bluuebunny/crossref_metadata_2025 huggingface dataset:
Development of density distributions in injection molded amorphous engineering plastics. Part I
Authors: Yu Jeong S. , Lim Marilu , Kalyon Dilhan M.
Published: December 2004

The gapwise density distributions of the injection molded specimens of two engineering thermoplastics, i.e., poly(phenylene ether) and poly(ether imide), were characterized employing the density gradient column technique. The samples were molded using a 40t Van Dorn injection molding machine. The effects of the thermal history on the density distribution of unconstrained quenched specimens were also investigated. In addition, various material properties, such as pressure‐volume‐temperature, isothermal contraction, and pressure induced densification behavior were characterized, for the two resins employed in this study. The moldings of the two resins exhibited different trends in their density distributions. These findings were explained in terms of the competing effects of cooling rate and the pressure history experienced by the engineering plastic resins during the molding cycle. The data collected were also used as input to mathematical modeling of density distributions in injection molded articles, which is reported in Part II of this article.
Development of density distributions in injection molded amorphous engineering plastics. Part II
Authors: Yu Jeong S. , Kalyon Dilhan M.
Published: December 2004

The experimental results obtained on the gapwise density distributions of freely quenched and injection molded specimens of two engineering thermoplastics presented in Part I of this paper were compared with simulation results. The effect of the thermal history on the density development in the freely quenched samples was investigated by employing the fictive temperature concept in conjunction with the experimentally determined material characteristics. The density distribution in freely quenched specimens of poly(ether imide) could be readily predicted. The combined effects of the cooling rate and the pressure history on the density distributions of injection molded samples were also investigated. A phenomenological model was developed to combine the effects of thermal and pressure history on the density distribution. Overall, the predicted results for injection molded specimens agreed well with the experimental results.
Effect of melt spinning and cold drawing on structure and properties of poly (aryl ether ketone) (PAEK) fibers
Authors: Hsiung C. M. , Cakmak M.
Published: December 2004

The effects of melt spinning and cold drawing on structure development and resulting properties of poly (aryl ether ketone) (PAEK) have been investigated. Melt spun and subsequently cold drawn fibers were characterized by differential scanning calorimetry, wide angle X‐ray diffraction, small angle X‐ray diffraction, and birefringence techniques. At low take‐up speeds, essentially amorphous fibers are produced. High take‐up speeds result in development of crystallinity in the as‐spun fibers. Cold drawing above the, Tg of PAEK causes further increase of crystallinity. Wide angle X‐ray patterns indicate progressive alignment of chains along the fiber axis in as spun as well as in cold‐drawn fibers with the draw down ratio and cold draw ratio. However, cold drawing was observed to broaden the WAXS peaks. SAXS patterns of cold drawn and fixed annealed fibers changed from two‐point to four‐point patterns indicating mosaic pattern formation of crystalline and amorphous regions. Mechanical properties including tensile strength, elongation at break, modulus, and yield strength were measured and correlated with fiber structure. Fracture surfaces of tensile tested fibers were observed using scanning electron microscopy and correlated with developed fiber structure.
Molecular and lamellar structure of an extrusion‐grade medium‐density polyethylene for gas distribution
Authors: Tränkner T. , Hedenqvist M. , Gedde U. W.
Published: December 2004

An extrusion‐grade medium‐density polyethylene was fractionated by size exclusion chromatography and selective solvent extraction. The fractions were studied by infrared spectroscopy, differential scanning calorimetry, and transmission electron microscopy. Infrared spectroscopy showed that chain branching was concentrated to the low molar mass material. Transmission electron microscopy showed the presence of roof‐shaped crystals in the low molar mass samples and curved S‐or C‐shaped lamellae in the high molar mass samples. These features could be used for identification of different molar mass species in the unfractionated sample.
Rubber modified epoxy resin. II: Phase separation behavior
Authors: Kim Dae Su , Kim Sung Chul
Published: December 2004

DGEBA (diglycidyl ether of bisphenol A)–ATBN (amine terminated butadiene acrylonitrile copolymer) blends exhibited upper critical solution temperature (UCST) behavior. Triethylene tetramine (TETA) was introduced as an amine curing agent of epoxy. The real‐time phase separation behavior of ATBN‐added epoxy system during cure was investigated using laser light scattering. SEM (scanning electron microscopy) and optical microscopy were also employed to observe the morphology of the epoxy blends. Since the DGEBA–ATBN blends showed UCST behavior, the degree of phase separation when cured at low temperature was higher than that when cured at high temperature. The domain correlation length increased as the curing temperature was lowered. Dynamic mechanical analysis (DMA) results indicated that the phase inversion occurred above 20 wt% of ATBN composition.
Rheology and physical properties of ternary blends containing a thermotropic liquid crystalline copolyester
Authors: Hong Soon Man , Kim Byoung Chul
Published: December 2004

Ternary blends of polyarylate (PAR) U‐Polymer 100, thermotropic liquid crystalline copolyester (LCP) Vectra A950, and a block copolyesterether Hytrel 7246 were investigated in terms of rheological properties, morphology, and mechanical properties. The PAR/Hytrel blend exhibited melting point depression and gave a unique single Tg over the entire range of blend compositions. Addition of Hytrel to the PAR/LCP blend decreased both dynamic viscosity and storage modulus over the normal processing temperature range. Further, it notably reduced the voids between the LCP domains and the matrix, and improved the mechanical properties. The optimum usage level of Hytrel proved to be 2 phr.
Analytical approximation of degradation profiles in polymer products
Authors: Jansen K. M. B.
Published: December 2004

A general, but simple, analytical technique is proposed for the solution of diffusion‐controlled reaction problems (as, for example, occur during the photooxidation of polymers). With this technique the stationary concentration and reaction rate profiles can be calculated for arbitrary reaction kinetics and concentration dependent diffusion coefficients. As an example, the photo‐oxidation of polyolefins is considered, which involves complex, concentration dependent, reaction kinetics. Excellent agreement between the analytical approximation and the numerical solution is obtained. Further, an analytical expression for the degradation profile (extend of reaction) is derived, which includes the starting‐up effect. It is shown that owing to instationary effects, the degradation profiles obtained with artificial weathering tests may differ considerably from those obtained with outdoor weathering experiments. It is therefore suggested that artificial weathering tests be used to measure the reaction rate parameter and calculate the degradation profile rather than measuring the degradation profile directly.
Synthesis and characterization of polyamides and poly(amide‐imide)s derived from 2,6‐bis(3‐aminophenoxy)benzonitrile or 2,6‐bis(4‐aminophenoxy)benzonitrile
Authors: Saxena Akanksha , Prabhakaran PV , Rao V Lakshmana , Ninan KN
Published: December 2004

A series of polyamides and poly(amide‐imide)s was prepared by direct polycondensation of ether and nitrile group containing aromatic diamines with aromatic dicarboxylic acids and bis(carboxyphthalimide)s respectively in N‐methyl 2‐pyrrolidone (NMP) using triphenyl phosphite and pyridine as condensing agents. New diamines, such as 2,6‐bis(4‐aminophenoxy)benzonitrile and 2,6‐bis(3‐aminophenoxy)benzonitrile, were prepared from 2,6‐dichlorobenzonitrile with 4‐aminophenol and 3‐aminophenol, respectively, in NMP using potassium carbonate. Bis(carboxyphthalimide)s were prepared from the reaction of trimellitic anhydride with various aromatic diamines in N,N′‐dimethyl formamide. The inherent viscosities of the resulting polymers were in the range of 0.27 to 0.93 dl g−1 in NMP and the glass transition temperatures were between 175 and 298 °C. All polymers were soluble in dipolar aprotic solvents such as dimethylsulfoxide, dimethylacetamide and NMP. All polymers were stable up to 350 °C with a char yield of above 40 % at 900 °C in nitrogen atmosphere. All polymers were found to be amorphous except the polyamide derived from isophthalic acid and the poly(amide‐imide)s derived from diaminodiphenylether and diaminobenzophenone based bis(carboxyphthalimide)s. Copyright © 2004 Society of Chemical Industry
Curing behaviour of syndiotactic polystyrene–epoxy blends: 1. Kinetics of curing and phase separation process
Authors: Salmon Nicolas , Carlier Véronique , Schut Jaap , Remiro Pedro M , Mondragon Ińaki
Published: December 2004

The modification of the curing behaviour and the phase separation process for an epoxy resin blended with a crystalline thermoplastic was investigated in the case of the diglycidylether of bisphenol‐A (DGEBA)/4,4′‐methylene bis(3‐chloro‐2,6‐diethylaniline) (MCDEA) blended with syndiotactic polystyrene (sPS) and cured at 220 °C. Phase separation taking place during curing of the blend was investigated by differential scanning calorimetry (DSC) and optical microscopy in order to get a better understanding of the complex interactions between cure kinetics of epoxy matrix and crystallisation of sPS, both influenced by blend composition. Results suggested that phase separation and crystallisation of sPS occurred at almost similar times, with phase separation just being ahead of crystallisation. DSC and near‐infrared measurements were used for the determination of the cure kinetics. Slow delays on the cure reactions were observed during the first minutes for the sPS‐containing blends compared with the neat DGEBA/MCDEA system but, after some time, the reaction rate became faster for the blends than for the neat matrix. Phase separation occurring in the mixtures may explain this particular phenomenon. Copyright © 2004 Society of Chemical Industry
Influence of the ethylene–(methacrylic acid)–Zn2+ ionomer on the thermal and mechanical properties of blends of poly(propylene) (PP)/ethylene–(vinyl alcohol) copolymer (EVOH)
Authors: Abad Maria J , Ares Ana , Barral Luis , Eguiazábal Jose I
Published: December 2004

The thermal and mechanical properties and the morphologies of blends of poly(propylene) (PP) and an ethylene–(vinyl alcohol) copolymer (EVOH) and of blends of PP/EVOH/ethylene–(methacrylic acid)–Zn2+ ionomer were studied to establish the influence of the ionomer addition on the compatibilization of PP/EVOH blends and on their properties. The oxygen transmission rate (O2TR) values of the blends were measured as well. PP and EVOH are initially incompatible as was determined by tensile tests and scanning electronic microscopy. Addition of the ionomer Zn2+ led to good compatibility and mechanical behaviour was improved in all blends. The mechanical properties on extruded films were studied for 90/10 and 80/20 w/w PP/EVOH blends compatibilized with 10 % of ionomer Zn2+. These experiments have shown that the tensile properties are better than in the injection‐moulded samples. The stretching during the extrusion improved the compatibility of the blends, diminishing the size of EVOH domains and enhancing their distribution in the PP matrix. As was to be expected, the EVOH improved the oxygen permeation of the films, even in compatibilized blends. Copyright © 2004 Society of Chemical Industry
Synthesis and characterization of UV‐curable acrylic resin containing fluorine groups
Authors: Park Soo‐Jin , Jin Fan‐Long
Published: December 2004

A novel fluorine‐containing acrylic resin, 4‐trifluoromethylphenyl glycerol dimethacrylate (TPGD), was synthesized and the structure was characterized by FTIR, 13C NMR, 1H NMR, and 19F NMR spectroscopy. The conversion of cure reaction, thermal stability, glass transition temperature (Tg), and electrical properties of the TPGD acrylic resin cured with UV radiation were investigated. The thermal stability and Tg of the UV‐cured specimens show a maximum value at 1 wt% photoinitiator, due to the formation of advanced network structures. The cured specimens had a relatively low dielectric constant, attributed to the decreased deformation polarizability of segment motion in the fluorine‐containing resin. Copyright © 2004 Society of Chemical Industry
The Technology of Droplet Measurement with Cascade Impactors
Authors: Büurkholz Armin
Published: December 2004

Cascade impactors are still the most suitable devices with which to measure fine droplet mists in gas ducts. This report describes the measurement technique and underlying principles. It is based largely on experience gained with a type of impactor that has been specially developed for droplet measurements, and also on applications of impactors in the chemical industry. Most of the measurement work has been undertaken in connection with environmental protection. The cascade impactor gives the mass‐related droplet size distributions and concentrations within a range extending from about 0.2 to 10 microns. Larger droplets are collected quantitatively in the sampling probe, which serves as a precollector.
Drop‐Size Distributions Produced by Flat‐Spray Nozzles
Authors: Schegk Claus‐Detlef , Lüoffler Friedrich , Umhauer Heinz
Published: December 2004

This study deals with measurements of the drop‐size distributions of different types of fan spray atomisers using a scattered‐light particle size counting analyser. The drop‐size distributions were determined at various locations in the spray cone. These local distributions change systematically from the fan's axis to its border. Superimposing these local distributions, adequately weighted, one acquires the entire distribution of all the drops. A comparison of the experimental results is made with those yielded by mathematical equations.
Studies of shaped charges with built‐in asymmetries. Part II: Modelling
Authors: Brown John , Edwards P. J. , Lee P. R.
Published: December 2004

A well‐characterized shaped charge was used to study the influence of asymmetrical initiation on the jet. An experimental study yielded flash radiographs of the jets from charges fired with the initiation point offset 2, 4, 6, 8 and 10 mm, respectively, from the central axis. The axial and lateral velocities of the jet particles were determined from the sets of radiographs. In a previous paper it was hypothesized that a simple relationship might exist between the departure vectors of the jet particles and the geometry of the impingement of the detonation front on the liner. Any part of the jet from an asymmetrically initiated shaped charge departs at an angle determined by the difference between the current angle between the actual detonation wave where it contacts the liner, and that which would have arisen had the initiation been perfectly axial. We set up a simple computer code which evaluates, for any given initiation offset distance, the instantaneous angles between the detonation front and the successive elements of the liner which are encountered as the wave sweeps along it. Since it is possible to map particle velocities in the jet on to those regions of the liner where they originated, simulated sets of axial and lateral jet velocities were readily generated. Agreement between theory and experiment is sufficiently close to suggest that our approximation is useful and can assist in understanding the jet dynamics of asymmetrically initiated shaped charges.
On application of the plate dent test for the performance evaluation of emulsion explosives
Authors: Ravi Shankar G. S. R. , Kumar A. S. , Krishna Mohan V.
Published: December 2004

The use of plate dent technique to evaluate w/o emulsion explosives is discussed in this paper. Experiments carried out with aluminium and mildsteel blocks show that the dent test results could give an idea about explosive performance. Attempts have been made to correlate the plate dent data with various detonation properties. Estimated detonation pressure did not yield a satisfactory correlation with either dent depth or dent volume. The role of detonation energy in governing the test result is highlighted. It is suggested that the plate dent test could be employed to assess the performance characteristics of large diameter, booster sensitive explosives.
Characteristic Properties of AN/GAP‐Propellants
Authors: Menke Klaus , Böhnlein‐Mauß Jutta , Schubert Hiltmar
Published: December 2004

Formulations based on ammonium nitrate and GAP are promising candidates for the development of high energetic, minimum smoke propellants with reduced sensitivity to be applied for radar and laser guided tactical missiles. The difficulties for the development of such a propellant system depend on the chemical nature and problems connected to the ingredients. Drawbacks are caused by the numerous phase changes of AN, its hygroscopicity, lower energy and low reactivity. The key problems for the development are the unfavourable combustion behaviour and sometimes bad stability of AN/GAP formulations.

Some of the main features of these propellants have been developed and illustrated in this paper. These are performance, chemical stability, combustion behaviour and detonation sensitivity. Four different kinds of pure and phase stabilized ammonium nitrates are compared regarding stability and combustion behaviour in propellant formulations with GAP and nitrate ester plasticizers. Satisfying solutions have been found for combustion behaviour and stability of AN/GAP‐propellants, if pure AN, atomized from the melt and new molybdenum oxide/vanadium oxide burning modifiers are successfully applied.
Explosive Systems Utilizing Semiconductor Bridge, SCB, Technology
Authors: Bickes R. W.
Published: December 2004

Sandia National Laboratories' semiconductor bridge, SCB, is a maturing technology now in use in several new applications. Those applications required explosive assemblies that were light weight, small volume, low cost, and needed only small quantities of electrical energy to function. Explosive assembly here refers to the combination of the firing set (the current source for the firing signal) and the explosive component. Because conventional firing systems could not meet the new reduced size, weight and energy requirements, SCB systems were developed for applications that range from Sandia devices to commercial igniters for fireworks. This paper is a brief overview of SCB technology with examples of SCB explosive systems designed to meet modern requirements.
Electric Detonators: EBW and EFI
Authors: Varesh Ron
Published: December 2004

Exploding Bridge Wire Detonators (EBW) and Exploding Foil Initiators (EFI) which were originally developed for military applications, have found numerous uses in the non‐military commercial market while still retaining their military use. While not as common as the more familiar hot wire initiators, EBW's and EFI's have definite advantages in certain applications. These advantages, and disadvantages, are discussed for typical designs.
Application of Fractal Geometry to Dynamical Impacting of condensed explosives and other materials
Authors: Guanren Zhang
Published: December 2004

The relation between fractal dimension D of impacting condensed explosive sample and its related physical parameters is derived. With this relation, and the frame photograph of impacting, the threshold energy required to initiate any physical or chemical process, such as melting, ignition or detonation can be calculated.
Prompt Shock Initiation of Cased Explosives by Projectile Impact
Authors: James H. R. , Haskins P. J. , Cook M. D.
Published: December 2004

Experimental results often show that a prompt shock response to projectile impact can be experienced by even relatively heavily cased explosives. This paper will discuss the predictive criteria that can be applied in such circumstances, and in particular will explore the different mechanisms which are present for rod and sphere impacts. Predicted initiation thresholds are shown to give good comparisons with experimental results, using, at most, two empirical shock sensitivity constants obtained from impacts of the uncased explosive.
Stabilizer Reaction is Cast Double Base Rocket Propellants. Part VIII: Characterization of propellant gassing properties during simulated aging
Authors: Sammour M. H.
Published: December 2004

The decomposition process of two cast double base (CDB) propellant compositions was measured in vacuum. The process of gas evolution during heating of propellant compositions in vacuum has been studied using Vacuum Stability Test (VST) and Gas chromatography/ Mass Spectrometry (GC‐MS) techniques. The results for the two different compositions aged at different storage temperatures for different periods of time were compared.

VST has been used to quantify the amount of gases evolved during heating of propellant (aged and unaged) compositions at 100°C in vacuum, while quantitative GC‐MS has been used to identify and quantify the evolved gases when the same propellant compositions were heated at 60 °C and 70 °C at low free volume.

The results have shown that the amount and type of gases evolved depend on the composition of propellant, percentage of stabilizer etc. Composition 1 evolved CO2, CO, N2, NO and N2O and produced the greater total gas volume, while Composition 2 evolved C02, CO and N2 only. In each case C02 was the predominant gas and Composition 1 produced more COz but less CO than Composition 2. It is suggested that these differences in gas evolution profiles are due to the presence of different ballistic modifiers in the two propellant compositions.

Gas evolution assessment using VST technique cannot be the strict measure of double base propellants stability.
Imidazolinone‐tolerant crops: history, current status and future
Authors: Tan Siyuan , Evans Richard R , Dahmer Mark L , Singh Bijay K , Shaner Dale L
Published: December 2004

Imidazolinone herbicides, which include imazapyr, imazapic, imazethapyr, imazamox, imazamethabenz and imazaquin, control weeds by inhibiting the enzyme acetohydroxyacid synthase (AHAS), also called acetolactate synthase (ALS). AHAS is a critical enzyme for the biosynthesis of branched‐chain amino acids in plants. Several variant AHAS genes conferring imidazolinone tolerance were discovered in plants through mutagenesis and selection, and were used to create imidazolinone‐tolerant maize (Zea mays L), wheat (Triticum aestivum L), rice (Oryza sativa L), oilseed rape (Brassica napus L) and sunflower (Helianthus annuus L). These crops were developed using conventional breeding methods and commercialized as Clearfield* crops from 1992 to the present. Imidazolinone herbicides control a broad spectrum of grass and broadleaf weeds in imidazolinone‐tolerant crops, including weeds that are closely related to the crop itself and some key parasitic weeds. Imidazolinone‐tolerant crops may also prevent rotational crop injury and injury caused by interaction between AHAS‐inhibiting herbicides and insecticides. A single target‐site mutation in the AHAS gene may confer tolerance to AHAS‐inhibiting herbicides, so that it is technically possible to develop the imidazolinone‐tolerance trait in many crops. Activities are currently directed toward the continued improvement of imidazolinone tolerance and development of new Clearfield* crops. Management of herbicide‐resistant weeds and gene flow from crops to weeds are issues that must be considered with the development of any herbicide‐resistant crop. Thus extensive stewardship programs have been developed to address these issues for Clearfield* crops. Copyright © 2005 Society of Chemical Industry
Time‐dependent quantum theory III. Model for vibrational relaxation in crystals
Authors: Schurr J. Michael
Published: December 2004

A one‐dimensional model consisting of a “diatomic” spring attached on one side to a rigid wall and on the other side to a linear array of mass‐springs is proposed as a model for the vibrational relaxation of small solute molecules in host lattices. A modification allowing a change in the equilibrium internuclear extension of the diatomic spring is also incorporated. The Hamiltonian divides naturally into pure diatomic, pure linear crystal, and the two mixed perturbation terms, one giving rise to stepwise vibrational cascade damping accompanied by phonon emission, and the other process, lattice relaxation, giving rise to phonon emission without any change of the quantum number of the diatomic spring. The cascade damping rate for a diatomic spring with a frequency less than the the maximum frequency of the linear crystal is calculated to second‐order, and it is shown that the perturbation series converges in this range.

An upper bound to the cascade damping rate for a diatomic spring with a frequency greater (i.e., 4.5 ×) than the cut‐off frequency of the linear crystal is determined to be very small, λ ≦ 104 sec −;1.

The rate for the lattice relaxation process corresponds to a line‐width λ = 6 cm −1 at 0K.

An explanation for the thermal quenching of the low‐temperature luminescence of SO2 is based upon induced cascade‐phonon emission.
On the energy difference between the lP and 3P states of the beryllium isoelectronic sequence
Authors: Tatewaki Hiroshi , Taketa Hirosiji , Sasaki Fukashi
Published: December 2004

Wave functions of the 1S (ground state), 3P and 1P states for the beryllium isoelectronic sequence have been obtained in various approximations.

The HF 2p orbitals for the 1P and 3P states are similar except for Be, where the 2p orbital is quite diffuse for the 1P state.

The difference between the experimental E(1P) – E(3P) and the HF E(1P) – E(3P) is 0.62 eV for Be and 1.17 ∼ 1.40 eV for B+ ∼ F5+. The disagreements are attributed to the correlation effects between the 2s and 2p electrons. This is confirmed by ci calculations.

It is shown that a limited basis SCF calculation reproduces the above feature of the HF results if we treat the orbital exponents as the variational parameters. The use of the Slater values for the orbital exponents is shown to be inadequate especially for the Be 1P state.

The conclusions of this paper will be useful for discussing the V–T separations of H2 and C2H4.
Origin of the irrational part contained in the angular numerical factors of matrix elements of the Coulomb operator
Authors: Sureau A.
Published: December 2004

By means of second quantization formalism and angular momenta coupling techniques, we show the reason why the irrational part of the coefficients of the Slater integrals Rk(ab, cd) in the expression \documentclass{article}\pagestyle{empty}\begin{document}$ (\Psi |\sum\limits_{i < j} {e^2 /r_{ij} |\Psi } ') $\end{document} is common to all values of k, a, b, c, d, and depends only on (Ψ∣ and ∣Ψ′).
A self‐consistent variation‐perturbation theory for open shell atomic systems: Calculation of polarizabilities and shielding factors
Authors: Mukherjee P. K. , Moitra R. K. , Mukherji A.
Published: December 2004

In this paper a fully coupled variation‐perturbation theory has been introduced for handling open‐shell atomic systems in the presence of static perturbations. The static dipolar and quadrupolar polarizabilities and shielding factors for Li, Be+, B2+, B, C+, Na and Al have been calculated and compared with available results. Important sources of discrepancies in previous calculations of shielding factors have been noticed and critically examined. The dipolar shielding factors calculated in this paper show satisfactory agreement with the theoretical N/Z ratio. In the absence of any theoretical test for the quadrupolar shielding factor, the accuracy of the calculations of γ∞, should be judged in the light of the accuracy of the corresponding β∞ values.
Continuous degeneracy and energy‐localization of molecular orbitals
Authors: England Walter
Published: December 2004

The energy‐localization method is examined for continuous degeneracy using a grouptheoretic approach. Conditions for the degenerate orbitals are obtained and an enumeration of symmetry groups where continuous degeneracy may occur is given. It is found that the orbitals may be equivalent under operations not contained in the total symmetry group. An alternative explanation for the free rotation of the lone pairs in F2 is offered.
Long range interaction energies using Gaussian basis sets and a one center method
Authors: Singh T. R. , Bukta J. F. , Meath W. J.
Published: December 2004

A one center method, based on the work of Karplus and Kolker, is discussed and used to calculate the induction energy, through O(R−8), for the H(ls) – H+ interaction employing two types of Gaussian basis sets constructed from functions of the form {rje−αr2}. The effective hydrogen atom excitation energies and transition multipole moment matrix elements generated in these calculations are used to calculate the dispersion energy for the H(ls) – H(ls) interaction, through O(R−10), and the R−9 triple dipole energy corresponding to the interaction of three H(ls) atoms. The results indicate that Gaussian functions can form good basis sets for obtaining long range forces for a variety of multipole interaction energies.
Self consistent calculation of dynamic multipole polarizabilities and excited state wave functions of open shell ions: Li sequence
Authors: Moitra R. K. , Mukherjee P. K.
Published: December 2004

A variational formulation of the Hartree–Fock–Roothaan (HFR) theory for open shell ions in presence of time dependent perturbations is presented. The theory has been used to calculate the dynamic polarizabilities of the first three ions of the Li sequence. The polarizability values, extrapolated to zero frequency, show good shell by shell agreement with the corresponding static results. The polarizability graphs display resonance behaviour at the transition frequencies of the ions, and a study of these points leads to analytic HF wave functions for their low lying excited states. The calculated transition frequencies are in excellent accord with the experimental values. The calculated oscillator strengths for the 2s → np transitions are in reasonable agreement with the extensive multiconfiguration calculations of Weiss and the available experimental results.
Internal symmetry groups of non‐rigid molecules
Authors: Gilles J.‐M. F. , Philippot J.
Published: December 2004

Hougen has established, for quasi‐rigid molecules, the relationship between permutationinversions acting on the molecular Hamiltonians written in Cartesian co‐ordinates and permutation‐rotations (perrotations) of symmetry acting on nuclear equilibrium configurations. We extend these relations to the case of non‐rigid molecules. For this, we introduce kinetic perrotations which act on nuclear equilibrium configurations in the same way as do Altmann's isodynamic operators. We show that isodynamic operators do not always form a group. Moreover, their action cannot be extended to the electrons. They cannot be used for the classification of molecular wave functions. This classification is achieved by using the group of Longuet‐Higgins and the group of the corresponding feasible perrotations.
The non‐crossing rule in molecular quantum mechanics
Authors: Naqvi K. Razi , Brown W. Byers
Published: December 2004

Previous mathematical proofs of the non‐crossing rule concerning the potential energy curves of a diatomic molecule are examined and criticised. A new treatment is presented which is simple and mathematically rigorous.
On the representations of the rotation group
Authors: Corio P. L.
Published: December 2004

The matrices of the irreducible representations of the 3‐dimensional rotation group are shown to be related to Krawtchouk's orthogonal polynomials of a discrete variable x = j – m', whose degrees are given by n = j + m. The relation follows directly from the recurrence formulas satisfied by the matrix elements and permits a concise development of the formal properties of the rotation matrices. In particular, an asymptotic relation for large j is developed that generalizes a formula first discussed for a special case by Wigner.
Coupled Hartree–Fock calculation of the electric dipole hyper‐polarizabilities: He sequence
Authors: Bhattacharya A. K. , Sengupta S. , Mukherji A.
Published: December 2004

The variation perturbation method in the coupled Hartree‐Fock (HF) scheme has been used to calculate the fourth‐order energies of He, Li+ and Be2+ ions subjected to a uniform external electric field. The hyper‐polarizabilities γh which are related to the fourthorder energies have been calculated neglecting intra‐atomic correlation. For He the observed value is γh = 53.6 ± 4.0 a.u. The present estimate in the coupled and uncoupled HF schemes yield 36.2 and 45.3 a.u. respectively. The other calculations using correlated ground state wave function gave values in the range 42‐44 a.u. The discrepancies between our result and those of others have been discussed.
An expansion for four‐center integrals over Slater‐type orbitals
Authors: Salmons Lydia S. , Ruedenberg Klaus
Published: December 2004

A new expression is given for the electron repulsion integral over Slater‐type orbitals on four different centers. It is based on the asymptotic expansion derived from the bipolar expansion of a previous paper. The expression has the form

where qp = {np, lp, mp}. Both F and σ are closed expressions. The quantity F is a combination of incomplete gamma functions, Laguerre polynomials and spherical harmonics. It depends upon the relative coordinates of a point P on the AB axis and a point Q on the CD axis. The functions σnlm(A, B) depend on the charge distribution (χAχB); they have the character of overlap integrals and are of the form
The generalized separated electron pair model. III. An application to three localization schemes for CO
Authors: Robb M. A. , Csizmadia I. G.
Published: December 2004

The separated electron pair (SEP) model (strongly orthogonal geminals) and methods for its systematic extension have been applied to three different localization schemes for CO. The optimum SEP wave function is obtained for the particular localization scheme that involves three equivalent bent bonds. The major corrections to the SEP model arise from one‐electron transfer terms. Two‐electron transfer terms were important only for those pairs that were not well localized. It was found that the separate definitions of the total intrapair and interpair correlation energies did not depend strongly on the choice of localization scheme.
Accurate calculation of Fourier transform of two‐center Slater orbital products
Authors: Monkhorst Hendrik J. , Harris Frank E.
Published: December 2004

A method is presented which leads to accurate Fourier transform values of any 1s−1s Slater‐type orbital overlap distribution. The numerical merits are discussed and illustrated by some examples.
Generalized Rayleigh–Schrödinger perturbation theory
Authors: Carbó Ramón
Published: December 2004

The equivalence of the perturbation formalism, in the Rayleigh‐Schrödinger frame‐work, between secular and generalized secular equations is analysed.
An economic storage and processing method for two‐electron integrals in LCAO‐MO calculations
Authors: Billingsley Frank P.
Published: December 2004

An economic algorithm for storing and processing two‐electron integrals arising in LCAO‐MO calculations is presented. The integrals are sorted prior to the SCF iterative scheme, classified according to equivalences in the orbital indices and finally stored on separate files that contain only integrals of one type. The novel approach of physically separating the integrals according to category is shown to be more efficient than random storage. Actual computing times for the new technique are tabulated for a representative number of molecular systems and compared with times obtained using previously reported methods.
Theoretical studies of diamagnetic properties of the hydrogen molecule ion. I. Approximate variation‐perturbation calculation
Authors: Garrett Thomas B. , Zeroka Daniel
Published: December 2004

A variation‐perturbation method, analogous to a technique devised by Das and Bersohn for the study of the hydrogen molecule, is developed for calculation of the diamagnetic susceptibility χ and magnetic shielding σ and is applied to a study of the hydrogen molecule ion. Two approximations are investigated–in a first approximation, χ = −0.37814α2a and σ = 1.112 × 10−5 c.g.s. units and in a second approximation, χ = −0.37569α2a and σ = 1.128 × 10−5 c.g.s. units.
Calculation of molecular quadrupole moments and a demonstration of the importance of overlap densities in the theory of polyatomic molecules
Authors: Rabinowitz James R. , Rein Robert
Published: December 2004

A computational method for calculating quadrupole moments from molecular wave functions in a Slater orbital basis set is described. Using both IEHT and CNDO wave functions quadrupole moments for a series of polyatomic molecules are calculated. They are compared with experimental results and the IEHT wave functions are found to give agreement with experiment while CNDO wave functions do not. The importance of bicentric densities (overlap densities) in the calculation of multipole moments is shown. This is followed by a discussion of the usefulness of these wave functions for a quantitative characterization of the electronic structure of large molecules.
The Renner effect in four‐atomic molecules
Authors: Petelin A. N. , Kiselev A. A.
Published: December 2004

The theory of the Renner effect in X2Y2 and X2YZ linear molecules is considered. The Renner equations are obtained with the help of the Born‐Oppenheimer method. It is shown that these equations contain two Renner parameters for an X2Y2 molecule and three Renner parameters for an X2YZ molecules. Assuming these parameters to be small enough, an approximate solution of the Renner equations is obtained with the help of perturbation theory. Some general qualitative results are obtained in the first order of the perturbation theory; the second order calculations are made for some specific cases. The theoretical results are used to consider experimental data concerning the vibrational structure of the 1IIu ‐ 1Σ electronic transition in C2H2 and C2D2 molecules. The frequencies of the bending vibrations and the Renner parameters are calculated for the electronic 1IIu‐state mentioned.
The n‐electron problem and matrices representing the symmetric groups
Authors: Gallup G. A.
Published: December 2004

The application of the representation theory of symmetric groups to the solution of quantum chemical problems is discussed. This is done using matrices which do not represent Sn in the normal sense, but which are much simpler to calculate than the Yamanouchi‐Kotani representation. A complete discussion of the calculation of these matrices is given.
Examination of the semi‐classical theory of circular dichroism
Authors: Duben Anthony J.
Published: December 2004

The solution of the time dependent Schrödinger equation, including renormalization of the wave function, is used to obtain quantum mechanical expressions for the optical rotation and the circular dichroism. The use and form of the radiative damping term is examined with respect to its effects in the circular dichroism formula.
Le champ autocoherent non hermitien
Authors: Gouyet J. F.
Published: December 2004

A theoretical study of the spin‐optimized self‐consistent field methods is given in a second quantization formalism using the occupation‐branching number representation and a biorthogonal basis treatment given by Moshinsky and Seligman. A diagrammatic presentation can then be introduced. Further investigation will be thus facilitated.
Effect of many‐body interactions on the stability of rare‐gas halides
Authors: Lombardi E. , Ritter R. , Jansen L.
Published: December 2004

Exchange perturbation theory of the Rayleigh‐Schrödinger type is applied, in first and second orders, to the problem of bonding in rare‐gas halides. The basic model is that of a four‐electron, three‐center system with one effective electron replacing the unpaired electrons of a halogen atom, and two spin‐paired electrons representing the closed shells of the rare‐gas atom. On the basis of exchange perturbation theory, the model verifies a direct parallelism between bonding in rare‐gas compounds and the phenomenon of super‐exchange in ionic solids with paramagnetic cations. It is found that the observed stability and specific geometric configuration of the xenon and krypton fluorides are readily reproduced by the model. In addition, the model explains why other dihalides cannot exist. The two principal components of the interaction energy are found to be indirect exchange between halogen atoms via the rare‐gas atoms (attractive in the stable configurations) and, in compounds with coordination higher than two, simultaneous interactions between three halogen atoms (always repulsive). The observed approximate constancy of the binding energy per bond in xenon fluorides with increasing coordination is accounted for.
Equation for the screened potential
Authors: Terasaka Toshitaka , Nedachi Youko
Published: December 2004

The equation for the screened potential in the RPA has been derived by using the method of functional differentiation of Martin and Schwinger. The contribution of the “oyster” diagram has been contained in this equation.
Product of group‐function expansions for correlated wave functions
Authors: Mehler E. L.
Published: December 2004

A theorem is proved which demonstrates the relationship between a product of group functions describing the correlated motion of a particular group of electrons in an N‐electron system and a wave function obtained from the exact wave function which describes the correlation of the same group of electrons. By considering such products of group functions as elements in a variational wave function, an expansion for correlated wave functions is suggested, which emphasizes the correlated motion of groups of electrons in the whole system.
Spin density distributions in some fluorinated radical cations
Authors: Kumari Usha , Ray N. K.
Published: December 2004

A theoretical study of π‐electron spin density distributions has been made for a series of fluoro‐substituted hydrocarbon radical cations using unrestricted Hartree‐Fock theory. Although some of the predicted proton splittings are not in very good agreement with experiment, the overall agreement with experiment can be passed as fairly satisfactory considering the approximate nature of the theory used. The experimental fluorine splittings can be well predicted by using a one‐parameter relationship between the isotropic fluorine splitting (aF) and the π‐electron spin density (ρCC) on the attached carbon. It has been further shown that both ρCC and the proportionality constant (Qeff) in the linear relation, are fairly insensitive to the parameter choice.
On the dimerization of BH3 and the associated delocalization (resonance) energy
Authors: Edmiston Clyde , Lindner Peter
Published: December 2004

SCF calculations utilizing a basis of all s‐type Gaussians have been performed to investigate the dimerization of BH3 to B2H6. Localized molecular orbitals and pseudonatural orbitals are calculated. The dimerization energy obtained (11.5 kcal/mole) supports the assumption that the non‐Hartree‐Fock interactions (electron correlation) play a dominant role (Exp = 40–60 kcal/mole).

The energy of the principal type of resonance structure based on the SCF‐MO's of the magnified image separated‐but‐distorted BH3 systems is rigorously calculated and found to be 150 kcal/mole higher in energy than the SCF energy of B2H6. Thus, resonance stabilization (delocalization) is shown to be extremely important to the stability of the “three‐center” bonds in B2H6, as has been suspected for many years.
Technique d'optimisation de l'energie SCF en fonction des exposants de slater
Authors: Bouscasse L. , Phan‐Tan‐Luu R. , Vincent E. J. , Metzger Et J.
Published: December 2004

We describe a method to optimize simultaneously Slater orbital exponents. The procedure is based on Newton's method and requires the derivatives of the energy as a function of the exponents. The calculation of these derivatives is described explicitly. The method has been applied to the hydrogen molecule.
Molecular integrals of relativistic effects with gaussian‐type orbitals
Authors: Matsuoka Osamu
Published: December 2004

A mathematical analysis is presented of molecular integrals of relativistic interactions in molecules. The integrals are based on Gaussian‐type orbitals and include those arising from variation of electron mass with velocity, one‐electron Fermi contact interaction, electron spin‐same‐orbit interaction, electron spin‐nuclear spin interaction, electron spin‐spin contact interaction, electron spin‐other‐orbit interaction, electron spin‐spin dipolar interaction and electron orbit‐orbit interaction. The integrals are expressed in suitable forms for use in computer. It is also pointed out that the integrals are written essentially in terms of the overlap, nuclear attraction, electron repulsion, or field integrals.
A “Level–Shifting” method for converging closed shell Hartree–Fock wave functions
Authors: Saunders V. R. , Hillier I. H.
Published: December 2004

A discussion of Hartree damping in closed‐shell Hartree‐Fock theory is given indicating when the method might force convergence of intrinsically divergent cases. An alternative, but closely related principle, “level shifting” is described, and the advantages of the latter procedure discussed.
Direct determination of pseudonatural orbitals
Authors: Palting Pancracio
Published: December 2004

It is shown how to obtain pseudonatural orbitals directly from the equations of motion. A sample calculation on the ground state of the Be atom is given.
An Ab Initio study of the permanganate ion
Authors: Mortola Albert P. , Basch Harold , Moskowitz Jules W.
Published: December 2004

An ab initio self‐consistent computation has been performed on the permanganate ion (MnO) in a large basis set of contracted gaussian functions. The ground state description as well as those of the first two excited states are discussed and compared with those obtained experimentally from photoelectron spectroscopy, ESCA, optical spectroscopy and magnetic circular dichroism.
Multipole structure of exchange polarization energy for H2+ Ion
Authors: Chałasiński G. , Jeziorski B.
Published: December 2004

The exchange polarization energy for the H2+ ion is expressed as an infinite sum of its angular components. At large internuclear distances R, a particular l‐component, referred to as induced 2l‐pole exchange energy, behaves asymptotically like

For larger R this suggests a rather slow l−4 rate of convergence of the series. However, as contrasted to the analogous expansion for the induction energy the convergence speeds up considerably with decreasing internuclear separation.

It is also shown that at sufficiently large R a given induced 2l‐pole exchange energy can be computed with a high accuracy using a polarization function obtained with neglect of charge overlap effects. Near the bottom of the van der Waals minimum over 99% of the exchange polarization energy can be produced using this simplified form of the polarization function.
Time‐dependent variational principle
Authors: Moccia R.
Published: December 2004

The time‐dependent variational principle due to Frenkel is derived from Hamilton's principle using a suitable general expression for the variational wave function. The connections with a recent comment of P. O. Löwdin and P. K. Mukherjee on the same subject are discussed.