bluuebunny/crossref_metadata_2025_split huggingface dataset:
A “canonical functions” approach to the eigenvalues of a system of two coupled Schrödinger equation
Authors: Fakhreddine Khaled , Kobeissi Hafez 
Published: January 2005

AbstractThe problem of the determination of eigenvalues for two coupled Schrödinger equations is considered. A new method to solve this problem is presented. This method replaces the use of the wave functions (with unknown initial values) by eight canonical functions αij and βij (i = 1,2; j = 1,2) having well‐defined initial values at an arbitrary “origin” r0. These functions are collected in four couples; each one is the solution of the given coupled equations. For a given E, an “eigenvalue functions” D(E) is defined by an analytical expression depending on αij (r) and βij (r) at r = 0 and r = ∞ only. The successive eigenvalues En of the given system are precisely the successive intersection of the graph D(E) with the E‐axis. The present method eliminates the conventional use of wave function initial values as well as the conventional problem of the prior guess of the limit points; it determines these points automatically. It eliminates also the use of trial values for E and the need of iterations for its correction. The numerical application of a standard example used by Friedman and co‐workers (1990) shows that the eigenvlues computed by the present method are highly accurate for low and high levels; the average relative discrepancy between computed and exact levels is about 3.4 × 10 −15 (this discrepancy never exceeds 1.6 × 10 −14), which is almost the precision of the computer. © 1994 John Wiley & Sons, Inc.
Quantum chemistry study on B14, B, and B14H
Authors: Li Qian Shu , Gu Feng Long , Tang Au Chin 
Published: January 2005

AbstractThe structure of B14, B, and B14H in octahedral symmetry has been investigated by ab initio calculations at the STO‐3G and 4–31G levels. The relationship of molecular orbitals among them has been analyzed and it can be found that the number of valence bonding orbitals of high borane obeys the Wade rule. The similarities and difference between boron clusters and carbon clusters are also discussed. © 1994 John Wiley & Sons, Inc.
Full configuration interaction study of the ground state of closed‐shell cyclic PPP polyenes
Authors: Bendazzoli Gian Luigi , Evangelisti Stefano , Gagliardi Laura 
Published: January 2005

AbstractFull configuration interaction (FCI) calculations are reported for the closed‐shell cyclic polyenes CNHN (N = 6, 10, 14, 18) in the Pariser–Parr–Pople (PPP) approximation, as a function of the hopping parameter β. A wide range of values of β is considered, from a highly correlated situation, β = 0, to a very weakly correlated limit, β = −10 eV. An estimate of the role of higher than two‐body connected cluster components was done, through a partial (i.e., limited to two‐body terms in the exponent) cluster analysis performed on the FCI wave function. The comparison with the approximate coupled pair theory that accounts for quadruply excited clusters [see P. Piecuch and J. Paldus, Theor. Chim. Acta 78, 65 (1990)] shows a good agreement in the whole range of the hopping parameter, particularly when the contribution of connected triples excitations is also taken into account. © 1994 John Wiley & Sons, Inc.
A theoretical investigation of some novel pilocarpine prodrugs
Authors: Ek holm Michaela , Konschin Henrik 
Published: January 2005

AbstractA new class of pilocarpine double prodrugs of the bispilocarpic acid diester type has been investigated. Molecular orbital and molecular mechanics calculations have been done to obtain information about the conformational preferences and general physicochemical properties. Geometries of the structures were obtained with the force field implemented in the CHEM‐X program and using the semiempirical quantum chemical program AMPAC and the AM1 method. A correlation between the van der Waals volume, van der Waals area, and log P of the bispilocarpic acid diester structures is observed. The structures of these biscompounds are compared with the structures of the corresponding monopilocarpic acid diesters. Electrostatic and electronic properties of the compounds will be discussed in the context of the interaction between the prodrugs and the hydrolyzing esterase enzymes. © 1994 John Wiley & Sons, Inc.
Protonation‐induced conformational flipping in hypermodified nucleic acid base N6−(N−glycylcarbonyl) adenine
Authors: Tewari Ravindra 
Published: January 2005

AbstractThe influence of accepting the hydrogen bond by N(3) of adenine on the conformational preferences of the N(6) substituent in modified nucleic acid base N6−(N−glycylcarbonyl)adenine (gc6Ade) has been modeled by the protonation of N(3). The preferred orientation of the glycylcarbonyl substituent changes on the protonation of N(3). The preferred conformation for the N(3) protonated base is the planar, intramolecular bifurcated hydrogen‐bonded structure involving the interaction of the ureido N(11)H with the N(1) of the purine and the O(13b) of the amino acid carboxyl. Another conformation of nearly equal stability, having the internal hydrogen bonding of O(13b) with the N(6)H, is also predicted. Such protonation or hydrogen‐bonding‐induced conformational flipping may enable the structural reorientation of the anticodon loop required for the functioning of tRNA. © 1994 John Wiley & Sons, Inc.
An extension of Frost–Musulin and Möbius–Zimmerman diagrams
Authors: Zhou Zhongxiang 
Published: January 2005

AbstractThe eigenspectrum of a Möbius graph is a complete inversion of a Hückel graph for odd‐numbered monocycles. For even‐numbered monocycles, the Coulson‐paired levels (xi, – xi) in a Hückel graph become the degenerate levels (x′1, x′1) in a Möbius graph. Here, we present the proof of a general theorem stating that the same eigenspectral relationship is found in a much wider class of graphs. © 1994 John Wiley & Sons, Inc.
Simulation of diffusion‐limited aggregation and reactions over its surfaces
Authors: Lee Shyi‐Long , Lee Chung‐Kung 
Published: January 2005

AbstractModifications of Witten–Sander diffusion‐limited aggregation (DLA) were proposed. Effects caused by releasing boundary shape, nonfixed seed, and rotating biased drift on the morphology of the resulting DLA were examined. The diffusion‐limited reaction on surfaces of DLA were also studied by performing a multifractal scaling analysis. © 1994 John Wiley & Sons, Inc.
Cooperativity and electron correlation effects on hydrogen bonding in infinite systems
Authors: Suhai Sándor 
Published: January 2005

AbstractStructural and electronic properties of hydrogen‐bonded infinite chains of hydrogen cyanide and formamide molecules have been investigated by the ab initio crystal orbital method using several, partly highly polarized, atomic basis sets of increasing size at the Hartree–Fock (HF) level and by including electron correlation effects in the second order of Møller–Plesset perturbation theory. The results obtained show that hydrogen bonding in molecular crystals of the type investigated is a highly cooperative phenomenon, both from the structural and energetic points of view. Comparison with clusters of up to four monomers demonstrate how various structural parameters converge toward their limiting values in the infinite system. The results obtained for infinite HCN chains show an excellent agreement with those observed for solid HCN, whereas the infinite formamide chain proves to be a reasonable model for the corresponding liquid phase. © 1994 John Wiley & Sons, Inc.
Electron correlations and pairing in low‐dimensional systems
Authors: Ukrainskii I. I. 
Published: January 2005

AbstractThe many‐electron system in one and two dimensions are studied within the geminal approach. The analytical expressions for the wave functions and ground‐state energies are obtained for a number of 1‐D and 2‐D systems: conjugated polymers, organic conductors, 2‐D conductors with square lattices, and others. It is shown that electron excitations of a kink type can exist in 2‐D systems with mixed valency. In this case, the correlation pairing of current carriers arises as a result of correlation effects leading to superconducting properties of the system. © 1994 John Wiley & Sons, Inc.
Molecular dynamics simulations of n‐Alkane melts confined between solid surfaces
Authors: Winkler Roland G. , Gerstmair Anja , Reineker Peter , Matsuda Tsunetoshi , Yoon Do Y. 
Published: January 2005

AbstractMolecular dynamics simulations of polyethylene chains (CnH2n+2 for n = 13, 16, 28, 60) have been carried out to investigate both equilibrium and dynamic properties of polymer melts confined between flat solid surfaces. We observe an oscillatory monomer density in the direction normal to the solid surfaces, which depends on the size of the monomers (i.e., on the volume density of the system). The packing manner of monomer segments, segment orientation, and local conformations of chains are found to be independent of chain length. In addition, preferential interfacial adsorption of chain ends is observed. The chains are flattened close to the surface and many molecules assume essentially two‐dimensional train configurations even in the case of C60H122 melts. The apparent self‐diffusivities of the centers of mass of the molecules depend on their distance from a surface. Molecules adjacent to a surface exhibit a reduced mobility perpendicular to the surface and an increased one parallel to it. The self‐diffusion constant parallel to a surface depends strongly on the size of the monomers. An increase of the united atom diameter by 10% reduces the diffusion constant by a factor of three, in good agreement with the experimental value. © 1994 John Wiley & Sons, Inc.
Density functional studies on hydrogen‐bonded complexes
Authors: Kieninger Martina , Suhai Sädor 
Published: January 2005

AbstractResults of density functional calculations will be reported on a variety of hydrogen‐bonded complexes, ranging from weak to strong hydrogen bonds. The charged bimolecular NH3NH complex and the dimers of water and methanol were investigated using a local approximation of the exchange‐correlation potential and two different nonlocal potentials with gradient corrections. In the case of the water dimers, the dependence of the results on the extension of the atomic basis set has also been investigated. The equilibrium structures of all complexes have been determined. Dipole moments, hydrogen‐bond lengths, and hydrogen‐bonding energies, calculated with corrections for the basis‐set superposition error using the counterpoise method, have been found to agree well with the corresponding experimental results. © 1994 John Wiley & Sons, Inc.
Calculation of excitation and photoionization spectra by quasi‐degenerate perturbation theory
Authors: Lisini Adriana , Decleva Piero 
Published: January 2005

AbstractThe ability of the QDPT CI method, in which the quasi‐degenerate perturbation theory is applied within the configuration interaction (CI) approach, in dealing with the calculation of excitation and photoionization spectra is shown through an overview of comparisons between the QDPT CI values and the full CI ones in the same basis set. A direct comparison with the experimental data is given for the core photoelectron spectrum of Ne and the valence photoelectron spectra of Ar and HCl. The quality of the results obtained is very satisfactory, both as regards the energies and the wave functions, indicating the validity and the flexibility of the method that can confidently be applied also in cases where strong correlation effects are present. © 1994 John Wiley & Sons, Inc.
Hypervirial theorem and matrix elements for the Coulomb potential
Authors: López‐Bonilla José L. , Morales Jesús , Rosales Marco A. 
Published: January 2005

AbstractIt is well known that hydrogen like atoms may be represented as Morse oscillators. Our aim in this article was to show how this result and the hypervirial theorem lead to a computational method with which the matrix elements for the Coulomb potential can be easily calculated. Also, a closed analytical expression for 〈n2l2|rk|n1l1〉 is obtained. © 1995 John Wiley & Sons, Inc.
On bound states in two‐body systems
Authors: Frolov Alexei M. , Smith Vedene H. 
Published: January 2005

AbstractThe Hamiltonian of an arbitrary two‐body nonrelativistic system is written in closed form in terms of generators of the noncompact O(2, 1) Lie algebra. The bound‐states problem in such systems is investigated with the help of the self‐adjoint irreducible representations of this algebra (positive discrete series). It is shown that the initial Schrödinger equation can be reduced to a simple eigenvalue problem, in which all matrices can be determined easily from the basic properties of the O(2, 1) algebra and by applying the explicit form of the potential interaction. Based on such algebraic considerations, we obtain a number of useful relations between the expectation values of the potential and kinetic energies for the so‐called prethreshold states, i.e., those bound (E < 0) states for which E ≈ 0. © 1995 John Wiley & Sons, Inc.
General criteria for assessing the accuracy of approximate wave functions and their densities
Authors: Núñez Marco A. 
Published: January 2005

AbstractBy means of examples, Löwdin showed that L2 convergence of approximate wave functions ψn to the exact ψ using the single limit limn→∞〈ψn, Aψn〉 = 〈ψ,Aψ〉 is not sufficient to compute accurate expectation values. It is shown that L2 convergence is indeed a sufficient condition to compute accurate expectation values using iterated limits limm→∝︁ limn→∝︁〈ψn, Aψm〉 = 〈ψ, Aψ〉 instead of a single limit. Practical conditions that guarantee the stability of single‐limit calculations are given. It is also shown that the L2 covergence of wave functions implies the convergence in the L1(R3)‐norm of their corresponding densities. This permits us to prove Weinhold's conjecture that the rate of convergence of densities are greater than that of wave functions. The results are extended to the momentum space, and their equivalence with those of position space is shown. Properties of Lp spaces are used to introduce the Cauchy criterion that permits us to check the convergence in norm of approximate wave functions and their densities, as well as to estimate exact errors. This is illustrated by a numerical example. © 1995 John Wiley & Sons, Inc.
Determination of the acid dissociation constants of p‐benzohydroquinone by the INDO method
Authors: Datta Sambhu N. , Mallik Buddhadeb 
Published: January 2005

AbstractThe stepwise acid dissociation constants for p‐benzohydroquinone (QH2) in aqueous media have been explicitly calculated for the first time, with the INDO parametrized SCF–MO method. We have optimized the geometries of QH2, QH−, and Q2− and of the QH2 · 6H2O, QH− · (H3O+) · 5H2O, and Q2− · (H3O+)2 · 4H2O systems that model the solvated species. The presence of the associated water molecules (and hydronium ions) account for the stabilization due to hydrogen bonding as well as for a part of the effect of interaction of these molecules with the respective reaction fields in an aqueous medium. To simulate the first solvation shell in a more complete manner, four more water molecules have been considered to be placed above and below the quinonoid ring and the optimized geometries of the resulting hydrated species, QH2 · 10H2O, QH− · (H3O+) · 9H2O, and QH− · (H3O+) · 8H2O, have been determined. The standard free‐energy changes calculated for the dissociation of QH2 into QH− and H+ is 0.0251 Hartree (65.9 kJ mol−1) and that of QH− into Q2− and H+ is 0.0285 Hartree (74.8 kJ mol−1). Experimentally observed dissociation constants for these two steps correspond to free‐energy changes of 0.0214 Hartree (56.2 kJ mol−1) and 0.0248 Hartree (65.1 kJ mol−1), respectively. © 1995 John Wiley & Sons, Inc.
Distortion of the Fermi surface of an anisotropic two‐dimensional Fermi gas
Authors: Wu Jin Zhong , Goodman Bernard 
Published: January 2005

AbstractWe report here the first quantitative theory of the change of anisotropic Fermi surfaces (FS) due to the dynamical e–e interaction. The new FS is constructed as a self‐consistent solution of the Dyson equation. This incorporates effects of “anomalous” diagrams, absent in the usual perturbation theory, but which are responsible for changing the FS. Calculations are presented for 2D electrons. Correlations reduce the anisotropy. © 1995 John Wiley & Sons, Inc.
Why irreversibility? The formulation of classical and quantum mechanics for nonintegrable systems
Authors: Prigogine Ilya 
Published: January 2005

AbstractNonintegrable Poincaré systems with a continuous spectrum (so‐called large Poincaré systems, LPS) lead to the appearance of diffusive terms in the frame of classical or quantum dynamics. These terms break time symmetry. They lead, therefore, to limitations to classical trajectory theory and of wave‐function formalism (Schrödinger's equation). These diffusive terms correspond to well‐defined classes of dynamical processes (i.e., so‐called vacuum‐vacuum transitions). The diffusive effects are amplified in situations corresponding to persistent interactions. As a result, we have to include, already, in the fundamental dynamical description the two basic aspects, probability and irreversibility, which are so conspicuous on the macroscopic level. We have to formulate both classical and quantum mechanics on the Liouville level of probability distributions (or density matrices). For integrable systems, we recover the usual formulation of classical or quantum mechanics. Instead of being primitive concepts, which cannot be further analyzed, trajectories and wave functions appear as special solutions of the Liouville–von Neumann equations. This extension of classical and quantum dynamics permits us to unify the two concepts of nature that we inherited from the nineteenth century, based, on the one hand, on dynamical time‐reversible laws and, on the other, on an evolutionary view associated to entropy. It leads also to a unified formulation of quantum theory, avoiding the conventional dual structure based on Schrödinger's equation, on the one hand, and on the “collapse” of the wave function, on the other. A dynamical interpretation is given to processes such as decoherence or approach to equilibrium without any appeal to extra dynamic considerations (such as many‐world theory, coarse graining, or averaging over the environment). There is a striking parallelism between classical and quantum theory. For large Poincaré systems (LPS), we have, in general, both a “collapse” of trajectories and of wave functions. In both cases, we need a generalized formulation of dynamics in terms of probability distributions or density matrices. Since the beginning of this century, we have known that classical mechanics had to be generalized to take into account the existence of universal constants. We now see that classical as well as quantum mechanics also have to be extended to include unstable dynamical systems such as LPS. As a result, we achieve a new formulation of “laws of physics” dealing no more with certitudes but with probabilities. This formulation is appropriate to describe an open, evolving universe. © 1995 John Wiley & Sons, Inc.
On the Dirac–Kepler problem: The Johnson–Lippmann operator, supersymmetry, and normal‐mode representations
Authors: Dahl Jens Peder , Jøorgensen Thomas 
Published: January 2005

AbstractThe relativistic Kepler problem is discussed, with emphasis on the exact supersymmetry of the problem. It is shown that the supersymmetry is generated by the Johnson–Lippmann operator. Two related operators are found to generate new supersymmetries in an extended function space. Each of these supersymmetries may be disguised as radial supersymmetries. The radial supersymmetries are discussed and it is shown that each of them defines a normal‐mode representation of the hydrogen‐atom radial functions. Thus, one obtains two different, but equivalent, analytical expressions for these functions. The expressions are well known, but are rederived here in the light of the new understanding. Finally, the nonrelativistic image of the relativistic supersymmetry is constructed and its generators shown to be identical with those recently presented in the literature. © 1995 John Wiley & Sons, Inc.
Configuration interaction studies using biorthogonal approach to VB basis
Authors: Kadolkar C. , Sarma C. R. , Rettrup S. 
Published: January 2005

AbstractIn the present article, we have attempted a systematic procedure for use of biorthogonal techniques to the configuration interaction studies in molecules using nonorthogonal valence bond (VB) orbitals. The procedure developed is integral‐driven and a program based on this has been developed. Test runs of the program have been carried out in case of full and truncated configuration spaces. © 1995 John Wiley & Sons, Inc.
Splitting of the characteristic polynomial (CP) using a computational technique to obtain the factors of the mirror plane and two‐, three‐, and n‐fold symmetric graph
Authors: Patra Swarna M. , Mishra Rama K. 
Published: January 2005

AbstractAll possible quadratic factors from the characteristic polynomial are generated. Selective extraction of the factors are smoothly achieved. Factors of the mirror plane and two‐, three‐, and n‐fold rotationally symmetric graphs are obtained without using any rule for the fragmentation pattern. The relationship among the irreducible representations of the two‐, three‐, and n‐fold operators are established through our computer program. © 1995 John Wiley & Sons, Inc.
Structural analysis of certain linear operators representing chemical network systems via the existence and uniqueness theorems of spectral resolution. I
Authors: Arimoto Shigeru , Fukui Kenichi , Taylor Keith F. , Mezey Paul G. 
Published: January 2005

AbstractThe present article develops a methodology and a unifying theorem to treat, on an equal footing, mathematical phenomena that were hitherto studied separately in each of the research fields of dynamical systems and quantum chemistry involving the spectral symmetry of alternant hydrocarbons. This article also serves as a foundation of a theoretical framework for the analysis of certain dynamical systems of chemical kinetic equations, which shall be made in the context of operator algebra in Parts II and III of this series of papers. © 1995 John Wiley & Sons, Inc.
Deltafunction model for the helium dimer
Authors: Lohr Lawrence L. , Blinder S. M. 
Published: January 2005

AbstractThe helium dimer 4He2 has recently been detected, confirming earlier ab initio predictions of stability for a single bound state with binding energy of 1.310 mK. The predicted potential minimum is at 2.96 Å, with a radial distribution function peaking at 6.96 Å. We model this system using a Dirac bubble potential, which also admits just one bound j = 0 state. With the bubble located at 6.96 Å, an overlap of 0.9994 with the ab initio wave function is obtained. An average internuclear distance of 52.6 Å is calculated, in good agreement with the ab initio result. The root mean square deviation from the mean, 48.0 Å, indicates an enormous spread of the radial wave function. Also consistent with our model is the absence of bound states for the isotopic variants 3He4He and 3He2. Cross sections for helium‐helium scattering are also computed, using both a partial‐wave expansion and the Born approximation. General trends in the energy dependence of the total cross section are accounted for, in qualitative agreement with experimental results. © 1995 John Wiley & Sons, Inc.