bluuebunny/crossref_metadata_2025 huggingface dataset:
A systematic study of basis set, electron correlation, and geometry effects on the electric multipole moments, polarizability, and hyperpolarizability of HCl
Authors: Maroulis George
Published: July 2002

The electric multipole moments, dipole and quadrupole polarizability and hyperpolarizability of hydrogen chloride have been determined from an extensive and systematic study based on finite-field fourth-order many-body perturbation theory and coupled-cluster calculations. Our best values for the dipole, quadrupole, octopole and hexadecapole moment at the experimental internuclear separation of Re=2.408 645a0 are μ=0.4238ea0, Θ=2.67ea02, Ω=3.94ea03, and Φ=13.37ea04, respectively. For the mean and the anisotropy of the dipole polarizability ααβ we recommend ᾱ=17.41±0.02 and Δα=1.60±0.03e2a02Eh−1. For the mean value of the first dipole hyperpolarizability βαβγ we advance β̄=−6.8±0.3e3a03Eh−2. Extensive calculations with a [8s6p6d3f/5s4p2d1f] basis set at the CCSD(T) level of theory yield the R-dependence of the Cartesian components and the mean of the second dipole hyperpolarizability γαβγδ(R)/e4a04Eh−3 around Re as γzzzz(R)=1907+1326(R−Re)+570(R−Re)2+10(R−Re)3−40(R−Re)4, γxxxx(R)=3900+747(R−Re)−65(R−Re)2−38(R−Re)3−7(R−Re)4, γxxzz(R)=962+222(R−Re)+88(R−Re)2+49(R−Re)3+5(R−Re)4, γ̄(R)=3230+841(R−Re)+151(R−Re)2+21(R−Re)3−9(R−Re)4, with z as the molecular axis. The present investigation suggests an estimate of (26.7±0.3)×102e4a04Eh−3 for the Hartree–Fock limit of the mean value γ̄ at Re. CCSD(T) calculations with basis sets of [8s6p6d3f/5s4p2d1f] and [9s7p5d4f/6s5p4d1f] size and MP4 calculations with the even larger [15s12p7d3f/12s7p2d1f] give (7.0±0.3)×102e4a04Eh−3 for the electron correlation effects for this property, thus leading to a recommended value of γ̄=(33.7±0.6)×102e4a04Eh−3. For the quadrupole polarizability Cαβ,γδ/e2a04Eh−1 at Re our best values are Czz,zz=41.68, Cxz,xz=26.11, and Cxx,xx=35.38, calculated with the [9s7p5d4f/6s5p4d1f] basis set at the CCSD(T) level of theory. The following CCSD(T) values were obtained with [8s6p6d3f/5s4p2d1f] at Re: dipole-quadrupole polarizability Aα,βγ/e2a03Eh−1, Az,zz=14.0, and Ax,zx=3.75, dipole-octopole polarizability Eα,βγδ/e2a04Eh−1, Ez,zzz=20.0, and Ex,xxx=3.0, and dipole-dipole-quadrupole hyperpolarizability Bαβ,γδ/e3a04Eh−2, Bzz,zz=−277, Bxz,xz=−261, Bxx,zz=246, and Bxx,xx=−416. A comparison of the mean polarizability and hyperpolarizability of some 18-electron systems shows that ᾱ(H2S)>ᾱ(HCl)>ᾱ(HOOH)>ᾱ(HOF)>ᾱ(Ar)>ᾱ(F2), and γ̄(H2S)>γ̄(HCl)>γ̄(HOOH)>γ̄(HOF)≈γ̄(Ar)>γ̄(F2).
State-resolved collisional relaxation of highly vibrationally excited pyridine by CO2: Influence of a permanent dipole moment
Authors: Wall Mark C. , Stewart Brian A. , Mullin Amy S.
Published: July 2002

The quenching of highly vibrationally excited pyridine through collisions with a 300 K bath of CO2 is investigated using high resolution transient infrared laser spectroscopy. Highly excited pyridine (Evib=37 950 cm−1) is prepared using pulsed ultraviolet (UV) excitation at 266 nm, followed by radiationless coupling to the ground electronic state. Energy gain into CO2 resulting from collisions with highly excited pyridine is probed using transient absorption techniques. Distributions of nascent CO2 rotational populations in both the ground (0000) state and the vibrationally excited (0001) state are determined from early time absorption measurements. Translational energy distributions of the recoiling CO2 in individual rovibrational states are determined through measurement of Doppler-broadened transient line shapes. These experiments investigate the influence of a large permanent dipole moment (μpyridine=2.2 D) on the collisional quenching dynamics of molecules with very large amounts of internal energy. A kinetic model is developed to describe rates for appearance of CO2 states resulting from collisions with excited pyridine as well as for quenching of excited pyridine at early times. These experiments show that collisions resulting in CO2 (0000) are accompanied by substantial excitation in rotation (Trot=1200 K for J=56–82) and translation (Ttrans=2900 K for J=78) while the vibrationally excited CO2 (0001) state has rotational and translational energy distributions near the initial 300 K distributions. Rate constants for the two energy transfer pathways are compared with previously published data on quenching collisions of excited (nonpolar) pyrazine, revealing only minor relative enhancement (∼2) in the vibrational excitation channel in pyridine relaxation. Overall quenching rates for excited pyridine are determined for both CO2 states investigated. These data show that the rotational and translational energy gain in CO2 is much more sensitive to collisional depletion of excited pyridine.
Chemiluminescent pathways in reactions of phosphorus, antimony, and bismuth with ozone to form dioxides and monoxides
Authors: Kampf Rodger P. , Parson John M.
Published: July 2002

Chemiluminescent (CL) reactions have been observed using molecular beams of phosphorus, antimony, and bismuth colliding with ozone as a scattering gas. The fluorescence spectra indicate the formation of electronically excited PO2, SbO2, and BiO2, and probably SbO and BiO, as well. None of the emitting states of the dioxides seem to correspond to previously characterized states. Since the beam source could generate variable ratios of atoms, dimers, and tetramers, the CL reactions can be attributed to P, Sb, Sb2, and Bi. The assignments of reactant species were aided by measurements of the total CL dependence on the beam time dependence. The time-dependent experiments also revealed CL reactions of antimony and bismuth, which are second order in ozone. Fits to the time-dependent spectra show that whereas the first-order CL reaction of P proceeds without a potential barrier, for Sbn and Bi, only the second-order CL reactions can occur without very high barriers.
Exact exchange in ab initio molecular dynamics: An efficient plane-wave based algorithm
Authors: Chawla Sanjay , Voth Gregory A.
Published: July 2002

A plane-wave based algorithm is presented for the efficient evaluation of exact (Hartree–Fock) exchange. The theory and numerical results show that the method scales linearly with the number of plane waves. A new, in principle exact, procedure is also defined for the construction of the exchange potential within a Vanderbilt pseudopotential (PP) scheme. The present plane-wave+PP approach can be used in ab initio molecular dynamics (AIMD) algorithms employing exact exchange, thus significantly extending the range of AIMD methodology.
Molecular dynamics study of the velocity cross-correlations in liquids
Authors: Verdaguer A. , Padró J. A. , Trullàs J.
Published: July 2002

Velocity cross-correlations for both soft-sphere fluids at different densities and temperatures and a simple molten salt are investigated by molecular dynamics simulation. Time correlation functions between the velocity of a tagged particle and velocities of particles within specified ranges of initial separations are calculated. In the case of the soft-sphere fluids, separation ranges corresponding to the first, second and third shells of neighbors are considered whereas up until six different shells are analyzed for the molten salt. The calculated functions allow us to build a picture of the spread of the initial momentum of a tagged particle over the successive shells of neighbors. It is observed that collisions with intermediate particles are the main mechanism for the transfer of momentum. A balance between the momentum exchanged by particles in a given shell with those in the two adjacent shells should be carried out in order to analyze the resulting velocity cross-correlation functions. The rate of transfer of momentum between distant particles increases with the density and temperature of the liquid. It has been noticed an incipient coherence, which is more marked for the ionic melt, between the motions of atoms in nonadjacent shells.
Methyl iodide A-band decomposition study by photofragment velocity imaging
Authors: Eppink André T. J. B. , Parker David H.
Published: July 2002

The methyl iodide A-band photodissociation process CH3I+hν→CH3(v,N,K)+I(2P3/2), I*(2P1/2) has been studied in a cold molecular beam. Full three-dimensional state-specific speed and angular distributions of the nascent fragments were recorded using (2+1) resonance-enhanced multi-photon ionization (REMPI) and velocity imaging, a new variant of ion imaging. By combining the I* quantum yield and anisotropy parameters for both I and I* channels, the relative absorption strength to the contributing electronic states (3Q0, Q13 and Q11) as well as the probability for curve crossing (3Q0→1Q1) are determined for excitation wavelengths across the full A band (240–334 nm). Parallel excitation to the Q03 state turns out to dominate the A band even more than previously thought.
Monte Carlo simulations of hydrogen adsorption in single-walled carbon nanotubes
Authors: Darkrim Farida , Levesque Dominique
Published: July 2002

Within the framework of a study on the properties of carbon nanotubes, a promising new material, we performed numerical simulation of hydrogen adsorption at room temperature in single-walled nanotubes. The structure of this material is favorable to the adsorption phenomenon because of the narrow size distribution of the nanotube diameters, which have dimensions on the order of the range of the carbon attractive interaction. We discuss the influence of the single-walled carbon nanotube diameters on the relative arrangement of carbon atoms and hydrogen molecules within an array of parallel single-walled carbon nanotubes. We also studied the influence on adsorption of the distance between the nearest-neighbor nanotubes.
Spin effects on the luminescence yield of organic light emitting diodes
Authors: Burin Alexander L. , Ratner Mark A.
Published: July 2002

The influence of the excitation spectrum on the quantum yield is investigated for organic molecules used in light emitting diodes (LEDs). The significance of the competition between radiative and nonradiative recombination channels is pointed out. A system of master equations is proposed to describe the relaxation of lower levels of the excited molecule, and the solution for the fluorescence yield is obtained assuming relatively weak vibronic coupling. The results are used to interpret the experimental data in oligothiophenes, and general approaches are proposed to increase the relative weight of the radiative decay channel and correspondingly enhance the working properties of organic light emitting diodes. In particular, the fluorescence quantum yield can exceed the simple estimate of 0.25.
Shifted-contour auxiliary field Monte Carlo for ab initio electronic structure: Straddling the sign problem
Authors: Baer Roi , Head-Gordon Martin , Neuhauser Daniel
Published: July 2002

The auxiliary field Monte Carlo (AFMC) technique has advantages over other ab initio quantum Monte Carlo methods for fermions, as it does not seem to require approximations for alleviating the sign problem and is directly applicable to excited states. Yet, the method is severely limited by a numerical instability, a numerical sign problem, prohibiting application to realistic electronic structure systems. Recently, the shifted contour auxiliary field method (SC-AFMC) was proposed for overcoming this instability. Here we develop a theory for the AFMC stabilization, explaining the success of SC-AFMC. We show that the auxiliary fields can be shifted into the complex plane in a manner that considerably stabilizes the Monte Carlo integration using the exact one-electron density. Practical stabilization can be achieved when an approximate Hartree–Fock density is used, proposing that an overwhelming part of the sign problem is removed by taking proper account of the Fermion mean-field contribution. The theory is demonstrated by application to H2.
Shifted-contour auxiliary-field Monte Carlo for molecular electronic structure
Authors: Rom Naomi , Fattal Eyal , Gupta Ashish K. , Carter Emily A. , Neuhauser Daniel
Published: July 2002

The shifted-contour auxiliary-field Monte Carlo (SCAFMC) approach has been recently developed by Rom, Charutz and Neuhauser as an extension of the auxiliary-field Monte Carlo (AFMC) method. AFMC replaces the difficult fully interacting electrons problem by an ensemble of simpler problems where the electrons interact with a fluctuating electric field but not with each other. SCAFMC is based on shifting the auxiliary-field contour of integration to pass through the (imaginary) stationary point, leading to numerical stability at long propagation times. The new approach converges to the full CI energy in electronic structure calculations (both ground and low-lying excited states). Here we expand the application of SCAFMC from atomic to molecular problems. First, we calculate ground-state energies of a highly correlated transition-metal system (Cr2) with a moderate (12 orbitals) active space size, and demonstrate that SCAFMC is able to extract the energies accurately. In addition, we use SCAFMC to calculate a C–C bond-stretch energy in ethane with complete active spaces of up to 28 orbitals.
A first-principles potential energy surface for Eley–Rideal reaction dynamics of H atoms on Cu(111)
Authors: Persson M. , Strömquist J. , Bengtsson L. , Jackson B. , Shalashilin D. V. , Hammer B.
Published: July 2002

We have performed first-principles total-energy calculations of low-dimensional sections of the electronically adiabatic potential energy surface (PES) that are relevant for the Eley–Rideal (ER) reaction of H atoms on a rigid Cu(111) surface. These calculations were performed within density-functional theory using a plane-wave and pseudopotential method and the generalized gradient approximation for the exchange-correlation energy. The calculated energy points for various configurations of one and two atoms on the Cu(111) surface were used to construct a model PES that can be used in ER reaction dynamics calculations.
Closed-loop critical curves in simple hard-sphere van der Waals-fluid models consistent with the packing fraction limit
Authors: Yelash Leonid V. , Kraska Thomas , Deiters Ulrich K.
Published: July 2002

Two new hard-sphere equations are proposed which, in combination with a van der Waals attraction term, lead to a biquadratic, respectively a cubic, equation of state. The new equations show the correct limiting behavior at low as well as at high densities; their poles are close to the physical packing fraction of hard spheres. Both equations of state were extended towards mixtures by one-fluid mixing rules, and their global phase behavior was investigated for the special case of equal-sized molecules. Both equations are able to predict closed-loop liquid–liquid immiscibility; the topology of the phenomenenon is the same as for the Carnahan–Starling equation. It appears the occurrence of closed-loop liquid–liquid immiscibility does not depend on the location of the pole nor on the degree of the equation of state used.
High level ab initio molecular orbital study of the structures and vibrational spectra of CH2Br and CH2Br+
Authors: Li Zhuangjie , Francisco Joseph S.
Published: July 2002

The equilibrium structures and harmonic vibrational frequencies for CH2Br and CH2Br+ have been determined using second-order Mo/ller–Plesset perturbation theory (MP2), Becke’s three parameter hybrid method employing the LYP correction functional (B3LYP) [A. D. Becke, J. Chem. Phys. 98, 5648 (1993)], and coupled-cluster theory with single and double excitations including perturbative corrections for the triple excitations CCSD(T) in conjunction with the triple-zeta double-polarized (TZ2P) and 6-311++G(3df,3pd) basis sets. Our computational results predict a very nearly planar structure for the CH2Br radical. At the CCSD(T)/6-311++G(3df,3pd) level of theory bond lengths of 1.076 and 1.851 Å are predicted for the C–H and C–Br bonds, and a 124.6° for the H–C–H angle in the CH2Br radical, which are in good agreement with the experimental values of 1.086 Å, 1.845 Å, and 124°, respectively. The calculated rotational constant value of B+C at the same level is found to agree with experiment. Like CHBr+ and CBr+, the C–Br bond length in the CH2Br+ cation is found to be shorter than that of the neutral species, due to the reduction of repulsion between carbon and bromine atoms. The vibrational frequencies for the C–Br stretching are expected to increase by more than 160 cm−1 when the CH2Br radical is ionized. The best estimate of the ionization potential for the CH2Br radical is 196.6 kcal mol−1, which agrees very well with the experimental value of 198.5±0.2 kcal mol−1.
Global nine-dimensional potential energy surface for the H5 system. II. Fit to an analytical expression
Authors: Tablero César , Aguado Alfredo , Paniagua Miguel
Published: July 2002

A global nine-dimensional potential energy surface (GPES) for the adiabatic ground state of the H5 system which fits the ab initio data, reported in the previous paper of this series, has been obtained (root-mean-square error 2.2 kcal/mol). The global fitting procedure is an extension of the corresponding procedure for triatomic and tetra-atomic systems including the functional form previously proposed by the authors. The H5 GPES obtained here is totally symmetric with respect to permutations of the hydrogen atoms and satisfies the criteria needed to be used in scattering calculations.
Theory for electron transfer from a mixed-valence dimer with paramagnetic sites to a mononuclear acceptor
Authors: Bominaar E. L. , Achim C. , Borshch S. A.
Published: July 2002

Polynuclear transition-metal complexes, such as Fe–S clusters, are the prosthetic groups in a large number of metalloproteins and serve as temporary electron storage units in a number of important redox-based biological processes. Polynuclearity distinguishes clusters from mononuclear centers and confers upon them unique properties, such as spin ordering and the presence of thermally accessible excited spin states in clusters with paramagnetic sites, and fractional valencies in clusters of the mixed-valence type. In an earlier study we presented an effective-mode (EM) analysis of electron transfer from a binuclear mixed-valence donor with paramagnetic sites to a mononuclear acceptor which revealed that the cluster-specific attributes have an important impact on the kinetics of long-range electron transfer. In the present study, the validity of these results is tested in the framework of more detailed theories which we have termed the multimode semiclassical (SC) model and the quantum-mechanical (QM) model. It is found that the qualitative trends in the rate constant are the same in all treatments and that the semiclassical models provide a good approximation of the more rigorous quantum-mechanical description of electron transfer under physiologically relevant conditions. In particular, the present results corroborate the importance of electron transfer via excited spin states in reactions with a low driving force and justify the use of semiclassical theory in cases in which the QM model is computationally too demanding. We consider cases in which either one or two donor sites of a dimer are electronically coupled to the acceptor. In the case of multiconnectivity, the rate constant for electron transfer from a valence-delocalized (class-III) donor is nonadditive with respect to transfer from individual metal sites of the donor and undergoes an order-of-magnitude change by reversing the sign of the intradimer metal–metal resonance parameter (β). In the case of single connectivity, the rate constant for electron transfer from a valence-localized (class-II) donor can readily be tuned over several orders of magnitude by introducing differences in the electronic potentials at the two metal sites of the donor. These results indicate that theories of cluster-based electron transfer, in order to be realistic, need to consider both intrinsic electronic structure and extrinsic interactions of the cluster with the protein environment.
Towards standard methods for benchmark quality ab initio thermochemistry—W1 and W2 theory
Authors: Martin Jan M. L. , de Oliveira Glênisson
Published: July 2002

Two new schemes for computing molecular total atomization energies (TAEs) and/or heats of formation (ΔHf∘) of first- and second-row compounds to very high accuracy are presented. The more affordable scheme, W1 (Weizmann-1) theory, yields a mean absolute error of 0.30 kcal/mol and includes only a single, molecule-independent, empirical parameter. It requires CCSD (coupled cluster with all single and double substitutions) calculations in spdf and spdfg basis sets, while CCSD(T) (i.e., CCSD with a quasiperturbative treatment of connected triple excitations) calculations are only required in spd and spdf basis sets. On workstation computers and using conventional coupled cluster algorithms, systems as large as benzene can be treated, while larger systems are feasible using direct coupled cluster methods. The more rigorous scheme, W2 (Weizmann-2) theory, contains no empirical parameters at all and yields a mean absolute error of 0.23 kcal/mol, which is lowered to 0.18 kcal/mol for molecules dominated by dynamical correlation. It involves CCSD calculations in spdfg and spdfgh basis sets and CCSD(T) calculations in spdf and spdfg basis sets. On workstation computers, molecules with up to three heavy atoms can be treated using conventional coupled cluster algorithms, while larger systems can still be treated using a direct CCSD code. Both schemes include corrections for scalar relativistic effects, which are found to be vital for accurate results on second-row compounds.
The isotropic–nematic transition and the phase separation of the tobacco mosaic virus particles with polysaccharide
Authors: Urakami Naohito , Imai Masayuki , Sano Yoh , Takasu Masako
Published: July 2002

The isotropic–nematic transition of the tobacco mosaic virus (TMV) particles by polysaccharide is related to a high inhibitory activity against TMV infection. We study the process of the isotropic–nematic transition of the TMV particles as a function of the polysaccharide concentration by Monte Carlo simulations in three-dimensional continuous space. In these simulations, we simplify the TMV particles and the polysaccharide molecules as the hard spherocylinders and semirigid chains, respectively, and we assume the simple interactions for the TMV particles and the polysaccharide chains. In our simulation, with increasing concentration of the polysaccharide the homogeneously dispersed TMV particles begin to segregate without orientational ordering, that is isotropic phase separation, and then transform to the nematic state of the TMV particles. The isotropic–nematic transition is caused by simple interactions such as the excluded volume effect, and the complicated biological interaction is not necessary.
Transient equations for multiple nucleation on solid electrodes: A stochastic description
Authors: D’Ajello P. C. T. , Munford M. L. , Pasa A. A.
Published: July 2002

We consider the phenomenon of heterogeneous nucleation in electrolytic cells. Through the proposition of a stochastic model, we derive an equation to describe the migration of solute ions and their reaction near the electrode surface. Defining particular boundary conditions, the stochastic equation is solved and the time dependent probability density is related to the flux of ions towards the growing nucleus. The flux of ions is identified as the current transient expression, which is adequate for a comparison with the experimental results. The theory is powerful enough to reproduce results obtained by electrodepositing cobalt on n-type silicon and to explain deviations from predictions of the standard model for three-dimensional nucleation diffusion limited growth.
Equation of state, phase transition, decomposition of β-HMX (octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine) at high pressures
Authors: Yoo Choong-Shik , Cynn Hyunchae
Published: July 2002

Pressure-volume relations and vibrational Raman spectra of unreacted HMX (octahydro-1, 3,5,7-tetranitro-1,3,5,7-tetrazocine) have been obtained in both quasihydrostatic conditions to 45 GPa and nonhydrostatic conditions to 10 GPa by using diamond-anvil cell, angle-resolved synchrotron x-ray diffraction, and micro-Raman spectroscopy. The results show that the high-pressure behavior of HMX strongly depends on the stress conditions. HMX is more compressible in hydrostatic conditions (B0=12.4 GPa and B′=10.4) than in nonhydrostatic conditions (B0=14.4 GPa, B′=13.3). This discrepancy in HMX compressibility can be explained in terms of chemical reactions occurring in nonhydrostatic conditions. The static isotherm is in good agreement with the shock Hugoniot, suggesting little temperature effect on the pressure–volume relation. The hydrostatic data suggest that β(monoclinic)-HMX undergoes two phase transitions: (i) a conformational transition at 12 GPa with no apparent abrupt volume change and (ii) a discontinuous one at 27 GPa with a 4% volume change. At 40 GPa, the b and c axes become nearly identical with the c/a ratio 1.62 and β=123°, approaching a nearly close-packed structure.
Adsorption of xenon and CH4 mixtures in zeolite NaA. 129Xe NMR and grand canonical Monte Carlo simulations
Authors: Jameson Cynthia J. , Jameson A. Keith , Kostikin Pavel , Baello Bernoli I.
Published: July 2002

Investigation of competitive adsorption is carried out using the Xe–CH4 mixture in zeolite NaA as a model system. The Xen clusters are trapped in the alpha cages of this zeolite for times sufficiently long that it is possible to observe individual peaks in the NMR spectrum for each cluster while the CH4 molecules are in fast exchange between the cages and also with the gas outside. The 129Xe nuclear magnetic resonance spectra of nine samples of varying Xe and CH4 loadings have been observed and analyzed to obtain the 129Xe chemical shifts and the intensities of the peaks which are dependent on the average methane and xenon occupancies. The distributions Pn, the fraction of cages containing n Xe atoms, regardless of the number of CH4 molecules are obtained directly from the relative intensities of the Xen peaks. From the observed 129Xe chemical shift of each Xen peak can be obtained the average number of CH4 molecules in the same cavity as n Xe atoms. Grand canonical Monte Carlo (GCMC) simulations of mixtures of Xe and CH4 in a rigid zeolite NaA lattice provide the detailed distributions and the average cluster shifts, as well as the distributions Pn. The agreement with experiment is reasonably good for all nine samples. The calculated absolute chemical shifts for the Xen peaks in all samples at 300 K range from 80 to 230 ppm and are in good agreement with experiment. We also consider a very simple strictly statistical model of a binary mixture, derived from the hypergeometric distribution, in which the component molecules are distinguishable but equivalent in competition for eight lattice sites per cage under mutual exclusion. The latter simple model provides a limiting case for the distributions, with which both the GCMC simulations and the properties of the actual Xe–CH4 system are compared. The ideal adsorbed solution theory gives a first approximation to the selectivity of the adsorption of the Xe and CH4 from a mixture of gases, but starts to fail at high total pressures, especially at low CH4 mole fraction in the bulk.
The structure of liquid methanol by H/D substitution technique of neutron diffraction
Authors: Adya Ashok K. , Bianchi Laurent , Wormald Christopher J.
Published: July 2002

Neutron diffraction (ND) measurements on liquid methanol (CD3OD,CD3O(H/D),CD3OH) under ambient conditions have been performed to obtain the total (intra-+intermolecular), Gdist(r) and intermolecular, Ginter(r) radial distribution functions (rdfs) for the three samples. The extent to which intermolecular structure is affected by using two different intramolecular models is discussed. The H/D substitution on hydroxyl–hydrogen (Ho) has been used to extract the partial distribution functions, GXHodist/inter(r) (X=C, O, and H—a methyl hydrogen) and GXXdist/inter(r) from the difference techniques of ND at both the distinct and intermolecular levels. The O–Ho bond length, which has been the subject of controversy in the past, is found purely from the partial distribution function, GXHodist(r) to be 0.98±0.01 Å. The C–H distance obtained from the GXXdist(r) partial is 1.08±0.01 Å. These distances determined by fitting an intramolecular model to the total distinct structure functions are 0.961±0.001 Å and 1.096±0.001 Å, respectively. The GXXinter(r) function, dominated by contributions from the methyl groups, apart from showing broad oscillations extending up to ∼14 Å is featureless, mainly because of cancellation effects from six contributing pairs. The Ho⋯Ho partial pair distribution function (pdf), gHoHo(r), also determined from the second-order difference, shows that only one other Ho atom can be found within a mean Ho⋯Ho separation of 2.36 Å. The average position of the O⋯Ho hydrogen bond determined purely from experimental GXHointer(r) partial distribution function, at 1.75±0.03 Å is found to lie in the range (1.75–1.95 Å) of values reported from computer simulation results.
Detection and characterization of alkyl peroxy radicals using cavity ringdown spectroscopy
Authors: Pushkarsky Michael B. , Zalyubovsky Sergey J. , Miller Terry A.
Published: July 2002

Cavity ringdown spectra of the Ã 2A′−X̃ 2A″ electronic transition in the IR are reported for the methyl and ethyl peroxy radicals. Analysis of partially resolved rotational structure for the origin band of the transition provides information about both the Ã and X̃ states of CH3O2⋅. An estimate for the absorption cross section is determined from the CRDS absorption and the rate of radical–radical recombination.
Theoretical study of the electronic structure of carbon dioxide: Bending potential curves and generalized oscillator strengths
Authors: Buenker Robert J. , Honigmann Michael , Liebermann Heinz-Peter , Kimura Mineo
Published: July 2002

The electronic spectrum of carbon dioxide is predicted by means of multireference single- and double-excitation configuration interaction (MRD–CI) calculations. Bending potential curves for a large number of electronic states are calculated and the generalized oscillator strengths (GOS) obtained for the corresponding transitions are compared with recent electron energy loss spectra (EELS) obtained by Tanaka and co-workers as well as with optical intensity data. The CO2 absorption spectrum is dominated by vertical Rydberg transitions from the linear ground state but valence excited states with bent equilibrium geometries are also found to be important. Emphasis is placed on the intense spectral features in the 11.0–11.4 eV region of the spectrum. The two most intense peaks are both found to originate from π–3pπ transitions, one of which only becomes allowed upon molecular bending. Good agreement with the EELS results is obtained for the variation of the GOS with K2 and for the associated transition energies.
Hindered diffusion of colloidal particles very near to a wall: Revisited
Authors: Bevan Michael A. , Prieve Dennis C.
Published: July 2002

Total internal reflection microscopy is a technique for monitoring changes in the distance between a single microscopic sphere and a flat plate by measuring the intensity of light scattered by the sphere when illuminated by an evanescent wave. A histogram of scattering intensities can be used to construct the potential energy profile as a function of distance relative to the most probable distance. Thus potential energies can be measured to within a fraction of kT while changes in distance can be measured to within 1 nm. An autocorrelation of the scattering intensities can be used to deduce an average diffusion coefficient of the sphere, which is found to be only a few percent of the Stokes–Einstein value, owing to the close proximity of the plate. The analysis of the intensity-autocorrelation function presented here can be used to deduce an absolute value for the most probable separation distance, without a priori knowledge of the functional form of the PE profile and in the presence of a constant background scattering intensity. This “hydrodynamic” separation distance is found to be within a few percent of the “optical” separation distance found independently by comparing the intensity at the most probable distance with the intensity of the same particle in contact with the plate. Since the particle does not need to be brought into contact with the plate, the hydrodynamic method is well suited for determining the absolute separation distance with deformable particles like liquid droplets, vesicles or biological cells. Moreover, the hydrodynamic separation can be immediately calculated without any additional experiments. However, accurate determination of the hydrodynamic separation requires an accurate value for the particle size, which must be determined independently.
High-accuracy approximation techniques for analytic functions
Authors: Schwartz Charles
Published: July 2002

A generalization of the familiar mesh point technique for numerical approximation of functions is presented. High accuracy and very rapid convergence may be obtained by thoughtful choice of the reference function chosen for interpolation between the mesh points. In particular, derivative operators are represented by highly nonlocal matrices; but this is no drawback when one has computing machines to perform the algebraic manipulations. Some examples are given from familiar quantum mechanical problems.
Imaging of discontinuities in the inverse scattering problem by inversion of a causal generalized Radon transform
Authors: Beylkin G.
Published: July 2002

This paper treats the linearized inverse scattering problem for the case of variable background velocity and for an arbitrary configuration of sources and receivers. The linearized inverse scattering problem is formulated in terms of an integral equation in a form which covers wave propagation in fluids with constant and variable densities and in elastic solids. This integral equation is connected with the causal generalized Radon transform (GRT), and an asymptotic expansion of the solution of the integral equation is obtained using an inversion procedure for the GRT. The first term of this asymptotic expansion is interpreted as a migration algorithm. As a result, this paper contains a rigorous derivation of migration as a technique for imaging discontinuities of parameters describing a medium. Also, a partial reconstruction operator is explicitly derived for a limited aperture. When specialized to a constant background velocity and specific source–receiver geometries our results are directly related to some known migration algorithms.
Memory-dependent nonlocal electromagnetic elastic solids and superconductivity
Authors: Eringen A. Cemal
Published: July 2002

Constitutive equations are developed for nonlinear (and linear) nonlocal electromagnetic elastic solids that possess continuous memory of past fields. The consequence of the second law of thermodynamics is studied. Phenomenological laws are given for special cases of nonlinear optics, nonlinear magnetism, conduction, and elastic dielectrics. A continuum theory is constructed for memory-dependent elastic superconductors.
Scattering from generalized point interactions using self-adjoint extensions in Pontryagin spaces
Authors: van Diejen J. F. , Tip A.
Published: July 2002

Generalized point interactions (GPI) appearing formally in (quantum) physics as pseudopotentials are given an operator theoretic basis. It is pointed out that in contrast to ordinary point interactions these GPI models are not self-adjoint generators in the physical Hilbert space ℋ0, but ‘‘live’’ instead in an apparently nonphysical Pontryagin space of the type Πm=ℋ0⊕Cm■Cm. The physical interpretation of the models lies in the association of a unitary S-operator on ℋ0 within a two-space setting. A general formalism for GPI is presented and used to answer questions, which were raised in the literature, on the underlying mathematical structure of some models involving pseudopotentials in higher dimensions. Quantum mechanical scattering from GPI, with the purpose of replacing a spherically symmetric short-range interaction potential in the low-energy regime, is discussed in detail. The possible power of using GPI to enable explicit calculations in quantum mechanical and electromagnetic multiple scattering from distortions that are small relative to the wavelength is briefly mentioned.
Weyl manifolds and connections
Authors: Hall G. S.
Published: July 2002

A study is made of Weyl connections and their associated holonomy groups. The extent to which a Weyl connection determines its associated metric and 1-form structures is also discussed. Finally, the related concept of a locally metric connection is introduced and some relations between metric, locally metric, and Weyl connections are established.
Generating functions of multivariable generalized Bessel functions and Jacobi-elliptic functions
Authors: Dattoli G. , Chiccoli C. , Lorenzutta S. , Maino G. , Richetta M. , Torre A.
Published: July 2002

It is pointed out that the Jacobi-elliptic functions are the natural basis to get generating functions of the multivariable generalized Bessel functions. Analytical and numerical results are given of interest for applications.
Long time behavior of nonlinear stochastic oscillators: The one-dimensional Hamiltonian case
Authors: Albeverio S. , Klar A.
Published: July 2002

The long time behavior of nonlinear, nondissipative systems, which are perturbed by a white noise force are discussed herein. Considering special nonlinear forces and an appropriate scaling, a stochastic convergence theorem is proven. In particular the convergence of the energy process of the system to a limit diffusion is discussed. This corresponds to convergence of the system to a stationary distribution. Furthermore, the limit process is investigated and an explicit formula for its transition probability density is given. An analytic approach to the convergence theorem in terms of a singular perturbation theorem for semigroups is also presented.
Time-asymptotic traveling-wave solutions to the nonlinear Vlasov–Poisson–Ampère equations
Authors: Lancellotti Carlo , Dorning J. J.
Published: July 2002

We consider the Vlasov–Poisson–Ampère system of equations, and we seek solutions for the electric field E(x,t) that are periodic in space and asymptotically almost periodic in time. Introducing the representation E(x,t)=T(x,t)+A(x,t) (where T and A are, respectively, the transient and time-asymptotic parts of E) enables us to decompose the nonlinear Poisson equation into a transient equation and a time-asymptotic equation. We then study the latter in isolation as a bifurcation problem for A with the initial condition and T as parameters. We show that the Fréchet derivative at a generic bifurcation point has a nontrivial null space determined by the roots of a Vlasov dispersion relation. Hence, the bifurcation analysis leads to a general solution for A given (at leading order) by a discrete superposition of traveling-wave modes, whose frequencies and wave numbers satisfy the Vlasov dispersion relation, and whose amplitudes satisfy a system of nonlinear algebraic equations. In applications, there is usually a finite number of roots to the dispersion relation, and the equations for the time-asymptotic wave amplitudes reduce to a finite dimensional bifurcation problem in terms of the amplitude of the initial condition.
A direct theory for the perturbed unstable nonlinear Schrödinger equation
Authors: Huang Nian-Ning , Chi Sien , Lou B. L. , Chen Xiang-Jun
Published: July 2002

A direct perturbation theory for the unstable nonlinear Schrödinger equation with perturbations is developed. The linearized operator is derived and the squared Jost functions are shown to be its eigenfunctions. Then the equation of linearized operator is transformed into an equivalent 4×4 matrix form with first order derivative in t and the eigenfunctions into a four-component row. Adjoint functions and the inner product are defined. Orthogonality relations of these functions are derived and the expansion of the unity in terms of the four-component eigenfunctions is implied. The effect of damping is discussed as an example.
A simple experiment to investigate two-dimensional mixing by Rayleigh–Taylor instability
Authors: Andrews M. J. , Spalding D. B.
Published: July 2002

A simple experiment to study the mixing of two different density fluids by the Rayleigh–Taylor instability has been performed. Several experiments are reported for nominally one-dimensional homogeneous mixing and for experiments characterized by a large two-dimensional motion superimposed on the mixing process. The one-dimensional experiments show a plane mixing region that expands by Rayleigh–Taylor instabilities. The two-dimensional experiments show a contraction in the width of the mixing interface that is a result of the stretching action of the large-scale motion. Image analysis techniques have been developed to provide quantitative measurements for use in a ‘‘two-fluid’’ model of the mixing phenomena.
Nonergodicity of point vortices
Authors: Weiss Jeffrey B. , McWilliams James C.
Published: July 2002

The motion of N point vortices in a two-dimensional fluid is a Hamiltonian dynamical system with a 2N-dimensional phase space. The equations of motion for point vortices in a two-dimensional square doubly periodic domain are derived from those for an open domain. The Hamiltonian has three known constants of the motion and is thus believed to be nonintegrable for four or more vortices. Trajectories are numerically integrated from several initial conditions containing six vortices with varying total energy. Ergodicity on the surface defined by the constants of the motion is directly tested by comparing time-average and ensemble-average vortex pair statistics. It is found that the dynamics is not ergodic. There is evidence that the nonergodicity is not due to a gross fragmentation of phase space as might result from a broken symmetry. Vortex pair statistics are also used to test the randomness of the chaotic motion. It is found that the time-averaged statistics of the vortices are clearly distinct from those of independent random walkers.
A proposed modification of the Germano subgrid-scale closure method
Authors: Lilly D. K.
Published: July 2002

The subgrid-scale closure method developed by Germano et al. is modified by use of a least squares technique to minimize the difference between the closure assumption and the resolved stresses. This modification removes a source of singularity and is believed to improve the method’s applicability.
Envelope solitons with stationary crests
Authors: Akylas T. R.
Published: July 2002

Recent analytical and numerical work has shown that gravity–capillary surface waves as well as other dispersive wave systems support symmetric solitary waves with decaying oscillatory tails, which bifurcate from linear periodic waves at an extremum value of the phase speed. It is pointed out here that, for small amplitudes, these solitary waves can be interpreted as particular envelope-soliton solutions of the nonlinear Schrödinger equation, such that the wave crests are stationary in the reference frame of the wave envelope. Accordingly, these waves (and their three-dimensional extensions) are expected to be unstable to oblique perturbations.
Landau damping in space plasmas
Authors: Thorne Richard M. , Summers Danny
Published: July 2002

Space plasmas typically possess a particle distribution function with an enhanced high-energy tail that is well modeled by a generalized Lorentzian (or kappa) distribution with spectral index κ. The modified plasma dispersion function Z*κ(ξ) [Summers and Thorne, Phys. Fluids B 3, ■■■■ (1991)] is employed to analyze the Landau damping of (electrostatic) Langmuir waves and ion-acoustic waves in a hot, isotropic, unmagnetized, generalized Lorentzian plasma, and the solutions are compared with the classical results for a Maxwellian plasma. Numerical solutions for the real and imaginary parts of the wave frequency ω0−iγ are obtained as a function of the normalized wave number kλD, where λD is the electron Debye length. For both particle distributions the electrostatic modes are strongly damped, γ/ω0≫1, at short wavelengths, kλD≫1. This collisionless damping becomes less severe at long wavelengths, kλD≪1, but the attenuation of Langmuir waves is much stronger for a generalized Lorentzian plasma than for a Maxwellian plasma. This will further localize Langmuir waves to frequencies just above the electron plasma frequency in plasmas with a substantial high-energy tail. Landau damping of ion-acoustic waves is only slightly affected by the presence of a high-energy tail, but is strongly dependent on the ion temperature. Owing to the simple analytical form of the modified plasma dispersion function when κ=2 (corresponding to a pronounced high-energy tail), exact analytical results for the real and imaginary parts of the wave frequency can be found in this case; similar solutions are not available for a Maxwellian plasma.
The modified plasma dispersion function
Authors: Summers Danny , Thorne Richard M.
Published: July 2002

In the linear theory of waves in a hot plasma if the zeroth-order velocity distribution function is taken to be Maxwellian, then there arises a special, complex-valued function of a complex variable ξ=x+iy, namely Z(ξ), known as the plasma dispersion function. In space physics many particle distributions possess a high-energy tail that can be well modeled by a generalized Lorentzian (or kappa) distribution function containing the spectral index κ. In this paper, as a natural analog to the definition of Z(ξ), a new special function Z*κ(ξ) is defined based on the kappa distribution function. Here, Z*κ(ξ) is called the modified plasma dispersion function. For any positive integral value of κ, Z*κ(ξ) is calculated in closed form as a finite series. General properties, including small-argument and large-argument expansions, of Z*κ(ξ) are given, and simple explicit forms are given for Z*1(ξ), Z*2(ξ), ..., Z*6(ξ). A comprehensive set of graphs of the real and imaginary parts of Z*κ(ξ) is presented. It is demonstrated how the modified plasma dispersion function approaches the plasma dispersion function in the limit as κ→∞, a result to be expected since the (appropriately defined) kappa distribution function formally approaches the Maxwellian as κ→∞. The function Z*κ(ξ) is expected to be instrumental in studying microinstabilities in plasmas when the particle distribution function is not only the standard generalized Lorentzian, but also of the Lorentzian type, including inter alia, the loss-cone, bi-Lorentzian, and product bi-Lorentzian distributions.