bluuebunny/crossref_metadata_2025_split huggingface dataset:
Improving an algebraic approach to calculate approximate Franck–Condon factors of diatomic molecules
Authors: Rivas‐Silva J. F. , Campoy G. , Palma A. 
Published: January 2005

AbstractUsing the BCH theorem, we express the Hamiltonian of a Morse oscillator as a complete series of powers of the creation and annihilation operators for the harmonic oscillator. In this way, we improve the results of a previous work that uses a Bogoliubov–Tyablikov tranformation to calculate the Franck–Condon factors by means of equivalent harmonic oscillators potentials. © 1992 John Wiley & Sons, Inc.
On coordinate transformations in steepest descent path and stationary point locations
Authors: Banerjee Ajit , Adams Noah P. 
Published: January 2005

AbstractTwo aspects of the problems of calculating steepest descent paths and locating stationary points on surfaces E(X), which are sources of some confusion in the literature, are addressed. These include writing proper expressions for the gradient and Hessian, and their transformation properties relative to coordinate transformations, based on the invariance of the surface E(X). The appropriate transformation is derived, based on a constrained energy minimization condition, to achieve what we call the Hessian eigenvalue representation. This not only allows decoupling of the variables, but also points to the minimization direction and preserves the eigenvalues of the Hessian. These results allow one to use the steepest descent path and stationary point location algorithms in any coordinate system and obtain invariant results. The validity of these considerations are also confirmed through numerical examples. The stationary condition with constrained kinematic path length is also shown to yield a Hessian eigenvalue representation for the normal modes for small vibrations. Lastly, we have constructed a mathematically consistent definition of mass‐weighted Cartesians where the intrinsic reaction path of Fukui is a steepest descent path. © 1992 John Wiley & Sons, Inc.
Products of class‐sums of the symmetric group: Generalizing the recurrence relations
Authors: Katriel Jacob 
Published: January 2005

AbstractThe formulation of a combinatorial theory of the structure of the class‐algebra of the symmetric group is pursued. Recurrence relations for reduced class‐coefficients involving imbedded cycles are presented. It is pointed out that for bridging cycles one can obtain elimination rules that involve symmetrization over sets of reduced class‐coefficients with common cycle‐structures but inequivalent index distributions. Consequently, some of these reduced class‐coefficients remain individually inaccessible. © 1993 John Wiley & Sons, Inc.
MAPLE symbolic computation of the long‐range many‐body intermolecular potentials: Three‐body induction forces between two atoms and a linear molecule
Authors: Piecuch Piotr 
Published: January 2005

AbstractGeneral theory of the long‐range intermolecular potentials, resulting from the use of the Rayleigh–Schrödinger perturbation theory at the multipole approximation level and the irreducible tensor formalism, is applied to describe the three‐body induction effects in a system composed of two atoms and a linear molecule. Explicit expressions for the leading van der Waals coefficients are derived by employing the symbolic computation language MAPLE. Both the general geometry and the special case of the isosceles triangular configuration are considered. Final equations are presented using the interface between MAPLE and the typesetting language LATEX. Some technical aspects associated with the use of MAPLE in theory of long‐range intermolecular potentials are briefly discussed. Explicit expressions obtained in this article should be useful in determination of the nonadditive induction effects in van der Waals clusters composed of two atoms and a diatomic molecule. In particular, they may be helpful in explaining the discrepancies between experiment and theory that are observed in high‐resolution microwave studies of the complex Ar ⃛Ar ⃛HCl. © 1993 John Wiley & Sons, Inc.
Intrinsic reaction coordinate of perturbed potential energy surfaces: Construction of perturbed energy profiles
Authors: Mestres Jordi , Duran Miquel 
Published: January 2005

AbstractThis contribution analyzes the changes in the intrinsic reaction coordinate (IRC) and in the potential energy profiles (PEP) caused by application of a uniform electric field evaluated using standard ab initio MO methods. Two typical organic processes have been studied, namely, the Friedel–Crafts and the Walden inversion reactions, which are modeled by suitable simple systems. The results for the Walden inversion reaction show that the IRC for the field‐free and that for perturbed processes are almost coincident; in this case, using the field‐free IRC to compute the perturbed energy profile is a very good approximation. On the contrary, for the Friedel–Crafts model reaction, the two IRCs differ slightly, so the energy profiles using the perturbed and the unperturbed IRCs are somewhat different. © 1993 John Wiley & Sons, Inc.
Accurate computation of eigenfunctions for Schrödinger operators in one dimension
Authors: Núñez Marco A. , Izquierdo B. Gustavo 
Published: January 2005

AbstractA numerical method is developed to obtain sequences of functions converging to the eigenfunctions of a Schrödinger operator in the Hilbert space L2(−∞, ∞), whose norm is used to introduce the criterion of convergence in the norm and we show that it guarantees the accurate computation of expected values of a symmetric operator. The method consists in solving the Dirichlet problem associated to the eigenvalue problem in the interval [−n, n] by the Ritz method, whose convergence to both eigenvalues and eigenfunctions is guaranteed by the compactness criterion. Using the asymptotic perturbation theory in L2(−∞, ∞), we prove the convergence of both eigenvalues and eigenfunctions of the Dirichlet problem to those of the unbounded system when the interval [−n, n] is expanded. The method is applied to the harmonic oscillator, the Mitra potential, as well as to the potential V(r) = r and the Coulomb and Yukawa potentials; in each case, the convergence of eigenvalues and eigenfunctions is shown. © 1993 John Wiley & Sons, Inc.
Rayleigh–Schrödinger perturbation theory for nonlinear Schrödinger equations with linear perturbation
Authors: Ángyán János G. 
Published: January 2005

AbstractRayleigh–Schrödinger‐type perturbation theory is developed for the nonlinear Schrödinger equation, which contains a linear perturbation operator. Typical applications involve the self‐consistent reaction‐field model of solvent effects. Consideration of external perturbations, like electric fields, allows. Calculation of the response properties of solvated species. The general formulae allow development of a consistent Møller‐Plesset perturbation theory of solvated molecules. © 1993 John Wiley & Sons, Inc.
A first‐principles approach to high‐Tc superconductivity. II. The superconducting ground state
Authors: Fritsche L. 
Published: January 2005

AbstractWe show that a consistent N‐electron theory of a solid can within the Born–Oppenheimer (BO) approximation lead only to normal conductivity or to an insulating state. If one leaves the BO approximation by turning on electron–phonon interaction, one can establish a lower‐lying new ground state that has the characteristic properties of the Bardeen–Cooper–Schrieffer (BSC) ground state. We demonstrate that an (N + Nn)‐particle Schrödinger equation that describes the motion of N electrons and Nn nuclei of a solid can lead only to phonon‐induced superconductivity. © 1993 John Wiley & Sons, Inc.
The low‐lying excitation energies of polyenes investigated with a chain‐length‐dependent screened potential
Authors: Siregar R. E. , Tjia M. O. 
Published: January 2005

AbstractThe chain‐length dependencies of 2Ag and 1Bu excitation energies as well as their unexpected inversion observed experimentally in trans‐polyenes have so far been explained satisfactorily only in terms of configuration interactions within the standard Pariser–Parr–Pople (PPP) parametrization scheme with at least double excitations involving prohibitively large computational labor for long polyenes. A simpler calculation allowing nonzero differential overlap and employing restricted (first‐order) single‐excitation configuration interaction with chain‐length‐dependent screened potential is shown to provide an adequate alternative for the studies of those basic spectroscopic features of polyene excited states. The screening factor is parametrized in accordance with the chain‐length‐dependent behavior of the electrical polarizabilities of polyenes derived within the standard PPP approximation scheme. © 1993 John Wiley & Sons, Inc.
Valence electronic states of NH2+ and PH2+ dications
Authors: Park Jong Keun , Sun Hosung 
Published: January 2005

AbstractThe ab initio second‐order effective valence‐shell Hamiltonian that is based on the multireference many‐body perturbation theory has been applied to determine adiabatic potential energy curves for the valence states of NH2+ and PH2+ dications. For PH2+, three low‐lying quasi‐bound states (X1∑+, a3 Π, A1Π) are found and their spectroscopic constants are characterized. In NH2+, no quasi‐bound states are found. The potential energy curves for NH2+ are compared with those for PH2+ to understand the difference between these two valence isoelectronic cations. © 1993 John Wiley & Sons, Inc.
Self‐consistent approximate solution of the second‐order contracted Schröudinger equation
Authors: Colmenero F. , Valdemoro C. 
Published: January 2005

AbstractThe general theoretical background for solving approximately the contracted Schrödinger equation (CSchE) in a self‐consistent (SC) way has recently been proposed [F. Colmenero and C. Valdemoro, Phys. Rev. A 47, 979 (1993)]. Here, a spin‐free procedure is developed and the convergence of the SC iterative process is analyzed using as test cases the beryllium atom and four isoelectronic ions in their ground states. Damping and extrapolation procedures are employed to improve and accelerate the convergence. The results obtained are in very close agreement with those obtained by means of the full configuration‐interaction (FCI) method. © 1994 John Wiley & Sons, Inc.
Improvement of methods for molecular dynamics integration
Authors: Janežič Dušanka , Orel Bojan 
Published: January 2005

AbstractAn application of symplectic implicit Runge–Kutta (RK) integration schemes, the s‐stage Gauss–Legendre Runge–Kutta (GLRK) methods of order 2s, for the numerical solution of molecular dynamics (MD) equation is described. The two‐stage fourth‐order GLRK method, the implicit midpoint rule, and the three‐stage diagonally implicit RK method of order four are studied. The fixed‐point iteraction was used for solving the resulting nonlinear system of equations. The algorithms were applied to a complex system of N particles interacting through a Lennard‐Jones potential. The proposed symplectic methods for MD integration permit a wide range of time steps, are highly accurate and stable, and are thus suitable for the MD integration. © 1994 John Wiley & Sons, Inc.
Thermal reaction rates with a two‐point flux–flux correlation function
Authors: Lefebvre R. , Moiseyev N. , Ryaboy V. 
Published: January 2005

AbstractThe thermal rate constant of a bimolecular reaction is shown to be expressible as the time limit of the time integral of a correlation function involving the reactive flux at two different points along the path leading from reactants to products. This extension provides some additional flexibility in the finite basis‐set representation of the rate given by Miller–Schwartz–Tromp [J. Chem. Phys. 79, 4889 (1983)]. Some of the features of this expression are examined in the case of one‐dimensional Eckart barrier. © 1994 John Wiley & Sons, Inc.
Some current problems in theoretical chemical physics to be solved
Authors: Löwdin Per‐Olov 
Published: January 2005

AbstractQuantum Chemistry can today boast the fact that ordinary chemists—by means of personal computers and programs available—can study many theoretical properties of molecules by solving the Schrödinger equation and get an advance idea of how to properly arrange their experiments to find new features. For small molecules, they can use ab initio programs of the Hartree–Fock type, and for large molecules, they can use semiempirical programs available. To achieve higher accuracy and to include electron correlation properly, however, one has in the ab initio approach to use configurational interaction methods and giant computers, whereas in the semiempirical methods, the effect of correlating is often taken into account in the adjustable parameters forming the basis for this approach. In connection with the ab initio methods, it is further emphasized that the resolvent methods combined with the partitioning technique provide an excellent conceptual and mathematical framework for getting solutions of any accuracy desired, but that most of the programming of this approach remains to be done. Ordinary wave mechanics is valid at absolute zero of temperature, and—in order to include such important chemical concepts as temperature, entropy, free energy, etc.—one has to go over to general quantum theory and the Liouvillian formalism. One can stil start from the Coulombic Hamiltonian, but it becomes of importance to include the nuclear motion properly and preferably on the same level as that of the electronic motion. It is further emphasized that the irreversibility problem is not yet fully solved, that the theory of the interaction between matter and electromagnetic fields still needs some improvements, and that the question of the proper introduction of relativistic corrections in the quantum theoretical treatment of molecular systems involving heavier atoms still has a great deal to desire. © 1994 John Wiley & Sons, Inc.
Statistical properties of spin‐adapted reduced Hamiltonians
Authors: Mas V. , Planelles J. , Karwowski J. , Rajadell F. 
Published: January 2005

AbstractThe first two moments of the spectral density distributions of the second‐ and the third‐order spin‐adapted reduced Hamiltonian (SRH) matrices have been calculated and compared with the corresponding quantities describing the full configuration interaction (FCI) Hamiltonian matrix. It has been demonstrated that the differences between the SRH and FCI spectral density distributions sharply increase with increasing difference between the number of electrons and the order of SRH. © 1994 John Wiley & Sons, Inc.
Temporal rearrangement of electronic densities in slow atomic collisions
Authors: Micha David A. 
Published: January 2005

AbstractElectronic rearrangement is a common occurrence in interactions of an atom with other atoms or with solid surfaces and in molecular photodissociation by visible and UV light. In this contribution, the emphasis is on the way properties change over time, as a system progresses from its initial to its final state in a collision. An overview is presented of our recent work describing electronic rearrangement in terms of coupled differential equations for electronic orbitals and nuclear degrees of freedom. An eikonal/(time‐dependent Hartree–Fock) approximation is described and a new compact formulation is given in terms of operators in Liouville space, for both small and extended molecular systems. A method is described for treating the coupling of degrees of freedom with very different time scales. The method is illustrated with selected results for temporal atomic population changes in ion–atom and ion–solid surface interactions. © 1994 John Wiley & Sons, Inc.
A microscopic theory for solution chemical reactions: Introduction of reactant and medium structures into generalized langevin equation formalism
Authors: Nagaoka Masataka , Okuno Yoshishige , Yoshida Naoto , Yamabe Tokio 
Published: January 2005

AbstractA microscopic formulation of solution chemical reactions, taking reactants and medium structures into consideration, is presented on the basis of microscopic understandings obtained by recent quantum chemical methods (i.e., ab initio molecular orbital theory, etc.). Assuming thermal equilibrium of the medium bath, an effective internal Hamiltonian is derived, and, further, its derivative with respect to internal normal coordinates is proved explicitly to give the same force field as is provided by the free‐energy surface or potential of mean force. The free‐energy surface can be expressed in the composite normal coordinate system (CNCS) consisting of some normal coordinate systems of isolated reactants and surrounding solvent molecules (i.e., medium solvent molecules). In CNCS, in use of diagonal elements obtained in the Hessian matrix of the free‐energy surface, effective normal‐mode frequencies, which reflect the equilibrium solvent effect, are estimated. Furthermore, on the generalized Langevin equation (GLE) treatment, a closed expression of the time‐dependent frictional coefficient is derived on a microscopic basis, reflecting the reactant and solvent structures. The nonequilibrium effect is estimated by an analytical expression similar to that in the Grote–Hynes theory. The rate constant is evaluated for a typical model system and it is shown that the equilibrium rate constants should be reduced by a factor 0.997. Finally, it is concluded that the present microscopic theory is reasonably applicable to the estimation of chemical reaction rate constants in solution. © 1994 John Wiley & Sons, Inc.
Many‐Electron, many‐photon theory of nonstationary states
Authors: Nicolaides C. A. , Mercouris T. H. , Komninos Y. , Petsalakis I. D. 
Published: January 2005

AbstractA number of physical processes, such as autoionization, predissociation, ac– or dc‐field‐induced ionization, multiphoton dissociation, or chemical transformations, can be formulated as problems involving a nonstationary state satisfying a time‐independent complex eigenvalue Schrödinger equation (CESE). The CESE gives rise to all the conceptual and practical difficulties associated with the polyelectronic structures of excited states, as well as novel ones due to the presence of external fields and to the physical significance of the continuous spectrum. In a series of articles from this institute, it has been shown how advanced electronic structure theory and methods suitable for excited states can be integrated in a practical way into selected elements of the rigorous theory of discrete states interacting with the continous spectrum in order to solve the CESE nonperturbatively and efficiently and compute properties such as positions and widths of inner hole or multiply excited states, multiphoton ionization rates, multichannel predissociation lifetimes, nonlinear static and frequency‐dependent polarizabilities, and tunneling rates. The present article constitutes a review of the basic features of this theory and its computational methods. © 1994 John Wiley & Sons, Inc.
Mathematical characterization and shape analysis of localized, fractal, and complex distributions in extended systems
Authors: Pipek János , Varga Imre 
Published: January 2005

AbstractThe availability of recent supercomputers and massively parallel computing facilities makes possible the calculation of the electronic structure of highly extended (mesoscopic) molecular networks. Disorder, which is practically always present in these systems, causes an extreme complexity of the wave function that typically shows multifractal behavior in the intermediate length scale. Multifractal analysis, however, is possible only on systems that cover several orders of length scales. Though such calculation can be carried out on model systems, it is beyond the bounds of present ab initio or semiempirical treatments. In this contribution, a shape‐analysis method of the wave function is given that is applicable both for localized and multifractal one‐particle states even in moderately large networks without a regular geometrical structure. No boxing of the distributions is necessary through several orders of magnitude of scaling distances. Multifractal behavior and different regularly decaying localization shape functions can be distinguished. Finite‐size multifractal distributions are also discussed. The described method is intended to serve as an easily applicable and efficient tool for bridging over the gap between the wave‐function analysis of systems containing macroscopic and moderately large number of particles. © 1994 John Wiley & Sons, Inc.
Analysis of chemical phenomena by solving constrained hartree‐fock equation. I. Method and application to resonance energy in linear polyenes
Authors: Ichikawa Hiroshi , Kagawa Hirotaka 
Published: January 2005

AbstractThe authors proposed a general method to analyze chemical phenomena in such static states as resonance and aromaticity, without changing the variational space of the trial wave function. Solution of the Hartree–Fock–Roothaan (HFR) equation for a molecular system gives the ground‐state electronic structure and its energy. One can impose constraint conditions, which have chemical meanings, on the HFR equation (the constrained HF equation). The presented method is to analyze the energy differences between usual and constrained HF solutions. This method has an advantage over conventional methods in that it neither varies the trial wave function nor the geometry. The method was applied to interpretation of resonance energy in unsaturated linear hydrocarbons to show that both vertical and adiabatic resonance energies are produced proportionally to the number of ethylene units and that they originate by the lowering of the kinetic energy of π electrons, namely, resonance releases the kinetic‐energy pressure of π electrons. This is consistent with the previous investigations © 1994 John Wiley & Sons, Inc.