we call classical Runge–Kutta–Nyström method the corresponding method with constant coefficients).     

Collision efficiencies of diffusing spherical particles: hydrodynamic,van der waals and electrostatic forces

A practical limitation of the application of Smoluchowski's classical estimate for the collisions probability of two diffusing spherical particles in Brownian motion is the non-consideration of interparticle forcves. For suspended particles in water such forces can arise from the disturbance the particle causes in the fluid (hydrodynamic forces), from the cloud of ions which surround an electrically charged particle (double layer forces) or they can be of molecular origin (van der Waals forces). In this paper corrections to Smoluckhowski's collision probability are computed when such forces operate Scoluchowski's collision probability are computed when such forces operate between two approaching particles of various sizes. Results for several values of the van der Waals energy of attraction and the ionic strength of the electrolyte are presented in a way convenient for particle collision modeling.     

Size-dependent reactivity of cobalt cluster ions with nitrogen monoxide: Competition between chemisorption and decomposition of NO

Reactions of NO molecules on cobalt cluster ions were studied in a beam-gas geometry by using a tandem mass spectrometer. Single-particle collision reactions of Co_mNO⁺ (m = 3–10) with NO were found to proceed in such a manner that NO decomposition dominates at m = 4–6 with the maximum reaction cross section at m = 5 and chemisorption dominates in m ≥ 7. On the other hand, in two-particle collision reactions of Co_n⁺ (n = 2–10) with NO, NO decomposition at n ≥ 5 and chemisorption of two NO molecules with Co atoms loss at n ≥ 8 were found to proceed. These results indicate that the size-dependency of the multiple collision reactions originates from secondary attacking of an NO molecule to primary products of the initial single collision reactions. The DFT calculation supports the scheme that both the decomposition and chemisorption of two-particle collision reactions proceed via a common intermediate, Co_mN₂O₂⁺, in which the two NO molecules are dissociatively chemisorbed on the cobalt cluster ion, and the size-dependency of the two-particle collision reactions is explained in terms of the structure of this reaction intermediate.     

Equations for the Molecular Mass Distribution of Hydrocarbons Formed in CO Hydrogenation on a Cobalt–Zirconium Catalyst

A mathematical model for Fischer–Tropsch synthesis is proposed. The model takes into account the most common deviations from classical Anderson–Schulz–Flory distribution and adequately describes the experimental molecular mass distributions of hydrocarbons formed in carbon monoxide hydrogenation on a cobalt catalyst supported on the zirconium form of silica gel.     

On the applicability of the classical trajectory equations in inelastic scattering theory

By using the classical trajectory equations and an average trajectory we have been able to predict the single quantum transitions for the one-dimensional atom—diatom collision problem to within 10–30%. The double quantum transitions P₀₂ are correct to within at least a factor of two.     

Attachment and ionization in a self-consistent treatment of the electron kinetics of a collision-dominated rf plasma

This paper deals with the self-consistent determination of the rf field amplitude for sustaining the steady-state collision-dominated weakley ionized plasmas in the bulk of the rf discharge and of the time-resolved behavior of the isotropic part of the distribution function as well as of relevant macroscopic quantities in plasmas whose particle loss is dominantly determined by electron attachment. The strict timeresolved treatment is based on the nonstationary Boltzmann equation of the electrons and its numerical solution including, apart from electron number conservative collision processes, the electron attachment and ionization. The investigations are related to an rf plasma in a model gas and in SF₆ and are performed for reduced rf field frequencies around 10 MHz Torr^–1 which are of particular interest from the point of application of rf discharges for plasma processing. The numerical results show that a large field amplitude of around 160 V cm^–1 Torr^–1 is necessary to maintain the discharge and that the isotropic distribution, the relevant collision frequencies for attachment and ionization, and the electron density undergo a large modulation during a period of the rf field.     

Generalized Christoffel–Darboux formulae and the frontier Kohn–Sham molecular orbitals

The Christoffel–Darboux formula for classical orthogonal polynomials is generalized to arbitrary sets of orthogonal functions in three dimensions, yielding an explicit link between frontier Kohn–Sham molecular orbitals and the Kohn–Sham density matrix. Methods using this result could significantly accelerate Kohn–Sham density functional theory calculations, as only a subset of the Kohn–Sham equations would need to be addressed. The result can also be seen as an explicit justification for the utility of frontier molecular orbital theory.     

A structurally driven spectral transform Lanczos method for mixed quantum—classical canonical simulations (MQCC): the thermodynamics of Kr10–H and the energies of Krn–H, (n:1→9)

We develop and test an approximate approach for canonical simulations of weakly bound atomic or molecular systems for which some degrees of freedom can be treated separately by quantum mechanics. The system chosen for testing is Kr₁₀–H, for which the adiabatic approximation applied to separate the hydrogen degrees of freedom works reasonably well. The hydrogen atom is bound to the Kr clusters at cold temperatures and we calculate several bound states for clusters in the n=1–9 range, in the global minimum configuration. The structural character of the mixed quantum classical simulation is substantially different than the classical simulation for Kr₁₀–H as a result of zero point energy effects. When quantum effects are included, the low temperature dynamics of Kr₁₀–H are dominated by a significant well to well hopping about an incomplete icosahedral krypton core.     

Simulating quantum dynamics in classical environments

Methods for simulating the dynamics of composite systems, where part of the system is treated quantum mechanically and its environment is treated classically, are discussed. Such quantum–classical systems arise in many physical contexts where certain degrees of freedom have an essential quantum character while the other degrees of freedom to which they are coupled may be treated classically to a good approximation. The dynamics of these composite systems are governed by a quantum–classical Liouville equation for either the density matrix or the dynamical variables which are operators in the Hilbert space of the quantum subsystem and functions of the classical phase space variables of the classical environment. Solutions of the evolution equations may be formulated in terms of surface-hopping dynamics involving ensembles of trajectory segments interspersed with quantum transitions. The surface-hopping schemes incorporate quantum coherence and account for energy exchanges between the quantum and classical degrees of freedom. Various simulation algorithms are discussed and illustrated with calculations on simple spin-boson models but the methods described here are applicable to realistic many-body environments.     

Ultrafast many-body energy transfer in the frequency domain

In this paper, we consider the response of many-body systems to ultrashort time scale impulsive perturbations. We focus on the interplay between the characteristic frequencies and time scales of the interacting degrees of freedom, and develop both a qualitative picture and a simple analytic theory in terms of a frequency domain perspective. We illustrate the general approach by considering a model many-body problem consisting of the impulsive collision of an atom with a harmonic chain, and treat the dynamics using classical mechanics. An analytic expression for the energy uptake of the chain is derived, and its predictions are compared with classical molecular dynamics simulations on a one-dimensional model of rare gas scattering from a Pt surface. Our approach highlights the importance of the overlap in frequency between the phonon spectrum of the solid, weighted by each mode's contribution to the surface atom displacement, and the power spectrum of the impulsive force felt by the surface during the collision. The analytic theory reproduces the high energy kinematic limit of binary atom–atom collisional energy transfer, and emphasizes the adiabatic “freezing out” of high frequency phonons as the collision energy is decreased.     

Application of Multivariate Calibration Techniques to HPLC Data for Quantitative Analysis of a Binary Mixture of Hydrochlorathiazide and Losartan in Tablets

New multivariate approaches have been applied to high-performance liquid chromatography (HPLC) with multiwavelength photodiode-array (PDA) detection. Multivariate calibration techniques such as partial least squares (PLS), principal component regression (PCR), classical least squares (CLS), and inverse least squares (ILS) was subjected to HPLC data for simultaneous quantitative analysis of synthetic binary mixtures and a commercial tablet formulation containing hydrochlorothiazide (HCT) and losartan potassium (LST). The combined use of HPLC and multivariate calibrations has been denoted HPLC–CLS, HPLC–ILS, HPLC–PCR, and HPLC–PLS. Successful chromatographic separation of the two active compounds and enalapril maleate, used as internal standard (IS), was accomplished by means of a 4.6 mm i.d. × 250 mm, 5 m particle, Waters Symmetry C₁₈ reversed-phase column and a mobile phase consisting of 60:40 acetate buffer (0.2 M, pH 4.8)–acetonitrile (v/v, 60:40). HPLC data based on the ratio of analyte peak areas to IS peak area were obtained by PDA detection at five-wavelengths (250, 255, 260, 265, and 270 nm). The HPLC–CLS, HPLC–ILS, HPLC–PCR, and HPLC–PLS calibration plots for hydrochlorothiazide and losartan potassium were constructed separately by using the peak-area ratios corresponding to the concentrations of each active compound. The HPLC multivariate calibrations obtained were tested for different synthetic mixtures containing HCT and LST in the presence of the IS. These multivariate chromatographic methods were also applied to a commercial pharmaceutical dosage form containing HCT and LST. The results obtained from the multivariate calibrations were compared with those obtained by use of another, classical HPLC method using single-wavelength detection.Revised: 29 September 2004 and 4 January 2005     

Development and characterisation of a new interface for coupling capillary LC with collision-cell ICP–MS and its application for phosphorylation profiling of tryptic protein digests

A comparison of different nebulisers for direct hyphenation of capillary and nano liquid chromatography (Cap-LC, Nano-LC) and quadrupole-based collision cell inductively coupled plasma mass spectrometry (CC-ICP–MS) for phosphorylation profiling of tryptic protein digests is described. Helium was used as cell gas and specially tuned instrumental conditions were used to achieve background minimisation at the mass of phosphorus, because of kinetic energy discrimination of the interfering polyatomic ions. The proposed set-up is based on a modified capillary electrophoresis interface and a home-made 4 mL spray chamber. It enables the use of gradient conditions with a highly concentrated organic mobile phase as often used in protein phosphorylation analysis, without the need to apply membrane desolvation for removal of the organic phase or further background minimisation. No significant signal suppression or other negative effects caused by the organic mobile phase occur, because of the low flow rates used in Cap-LC and the robust plasma conditions of the CC-ICP–MS instrument. A tryptic digest of beta-casein was investigated as model compound to demonstrate the applicability of the proposed set-up for phosphorylation profiling in protein analysis using quadrupole based collision-cell ICP–MS as phosphorus-specific detector. Detection limits for phosphorylated peptides down to the sub picomole level were obtained. As a complementary technique, electrospray ionisation tandem mass spectrometry (ESI–MS–MS) with data base searching was used for further characterisation of the phosphorylated peptides detected.     

Symplectic Methods for the Numerical Solution of the Radial Shrödinger Equation

In this paper new symplectic-schemes for the numerical solution of the radial Shrödinger equation are proposed. In particular, symplectic integrators for Hamiltonian systems have been developed. Based on this approach, second- and third-order methods are proposed. These methods are more accurate than the existing ones. We compare these methods not only with the existing symplectic methods, but also with a classical Runge–Kutta–Nyström method.     

Inorganic particulates in removal of toxic heavy metal ions

Adsorption behavior of zinc ions on hydrous zirconium oxide (HZO) in aqueous solution has been studied as a function of concentration (10^–2–10^–8M), temperature (303–333 K) and pH 3–8 of adsorptive solution applying radiotracer technique. The kinetics of adsorption follows first order rate law and agrees well with the classical Freundlich isotherm in the entire range of adsorptive concentration. The removal was found to be increasing with pH of the adsorptive solution while it was suppressed in the presence of acid concentrations. The overall process is found to be endothermic and irreversible in nature.     

Application of dynamical Lie algebraic method to atom–diatomic molecule scattering

The dynamical Lie algebraic approach developed by Alhassid and Levine combined with intermediate picture is applied to the study of translational–vibrational energy transfer in the collinear collision between an atom and an anharmonic oscillator. We find that the presence of the anharmonic terms indeed has an effect on the vibrational probabilities of the oscillator. The computed probabilities are in good agreement with those obtained using exact quantum method. It is shown that the approach of dynamical Lie algebra combining with intermediate picture is reasonable in the treating of atom–anharmonic oscillator scattering.     

Semiclassical quantum unimolecular reaction rate theory revisited

We describe a semiclassical quantum unimolecular reaction rate theory derived from the corresponding classical theory developed by Davis, Gray, Rice and Zhao (DGRZ). The analysis retains the intuitively useful mechanistic distinctions between intramolecular energy transfer and reaction, with the consequence that the semiclassical quantum theory version neglects some interference effects in the reaction dynamics. In the limiting case that intramolecular energy transfer is very fast compared to the rate of reaction we show that the DGRZ representation of the rate constant can be transformed, using the Weyl correspondence between quantum operators and classical variables, to the quantum flux–flux correlation function representation of the rate constant. In the more general case that the rate of intramolecular energy transfer influences the reaction dynamics, the semiclassical representation of the Wigner function for a classical system with both quasiperiodic and chaotic motion is used to obtain the reaction rate constant. Our analysis identifies the quantum analogue of the classical bottleneck to intramolecular energy transfer with the scars of unstable periodic orbits; it leads to a flux–flux correlation function representation of the rate constant for intramolecular energy transfer.     

Synthesis and properties of peptide fragments of the S-region of the surface protein of the heptatitis B virus

A peptide fragment with the 140–146 sequence of the main component of the surrace protein of the hepatitis B virus (HBsAG) and a number of its structural analogues have been synthesized by the classical method in solution. Conjugates of the peptides synthesized with bovine serum albumin and with a synthetic polypeptide analogue of polytuftsin have been obtained. The ability of the preparations to bind antibodies from the blood sera of hepatitis B patients has been studied. The possibility has been shown of their use for revealing antibodies to the heptatitis B virus in solid-phase enzyme-mediated immunoassay.Leningrad State University. Translated from Khimiya Prirodnykh Soedinenii, Nos. 3,4, pp. 406–413, May–August, 1992.     

Exploring rearrangements along the fragmentation pathways of diuron anion: A combined experimental and computational investigation

Diuron (3-(3,4-dichlorophenyl)-1,1-dimethylurea), a common herbicide from phenyl urea class, was investigated by studying the formation of several negative ions [M−H]⁻ in the gas phase and the fragmentation behaviour of the thermodynamically most probably formed isomeric anions upon linear ion acceleration/collision experiments. The collision induced dissociation experiments (CID) were carried out in a hexapole–quadrupole–hexapole hybrid system coupled to 12 T magnet with infinity ICR cell for high resolution measurements. Two distinctive main pathways were observed in the MS/MS spectrum. Sustained off-resonance irradiation (SORI) experiments inside the ICR cell reinforce the fragmentation channels obtained from linear ion acceleration experiments. The fragmentation pathways were also completely investigated by the use of B3LYP/6-311+G(2d,p)//B3LYP/6-31+G(d) level of theory. Elimination of dimethylamine takes place in a two-step process, by which two successive 1,3 proton shifts occur. The second 1,3 proton shift is concerted with the departure of dimethylamine. The driving force for the (CH₃)₂NH elimination is the formation of isocyanate group. The formed primary product ion can further decompose to release HCl through a new transition state. A stable new aromatic product ion is formed with 10π electrons. Loss of C₃H₅NO neutral from another anionic isomer of the precursor ion was also observed and is characteristic for the amide terminal of the diamide functional group. A concerted mechanism is proposed, by which N–C bond breakage and cyclization of the eliminated neutral fragment C₃H₅NO takes place simultaneously to form 1-methyl-aziridin-2-one.     

Synthesis of a suggested aggression peptide

Four different schemes for the synthesis by the classical method of pyroglutamylasparaginylglycine — a suggested aggression peptide have been described. The best is a scheme using C- and N-terminal protective groups of the benzyl type at the stage of obtaining the protected tripeptide. Literature information according to which the compound possesses biological activity has been refuted.A. A. Zhdanov Leningrad State University. Translated from Khimiya Prirodnykh Soedinenii, No. 2, pp. 253–255, March–April, 1988.