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  • 2010-2014  (24)
  • 1995-1999  (849)
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  • Atomic, Molecular and Optical Physics  (830)
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  • ddc:510
  • 1
    Publication Date: 2020-12-11
    Description: Convexity is an important property in nonlinear optimization since it allows to apply efficient local methods for finding global solutions. We propose to apply symbolic methods to prove or disprove convexity of rational functions over a polyhedral domain. Our algorithms reduce convexity questions to real quantifier elimination problems. Our methods are implemented and publicly available in the open source computer algebra system REDUCE. Our long term goal is to integrate REDUCE as a workhorse'' for symbolic computations into a numerical solver.
    Keywords: ddc:510
    Language: English
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  • 2
    Publication Date: 2016-06-30
    Description: Applications which need exclusive access to a shared resource in distributed systems require a fault-tolerant and scalable mechanism to coordinate this exclusive access. Examples of such applications include distributed file systems and master/slave data replication. We present Flease, an algorithm for decentralized and fault-tolerant lease coordination in distributed systems. Our algorithm allows the processes competing for a resource to coordinate exclusive access through leases among themselves without a central component. The resulting system easily scales with an increasing number of nodes and resources. We prove that Flease ensures exclusive access, i.e. guarantees that there is at most one valid lease at any time.
    Keywords: ddc:510
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  • 3
    Publication Date: 2020-08-05
    Description: We propose an efficient column generation method to minimize the probability of delay propagations along aircraft rotations. In this way, delay resistant schedules can be constructed. Computational results for large-scale real-world problems demonstrate substantial punctuality improvements. The method can be generalized to crew and integrated scheduling problems.
    Keywords: ddc:510
    Language: English
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  • 4
    Publication Date: 2022-01-07
    Description: In optimal control problems with nonlinear time-dependent 3D PDEs, full 4D discretizations are usually prohibitive due to the storage requirement. For this reason gradient and quasi-Newton methods working on the reduced functional are often employed. The computation of the reduced gradient requires one solve of the state equation forward in time, and one backward solve of the adjoint equation. The state enters into the adjoint equation, again requiring the storage of a full 4D data set. We propose a lossy compression algorithm using an inexact but cheap predictor for the state data, with additional entropy coding of prediction errors. As the data is used inside a discretized, iterative algorithm, lossy coding maintaining an error bound is sufficient.
    Keywords: ddc:510
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  • 5
    Publication Date: 2020-03-11
    Description: Bovine fertility is the subject of extensive research in animal sciences, especially because fertility of dairy cows has declined during the last decades. The regulation of estrus is controlled by the complex interplay of various organs and hormones. Mathematical modeling of the bovine estrous cycle could help in understanding the dynamics of this complex biological system. In this paper we present a mathematical model of the bovine estrous cycle that includes the processes of follicle and corpus luteum development and the key hormones that interact to control these processes. Focus in this paper is on development of the model, but also some simulation results are presented, showing that a set of equations and parameters is obtained that describes the system consistent with empirical knowledge. Even though the majority of the mechanisms that are included are only known qualitatively as stimulatory or inhibitory effects, the model surprisingly well features quantitative observations made in reality. This model of the bovine estrous cycle could be used as a basis for more elaborate models with the ability to study effects of external manipulations and genetic differences.
    Keywords: ddc:510
    Language: English
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  • 6
    Publication Date: 2022-03-14
    Description: Learning during search allows solvers for discrete optimization problems to remember parts of the search that they have already performed and avoid revisiting redundant parts. Learning approaches pioneered by the SAT and CP communities have been successfully incorporated into the SCIP constraint integer programming platform. In this paper we show that performing a heuristic constraint programming search during root node processing of a binary program can rapidly learn useful nogoods, bound changes, primal solutions, and branching statistics that improve the remaining IP search.
    Keywords: ddc:510
    Language: English
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  • 7
    Publication Date: 2020-08-05
    Description: We propose a novel integer programming approach to transfer minimization for line planning problems in public transit. The idea is to incorporate penalties for transfers that are induced by “connection capacities” into the construction of the passenger paths. We show that such penalties can be dealt with by a combination of shortest and constrained shortest path algorithms such that the pricing problem for passenger paths can be solved efficiently. Connection capacity penalties (under)estimate the true transfer times. This error is, however, not a problem in practice. We show in a computational comparison with two standard models on a real-world scenario that our approach can be used to minimize passenger travel and transfer times for large-scale line planning problems with accurate results.
    Keywords: ddc:510
    Language: English
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  • 8
    Publication Date: 2016-06-09
    Description: The aim of this paper is to devise an adaptive timestep control in the contact--stabilized Newmark method (CONTACX) for dynamical contact problems between two viscoelastic bodies in the framework of Signorini's condition. In order to construct a comparative scheme of higher order accuracy, we extend extrapolation techniques. This approach demands a subtle theoretical investigation of an asymptotic error expansion of the contact--stabilized Newmark scheme. On the basis of theoretical insight and numerical observations, we suggest an error estimator and a timestep selection which also cover the presence of contact. Finally, we give a numerical example.
    Keywords: ddc:510
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  • 9
    Publication Date: 2020-08-05
    Description: Railway scheduling is based on the principle of the construction of a conflict-free timetable. This leads to a strict definition of capacity: in contrast with road transportation, it can be said in advance whether a given railway infrastructure can accommodate - at least in theory - a certain set of train requests. Consequently, auctions for railway capacity are modeled as auctions of discrete goods -- the train slots. We present estimates for the efficiency gain that may be generated by slot auctioning in comparison with list price allocation. We introduce a new class of allocation and auction problems, the feasible assignment problem, that is a proper generalization of the well-known combinatorial auction problem. The feasible assignment class was designed to cover the needs for an auction mechanism for railway slot auctions, but is of interest in its own right. As a practical instance to state and solve the railway slot allocation problem, we present an integer programming formulation, briefly the ACP, which turns out to be an instance of the feasible assignment problem and whose dual problem yields prices that can be applied to define a useful activity rule for the linearized version of the Ausubel Milgrom Proxy auction. We perform a simulation aiming to measure the impact on efficiency and convergence rate.
    Keywords: ddc:510
    Language: English
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  • 10
    Publication Date: 2022-01-07
    Description: This paper presents concepts and implementation of the finite element toolbox Kaskade 7, a flexible C++ code for solving elliptic and parabolic PDE systems. Issues such as problem formulation, assembly and adaptivity are discussed at the example of optimal control problems. Trajectory compression for parabolic optimization problems is considered as a case study.
    Keywords: ddc:510
    Language: English
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  • 11
    Publication Date: 2020-08-05
    Description: In this paper a bottom-up approach of automatic simplification of a railway network is presented. Starting from a very detailed, microscopic level, as it is used in railway simulation, the network is transformed by an algorithm to a less detailed level (macroscopic network), that is sufficient for long-term planning and optimization. In addition running and headway times are rounded to a pre-chosen time discretization by a special cumulative method, which we will present and analyse in this paper. After the transformation we fill the network with given train requests to compute an optimal slot allocation. Then the optimized schedule is re-transformed into the microscopic level and can be simulated without any conflicts occuring between the slots. The algorithm is used to transform the network of the very dense Simplon corridor between Swiss and Italy. With our aggregation it is possible for the first time to generate a profit maximal and conflict free timetable for the corridor across a day by a simultaneously optimization run.
    Keywords: ddc:510
    Language: English
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  • 12
    Publication Date: 2020-12-11
    Description: In solving large polynomial algebraic systems that are too big for standard Gröbner basis techniques one way to make progress is to introduce case distinctions. This divide and conquer technique can be beneficial if the algorithms and computer programs know how to take advantage of inequalities. A further hurdle is the form of the resulting general solutions which often have unnecessarily many branches. In this paper we discuss a procedure to merge solutions by dropping inequalities which are associated with them and, if necessary, by re-parametrizing solutions. In the appendix the usefulness of the procedure is demonstrated in the classification of quadratic Hamiltonians with a Lie-Poisson bracket $e(3)$. This application required the solution of algebraic systems with over 200 unknowns, 450 equations and between 5000 and 9000 terms.
    Keywords: ddc:510
    Language: English
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  • 13
    Publication Date: 2020-12-11
    Description: In the paper arguments are given why the concept of static evaluation (SE) has the potential to be a useful extension to Monte Carlo tree search. A new concept of modeling SE through a dynamical system is introduced and strengths and weaknesses are discussed. The general suitability of this approach is demonstrated. A Remark: Among users of the Internet Go server KGS the abbreviation SE is used for 'Score Estimator'. Although different from 'Static Evaluation' a score estimator is easily obtained from static evaluation by adding up probabilities of chains to be alive at the end of the game or points to be owned by White or Black
    Keywords: ddc:510
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  • 14
    Publication Date: 2020-12-11
    Description: Linear Poisson brackets on e(3) typical of rigid body dynamics are considered. All quadratic Hamiltonians of Kowalevski type having additional first integral of fourth degree are found. Quantum analogs of these Hamiltonians are listed.
    Keywords: ddc:510
    Language: English
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  • 15
    Publication Date: 2020-12-11
    Description: A classification problem is proposed for supersymmetric %scaling\/-\/in\-va\-ri\-ant evolutionary PDE that satisfy the assumptions of nonlinearity, nondegeneracy, and homogeneity. Four classes of nonlinear coupled boson\/-\/fermion systems are discovered under the weighting assumption $|f|=|b|=|D_t|=\oh$. The syntax of the \Reduce\ package \SsTools, which was used for intermediate computations, and the applicability of its procedures to the calculus of super\/-\/PDE are described.
    Keywords: ddc:510
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  • 16
    Publication Date: 2020-12-11
    Description: We consider the problem of constructing Gardner's deformations for the $N{=}2$ supersymmetric $a{=}4$--\/Korteweg\/--\/de Vries equation; such deformations yield recurrence relations between the super\/-\/Hamiltonians of the hierarchy. We prove the non\/-\/existence %P.~Mathieu's Open problem on constructing for of supersymmetry\/-\/invariant %Gardner's deformations that %solutions, retract to Gardner's formulas for the KdV equation %whenever it is assumed that, under the %respective component reduction. % in the $N{=}2$ super\/-\/field. the solutions . At the same time, we propose a two\/-\/step scheme for the recursive production of the integrals of motion for the $N{=}2$,\ $a{=}4$--\/SKdV. First, we find a new Gardner's deformation of the Kaup\/--\/Boussinesq equation, which is contained in the bosonic limit of the super\/-\/%$N{=}2$,\ $a{=}4$--\/SKdV hierarchy. This yields the recurrence relation between the Hamiltonians of the limit, whence we determine the bosonic super\/- /Hamiltonians of the full $N{=}2$, $a{=}4$--\/SKdV hierarchy.
    Keywords: ddc:510
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  • 17
    Publication Date: 2020-08-05
    Description: We provide an introduction into the mathematics of and with paths. Not on the shortest, but hopefully on an entertaining path!
    Keywords: ddc:510
    Language: English
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  • 18
    Publication Date: 2020-08-05
    Description: Wir stellen in dieser Arbeit ein mathematisches Optimierungsmodell zur Bestimmung eines optimalen Linienplans vor, das sowohl die Fahrzeiten und die Anzahl der Umstiege berücksichtigt als auch die Kosten des Liniennetzes. Dieses Modell deckt wichtige praktische Anforderungen ab, die in einem gemeinsamen Projekt mit den Verkehrsbetrieben in Potsdam (ViP) formuliert wurden. In diesem Projekt wurde der Linienplan 2010 für Potsdam entwickelt. Unsere Berechnungen zeigen, dass die mathematische Optimierung in nichts einer "Handplanung" des Liniennetzes nachsteht. Im Gegenteil, mit Hilfe des Optimierungsprogramms ist es möglich, durch Veränderung der Parameter mehrere verschiedene Szenarien zu berechnen, miteinander zu vergleichen und Aussagen über minimale Kosten und Fahrzeiten zu machen.
    Keywords: ddc:510
    Language: German
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  • 19
    Publication Date: 2020-12-11
    Description: The paper gathers evidence showing different dimensions of the game of Go: the continuous and discrete nature of the game and different types of relations between state variables happening on ultra local, local, regional, and global scales. Based on these observations a new continuous local model for describing a board position is introduced. This includes the identification of the basic variables describing a board position and the formulation and solution of a dynamical system for their computation. To be usable as a static evaluation function for a game playing program at least group-wide (regional)aspects will have to be incorporated.
    Keywords: ddc:510
    Language: English
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  • 20
    Publication Date: 2020-08-05
    Description: The track allocation problem, also known as train routing problem or train timetabling problem, is to find a conflict-free set of train routes of maximum value in a railway network. Although it can be modeled as a standard path packing problem, instances of sizes relevant for real-world railway applications could not be solved up to now. We propose a rapid branching column generation approach that integrates the solution of the LP relaxation of a path coupling formulation of the problem with a special rounding heuristic. The approach is based on and exploits special properties of the bundle method for the approximate solution of convex piecewise linear functions. Computational results for difficult instances of the benchmark library TTPLIB are reported.
    Keywords: ddc:510
    Language: English
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  • 21
    Publication Date: 2020-08-05
    Description: This paper presents a case study on a railway timetable optimization for the very dense Simplon corridor, a major railway connection in the Alps between Switzerland and Italy. Starting from a detailed microscopic network as it is used in railway simulation, the data is transformed by an automatic procedure to a less detailed macroscopic network, that is sufficient for the purpose of capacity planning and amenable to state-of-the-art integer programming optimization methods. In this way, the macroscopic railway network is saturated with trains. Finally, the corresponding timetable is re-transformed to the microscopic level in such a way that it can be operated without any conflicts among the slots. Using this integer programming based micro-macro aggregation-disaggregation approach, it becomes for the first time possible to generate a profit maximal and conflict free timetable for the complete Simplon corridor over an entire day by a simultaneous optimization of all trains requests. This also allows to to undertake a sensitivity analysis of various problem parameters.
    Keywords: ddc:510
    Language: English
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  • 22
    Publication Date: 2016-06-09
    Description: The thesis presents the analysis of a reduced model for modulation of internal gravity waves by deep convective clouds. The starting point for the derivation are conservation laws for mass, momentum and energy coupled with a bulk micro-physics model describing the evolution of mixing ratios of water vapor, cloud water and rain water. A reduced model for the identified scales of the regime is derived, using multi-scale asymptotics. The closure of the model employs conditional averaging over the horizontal scale of the convective clouds. The resulting reduced model is an extension of the anelastic equations, linearized around a constant background state, which are well-known from meteorology. The closure of the model is achieved purely by analytical means and involves no additional physically motivated assumptions. The essential new parameter arising from the coupling to a micro-physics model is the area fraction of saturated regions on the horizontal scale of the convective clouds. It turns out that this parameter is constant on the employed short timescale. Hence the clouds constitute a constant background, modulating the characteristics of propagation of internal waves. The model is then investigated by analytical as well as numerical means. Important results are, among others, that in the model moisture (i) inhibits propagation of internal waves by reducing the modulus of the group velocity, (ii) reduces the angle between the propagation direction of a wave-packet and the horizontal, (iii) causes critical layers and (iv) introduces a maximum horizontal wavelength beyond which waves are no longer propagating but become evanescent. The investigated examples of orographically generated gravity waves also feature a significant reduction of vertical momentum flux by moisture. The model is extended by assuming systematically small under-saturation, that is saturation at leading order. The closure is similar to the original case but requires additional assumptions. The saturated area fraction in the obtained model is no longer constant but now depends nonlinearly on vertical displacement and thus on vertical velocity.
    Keywords: ddc:510
    Language: English
    Type: doctoralthesis , doc-type:doctoralThesis
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  • 23
    Publication Date: 2022-03-14
    Description: We propose a hybrid approach for solving the resource-constrained project scheduling problem which is an extremely hard to solve combinatorial optimization problem of practical relevance. Jobs have to be scheduled on (renewable) resources subject to precedence constraints such that the resource capacities are never exceeded and the latest completion time of all jobs is minimized. The problem has challenged researchers from different communities, such as integer programming (IP), constraint programming (CP), and satisfiability testing (SAT). Still, there are instances with 60 jobs which have not been solved for many years. The currently best known approach, lazyFD, is a hybrid between CP and SAT techniques. In this paper we propose an even stronger hybridization by integrating all the three areas, IP, CP, and SAT, into a single branch-and-bound scheme. We show that lower bounds from the linear relaxation of the IP formulation and conflict analysis are key ingredients for pruning the search tree. First computational experiments show very promising results. For five instances of the well-known PSPLIB we report an improvement of lower bounds. Our implementation is generic, thus it can be potentially applied to similar problems as well.
    Keywords: ddc:510
    Language: English
    Type: reportzib , doc-type:preprint
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  • 24
    Publication Date: 2023-11-03
    Description: In contrast to the well known meshbased methods like the finite element method, meshfree methods do not rely on a mesh. However besides their great applicability, meshfree methods are rather time consuming. Thus, it seems favorable to combine both methods, by using meshfree methods only in a small part of the domain, where a mesh is disadvantageous, and a meshbased method for the rest of the domain. We motivate, that this coupling between the two simulation techniques can be considered as saddle point problem and show the stability of this coupling. Thereby a novel transfer operator is introduced, which interacts in the transition zone, where both methods coexist.
    Keywords: ddc:510
    Language: English
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  • 25
    Electronic Resource
    Electronic Resource
    Springer
    European food research and technology 209 (1999), S. 389-392 
    ISSN: 1438-2385
    Keywords: Key words Gelation ; Polymerization ; Whey proteins
    Source: Springer Online Journal Archives 1860-2000
    Topics: Process Engineering, Biotechnology, Nutrition Technology
    Notes: Abstract  The influence of protein concentration on the properties of gels obtained by a two-stage heating process was determined. In the first stage, whey protein dispersion (3–10%) was heated at pH 8.0, and in the second stage it was diluted to 3% protein, adjusted to pH 7.0 and heated again. Increased protein concentration in the first stage of polymerization resulted in the gels obtained in the second stage having a lower phase angle, increased storage modulus and increased hardness. Increased protein concentration also resulted in gels with an increased optical density, which suggests thathigher protein concentration leads to more and larger aggregates. Gels obtained from dispersions preheated at a higher protein concentration had higher permeability coefficient (B gel) values. The increase in B gel suggests that the higher protein concentration increased the size of the aggregates, which in a second stage of heating formed a gel matrix with a larger pore size.
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  • 26
    Electronic Resource
    Electronic Resource
    Springer
    Theoretical chemistry accounts 102 (1999), S. 285-292 
    ISSN: 1432-2234
    Keywords: Key words: Ethylene insertion ; ab initio MO calculations ; Sm complexes ; Polymerization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract. Ethylene insertion into the Sm–C bond of H2SiCp2SmCH3, a model reaction of an olefin polymerization propagation step, has been studied by ab initio molecular orbital methods. The small electronegativity of the Sm atom makes the Sm–C bond ionic, the methyl group being negatively charged by −0.75. The reaction passes through a loose ethylene complex with a binding energy of 15 kcal/mol and then a tight four-centered transition state with an agostic interaction between the Sm atom and one of the methyl CH bonds. A small activation energy of 14 kcal/mol is required to pass through this transition state, indicating that this is an easy reaction. Compared with the reactions with group 4 cationic silylene-bridged metallocenes the activation energy is higher and the reaction is less exothermic. The origin of these differences is discussed. The results of molecular mechanics calculations on regio- and stereoselectivities in the insertion reaction of propylene are also reported.
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  • 27
    ISSN: 1611-4663
    Keywords: Coriolus versicolor ; Na2SO3-HCHO-AQ pulping effluent ; Polymerization ; Lignosulfonate ; Laccase
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract A strain of the fungusCoriolus versicolor was inoculated periodically into potato dextrose agar (PDA) slants containing the effluent to enhance the natural ability to grow in the effluent. The acclimated strain grown in the 50% effluent-containing PDA slant and the original strain were employed to treat the effluent. The acclimated strain could grow in a higher concentration of the effluent than the original unacclimated one. Both the original and acclimated strains improved the dispersing ability of the effluent, especially the acclimated strain because of its higher laccase secretion. The dispersing ability of the SFP effluent was improved to a level comparable to a commercial lignosulfonate product because it was strongly polymerized by the fungus. During the fungal treatment, more than 50% of the sugars were removed from the effluent, thereby increasing the purity of the SFP lignin product.
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  • 28
    ISSN: 1435-1536
    Keywords: Key words Reaction kinetics in microgravity ; Colloidal silica spheres ; Polymerization ; Transmitted-light intensity ; Dynamic light scattering
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract Polymerization reactions of colloidal silica spheres via the hydrolysis and dehydration processes of tetraethyl orthosilicate with ammonia and a tiny amount of water in ethyl alcohol have been studied in microgravity by the parabolic flights of a MU-300 rear-jet aircraft. Induction periods and polymerization rates are determined by fast-scanning transmitted-light-intensity measurements and the fast-scanning dynamic light-scattering method. Direct observation of the reaction mixtures is also made with a charge-coupled device video camera. Reproducible and reliable data are obtained in microgravity compared with those in gravity. Increases in the induction times and decreases in the polymerization rates are observed in microgravity compared with those in gravity. One of the main reasons for these observations is the fact that the translational Brownian movement of the reactants and/or product spheres is free from downward translational movement in microgravity. Very weak convection of the reaction suspensions in microgravity is another important factor.
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  • 29
    ISSN: 1435-1536
    Keywords: Key words Allyldimethyldodecylammonium bromide ; Liquid crystals ; Polymerization ; Polymerizable surfactant
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract Allyldimethyldodecylammonium bromide was polymerized by γ-ray irradiation in both hexagonal and cubic mesophases, and the conversion–time curves were obtained. The maximum conversion was about 35%, and the polymer remained in the liquid-crystalline structure formed by the nonpolymerized monomers. The influence of polymerization on the distribution of water in the different types related to the hydrophilic surfaces of microstructures was studied using Fourier transform infrared spectroscopy. The incomplete polymerization was explained by steric constraints in the liquid-crystalline structures.
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  • 30
    Electronic Resource
    Electronic Resource
    Springer
    Colloid & polymer science 277 (1999), S. 203-209 
    ISSN: 1435-1536
    Keywords: Key words Microemulsions ; Vinylacetate ; Acrylic acid structure ; Polymerization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract The composition ranges over which microemulsions are formed in systems containing vinyl acetate, acrylic acid, water with nonylphenol ethoxylated with 25 mol ethylene oxide monomaleate as surfactant were studied. Conductometric and refractometric investigations have shown the existence of some aqueous/organic, bicontinuous and organic/aqueous microemulsions. The types of precursor microemulsions influence the conversion of monomers. In the presence of a crosslinking agent, diethylene glycol bis maleate, hydrogels are formed whose water absorption depends on the composition of the initial microemulsions. The kinetics of water absorption suggests the modification of polymer network structures as a function of the crosslinked monomer content and the ratio of organic to aqueous phases.
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  • 31
    Publication Date: 2016-06-09
    Keywords: ddc:510
    Language: English
    Type: doctoralthesis , doc-type:doctoralThesis
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  • 32
    ISSN: 1572-8935
    Keywords: Anionic ; Polymerization ; Hydrogenation ; Head-to-head ; 2,3-Dimethyl-1,3-butadiene ; Polypropylene
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract Poly(2,3-Dimethyl-1,3-butadiene) (PDMB) with varying contents of 1,4-and 1,2-structures has been anionically synthesized using either n-butyllithium or sec-butyllithium as an initiator. The addition of tetrahydrofuran could enhance the rate of synthesis and effect the microstructure. The Tm was higher for PDMB with a lower content of 1,2-structure, and the Tg was lower. This PDMB was then hydrogenated with a nickelocene/n-butyllithium catalyst system leading to the formation of HPDMB. The trans 1,4-structure unit was more difficult to hydrogenate due to its steric hindrance. Repetitive hydrogenation was necessary in order to achieve a high degree of hydrogenation. The hydrogenated PDMB is an amorphous elastomeric material. The Tg’s were found to decrease with an increase in the degree of hydrogenation, concurrent with a gradual disappearance of the Tm’s. Since a HPDMS with a low content of 1,2-structure resembles a head-to-head polypropylene, our data suggest that the Tg of an atactic head-to-head polypropylene lie between −30 and −35 °C.
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  • 33
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    Chromatographia 47 (1998), S. 470-474 
    ISSN: 1612-1112
    Keywords: Affinity chromatography ; Polymerization ; Imprinted polymer networks ; Colloid ; Silica
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Summary The article covers the methods that are currently available for the preparation of molecularly imprinted polymers. The disadvantages of the conventional grinding of bulk polymerized blocks of imprinted polymer are first identified. The newer methods are divided into four sections: suspension polymerization; modified surfaces; polymer colloids and finally miscellaneous techniques such as the use of linear polymers. Each alternative method is compared with the grinding method and the relative advantages and disadvantages identified.
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  • 34
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    Sexual plant reproduction 10 (1997), S. 136-141 
    ISSN: 1432-2145
    Keywords: Key words Ginkgo biloba L. ; Tubulin ; Purification ; Polymerization ; Pollen
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Abstract  Tubulin was purified by a combination of acetone powder preparation, DEAE Sephadex A-50 chromatography, Sephacryl S-300 gel filtration, and Mono Q anion exchange chromatography from the pollen of ginkgo (Ginkgo biloba L.), a typical gymnosperm. The average yield of tubulin is 2 mg per 100 g of pollen grain. The purified tubulin is electrophoretically homogeneous. It seems to be composed of two subunits on SDS-PAGE and is resolved as two major spots on two-dimensional electrophoresis, preliminarily indicating that there are no obvious tubulin isotypes in ginkgo pollen. The apparent molecular weights of the two subunits are about 54 kDa and 52 kDa respectively, estimated from the SDS-PAGE. It was also demonstrated that tubulin from ginkgo pollen is immunochemically related to animal brain tubulin, and the purified tubulin was polymerized to microtubular aggregates in the presence of taxol and GTP in vitro.
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  • 35
    ISSN: 1432-1017
    Keywords: Key words Diacetylenic lipids ; Polymerization ; Microfluorescence ; Filmbalance ; AFM
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Physics
    Notes: Abstract Molecular films from polymeric materials play an important role in basic research as well as in technology. We have synthesized the double chain diacetylenic ammonium lipid N-bis-(10, 12-pentacosadiinoyl)-oxy-ethyl)-N-methyl-amine (ONCO). We have characterized monomolecular films at the air/water interface by means of microfluorescence filmbalance techniques and by atomic force microscopy (AFM). ONCO forms stable monomolecular films that exhibit a fluid-solid phase transition with a transition enthalpy of 90 kJ/mol at 10 °C and neutral pH. The coexistence pressure was found to decrease with decreasing protonation, which is in contrast to the commonly found Coulomb mechanism. A change in the chain packing due to a different nitrogen bond angle is discussed as a possible mechanism. This model is cor-roborated by the finding that crystals at high and at low pH differ in their polymerization properties as measured by microfluorescence.
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  • 36
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    Berichte der deutschen chemischen Gesellschaft 130 (1997), S. 399-404 
    ISSN: 0009-2940
    Keywords: Disilylamides ; Group 4 Complexes ; Polymerization ; Metallacycles ; Titanium ; Zirconium ; Chemistry ; Inorganic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A series of metallacyclodisiladiazanes has been prepared. Lithiated (SiMe2NHtBu)2 (1) reacts with TiCl4 · 2 THF to give (SiMe2NtBu)2TiCl (4). Methylation or fluorination of 4 leads to (SiMe2NtBu)2TiMe2 (8) and (SiMe2MtBu)2TiF2 (9), respectively. The reaction of ZrCl4 · 2 THF with lithiated 1 or [SiMe2NH(4-FC6J4)]2 (2) yields (SiMe2NtBu)2ZrCl2 (5) and [SiMe2N(4-FC6H4)]ZrCl2 · THF (7), respectively. The lithiated ligand [SiMe2NH(2,6-iPr2C6H3)]2 (3) reacts with noncoordinated ZrCl4 to give [SiMe2N(2,6-iPr2C6H3)]2ZrCl2 (6). X-ray structural analysis of 9 showed it to be a fluorine-bridged dimer in the solid state. Compounds 4, 6, 8 and 9 were found to be catalysts for the polymerization of ethylene.
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  • 37
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    Berichte der deutschen chemischen Gesellschaft 130 (1997), S. 291-294 
    ISSN: 0009-2940
    Keywords: Halogenoacetates ; Silver salts ; Solid-state reactions ; Polymerization ; Chemistry ; Inorganic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The structure of silver chloroacetate was determined by single-crystal X-ray structure analysis. This represents the first salt of a monohalogenoacetic acid with a monovalent metal whose structure was determined with high precision. The salt undergoes a thermally induced solid-state polymerization to polyglycolide under elimination of silver chloride. A probable mechanism for a structure-determined reaction in the solid state is discussed.
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  • 38
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    Liebigs Annalen 1997 (1997), S. 81-85 
    ISSN: 0947-3440
    Keywords: Halogenocarboxylates ; Solid-state reactions ; Polyesters ; Thermal analysis ; Polymerization ; Chemistry ; Organic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Heating of the sodium salts of chlorocarboxylic acids leads to exothermic elimination of sodium chloride and oligomerization of the organic backbone of the molecule. Thermochemical data of sodium 2-chloropropionate (1), sodium 3-chloropropionate (2) and sodium 2-chlorobutyrate (3) were derived. The reaction products were characterized by IR and NMR spectroscopy, and the degree of polymerization was determined by gel permeation chromatography (GPC).
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  • 39
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    International Journal of Quantum Chemistry 62 (1997), S. 1-11 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Roothaan-Hartree-Fock (RHF) calculations are carried out for the ground states of the atoms from helium to xenon using a minimal basis set of Slater-type functions whose principal quantum numbers are allowed to take variationally optimal noninteger values. The resulting energies are substantially superior to those obtained previously under the usual restriction that principal quantum numbers be positive integers. The energy lowering relative to the single-zeta wave functions of Clementi and co-workers ranges from 0.0066 Eh in He to 11.2 Eh in Xe. Our results are superior to those obtained by Höjer using a minimal basis set of unconventional binomially screened basis functions. Noninteger principal quantum numbers benefit d-orbitals the most; physically realistic negative d-orbital energies are obtained in all cases including those transition-metal atoms for which a conventional single-zeta STF basis leads to positive d-orbital energies. © 1997 John Wiley & Sons, Inc.
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  • 40
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    International Journal of Quantum Chemistry 62 (1997), S. 23-27 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: An ab initio study on the reaction of the ground state (3D) and the excited state (1D) of Sc+ with methane was performed. Reaction channels on the singlet and triplet potential surface (PES) and the reaction mechanism are examined and discussed. Three regions of the potential surface was studied: the molecular complex, the C(SINGLE BOND)H insertion products, and the transition states for the reaction. Comparisons between singlet and triplet PESs show that the excited state (1D) of Sc+ has more reactivity with methane than does the ground state (3D) due to the spin quantum number conservation with the more stable insertion intermediate. © 1997 John Wiley & Sons, Inc.
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  • 41
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    International Journal of Quantum Chemistry 62 (1997), S. 67-76 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The importance of the hybridization displacement charge (HDC) in describing molecular electrostatic potential (MEP) maps was demonstrated by studying six molecules; pyrazine N-oxide, para-nitropyridine, 5-nitropyrimidine, 3-nitropyridazine, N2, and N2O. It is shown that continuously distributed HDC-corrected Löwdin charges reproduce the MEP features of these molecules, most of which have competing electrophilic sites, in agreement with ab initio results. Further, it is found that for homonuclear diatomic molecules MEP minima can be located properly using HDC-corrected Löwdin (or HDC-corrected Mulliken) continuously distributed charges, but these features cannot be obtained using the conventional Löwdin (or Mulliken) charges. It was shown that the order of molecular electric field (MEF) values near the different electrophilic sites becomes changed when one moves away from the molecules. Thus, pyridine-type nitrogen atoms are the preferred binding sites close to the molecules, while at large distances, effects of oxygen atoms of the NO groups become dominant. © 1997 John Wiley & Sons, Inc.
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  • 42
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    International Journal of Quantum Chemistry 62 (1997), S. 115-124 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Some types of atomic vibrations in a chain of the DNA type constructed of G-C pairs were studied. These are the atomic vibrations of the lateral groups of guanine and N(3)H(1)H(2) of cytosine connected by the hydrogen bond h-b-1 and the vibrations of the centers of masses of bases in the direction parallel to bonds h-b-i, i = 1-3. The vibrations mix partially due to the dependence of the energy of the bond h-b-1 on its length and split into two bands because of the interaction between neighboring base pairs. It was shown that the excitation of the bond h-b-1 results in the splitting off of the two local vibrations and in a small deformation of the chain in the vicinity of the pair with the localized hydrogen bond. The law of the dispersion of band vibrations, values of the split-off frequencies, and degree of poly(dG)-poly(dC) chain deformation were determined. © 1997 John Wiley & Sons, Inc.
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  • 43
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    International Journal of Quantum Chemistry 62 (1997), S. 273-278 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Analytical solutions to the Yukawa-like screened Coulomb nuclear attraction and electron repulsion molecular basic integrals, as well as to the basic integrals required to compute the virial coefficient, over Gaussian basis functions, are derived and cast into a practical closed form, suitable to interface with modern codes for the calculation of molecular electronic structure. © 1997 John Wiley & Sons, Inc.
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  • 44
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    International Journal of Quantum Chemistry 62 (1997), S. 303-314 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: He I photoelectron (PE) spectra of four carboxylic acids and five esters are measured. Semiempirical and ab initio quantum chemical calculations are used for the interpretation of the spectra. The complex approach which uses empirically established relationships (the dependence of valence electron ionization energies on proton affinities in the gas phase, on the core level ionization energies, and on the structure) was developed. © 1997 John Wiley & Sons, Inc.
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  • 45
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    International Journal of Quantum Chemistry 62 (1997), S. 323-328 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Simple molecular orbital calculations are employed in searching electronic parameters which may characterize the chemical carcinogens. Using frontier orbitals, the carcinogen-DNA bond formation is described as an electron transfer from the highest occupied molecular orbital (HOMO) of DNA to the lowest unoccupied molecular orbital (LUMO) of the carcinogen. Analysis of the DNA bases units shows that the electron donation occurs preferentially at the guanine site. The calculated low LUMO energy of several carcinogens indicate correctly the electrophilic character of these compounds. The difference between the carcinogen and the ultimate carcinogen is analyzed. Epoxides, free radicals, alkylating agents, and other metabolite forms are studied. A reasonable correlation is found between the LUMO energy and the carcinogenic function. © 1997 John Wiley & Sons, Inc.
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  • 46
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    International Journal of Quantum Chemistry 63 (1997), S. 1107-1122 
    ISSN: 0020-7608
    Keywords: relativistic pseudopotentials ; heavy atoms ; method of molecular calculation ; electronic structure ; Gaussian approximation ; Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The Gaussian expansions of the generalized relativistic effective core potential (GRECP) components are reported for elements Hg through Rn. The accuracy of the analytical GRECPs is estimated by calculations of atomic transition energies with the numerical one-configurational wave functions in comparison with Dirac-Fock calculations. The results of the corresponding calculations with the RECPs of other groups are also given. An “averaged error” in the reproduction of the transition energies without the change of the occupation number of the 5d-shell is an order of magnitude smaller than that for the RECPs of other groups. As is demonstrated for the transitions with the change of the occupation number of the 5d-shell in mercury, the largest absolute error of the GRECP is only 1.5-2 times smaller than that of the energy-adjusted pseudopotential (PP) or the RECP of Ross et al. with the same space of explicitly treated electrons. However, the dispersion of these errors is 19⋅10-4 au for the energy-adjusted PP, 35⋅10-4 au for the RECP of Ross et al. and only 4⋅10-4 au for the GRECP. One-configurational spin-averaged calculations of the molecular properties for HgH and HgH+ are carried out and compared with the corresponding results of Häussermann et al.   © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 1107-1122, 1997
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  • 47
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    International Journal of Quantum Chemistry 63 (1997), S. 1123-1131 
    ISSN: 0020-7608
    Keywords: MD simulations ; liquid surface ; formamide ; molecular orientation ; molecular surface density ; Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Molecular dynamics simulations of liquid formamide(HCONH2) were carried out using the GROMOS software. The formamide molecule is represented by all of its atoms with all internal degrees of freedom. In contrast to other simulations dealing with bulk properties, this study focuses on the interface liquid-vacuum for the first time. We show that the molecular plane is tilted out of the surface, exposing the HCO group to the vacuum.   © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 1123-1131, 1997
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  • 48
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    International Journal of Quantum Chemistry 62 (1997), S. 29-45 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The H2 interaction with the Pd dimer and trimer were studied using multiconfigurational self-consistent field (MC-SCF) calculations with the relativistic effective core potential (RECP); the correlation energy correction was included in the extended multireference configuration interaction (MRCI), variational and perturbative to second order. Here, we considered the Pd2 first six states: 3Σ+u, 1Σ+g, 3Πg, 3Δxy, 1Σ+u, and 3Σ+g. For them, the four geometrical approaches included were the side-on H2 toward Pd2, for the hydrogen molecule in and out the Pd dimer plane; the perpendicular end-on H2 toward Pd2; and the perpendicular end-on Pd2 to H2. The Pd2 ground state is 3Σ+u, which only captures H2 in the C2v end-on approach, softly relaxing the H(SINGLE BOND)H bond. The closed-shell 1Σ+g captures the H2 molecule in all the approaches considered: The side-on approach of this state presents deep wells and relaxes the H(SINGLE BOND)H bond, and the end-on approach captures H2 with a relatively longer H(SINGLE BOND)H distance and also a deep well. The 3Πg state was the only one which did not capture H2. For the triangular Pd3 clusters, H2 was approached in the C2v symmetry in and out of the Pd3 plane. In the triangular case, H2 was absorbed in both spin states, with deep wells and relaxing the H(SINGLE BOND)H distance. The linear Pd3 singlet and triplet states capture outside of the Pd3 and break the H(SINGLE BOND)H bond. © 1997 John Wiley & Sons, Inc.
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  • 49
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    International Journal of Quantum Chemistry 62 (1997), S. 89-96 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: We presented a calculation of the total and partial decay widths of vibrational predissociation (VP) of the HeI2 molecule for low initial vibrational excitations from the lowest van der Waals (vdW) state with total angular momentum J = 0. A time-dependent golden rule wave-packet method was employed in our numerical calculations for the decay widths. The computed total decay widths, lifetimes, and rates of VP are in fairly good agreement with those extrapolated from the experimental data available. Predicted total decay widths as a function of initial vibrational levels exhibit a highly nonlinear behavior. These results demonstrate that a quantum mechanical decay mode for low vibrational excitation remains as well. The total propagation time needed in the time-dependent golden rule wave-packet calculations is much shorter than is the lifetime of the predissociation of HeI2. It is shown that the final-state interaction between the fragments is important for determining the final rotational-state distribution (partial decay width). We find that the major peak position in the final rotational-state distribution shifts to lower rotational energy levels with increase of the initial vibrational quantum number, which is evidently different from that for higher vibrational levels. This fact can be clearly explained by the dependence of the amount of kinetic energy released to the product degrees of freedom on the initial vibrational state. © 1997 John Wiley & Sons, Inc.
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  • 50
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    International Journal of Quantum Chemistry 63 (1997), S. 1065-1078 
    ISSN: 0020-7608
    Keywords: very precise eigenvalues ; very accurate grid method ; general solution for Schrödinger equations ; rapidly convergent treatment for helium eigenvalues ; superconvergence ; optimization of grids ; treatment of continuum ; Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: An extension to the theory of Schrödinger equations has been made which enables the derivation of eigenvalues from a consideration of a very small part of geometric space. The concomitant unwanted continuum effects have been removed. The theory enables very convergent or “superconvergent” calculations. In the case of the helium ground state, E=-2.90372437703411987 Eh was obtained from 251 terms. The result is comparable to that from the largest variation calculations so far carried out reinforced by extrapolation techniques. The theory is extensible to atoms and molecules irrespectively of the number of electrons or nuclear centers. In these cases, the advantage of “superconvergent” calculations will be more pronounced than in the case of helium.   © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 1065-1078, 1997
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  • 51
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    International Journal of Quantum Chemistry 62 (1997), S. 239-244 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: We calculate the resonant and antibound state energies for a Morse potential with a centrifugal barrier using Siegert boundary conditions. Starting with a complex wave number k (purely imaginary for bound and antibound states), we integrate numerically from the origin up to a matching point using Numerov's method. The inward integration is performed using the corresponding (first-order) Riccati equation. The complex eigenvalues are found by matching the two logarithmic derivatives. We find narrow shape resonances within the well, above the dissociation limit, and broad resonances above the centrifugal barrier. Antibound states are found even with J = 0. © 1997 John Wiley & Sons, Inc.
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  • 52
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    International Journal of Quantum Chemistry 62 (1997), S. 265-272 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Numerical experiments with a nonlinear (λχ4) oscillator which has its harmonic frequency changing randomly with time reveal certain interesting features of its dynamics of quantum evolution. When λ = 0, the level populations are seen to oscillate. But, as the nonlinear coupling is switched on (λ 〉 0), a threshold is reached at λ = λc when the evolution is seen to be characterized by an abrupt transition dominantly to the highest available state of the unperturbed (initial) oscillator. It is shown that this transition probability is maximized at a particular value of λ. The time threshold for this transition decreases with increasing nonlinear coupling strength. The numerically obtained structures of the underlying quantum-phase spaces of the linear and nonlinear random oscillators are examined. Possible use of these results in a problem of chemical origin is explored. © 1997 John Wiley & Sons, Inc.
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  • 53
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    International Journal of Quantum Chemistry 62 (1997), S. 279-289 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Testosterone (17β-hydroxy-4-androsten-3-one) was studied by the semiempirical AM1 and PM3 and ab initio STO-3G*, 3-21G*, and 6-31G* methods. The goals were to compare those methods and to know the electronic structure of the hormone. Full geometry optimization was performed, and two crystal conformers (T1 and T2), and experimental dipole moment in solution were used for comparison. One conformer with a dipole moment similar to the solvated conditions was generated. Total energy, entalphies, dipole moments, charges, electrostatic potentials, and highest occupied molecular orbitals (HOMO) and lowest unoccupied molecular orbital (LUMO) were calculated. Root-mean-square (RMS) index of the theoretical molecules against T1 and T2 showed best results with the 3-21G* and 6-31G* methods, while AM1 gave better energies than PM3. Dipole moments were directed toward the OH group and the botton face of the A ring. The frontier orbitals were located along the C4-C5 π bond, particularly the LUMO was split between C4 and C5, predicting the action of enzymes at C5 yielding to 5α and 5β-reduced androgens. Electrostatic potentials might be also of biological importance since they are coincidental with the dipole-moment orientation. Finally, it is interesting that the solvatedlike conformer, its properties, and the OH group laid between the same group of T1 and T2 and with a total energy between the crystals and the gas phase or in vacuo conditions. This results might also explain the biology of testosterone and use them to model the hormone-receptor interaction. © 1997 John Wiley & Sons, Inc.
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    International Journal of Quantum Chemistry 62 (1997), S. 315-322 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Two alternative dehydration reactions C(OH)4 → (HO)2CO + H2O and C(OH)4 + H2O → (HO)2CO + 2H2O are studied by ab initio Becke3LYP/6-311 + G** and MP2/6-31G** methods. Calculated energy and geometry characteristics of intermediates and transition states predict a catalytic effect of one water molecule and the exothermism of the transformations. Relevant HF/6-311 + G**, HF/6-31G**, HF/6-31G, and HF/3-21G calculations were performed for comparison. © 1997 John Wiley & Sons, Inc.
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  • 55
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    International Journal of Quantum Chemistry 62 (1997), S. 97-113 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Restricted geometry optimizations at the ab initio SCF level with the 3-21G basis set were employed to investigate the conformation space of flavone acetic acid (FAA) and its related compounds. All the conformations are produced from a conformation which is, according to our previous work, probably the active conformation in terms of antitumor activity shown by these compounds. Detailed studies on FAA were carried out while only brief discussions are made on the analogs. The main results obtained are that (1) FAA is a very flexible molecule, e.g., with the energy barrier up to about 3 kcal mol-1 from the reference conformation, the important torsional angle τ1 can change from 27.0° to 117.0°, τ2 from -168.0° to 2.0°, and τ3 from -50.0° to 30.0°; (2) the hydrogen-bonding effect plays an important role in determining lower-energy conformations; (3) among all the FAA conformations considered, some are active and some are inactive; (4) it seems that the analogs will have similar behavior to FAA when the torsional angle τ3 is restricted to the values which are around the equilibrium values; and (5) the hypothesis put forward previously has been further developed in this work. Now, we postulate that efficient charge transfers will lower the energy and that proper charge transfers will activate the molecule. There are mainly two different types of charge transfer corresponding to two different types of conformation, which are specified in this article. © 1997 John Wiley & Sons, Inc.
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  • 56
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    International Journal of Quantum Chemistry 62 (1997), S. 55-65 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: We compare geometry configurations, vibrational properties, and electronic structures of (HF)2 in a free state and inside argon atom shells Arn. For the first stage, molecular dynamics calculations for the (HF)2 · Ar62 heterocluster are performed with the help of model potentials HF(SINGLE BOND)HF, Ar(SINGLE BOND)Ar, and Ar(SINGLE BOND)HF. Then, ab initio quantum chemistry analysis is carried out for the smaller systems (HF)2 · Ar15 and (HF)2 · Ar6 when keeping the argon atoms closest to the trapped dimer. We conclude that the hydrogen-bonded complex (HF)2 gains some extra stability inside the argon shells, originating primarily from a decrease of intermolecular distance RFF. Electronic structure calculations are in accord with the changes in dynamical properties, namely, a noticeable increase in the vibrational frequency assigned to the F(SINGLE BOND)F stretching mode (+25 cm-1) and decrease in rms deviations for the corresponding coordinate δFF. In addition to these changes, the argon atoms of the nearest solvent shell donate a small fraction of electron charge which is spent for an increase of population of the antibonding orbital σ*Hf(SINGLE BOND)Ff of the free monomer unit and shift orbital energies primarily of the lone-pair fluorine species. These shifts are greater than the changes due to geometry alterations and the possible inaccuracies of the calculation scheme. © 1997 John Wiley & Sons, Inc.
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  • 57
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    International Journal of Quantum Chemistry 62 (1997), S. 13-21 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: An analysis of the anisotropic Heisenberg model is carried out by solving the Bethe ansatz solution of the model numerically as a function of the anisotropy parameter for finite N. A brief introduction to the limit of the infinite chain is presented. The energy for a few special limiting cases of the anisotropy parameter in the Hamiltonian are worked out. Numerical results for finite cycles as well as for the infinite chain are given. Comparison can then be made with the case of finite increasing N. © 1997 John Wiley & Sons, Inc.
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  • 58
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    International Journal of Quantum Chemistry 62 (1997), S. 47-53 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The MELD program is employed to evaluate the Slater average potential v(r) felt by an electron at the point r within an atom. The characteristic radius R of the atom is then defined by the classical turning point equation v(R) = -I, where I denotes the first ionization potential of the atom. The atomic radii defined in this way have a close correlation with the van der Waals atomic radii. © 1997 John Wiley & Sons, Inc.
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  • 59
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    International Journal of Quantum Chemistry 62 (1997), S. 77-88 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Highly accurate upper bounds for several 2Pe states of the Li isoelectronic series obtained by extensive Hylleraas-Cl calculations are given. The best value for the 22Pe state (1s2p2) of Li is -5.21373920 au. The evaluation of the occurring integrals is given explicitly. Additionally, we present some expectation values and isotope energies of the Li isoelectronic series. © 1997 John Wiley & Sons, Inc.
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  • 60
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    International Journal of Quantum Chemistry 62 (1997), S. 245-259 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: An efficient expansion method for the evaluation of VB matrix elements is introduced. The overlaps of VB wave functions of N electrons can be treated as algebrants, i.e., generalized determinants, of N × N matrices. An algebrant can be expanded with subalgebrants of lower orders in a successive way. By choosing Rumer spin bases and appropriately arranging the expansion, it is found that the number of unique subalgebrants involved in the expansion increases in a quite moderate way with N. In contrast to the traditional symmetric group approach, which explicitly utilizes all N! representation matrices, the new strategy incorporates the group theoretical factors in a simple way in the successive expansion. As only the unique subalgebrants are further expanded, the computational effort required by the new strategy scales in a very acceptable manner with the increasing number of electrons. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 62: 245-259, 1997
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  • 61
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    International Journal of Quantum Chemistry 62 (1997), S. 261-264 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Characters of irreducible representations (irreps) of the symmetric group corresponding to the two-row Young diagrams, i.e., describing transformation properties of N-electron eigenfunctions of the total spin operators, have been expressed as explicit functions of the number of electrons N and of the total spin quantum number S. The formulas are useful in various areas of theory of many-electron systems, particularly in designing algorithms for evaluation of spectral density moments. © 1997 John Wiley & Sons, Inc.
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  • 62
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    International Journal of Quantum Chemistry 62 (1997), S. 291-296 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The geometries and S-H, S-S, and S-C bond dissociation energies for hydrogen sulfide, hydrogen disulfide, methanethiol, dimethyl disulfide, and dimethyl disulfide were calculated with both ab initio (ROHF and MP2), hybrid (BHandH, BHandHLYP, Becke3LYP and Becke3P86), and nonlocal (BLYP and BP86) density functional theory (DFT) methods. In all studies the 6-31 + G(d) basis set is used. The computed results are compared to the experimentally obtained values, targeting the selection of a suitable ab initio or DFT method for the study of these systems. © 1997 John Wiley & Sons, Inc.
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  • 63
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    International Journal of Quantum Chemistry 62 (1997), S. 297-302 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The mechanism and kinetics for the decomposition of β-hydroxypropaldehyde, primary and secondary β-hydroxyketones, were studied by using ab initio RHF/6-31G and RHF/6-31G* methods. The activation barriers of these reactions were refined to be 39.57, 40.10, and 36.80 kcal mol-1 at the MP2/ /RHF/6-31G* level, respectively. The calculated results show that each decomposition is a concerted process with hydrogen transferring and bond breaking via a six-membered cyclic transition state. The thermal rate constants of the decomposition of primary and secondary β-hydroxyketones were obtained by calculating microcanonical probability fluxes through each transition state. It is theoretically confirmed that methyl substitution at the hydroxyl carbon of β-hydroxyketones causes a small enhancement in rates. The theoretical investigations of the mechanism and the rate constants are in agreement with the experimental results. © 1997 John Wiley & Sons, Inc.
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  • 64
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    International Journal of Quantum Chemistry 63 (1997), S. 1079-1089 
    ISSN: 0020-7608
    Keywords: large-order perturbation theory ; lie algebra ; three-body problem ; symbolic computations ; helium atom ; Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The method of o(4, 2) operator replacements is generalized. As a result, the series whose limiting values when the variable goes to  +∞ should correspond to the two-electron atom energies now have rational coefficients. This generalization allows one also to compute the series for the case of singlet S symmetry, a case which could not be considered in the previous original formulation of the method. Series with rational coefficients for the helium singlet and triplet S ground-state energy are calculated up to order 41 and 45, respectively. Moreover, symbolic computations also allow one to give the first few coefficients of these series for arbitrary values of the nuclear charge Z. Finally, a new method for analytic continuation to the limit  +∞ is presented for the energies of the helium singlet and triplet ground states.   © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 1079-1089, 1997
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  • 65
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    International Journal of Quantum Chemistry 63 (1997), S. 1099-1106 
    ISSN: 0020-7608
    Keywords: metathesis reactions ; bond order ; free valence ; minimum energy path ; nonsynchronization ; Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A few simple atom-transfer reactions (i.e., Ȧ+X-A→A-X+Ȧ) are studied by quantum mechanical ab initio methods. Emphasis is given to the detailed analysis of density matrices rather than to the energetics. Results reveal that during these reactions a small free valence always develops on the migrating atom at the transition state. The barriers in these reactions arise from the greater extent of bond cleavage in the reactant than that of bond formation in the transition state. Analysis of bond orders estimated from bond lengths using Pauling's relation also leads to the fact that the bond-cleavage process is more advanced than is the bond-formation process in these reactions.   © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 1099-1106, 1997
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  • 66
    Publication Date: 2020-08-05
    Description: The present dissertation deals with the structure of polyhedral subdivisions of point configurations. Of particular interest are the global properties of the set of all subdivisions of a given point configuration. An important open problem in this context is the following: can one always transform any triangulation of a given point configuration to any other triangulation of the same configuration by means of bistellar operations? In other words, is the set of all triangulations of a given point configuration always bistellarly connected? The results presented in this thesis contribute progress from two directions. \begin{itemize} \item The set of all subdivisions that are induced by a polytope projection is in general not bistellarly connected in a generalized sense. This result is obtained by constructing a counterexample to the so-called Generalized Baues Conjecture.'' \item The set of all triangulations of a cyclic polytope forms a bounded poset. The covering relations are given by increasing bistellar operations. Thus we get an affirmative answer to the above question in the case of cyclic polytopes. \end{itemize} In the introduction, the mathematical environment of the structures under consideration is illuminated. The "Generalized Baues Conjecture" has connections to various mathematical concepts, such as combinatorial models for loop spaces, discriminants of polynomials in several variables, etc. The triangulation posets of cyclic polytopes are natural generalizations of the well-studied Tamari lattices in order theory. Moreover, there is a connection to the higher Bruhat orders, which have similar structural properties. As a by-product, the investigations yield the shellability of all triangulations of cyclic polytopes without new vertices. This is in particular interesting because most triangulations of cyclic polytopes are non-regular.
    Description: Die vorliegende Dissertation beschäftigt sich mit strukturellen Fragen in der Theorie der polyedrischen Unterteilungen von Punktkonfigurationen. Hierbei sind vor allem globale Eigenschaften der Menge aller Unterteilungen einer gegebenen Punktkonfiguration von Interesse. Eine wichtige ungelöste Frage in diesem Zusammenhang ist die folgende: Ist es immer möglich, von einer beliebigen Triangulierung einer gegebenen Punktkonfiguration zu jeder anderen Triangulierung derselben Konfiguration zu gelangen, indem man sogenannte bistellare Operationen durchführt? Mit anderen Worten, ist die Menge aller Triangulierungen einer gegebenen Punktkonfiguration stets bistellar zusammenhängend? Die Ergebnisse der vorliegenden Doktorarbeit liefern auf zwei Seiten dieser nach wie vor offenen Frage Fortschritte: \begin{itemize} \item Die Menge aller durch eine Polytopprojektion induzierten Unterteilungen ist nicht immer --- in einem verallgemeinerten Sinne --- bistellar zusammenhängend. Dieses Resultat wird durch ein Gegenbeispiel zur sogenannten "Verallgemeinerten Baues Vermutung"' erzielt. \item Die Menge aller Triangulierungen eines zyklischen Polytops bildet eine beschränkte Halbordnung. Die Ueberdeckungsrelationen sind gerichtete bistellare Operationen. Für zyklische Polytope ist die obige Frage nach bistellarem Zusammenhang also positiv beantwortet. \end{itemize} In der Einleitung wird das mathematische Umfeld der betrachteten Strukturen näher beleuchtet: Die "Verallgemeinerte Baues Vermutung" steht in Verbindung mit verschiedensten mathematischen Konzepten, angefangen von kombinatorischen Modellen von Schleifenräumen bis hin zu Diskriminanten von Polynomen in mehreren Variablen. Die Triangulierungs-Halbordnungen von zyklischen Polytopen sind zugleich natürliche Verallgemeinerungen der gut studierten Tamari-Verbände in der Ordnungstheorie. Ausserdem existiert ein Zusammenhang mit den höheren Bruhat-Ordnungen, die ähnliche Struktureigenschaften aufweisen. Ein Nebenprodukt der Untersuchungen ist die Schälbarkeit aller Triangulierungen von zyklischen Polytopen ohne neue Ecken. Das ist um so interessanter, da die meisten Triangulierungen von zyklischen Polytopen nicht-regulär sind.
    Keywords: ddc:510
    Language: English
    Type: doctoralthesis , doc-type:doctoralThesis
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    Format: application/postscript
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  • 67
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    Berichte der deutschen chemischen Gesellschaft 129 (1996), S. 1123-1129 
    ISSN: 0009-2940
    Keywords: Halogenoacetates ; Solid-state reactions ; Polyglycolide ; Thermal analysis ; Polymerization ; Chemistry ; Inorganic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Nine salts of halogenoacetic acids MOOC-CH2—X were prepared and characterized by their thermochemical reactivity. It was found that in seven cases elimination of MX led to polymerization of the organic part of the molecule. The resulting polyester, polyglycolide, could be isolated easily by washing the reaction product with water. It has a distinct porous morphology. The reaction takes place at moderate temperatures (100—200°C).
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  • 68
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    International Journal of Quantum Chemistry 57 (1996), S. 7-15 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The solution of the Schrödinger equation for the d-dimensional hydrogen atom in a d-dependent potential defined by Gauss' law has been studied by the shifted 1/d method and the δ expansion. These methods provide analytical formulas for the eigenvalues and eigenfunctions which have been tested against “exact” numerical values obtained recently. The comparison shows that the results obtained with the analytical expressions are in excellent accord with the numerical ones and, on the other hand, provide a theoretical justification for a proposed empirical expression for the energies of the two-dimensional hydrogen atom with a logarithmic potential energy function. © 1996 John Wiley & Sons, Inc.
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  • 69
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    International Journal of Quantum Chemistry 57 (1996), S. 17-33 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: An analysis of the structure of the optimized effective Kohn-Sham exchange potential vx and its gradient approximations is presented. The potential is decomposed into the Slater potential vs and the response of vs to density variations, vresp. The latter exhibits peaks that reflect the atomic shell structure. Kohn - Sham exchange potentials derived from current gradient approaches for the exchange energy are shown to be quite reasonable for the Slater potential, but they fail to approximate the response part, which leads to poor overall potentials. Improved potentials are constructed by a direct fit of vx with a gradient-dependent Padé approximant form. The potentials obtained possess proper asymptotic and scaling properties and reproduce the shell structure of the exact vx. © 1996 John Wiley & Sons, Inc.
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  • 70
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    International Journal of Quantum Chemistry 57 (1996), S. 43-51 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Analytical exact expressions are obtained for matrix elements of the modified Pöschl-Teller oscillator over different operators including powers of the hyperbolic functions sinh(α x), cosh(α x), and tanh(α x) and the differential operators d/dx and d2/dx2. These expressions are derived using explicitly the Pöschl-Teller eigenfunctions. In addition, several recursion relations connecting different Pöschl-Teller matrix elements are obtained using the factorization and hypervirial techniques. It is shown that these relations can be used to make easier the computation of the matrix elements. © 1996 John Wiley & Sons, Inc.
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  • 71
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    International Journal of Quantum Chemistry 57 (1996), S. 53-61 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The D-dimensional Coulomb system serves as a starting point for generating generalized atomic shells. These shells are ordered according to a generalized Madelung rule in D dimensions. This rule together with an Aufbau Prinzip is applied to produce a D-dimensional periodic table. A model is developed to rationalize the ordering of the shells predicted by the generalized Madelung rule. This model is based on the introduction of a Hamiltonian, invariant under the q-deformed algebra Uq(so(D)), that breaks down the SO(D + 1) dynamical symmetry of the hydrogen atom in D dimensions. The D = 2 case (Flatland) is investigated in some detail. It is shown that the neutral atoms and the (moderately) positive ions correspond to the values q = 0.8 and q = 1, respectively, of the deformation parameter q. © John Wiley & Sons, Inc.
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  • 72
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    International Journal of Quantum Chemistry 57 (1996), S. 137-137 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 73
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    International Journal of Quantum Chemistry 57 (1996), S. 1-2 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 74
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    International Journal of Quantum Chemistry 57 (1996), S. 123-135 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Ab initio calculations at the scf level were carried out to compute the polarization potential map (mpp) of the nucleic acid bases: cytosine, thymine, uracil, adedine, and guanine. For this purpose, the Dunning's 9s5p basis set contracted to a split-valence, was selected to perform the calculations. The molecular polarization potential (mpp) at each point was evaluated by the difference between the interaction energy of the molecule with a unit point charge and the molecular electrostatic potential (mep) at that point. meps and mpps for the different molecules were computed with a density of 5 points/Å2 on the van der Waals surface of each molecule, defined using the van der Waals radii. Due to the symmetry of the molecules, only half the points were computed. The total number of points calculated was 558 for cytosine, 621 for thymine, 526 for uracil, 666 for adenine, and 699 for guanine. The results of these calculations are analyzed in terms of their implications on the molecular interactions between pairs of nucleic acid bases. © 1996 John Wiley & Sons, Inc.
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  • 75
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    International Journal of Quantum Chemistry 57 (1996) 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 76
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    International Journal of Quantum Chemistry 57 (1996), S. 139-139 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 77
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    International Journal of Quantum Chemistry 57 (1996), S. 141-155 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The matrix differential calculus is applied for the first time to a quantum chemical problem via new matrix derivations of integral formulas and gradients for Hamiltonian matrix elements in a basis of correlated Gaussian functions. Requisite mathematical background material on Kronecker products, Hadamard products, the vec and vech operators, linear structures, and matrix differential calculus is presented. New matrix forms for the kinetic and potential energy operators are presented. Integrals for overlap, kinetic energy, and potential energy matrix elements are derived in matrix form using matrix calculus. The gradient of the energy functional with respect to the correlated Gaussian exponent matrices is derived. Burdensome summation notation is entirely replaced with a compact matrix notation that is both theoretically and computationally insightful. © 1996 John Wiley & Sons, Inc.
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  • 78
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    International Journal of Quantum Chemistry 57 (1996), S. 157-172 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The size-extensive quadratic CI method with single(s), double(D), and triple (T) excitations, QCISDT, is compared with QCISD, QCISD(T), CCSDT-n, and CCSDT. It is shown that QCISDT results are more accurate than are either QCISD or QCISD(T) results. In particular, QCISDT turns out to be more stable than are QCISD and QCISD(T) in cases with considerable multireference character. QCISDT and CCSDT results are of similar accuracy with slight advantages for the former method. Since QCISDT is much easier to implement on a computer than is CCSDT, it is an attractive alternative to CCSDT. © 1996 John Wiley & Sons, Inc.
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  • 79
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    International Journal of Quantum Chemistry 57 (1996), S. 173-182 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: This article presents remarks on the meaning of stopping power and of its magnitude. More precisely, the first set of remarks concerns the connection of stopping power with elements of particle-transport theory, which describes particle transport and its consequences in full detail, including its stochastic aspects. The second set of remarks concerns the magnitude of the stopping power of a material and its relation with the material's electronic structure and other properties. © 1996 John Wiley & Sons, Inc.
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  • 80
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    International Journal of Quantum Chemistry 57 (1996), S. 219-227 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: For the first hydrogen bond of the guanine-cytosine (G-C) pair, the potential function V(r, R) is found for the nonequilibrium bond length R. A new form of the semiempirical potential function, Clementi's calculations for V(r, R0) and some experimental data are used. New wave functions and energy levels as a function of the H-bond length for the ground and several excited states are obtained. This allows one to obtain frequencies and amplitudes of some vibrations of the G-C pair side groups involved in the formation of the hydrogen bond when the latter is not excited and when it is excited to the first energy level. © 1996 John Wiley & Sons, Inc.
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    International Journal of Quantum Chemistry 57 (1996), S. 229-233 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Restricted open-shell Hartree-Fock and unrestricted Hartree-Fock calculations of the electric-field gradient in atoms B, N, O, Al, S, and Cl were performed by relieving the spherical symmetric constraint. The Sternheimer's core polarization effect is then automatically taken into account. The orbitals produced by the axial symmetric self-consistent field are found to have axial symmetry of s-d and p-f mixing types. However, the nonequivalence of the three p orbitals also gives rise to ambiguity. © 1996 John Wiley & Sons, Inc.
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    International Journal of Quantum Chemistry 57 (1996), S. 235-243 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The diagonalization of a class of lattice spin models of a particular structure is first reviewed and secular polynomials for these models are calculated explicitly from the corresponding secular matrices. The structure of the eigenvectors of the given secular matrices is investigated and used to determine the eigenvalues theoretically, and proofs which have not appeared are presented. These results can be compared to the results obtained from the full secular polynomials. © 1996 John Wiley & Sons, Inc.
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  • 83
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    International Journal of Quantum Chemistry 57 (1996) 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 84
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    International Journal of Quantum Chemistry 57 (1996), S. 259-259 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 85
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    International Journal of Quantum Chemistry 57 (1996), S. 263-263 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 86
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    International Journal of Quantum Chemistry 57 (1996), S. 377-389 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The recently introduced set of quadratic ionic and covalent valence indices from changes in the pair-diagonal part of the molecular (Hartree-Fock) two-electron density matrix, ΔΓ(2)(a, b) (orthogonal atomic orbital [OAO] basis set), relative to separated atoms limit (SAL), is extended to cubic valence numbers; they are calculated from the corresponding changes in the three-electron density matrix, ΔΓ(3)(a,b,c). The two- and three-electron indices are given by the corresponding contributions to ΔΓ(2), and ΔΓ(3), which are quadratic and cubic in terms of relevant changes in the one-electron density matrix. The new valence measures are partitioned into one-, two-, and three-center contributions comprising purely ionic (covalent) and mixed ionic-covalent terms. For integral OAO occupations in the SAL, the sum of all three-electron contributions vanishes exactly in the UHF approximation; for fractional occupations, they give rise to a rather small correction to the overall two-electron valence index. The properties of cubic valence numbers are tested on a model three-orbital description of a symmetric (ABA), collinear transition state and on the OQ2 (Q = 1,0, -1) and O2(bond)H+ systems. Preliminary results for B2H6 are also given. © 1996 John Wiley & Sons, Inc.
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  • 87
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    International Journal of Quantum Chemistry 60 (1996), S. 235-248 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Extremal pair functions for an n-electron wave function of a closed-shell state are defined as linear combinations of spin-orbital-product pair functions that make some functionals (e.g., r212 or r-112) extremal. They are related to the natural spin geminals in the uncorrelated limit and are useful both for an analysis of wave functions in view of an understanding of the chemical bond and for the treatment of electron correlation. Numerical examples are shown and discussed for He2 as well as the 10-electron systems Ne, HF, H2O, NH3, and CH4. © 1996 John Wiley & Sons, Inc.
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  • 88
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    International Journal of Quantum Chemistry 60 (1996), S. 287-295 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The generalized Langevin equations are presented by considering such microscopic motions of molecules described by the microscopic Hamiltonian whose potential function is quadratic and internal degree of freedom is multidimensional. Considering the long time behavior of the reactive mode, the Grote-Hynes equation has been derived from the generalized Langevin equations. Furthermore, we have proved that solving the Grote-Hynes equation is equivalent to solving the eigenvalue problem for the whole system, and then the Grote-Hynes treatment coincides with the transition-state theory for the whole system. © 1996 John Wiley & Sons, Inc.
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  • 89
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    International Journal of Quantum Chemistry 60 (1996), S. 307-320 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Motivated by McWeeny's pioneering work on the solution of the Schrödinger equation in momentum space and his early treatment of X-ray scattering factors from the electron distribution ρ(r) in both isolated and bonded atoms, the relation between momentum space moments 〈pn〉 and ρ(r) is first developed semiclassically, as in the forerunner of density functional theory, the Thomas-Fermi method. The relation between 〈p〉 and the Dirac-Slater exchange energy prompts the treatment of an exact nonlocal relation between kinetic and exchange energies in Hartree-Fock theory. The Hiller-Sucher-Feinberg identity serves then to introduce the differential form of the virial theorem in a many-electron system. Following very recent work of Holas and March, this is used to obtain the exact exchange-correlation potential as a path integral expressed in terms of low-order density matrices. © 1996 John Wiley & Sons, Inc.
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  • 90
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    International Journal of Quantum Chemistry 60 (1996), S. 359-372 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The realization of a Clifford algebra in laboratory space is considered and it is demonstrated that the elements of the algebra cannot, as often assumed, be directly identified with vectors in this space, but, rather, that they form the parametric space of the symmetry operations of the Euclidean group as performed in the laboratory space. Details of this parametrization are established and expressions are given that determine the action of the Euclidean-group operations (screws included) on laboratory-space vectors in terms of the elements of the Clifford algebra. A discussion of Clifford vectors, bivectors, and pseudoscalars and their relation to the Gibbs vectors is provided. The correct definition of axial and polar vectors within the Clifford algebra is carefully discussed. It is shown how simple it is to generate finite point groups in 4-dimensional space by means of the Clifford algebra. © 1996 John Wiley & Sons, Inc.
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  • 91
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    International Journal of Quantum Chemistry 60 (1996), S. 393-400 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Spin-coupled calculations are carried out for the nitryl halides FNO2 and CINO2. The picture that emerges suggests that the nitrogen atoms use all five valence electrons in covalent bonding. The description of the NO2 group appears to be essentially transferable between the two molecules. No evidence is found for active d-orbital participation in the bonding in either of these molecules or in FPO2. We assess the geometries, charge distributions, and dipole moments of various X3NO and X3PO species (X = H, CH3, or F). We propose a simple rationalization of the dipole moment data without invoking supposed dπ-pπ bonding. © 1996 John Wiley & Sons, Inc.
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  • 92
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    International Journal of Quantum Chemistry 60 (1996), S. 409-419 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The photoionization cross sections and asymmetry parameters of the three main valence ionization processes in HI, corresponding to the formation of, respectively, 6π, 11σ, and 10σ holes, were calculated in the random-phase approximation (RPA). Our particular computational procedure, based on solving the integral equation for the half on the shell K-matrix upon a grid of points supplied by an L2 basis set calculation, affords recovery of the electronic continuum degeneracy of the final states. This makes it possible to compute the differential ionization cross section at any energy up to the fourth ionization threshold, allowing for the interaction of the three channels considered. The total cross section obtained by applying the Stieltjes imaging procedure to the discrete spectrum yielded by the RPA is also reported. © 1996 John Wiley & Sons, Inc.
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  • 93
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    International Journal of Quantum Chemistry 60 (1996), S. 453-466 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: An extended geminal model has been applied to determine the interatomic potential for the X1Σ+g state Be2. By adopting a [11s, 9p, 6d, 4f, 2g] contracted Gaussian-type basis, the following potential minimum parameters are obtained: Re = 4.67 a.u. (4.63 a.u.) and De = 3.70 mH (3.82 ± 0.05 mH), experimental values in parentheses. A calculation with a nuclei-centered [9s, 7p, 4d, 2f, 1g] GTO basis plus two sets of bond-type function, each set comprising diffuse (2s, 2p, 2d, 2f, 1g) GTOs, yielded -3.79 mH as the value of the potential at R = 4.63 a.u. On the basis of an error analysis the best theoretical estimate of the binding energy is determined to be 3.83 ± 0.08 mH. The calculated value for the fundamental vibrational frequency is v0→1 = 224.7 cm-1 (exp. = 224 ± 3 cm). © 1996 John Wiley & Sons, Inc.
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  • 94
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    International Journal of Quantum Chemistry 60 (1996), S. 487-492 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The second electric dipole hyperpolarizability of the lithium atom is calculated using a series of multiconfiguration SCF wave functions with an increasing number of active space orbitals. In agreement with other recent calculations, we find a very large correlation correction to the hyperpolarizability. We analyze the frequency dependence of the dc Kerr hyperpolarizability γK(ο) = γ (- ο ο, 0, 0) and observe very significant dispersion effects. © 1996 John Wiley & Sons, Inc.
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  • 95
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    International Journal of Quantum Chemistry 60 (1996), S. 505-512 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The S0 and S1 potential energy surfaces of pentalene were studied using MMVB - a hybrid force-field/parametrized valence bond (VB) method designed to simulate CASSCF calculations for ground and covalent excited states. The results were calibrated against full CASSCF calculations. Four distinct critical points were optimized: on S0, a C2h minimum (with alternating single and double bonds) and a D2h transition structure; and on S1, a D2h minimum and an adjacent S1/S0 conical intersection. A VB exchange density matrix (which is independent of the choice of the spin-coupled basis) was used to rationalize the S0 and S1 surface topologies. Craig defined pseudoaromatic molecules to be those with nontotally symmetric electronic ground states. For pentalene, this is true for both CASSCF and MMVB calculations: the CASSCF S0 transition structure is an open-shell B1x singlet, and the VB ground state is dominated by a spin-coupling which transforms as B1g. A C2v minimum and a D2h transition structure were located on the CASSCF S2 potential energy surface. This state cannot be represented by MMVB because of the importance of ionic configurations. The characters of the S1 S2 states of pentalene are shown to be reverse of the S1 and S2 states of benzene. © 1996 John Wiley & Sons, Inc.
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  • 96
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    International Journal of Quantum Chemistry 60 (1996), S. 579-592 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Position and momentum space plots are presented for localized molecular orbitals in hydrocarbons, boranes, a carborane, and two octahedral transition metal complexes. The p-space representation proves to be valuable for visualizing such orbitals since it highlights the differences in their character from one molecule to another. Factors influencing the form of the orbitals in p space, including the oscillatory behavior caused by contributions to an orbital from more than one center, are examined in detail. © 1996 John Wiley & Sons, Inc.
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  • 97
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    International Journal of Quantum Chemistry 60 (1996) 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 98
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    International Journal of Quantum Chemistry 60 (1996), S. 609-616 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Coupled Hartree-Fock theory is used to compute and map the current density induced in planar hydrocarbons by an external magnetic field. Results of useful accuracy can be obtained with modest (6-31G**) basis sets by employing a continuous gauge transformation. Maps are presented and discussed for benzene, naphthalene, anthracene, tetracene, pentacene, heptacene, and biphenylene. © 1996 John Wiley & Sons, Inc.
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  • 99
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    International Journal of Quantum Chemistry 60 (1996), S. 617-634 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The group-function theory, as proposed by McWeeny for the study of weak intermolecular interactions and developed by Huzinaga in the context of valence-electron methods, is shown to be applicable to the ab initio study of tunable solid-state laser materials made of defective ionic crystals. The applicability of the theory relies on the existence of local electronic states (to which the demonstrated/potential laser activity is ascribed), which are essentially localized in a small cluster of atoms including the defect and whose electron correlation interactions with the surrounding crystal components are negligible. According to the group-function formalism, it is possible (a) to neglect electron correlation effects beyond the defect cluster and (b) to define a quantum mechanical embedding potential which embodies the rest of the so-called host effects. Computationally, the theory becomes applicable as the embedding potential is approximated through ab initio model potentials (AIMP). The results of AIMP embedded-cluster calculations demonstrate that it is possible to calculate the local structure and spectroscopy of the active defect at an ab initio level, the attainable accuracy being comparable to the usual one in molecular ab initio studies in the gas phase. Also, in this article, we present a systematic study of the local distortions produced upon doping divalent first-series transition-metal ions in rock-salt oxides, MO:Me2+ (M=Mg, Ca, Sr; Me=Sc-Zn) and Tl+ in KMgF3 and KF hosts. This study leads to the calculation of the local structures of the defects in these materials, which have not been measured. The results suggest that the use of the mismatch of the empirical ionic radii of the impurity and the substituted ion in order to predict local distortions in doped ionic crystals is not significant when it is smaller than 0.1 Å, and when it is larger, it should be weighted by a reduction factor depending on the host. For the first-series divalent transition-metal ion impurities, this factor is shown to be 0.15 for SrO, 0.25 for CaO, and around 0.50 for MgO. © 1996 John Wiley & Sons, Inc.
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  • 100
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    International Journal of Quantum Chemistry 60 (1996), S. 649-655 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Using ab initio HF/6-31G** and MP2/6-31G** calculations alternative reactions HC(OH)3 → HCO2H + H2O and HC(OH)3 + H2O → HCO2H + 2H2O are investigated and the results are compared with relevant PM3, HF/3-21G, and HF/6-31G data. Reactant and product complexes as well as transition states are located on corresponding potential energy surfaces. © 1996 John Wiley & Sons, Inc.
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