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Hamiltonian
Kinds of Hamiltonian Terms modified by Hamiltonian Selected AbstractsGeometric algebra and transition-selective implementations of the controlled-NOT gateCONCEPTS IN MAGNETIC RESONANCE, Issue 1 2004Timothy F. Havel Geometric algebra provides a complete set of simple rules for the manipulation of product operator expressions at a symbolic level, without any explicit use of matrices. This approach can be used not only to describe the state and evolution of a spin system, but also to derive the effective Hamiltonian and associated propagator in full generality. In this article, we illustrate the use of geometric algebra via a detailed analysis of transition-selective implementations of the controlled-NOT gate, which plays a key role in NMR-based quantum information processing. In the appendices, we show how one can also use geometric algebra to derive tight bounds on the magnitudes of the errors associated with these implementations of the controlled-NOT. © 2004 Wiley Periodicals, Inc. Concepts Magn Reson Part A 23A: 49,62, 2004 [source] Assembly of Dinuclear CuII Rigid Blocks by Bridging Azido or Poly(thiocyanato)chromates: Synthesis, Structures and Magnetic Properties of Coordination Polymers and Polynuclear ComplexesEUROPEAN JOURNAL OF INORGANIC CHEMISTRY, Issue 8 2010Sergey V. Kolotilov Abstract Reaction of a dinuclear cationic copper(II) complex of 4,4,-[2-(3-hydroxyiminobutyl)imino]biphenyl [CuII2(LH)2]2+ with N3, resulted in the formation of a dinuclear azido [CuII2(LH)2(N3)2(H2O)2] complex or a 2D coordination polymer [CuII2(LH)2(N3)2]n. Reaction of the dinuclear complex with [CrIII(NCS)6]3, or [CrIII(NCS)4(NH3)2], produced a 2D polymer {[CuII2(LH)2(CH3CN)2]3[CrIII(NCS)6]2}n or a 1D chain, constructed from tetranuclear units {[CuII2(LH)2][CrIII(NCS)4(NH3)2]2}n. Structures of the compounds were determined by X-ray crystallography and complexes were characterised by the temperature dependency of the magnetic susceptibility and by ESR spectroscopy. Magnetic properties of homometallic compounds were fit with the model of a dimer with the Hamiltonian , = ,J,1·,2. For heterometallic complexes ,MT curves were fit as the superposition of magnetism resulting from both [CuII2(LH)2]2+ and the adjacent CrIII -containing anion. J values for the complexes lie in the range from ,12.74(4) to ,17.77(8) cm,1. It was shown that the 4,4,-biphenyl bridge efficiently mediates exchange interactions. [source] Origin of the Paramagnetic Properties of the Mixed-Valence Polyoxometalate [GeV14O40]8, Reduced by Two Electrons: Wave Function Theory and Model Hamiltonian CalculationsEUROPEAN JOURNAL OF INORGANIC CHEMISTRY, Issue 34 2009N. Suaud Abstract The aim of the work is to give an explanation of the magnetic properties of a mixed-valence [GeV14O40]8, polyoxometalate reduced by two electrons, which, in contrast to what happens in other two-electron-reduced polyoxometalates, does not show any magnetic coupling between the two unpaired electrons. For this purpose, a quantitative evaluation of the microscopic electronic parameters (electron transfer, magnetic coupling, magnetic orbital energy, and Coulomb repulsion) of the mixed-valence polyoxometalate cluster is performed. The parameters are extracted from valence-spectroscopy large configuration interaction (CI) calculations on embedded fragments. Then, these parameters are used in an extended t - J model Hamiltonian suited to model the properties of the whole anion. The analysis of the wave functions of the lowest singlet and triplet states and of the microscopic parameters emphasizes that the electron delocalization in this mixed-valence cluster is such that each unpaired electron is almost trapped in a different half of the polyoxovanadate, thus disabling any exchange interaction between them.(© Wiley-VCH Verlag GmbH & Co. KGaA, 69451 Weinheim, Germany, 2009) [source] [(Pyridylcarbonyl)pyridyl]triazolopyridines, Useful Ligands for the Construction of Polynuclear Coordination Compounds , Synthesis, Crystal Structure and Magnetic Properties of a Novel Tetranuclear Copper(II) Cubane,EUROPEAN JOURNAL OF INORGANIC CHEMISTRY, Issue 29 2007Belén Abarca Abstract A new tetranuclear cubane Cu4O4 complex has been synthesised from assembly of CuII ions and the polydentate ligand (pyridin-2-yl){6-([1,2,3]triazolo[1,5- a]pyridin-3-yl)pyridin-2-yl}methanone. Crystallographic analysis indicates that the Cu4O4 unit has an S4 symmetry. The magnetic properties have been analysed using the H = ,2,i,jJijSiSj spin Hamiltonian. Two distinct coupling constants, 2J1,3 = ,37.4 cm,1 and 2J1,2 = ,2.6 cm,1, obtained from the fitting of the experimental data have been rationalised on the basis of a density functional study of magnetostructural correlations in cubane complexes containing the Cu4O4 core. (© Wiley-VCH Verlag GmbH & Co. KGaA, 69451 Weinheim, Germany, 2007) [source] HAMILTON'S FORCES OF NATURAL SELECTION AFTER FORTY YEARSEVOLUTION, Issue 6 2007Michael R. Rose In 1966, William D. Hamilton published a landmark paper in evolutionary biology: "The Moulding of Senescence by Natural Selection." It is now apparent that this article is as important as his better-known 1964 articles on kin selection. Not only did the 1966 article explain aging, it also supplied the basic scaling forces for natural selection over the entire life history. Like the Lorentz transformations of relativistic physics, Hamilton's Forces of Natural Selection provide an overarching framework for understanding the power of natural selection at early ages, the existence of aging, the timing of aging, the cessation of aging, and the timing of the cessation of aging. His twin Forces show that natural selection shapes survival and fecundity in different ways, so their evolution can be somewhat distinct. Hamilton's Forces also define the context in which genetic variation is shaped. The Forces of Natural Selection are readily manipulable using experimental evolution, allowing the deceleration or acceleration of aging, and the shifting of the transition ages between development, aging, and late life. For these reasons, evolutionary research on the demographic features of life history should be referred to as "Hamiltonian." [source] Dependence of s -waves on continuous dimension: The quantum oscillator and free systemsFORTSCHRITTE DER PHYSIK/PROGRESS OF PHYSICS, Issue 12 2006K.B. Wolf Abstract Wavefunctions with rotational symmetry (i.e., zero angular momentum) in D dimensions, are called s -waves. In quantum quadratic systems (free particle, harmonic and repulsive oscillators), their radial parts obey Schrödinger equations with a fictitious centrifugal (for integer D , 4) or centripetal (for D = 2) potential. These Hamiltonians close into the three-dimensional Lorentz algebra so(2,1), whose exceptional interval corresponds to the critical range of continuous dimensions 0 < D < 4, where they exhibit a one-parameter family of self-adjoint extensions in ,2(,+). We study the characterization of these extensions in the harmonic oscillator through their spectra which , except for the Friedrichs extension , are not equally spaced, and we build their time evolution Green function. The oscillator is then contracted to the free particle in continuous- D dimensions, where the extension structure is mantained in the limit of continuous spectra. Finally, we compute the free time evolution of the expectation values of the Hamiltonian, dilatation generator, and square radius between three distinct sets of ,heat'-diffused localized eigenstates. This provides a simple group-theoretic description of the purported contraction/expansion of Gaussian-ring s -waves in D > 0 dimensions. [source] Modeling Electron and Hole Transport in Fluoroarene-Oligothiopene Semiconductors: Investigation of Geometric and Electronic Structure Properties,ADVANCED FUNCTIONAL MATERIALS, Issue 2 2008E. Koh Abstract A theoretical study using density functional theory is undertaken to gain insight into how the structural, electronic, and electron-transfer characteristics of three Fluoroarene-oligothiophene semiconductors influence the preferred transport of electrons versus holes in field-effect transistor applications. The intermolecular electronic coupling interactions are analyzed through both a simplified energy-splitting in dimer (ESID) model and as a function of the entire dimer Hamiltonian in order to understand the impact of site energy differences; our results indicate that these differences are generally negligible for the series and, hence, use of the ESID model is valid. In addition, we also investigate the reduction and oxidation processes to understand the magnitudes of the intramolecular reorganization energy for the charge-hopping process and expected barrier heights for electron and hole injection into these materials. From the electronic coupling and intramolecular reorganization energies, estimates of the nearest-neighbor electron-transfer hopping rate constant for electrons are obtained. The ionization energetics suggest favored electron injection for the system with perfluoroarene groups at the end of the thiophene core, in agreement with experiments. The combined analyses of the electron-transfer properties and ionization processes suggest possible ambipolar behavior for these materials under favorable device conditions. [source] Hamiltonian-based error computationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 4 2006Y. L. Kuo Abstract This paper presents two sets of the Hamiltonian for checking errors of approximated solutions. The first set can be applied to those problems having any number of independent and dependent variables. This set of the Hamiltonian can effectively indicate the errors of approximated solutions when requiring a high accuracy. The second set of the Hamiltonian has the invariant property when the Lagrangian is not an explicit function of time, even for non-conservative systems. Both sets can be formulated as error indicators to check errors of approximated solutions. Three illustrative examples demonstrate the error analyses of finite element solutions. Copyright © 2005 John Wiley & Sons, Ltd. [source] Lie-Poisson integrators: A Hamiltonian, variational approachINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 13 2010Zhanhua Ma Abstract In this paper we present a systematic and general method for developing variational integrators for Lie-Poisson Hamiltonian systems living in a finite-dimensional space ,,*, the dual of Lie algebra associated with a Lie group G. These integrators are essentially different discretized versions of the Lie-Poisson variational principle, or a modified Lie-Poisson variational principle proposed in this paper. We present three different integrators, including symplectic, variational Lie-Poisson integrators on G×,,* and on ,,×,,*, as well as an integrator on ,,* that is symplectic under certain conditions on the Hamiltonian. Examples of applications include simulations of free rigid body rotation and the dynamics of N point vortices on a sphere. Simulation results verify that some of these variational Lie-Poisson integrators are good candidates for geometric simulation of those two Lie-Poisson Hamiltonian systems. Copyright © 2009 John Wiley & Sons, Ltd. [source] An assumed-gradient finite element method for the level set equationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 8 2005Hashem M. Mourad Abstract The level set equation is a non-linear advection equation, and standard finite-element and finite-difference strategies typically employ spatial stabilization techniques to suppress spurious oscillations in the numerical solution. We recast the level set equation in a simpler form by assuming that the level set function remains a signed distance to the front/interface being captured. As with the original level set equation, the use of an extensional velocity helps maintain this signed-distance function. For some interface-evolution problems, this approach reduces the original level set equation to an ordinary differential equation that is almost trivial to solve. Further, we find that sufficient accuracy is available through a standard Galerkin formulation without any stabilization or discontinuity-capturing terms. Several numerical experiments are conducted to assess the ability of the proposed assumed-gradient level set method to capture the correct solution, particularly in the presence of discontinuities in the extensional velocity or level-set gradient. We examine the convergence properties of the method and its performance in problems where the simplified level set equation takes the form of a Hamilton,Jacobi equation with convex/non-convex Hamiltonian. Importantly, discretizations based on structured and unstructured finite-element meshes of bilinear quadrilateral and linear triangular elements are shown to perform equally well. Copyright © 2005 John Wiley & Sons, Ltd. [source] Efficiency of nested Markov chain Monte Carlo for polarizable potentials and perturbed HamiltoniansINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 13 2010Florent Calvo Abstract Nested Markov chain Monte Carlo is a rigorous way to enhance sampling of a given energy landscape using an auxiliary, approximate potential energy surface. Its practical efficiency mainly depends on how cheap and how different are the auxiliary potential with respect to the reference system. In this article, a combined efficiency index is proposed and assessed for two important families of energy surfaces. As illustrated for water clusters, many-body polarizable potentials can be approximated by simplifying the polarization contribution and keeping only the two-body terms. In small systems, neglecting polarization entirely is also acceptable. When the reference potential energy is obtained from diagonalization of a quantum mechanical Hamiltonian, a first-order perturbation scheme can be used to estimate the energy difference occuring on a Monte Carlo move. Our results indicate that this perturbation approximation performs well provided that the number of steps between successive diagonalization is adjusted beforehand. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem 110:2342,2346, 2010 [source] Ab initio quantum-mechanical prediction of the IR and Raman spectra of Ca3Cr2Si3O12 Uvarovite garnetINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 2 2010L. Valenzano Abstract The IR and Raman spectra of uvarovite (Ca3Cr2Si3O12) garnet were simulated with the periodic ab initio CRYSTAL code by adopting an all-electron Gaussian-type basis set and the B3LYP Hamiltonian. The two sets of 17 F1u Transverse-Optical (TO) and Longitudinal-Optical (LO) frequencies are generated, together with their intensities. As regards the IR experimental spectrum, only five peaks are available, that are in excellent agreement with the calculated data (mean absolute difference smaller than 5.2 cm,1). The analysis of the TO-LO eigenvalue overlaps permits to establish a correspondence between LO and TO modes. The set of experimental Raman peaks is much reacher (23 out of 25) and the agreement with our calculations excellent ( smaller than 6 cm,1). Isotopic substitution is used to identify the zones of the spectrum where Cr and Ca contributions are relevant. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010 [source] Davydov's solitons in a homogeneous nucleotide chainINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 1 2010Victor D. Lakhno Abstract Charge transfer in homogeneous nucleotide chains is modeled on the basis of Holstein Hamiltonian. The path length of Davydov solitons in these chains is being studied. It is shown that in a dispersionless case, when the soliton velocity V is small, the path length grows exponentially as V decreases. In this case, the state of a moving soliton is quasisteady. In the presence of dispersion determined by the dependence ,2 = , + V,2, the path length in the region 0 < V < V0 is equal to infinity. In this case, the phonon environment follows the charge motion. In the region V > V0, the soliton motion is accompanied by emission of phonons which leads to a finite path length of a soliton. The latter tends to infinity as V , V0 + 0 and V , ,. The presence of dissipation leads to a finite soliton path length. An equilibrium velocity of soliton in an external electric field is calculated. It is shown that there is a maximum intensity of an electric field at which a steady motion of a soliton is possible. The soliton mobility is calculated for the stable or ohmic brunch. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010 [source] Convergence radii of the polarization expansion of intermolecular potentialsINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 15 2009William H. Adams Abstract A new method is presented to evaluate convergence radii of the polarization expansion of interaction energies for pairs of atoms or molecules. The method is based on an analysis of the variation of the perturbed state vector as a function of the coupling constant , and does not require a calculation of perturbation corrections to high order. The convergence radii at infinite interatomic/intermolecular distances R, as well as a remarkably accurate representation of the R dependence of the convergence radii are obtained from simple calculations involving only monomer wave functions. For the interaction of the lithium and hydrogen atoms, the obtained convergence radii agree well with those obtained previously from the large-order calculations of Patkowski et al. (Patkowski et al., J Chem Phys, 2002, 117, 5124), but are expected to be considerably more accurate. Rigorous upper bounds and reasonable approximations to the convergence radii at R = , are obtained for the pairs of lithium, beryllium, boron, neon, and sodium atoms, as well as for the dimer consisting of two LiH molecules. For all the systems studied, the convergence radii are significantly smaller than the unity and rapidly decrease with the increase of the nuclear charge. It is hoped that the results of this investigation will help to analyze and eventually to compute the convergence radii of the symmetry-adapted perturbation theories which utilize the same partitioning of the Hamiltonian as the polarization expansion. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009 [source] Laser control of photodissociation process in diatomic moleculeINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 14 2009A. Tawada Abstract In this work, we first aim to realize the complete laser-induced photodissociation of the OH molecule, and then intend to control the wavepacket generated on the continuum state, i.e., to achieve the laser control of the above-threshold dissociation (ATD) spectrum. To numerically solve the Schrödinger equation, we adopt the split operator method (SOM), which conserves the norm of the state vector, and can treat both discrete and continuum states simultaneously and correctly. This photodissociation process induced by the multiphoton absorption involves the ATD spectrum due to the continuum-continuum transition by the intense electric field. First, we investigate the detailed mechanism of the complete photodissociation with the one-color laser pulse by changing the laser parameters. Then, we investigate the control of the ATD spectrum by using the two-color laser field, where we focus on the role of the relative phase and position of two laser pulses. To analyze the population of both discrete and continuum states involved in the resultant wavepacket, we show the effective method by means of the quasicontinuum state on the Morse potential obtained by numerically diagonalizing the Fourier grid Hamiltonian (FGH). © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009 [source] Effective collision strengths for electron-impact excitation of transitions within the ground 1s2 2s2 2p4 manifold of O-like Fe18+INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 9 2009Juan A. Santana Abstract Collision strengths have been computed for the electron impact excitations of parity and spin forbidden transitions within the ground 1s22s22p4 manifold of Fe XIX (Fe18+). The calculations were carried out using a relativistic R-matrix close-coupling method based on the effective many-body Hamiltonian. Twenty-six target states were included in the close-coupling expansion. Effective collision strengths, assuming a Maxwellian electron velocity distribution, were evaluated for all transitions within the ground configuration. Good agreement is found with previous Breit-Pauli R-matrix calculations at low electron temperatures, 5.0 , log Te , 6.0 K, for all the transitions, whereas significant differences are found for electron temperatures in the range 6.0 , log Te , 7.0 K. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009 [source] Theoretical investigation of carotenoid ultraviolet spectraINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 4 2009Joăo B. L. Martins Abstract We have determined the , band-gaps of the main carotenoids present in poly(methyl)methacrylate/buriti blends, namely, trans- ,-carotene, 13- cis- ,-carotene, 9- cis- ,-carotene, phytofluene, and zeaxanthin. Semiempirical, model Hamiltonian, and density functional calculations were carried out to study these structures. The geometries were fully optimized using AM1, PM3, and B3LYP/6-31G(d,p) methods. The TD-DFT and ZINDO/S methods were applied for the calculation of the electronic absorption spectra of the optimized B3LYP geometries. The calculated spectra using the polarizable continuum model for the solvent effects were compared with the available experimental. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009 [source] New perspectives on the fundamental theorem of density functional theoryINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 15 2008Xiao-Yin Pan Abstract The fundamental theorem of time-independent/time-dependent density functional theory due to Hohenberg,Kohn (HK)/Runge,Gross (RG) proves the bijectivity between the density ,(r)/,(rt) and the Hamiltonian /(t) to within a constant C/function C(t), and wave function ,/, (t). The theorems are each proved for scalar external potential energy operators. By a unitary or equivalently a gauge transformation that preserves the density, we generalize the realm of validity of each theorem to Hamiltonians, which additionally include the momentum operator and a curl-free vector potential energy operator defined in terms of a gauge function , (R)/, (Rt). The original HK/RG theorems then each constitute a special case of this generalization. Thereby, a fourfold hierarchy of such theorems is established. As a consequence of the generalization, the wave function ,/, (t) is shown to be a functional of both the density ,(r)/,(rt), which is a gauge-invariant property, and a gauge function ,(R)/,(Rt). The functional dependence on the gauge function ensures that as required by quantum mechanics, the wave function written as a functional is gauge variant. The hierarchy and the dependence of the wave function functional on the gauge function thus enhance the significance of the phase factor in density functional theory in a manner similar to that of quantum mechanics. Various additional perspectives on the theorem are arrived at. These understandings also address past critiques of time-dependent theory. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008 [source] The electronic and optical properties of oligo(trans -1,2-di(2-thienyl)-1,3-butadiene): A theoretical studyINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 13 2008Nei Marçal Abstract In the present work we investigated the theoretical electronic structure of poly(trans -1,4-di(2-thienyl)-1,3-butadiene) (PTB) and determined the optical properties of its neutral and doped oligomers. Geometrical optimizations were at the semiempirical level by using the Austin method 1 (AM1). The band structure of , electrons regarding to the neutral PTB polymer was obtained by using a tight-binding Hamiltonian. The densities of electronic states (DOS) for neutral and doped copolymers were calculated by using the negative factor counting technique. The spatial charge distribution of the oligomeric chain was also analyzed. The energy of the electronic transitions and their associated oscillator strength values were calculated for the neutral, double, and single charged oligomers to determine the UV,vis absorption spectra. The calculations were performed using the intermediate neglect of differential overlap Hamiltonian in combination with the single configuration-interaction technique in order to include correlation effects. The band gap obtained in the PTB was about 2.101 eV for the optics absorption and 1.73 eV for the DOS. The bipolaron states appear in the gap, about 0.57 eV and 0.48 eV below and above the conduction and valence bands, respectively. When the dopants concentration is increased the DOS showed that the energy gap tends to vanish, which may lead to semiconductor,metal transition. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008 [source] Improvements of parametric quantum methods with new elementary parametric functionalsINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 10 2008Fernando Ruette Abstract A series of elementary parametric functionals (EPFs) for resonance integral, electron-electron repulsion, electron-nucleus attraction, core-core interaction, and bond correlation correction were included in the new version of CATIVIC method [Int J Quantum Chem 2004, 96, 321]. In the present work, a systematic way to improve the precision of parametric quantum methods (PQMs) by using several EPFs in the parameterization of a set of molecules is proposed. Based on the fact that a linear combination of elementary functionals from the exact Hamiltonian is also a functional, a linear combination of EPFs has been proved that can enhance the accuracy of PQMs by considering the convex condition. A general formulation of simulation techniques for molecular properties is presented and a formal extension of the minimax principle to PQMs is also considered. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008 [source] Comment on the connected-moments polynomial approachINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 7 2008M. G. Marmorino Abstract Bartashevich has recently proposed two new methods for approximating eigenvalues of a Hamiltonian. The first method uses Hamiltonian moments generated from a trial function and his second method is a generalization of local energy methods. We show that the first method is equivalent to a variational one, a matrix eigenvalue problem using a Lanzcos subspace. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008 [source] Dipole induced photodetachment dynamics of halide anionsINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 1 2008Chandan Kumar MondalArticle first published online: 1 MAY 200 Abstract In this article the dynamics of photodetachment from closed shell anion in the presence of two color (bichromatic) laser field have been explored in the context of polar environmental situation. The electronic states of halide ions are modeled by a one dimensional Hamiltonian with a potential V(x) = ,V0e. The two parameters V0 and , are fixed by requiring V(x) to reproduce the experimentally observed ground state ionization energy of the halide ion concerned. The potential so generated are shown to support only one bound state. The time-dependent Fourier grid Hamiltonian method is used to follow the detachment dynamics with fairly high intensities of light. The environmental effects on the dynamics are sought to be modeled by two ways i) allowing the well depth (V0) to fluctuate randomly V0(t) = V0[1+,VR(t)]; R(t) randomly fluctuates between +1 and ,1 with time, when ,V (strength of fluctuation) is fixed and ii) in the presence of perturbation produced by a neighboring solvent dipole, which changes the effective potential. The detachment rate constant is studied as a function of important system parameters of the used light field. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2008 [source] Time evolution of the Neel stateINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 13 2007A. A. Soluyanov Abstract A quasionedimentional spin chain s = ˝ is considered as a lattice consisting of two sublattices. The attention is paid to the states, which are pure spin states of the whole lattice and both sublattices, the value of the sublattices' spins being maximum. It is shown that the Neel state can be considered as a superposition of such states. The exact equation for this superposition coefficients is developed. The possibility of the Neel state to be the eigenstate of a Hamiltonian is discussed. Several model Hamiltonians are examined, the well known ones and few novel Hamiltonians being considered. The time evolution of the Neel state in different models is studied with the help of Fock-Krylov method. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2007 [source] Exponentially accurate quasimodes for the time-independent Born,Oppenheimer approximation on a one-dimensional molecular systemINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 5 2005George A. Hagedorn Abstract We consider the eigenvalue problem for a one-dimensional molecular-type quantum Hamiltonian that has the form where h(y) is an analytic family of self-adjoint operators that has a discrete, nondegenerate electronic level ,(y) for y in some open subset of ,. Near a local minimum of the electronic level ,(y) that is not at a level crossing, we construct quasimodes that are exponentially accurate in the square of the Born,Oppenheimer parameter , by optimal truncation of the Rayleigh,Schrödinger series. That is, we construct an energy E, and a wave function ,,, such that the L2 -norm of ,, is ,,(1) and the L2 -norm of (H(,) , E,),, is bounded by , exp(,,/,2) with , > 0. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005 [source] The derivation of the characteristic function and the spectral density distribution of a Hamiltonian of N -coupled morse oscillators: The large N -limitINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 1 2005gorzata Bancewicz Abstract This paper reports a derivation of the characteristic function and the frequency function of spectral density distribution of a Hamiltonian representing a system of N -coupled Morse oscillators. The procedure utilized previously evaluated large- N expressions for spectral density distribution moments. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005 [source] Toward a BSSE-free description of strongly interacting systemsINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 4 2002G.J. Halász Abstract The so-called "chemical Hamiltonian approach" (CHA) gives perfect a priori BSSE-free description of weak intermolecular interactions, but has been found inappropriate for describing strong interactions taking place within a molecule. Here, we propose a simple modification of the CHA/F BSSE-free SCF method, which retains all the good properties of the CHA/F method for the intermolecular case but can be used also to describe covalent and ionic interactions. This is vital for calculating whole potential surfaces of chemical reactions in a consistent manner, which was found impossible by using the a posteriori counterpoise correction method. Model calculations are presented for covalent and ionic chemical bonds and for a rare gas,proton system. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002 [source] Theoretical studies on transimination of vitamin B6 analogsINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 1 2002Antoni Salvŕ Abstract The transimination reaction of vitamin B6 analogs has been studied by semiempirical quantum mechanics calculations (PM3 Hamiltonian) on a model reactive system consisting of the Schiff base made from a pyridoxal-5'-phosphate (PLP) model compound, methylamine and two auxiliary water molecules. The mechanism of this reaction has been theoretically established through the description of the energy and the geometric parameters of the intermediates and transition-state structures in the gas phase and in water solution by means of the use of two different solvation models. The description of the reaction pathway for transimination through the structures that have resulted from the calculations supports the existence of a geminal diamine as the main intermediate. The reaction also involves the occurrence of internal hydrogen transfers and water-mediated hydrogen transfers as rate-limiting steps. This study highlights the key role of water molecules not only in the formation of selected hydrogen bonds but also as true reactives. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002 [source] BSSE-free description of the formamide dimersINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 6 2001A. Bende Abstract The different configurations (linear, zig-zag, and cyclic) of formamide dimers have been studied at the level of both Hartree,Fock (HF) and second order Mřller,Plesset perturbation theory (MP2). The widely used a posteriori Boys,Bernardi "counterpoise" (CP) correction scheme has been compared with our a priori methods utilizing the "chemical Hamiltonian approach" (CHA). The appropriate interaction energies have been calculated in six different basis sets (6-31G, 6-31G**, DZV, DZP, TZV, and cc-pVDZ). © 2001 John Wiley & Sons, Inc. Int J Quant Chem, 2001 [source] Electron structure of polysilanes.INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 2 2001Are these polymers one-dimensional systems? Abstract Electron structures of polysilane, 1-methyl polysilane, 1,1-dimethyl polysilane, 1-phenyl polysilane, 1,1-diphenyl polysilane, and 1-methyl 1-phenyl polysilane in solid state were calculated using the cyclic cluster orbital method (CCO), based on a Hartree,Fock approach using a quasirelativistic INDO Hamiltonian applied to cyclic clusters. Effect of the redistribution of electron density on the silicon backbone chains after the substitution of hydrogen by methyl and phenyl groups has been investigated. Going from one- to three-dimensional models, significant changes appear in calculated electron distributions, as well as in the band structure topologies of the corresponding polymers. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem 84: 157,168, 2001 [source] Symplectic molecular dynamics integration using normal mode analysisINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 1 2001anka Jane Abstract The split integration symplectic method (SISM) for molecular dynamics (MD) integration using normal mode analysis based on a factorization of the Liouville propagator is presented. This approach is quite distinct from others that use fractional-step methods, owing to the analytical treatment of high-frequency motions. The method involves splitting the total Hamiltonian of the system into a harmonic part and the remaining part. Then the Hamilton equations are solved using a second-order generalized leapfrog integration scheme in which the purely harmonic Hamiltonian (which represents the main contribution of the chemical bonds and angles) is treated analytically, i.e., independent of the step size of integration, by a normal mode analysis that is carried out only once, at the beginning of calculation. The whole integration step combines analytical evolution of the harmonic part of the Hamiltonian with a correction arising from the remaining part. The proposed algorithm requires only one force evaluation per integration step. The algorithm was tested on a simple system of linear chain molecules. Results demonstrate the method makes possible the integration of the MD equations over larger time steps without loss of stability while being economical in computer time. © 2001 John Wiley & Sons, Inc. 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