Search

A study is made of the adsorption states of light atoms (H,D,He) on perfect quantum crystals (H2,D2,He,Ne). The quantum nature of the crystal is taken into account at the outset of the theory and the adsorption states are calculated as the bound states of a single atom in the potential created by the semi-infinite solid (rigid lattice approximation). The three-dimensional Schrödinger equation is solved to obtain the binding energies of the various hydrogen and helium isotopes on the (111) and (100) faces of the following quantum crystals: H2, D2, He, Ne. The major sources of uncertainty in the results are discussed in the paper: by increasing importance they are the neglect of many body interactions, the neglect of the coupling of the adatom with the surface, and finally the uncertainties in most of the pair potentials. A good agreement is obtained with available experimental results. [ABSTRACT FROM AUTHOR]

We develop methodology for performing time dependent quantum mechanical calculations by representing the wave function as a sum of Gaussian wave packets (GWP) each characterized by a set of parameters such as width, position, momentum, and phase. The problem of computing the time evolution of the wave function is thus reduced to that of finding the time evolution of the parameters in the Gaussians. This parameter motion is determined by minimizing the error made by replacing the exact wave function in the time dependent Schrödinger equation with its Gaussian representation approximant. This leads to first order differential equations for the time dependence of the parameters, and those describing the packet position and the momentum of each packet have some resemblance with the classical equations of motion. The paper studies numerically the strategy needed to achieve the best GWP representation of time dependent processes. The issues discussed are the representation of the initial wave function, the numerical stability and the solution of the differential equations giving the evolution of the parameters, and the analysis of the final wave function. Extensive comparisons are made with an approximate method which assumes that the Gaussians are independent and their width is smaller than the length scale over which the potential changes. This approximation greatly simplifies the calculations and has the advantage of a greater resemblance to classical mechanics, thus being more intuitive. We find, however, that its range of applications is limited to problems involving localized degrees of freedom that participate in the dynamic process for a very short time. Finally we give particular attention to the notion that the GWP representation of the wave function reduces the dynamics of one quantum degree of freedom to that of a set of pseudoparticles (each represented by one packet) moving according to a pseudoclassical (i.e., classical-like) mechanics whose... [ABSTRACT FROM AUTHOR]

In this paper we suggest an approximation to the Wigner Path integral using quantum trajectories. We discuss the results in terms of Bohm’s theory and Takabayasi’s study of the relation between Bohm and Wigner theory. We discuss how this new approach is an approximation to Bohm’s theory and discuss its validity. We also suggest a method of evaluation and where such an approach would be useful. [ABSTRACT FROM AUTHOR]

This paper explores the application of quantum mechanical perturbation theory to the determination of reactive transition probabilities. The very simple problem of particle reflection and transmission at a one-dimensional potential barrier is examined over a wide range of energies and for alternate perturbative schemes. The first scheme is conventional; the second is based on a quasi-adiabatic (QA) description of the dynamics. We find that for a choice of model parameter values, loosely based on the H+H2 system, the first (conventional) scheme provides quantitatively accurate results. However, at higher system masses, the first scheme results are in only moderate agreement with exact results and are highly sensitive to the variation of distortion potential parameters. For the high system mass case, the QA results are in much better agreement with the exact results. However, the QA results are also highly sensitive to the variation of QA potential parameters. We discuss finally a number of avenues for further investigation. [ABSTRACT FROM AUTHOR]

This paper investigates the applicability of the concepts of classical ergodicity and the results of semiclassical ergodic theory to quantum mechanical systems that are away from the classical limit and that do not necessarily become ergodic as h → 0. To carry out this study, a new quantity, called the ‘‘constancy’’ FA of classical property A, is introduced. This constancy is defined in terms of the autocorrelation function of A and its statistical equilibrium value. It measures, on an absolute scale, the extent to which the dynamics of A behave statistically. The FA for a set of quadratically integrable properties A can be used to define the ‘‘degree of ergodicity’’ of a classical system with respect to this set. This analysis motivates introduction of the quantum analog of FA as a means of judging the applicability of classical ergodicity concepts to quantum mechanical systems. To illustrate these ideas, calculations for the Henon–Heiles system are carried out which compare the quantum and classical analogs of the constancies and of the ‘‘almost microcanonical’’ autocorrelation functions from which they are formed. The results indicate that the quantum and classical systems exhibit similar forms of partial ergodicity at high energy. This conclusion supports the approach introduced here for identifying the quantum implications of classical ergodicity. As a consequence of the good quantum-classical agreement, the partially ergodic nature of the classical behavior is reflected in the distribution of certain quantum-mechanical matrix elements. At lower energy, the applicability of classical ergodicity concepts to this system is more limited due to differences in the quantum and classical dynamics. The kinds of quantum-classical discrepancies that limit the implications of classical ergodicity for quantum systems are identified. [ABSTRACT FROM AUTHOR]

This paper describes an accurate study of the electronic interaction energies of NaCl, from computations with extensive basis set optimizations for the molecule, at the configuration interaction (CI) level. In the analysis of the resultant potential energy surface for predictions of gas-phase spectroscopic properties, the properties demonstrate the accuracy of the present two-body interaction energies and indicate that, unlike the predecessors, they are sufficiently accurate to be combined with future three-body and four-body potential calculations for study of microscopic many-body effects, widely known to be present in the condensed phases of NaCl. [ABSTRACT FROM AUTHOR]

We have studied the accuracy and the numerical stability of several methods for solving time dependent quantum problems in which a localized system is disturbed for a finite time. The methods assume that the wave function can be represented throughout the interaction time as a sum of Gaussian wave packets; the time evolution of the wave function is given by the evolution of the parameters in each packet. One of the methods propagates the packets independently and the other couples them by using a variational principle. Applications were made to calculate the time evolution of the ground state of a Morse oscillator and of a linear combination of the first four Morse states, and to calculate the vibrational excitation by coupling to a strong laser field. We have found that the coupled packets method provides accurate, numerically stable solutions for these problems, while the decoupled packet method fails for some of them. We have investigated the dependence of the results on the method used to fit the initial wave function to the sum of Gaussians and found that the nonlinear, least square fitting is superior to other methods. A particularly important observation is that the results obtained by the coupled Gaussians method are improved as the number of packets is increased but the propagation equations become unstable if too many packets are used to fit the wave function. Methods for monitoring and avoiding such instabilities are discussed in the paper. Our overall conclusion is that the use of the coupled, frozen Gaussians method may play an important role in the study of time dependent quantum processes in which localized quantum degrees of freedom are disturbed for a moderately long time (i.e., ten times the time constant of the system). [ABSTRACT FROM AUTHOR]

This paper presents a general theoretical formalism for describing quantum reactive scattering in four atom reactions of the type A+BCD→AB+CD based on the coupled channel distorted wave method (CCDW). In this formalism, we have derived expressions for the Schrödinger equation in body-fixed axis (bfa) coordinate systems associated with the A+BCD and AB+CD arrangement channels, and we have reduced the CCDW scattering matrix to a six dimensional internal coordinate quadrature in terms of the bfa wave functions. Explicit expressions for the nonreactive (coupled channel) centrifugal and potential coupling matrices are derived for both A+BCD and AB+CD using the bfa frame isomorphic Hamiltonian. The interconnection between A+BCD and AB+CD coordinate systems is explored in detail, and it is found that the resulting CCDW scattering matrix is similar in form to that derived earlier for atom–diatom collisions, with the main conceptual difference associated with use of an Eckart frame to define the vibrational wave functions for BCD. The relation between the Eckart and scattering frames is discussed in depth. Also, the imposition of parity decoupling in the CCDW calculation is developed for both the CC Hamiltonian matrices and the distorted wave overlap. [ABSTRACT FROM AUTHOR]

In this paper, we study the collective single-quantum excitations of a ring of N identical molecular units, of arbitrary radius R relative to the radiation wavelength λ. We first calculate the single-quantum eigenstates of the system for N=2,...,6 and N large, their energies and their lifetimes due to interaction with the radiation field. For large N, we study the collective emission by the ring as a function of direction, comparing the pattern with that created by a collectively excited linear chain of molecular units. Finally, we calculate the emission spectrum of the ring for arbitrary initial excitation, and the spectrum of the radiation absorbed by the ring from an external electromagnetic field. [ABSTRACT FROM AUTHOR]

The concept of local pressure in an electronic system is extended and developed, starting from an integral relation of Bartolotti and Parr (Ref. 11) and using the local thermodynamic language of Ghosh, Berkowitz, and Parr (GBP) (Ref. 3), who have shown that for an ideal, noninteracting microscopic system the internal pressure at a point r is purely kinetic and given by ps=ρ(r)kT(r), where T(r) is an appropriately defined local temperature. In the present paper, we show that this equation, exact for the noninteracting, ideal system within the local thermodynamic transcription is a first order truncation of the real, interacting system pressure density functional, which contains explicit correlation and exchange pressure contributions, which act as ‘‘deviations from ideality’’ in the real system. From analogy with the macroscopic situation, the pressure density functional is written as a virial expansion in terms of the density. [ABSTRACT FROM AUTHOR]

Reduced dimensionality exact quantum and quasiclassical reaction probabilities and rate constants are presented for the O(3P)+HD(ν=0,1)→OH+D and OD+H reactions. The effective potential energy surface used is the ab initio collinear MODPOLCI surface with the ground state adiabatic bending energy added in, as in the previous paper in this series. The rate constants are compared with the recent experiments of Gordon et al. [ABSTRACT FROM AUTHOR]

Reduced dimensionality exact quantum and quasiclassical trajectory isotope effects are presented for the O(3P)+H2, D2, and HD reactions. Two potential energy surfaces are used: the ab initio MODPOLCI and the semiempirical LEPS surfaces studied in previous papers in this series. Isotope effects are also calculated by conventional transition state theory with a Wigner tunneling correction. All the calculated results are compared to recent experimental measurements of the isotope effects. The measured values show that H atom abstraction is essentially the same from HH or HD, as is the D atom abstraction from either DD or DH. Only the reduced dimensionality quantum calculations on the MODPOLCI surface are in agreement with these results. [ABSTRACT FROM AUTHOR]

The reaction Li+HF→LiF+H is studied using three-dimensional quantum reactive scattering theory. The rotational and bending motions are treated using the bending corrected rotating nonlinear model (BCRNM) developed in the body of this paper. Reaction probabilities and total reaction cross sections are calculated for energies up to 1 eV. Reaction cross sections are compared with experimental results at 0.38 and 0.63 eV. Results are in excellent agreement with experiment at the lower energy. We calculate a total reaction cross section σ of 0.72 Å2 vs the measured value of 0.80 Å2. At the higher energy, the BCRNM overestimates the cross section: We calculate σ=2.46 Å2, while the experimental value is σ=0.97 Å2. [ABSTRACT FROM AUTHOR]

Classical resonances arising from the interaction of three nonlinearly coupled oscillators are studied from both a theoretical and numerical perspective. In particular, our study focuses on ternary classical resonances defined by n1ω1 +n2ω2 -n3ω3 =0. We discuss some of the experimental and quantum mechanical consequences of binary and ternary classical resonances (e.g., Fermi resonances and vibration–rotation coupling). Numerically we show that it is possible to construct a three-dimensional map such that ternary classical resonances can be systematically found. Theoretically, we show that canonical transformations exist between resonant and nonresonant motion. These transformations predict various structural features of the three-dimensional numerical maps which are subsequently observed in a model numerical calculation. Finally we argue that the methods and ideas presented in this paper are generic and can be used for more general systems. [ABSTRACT FROM AUTHOR]

This paper addresses the general problem of zeroth order representation of resonant dynamics. We investigate the classical, quantum mechanical, and semiclassical transformation properties of two-dimensional isotropic and anisotropic uncoupled harmonic oscillators. The classical and quantal theories are presented in a manner that emphasizes the strong correspondence between the two, and in particular, the SU(2) symmetry exhibited by both the classical and quantum oscillators. The classical canonical transformations relating the action-angle variables appropriate for normal, local, and precessional motion of the isotropic oscillator are derived by explicit calculation of the generating functions. By employing a simple mapping relating the anisotropic and isotropic oscillators, expressions for action-angle variables appropriate for the topology of an arbitrary m:n resonance are determined. The resulting invariant tori are compared with the corresponding quantum mechanical wave functions and phase space densities. The relationship between the classical and quantum mechanical theories is illustrated by determining semiclassical approximations to the unitary transformation matrix elements, which are given in terms of the classical generating functions. Applications to problems of current interest, such as the adiabatic switching method for semiclassical quantization of nonseparable systems, are briefly discussed. [ABSTRACT FROM AUTHOR]

We consider in the present paper an extension of numerical path integral methods for use in computing finite temperature time correlation functions. We demonstrate that coordinate rotation techniques extend appreciably the time domain over which Monte Carlo methods are of use in the construction of such correlation functions. [ABSTRACT FROM AUTHOR]

Quantum electrodynamics of an atom near a surface is a timely problem in current theoretical research. It appears, however, that a full dynamical theory, which includes both the time evolution of the atomic density operator and the details of the fluorescence radiation (temporal photon distribution) has never been formulated. In this paper the quantum theory of an atom near a perfect conductor is presented, and it is indicated how the formalism can be modified to account for more realistic optically active substrates. An expression is derived for the atomic spontaneous-decay Liouville operator from the Hamiltonian, which recovers the familiar results for the lifetimes and energy shifts. Furthermore, the emitted power is calculated as a function of time from the explicit expression for the radiation field. Comparison of the atomic-decay rates with the power of the emitted radiation shows the consistency of the theory, as far as the properties of the fluoresence are concerned. An unusual energy interference in the fluorescence, which is emitted by a multilevel atom, is predicted. Similarities and discrepancies with other theories are pointed out, and it is shown that especially the mirror theory has a very restricted applicability. [ABSTRACT FROM AUTHOR]

This paper presents systematic developments in the previously initiated line of research concerning a quantum Monte Carlo (QMC) method based on the use of a pure diffusion process corresponding to some reference function and a generalized Feynman–Kac path integral formalism. Not only mean values of quantum observables, but also response properties are expressed using suitable path integrals involving the diffusion measure of the reference diffusion process. Moreover, by relying on the ergodic character of this process, path integrals may be evaluated as time-averages along any sample trajectory of the process. This property is of crucial importance for the computer implementation of the method. As concerns the treatment of many-fermion systems, where the Pauli principle must be taken into account, we can use the fixed-node approximation, but we also discuss the potentially exact release-node procedure, whereby some adequate symmetry is imposed on the integrand (of the generalized Feynman–Kac formula), associated with a possibly refined choice of the reference function. [ABSTRACT FROM AUTHOR]

This work describes an approximate and temporary form of ergodicity, called pseudoergodicity. This is a classical phenomenon that is of particular interest since it has a straightforward quantum analog and can be expected to influence the dynamics of a quantum system more directly than rigorous ergodicity. A procedure is described for locating phase space regions where classical motion is pseudoergodic (pe) and this technique is applied to the Henon–Heiles system excited to near its escape energy. Certain pe zones containing chaotic trajectories appear to coincide with the vague tori of Reinhardt and co-workers while other such zones have less familiar forms. When the Henon–Heiles system is observed for long times, a single pe region becomes larger than others, thus marking incipient ergodicity on much of the energy shell. The classical pe regions are compared to quantum pe zones, calculated by a slight modification of a technique presented in an earlier paper. It is found that certain classical pe regions have close quantum analogs while others do not, for reasons probably related to the short time scale for quantum-classical correspondence. Among the classical regions that do not have quantum analogs is the aforementioned dominant pe zone. The implication is that the present quantum system does not display behavior similar to the truly large-scale ergodicity that occurs in the classical system. [ABSTRACT FROM AUTHOR]

The Husimi function provides a phase-space view of quantum systems. This paper considers a number of its properties, including ways in which it can be expanded in terms of basis functions. A spectral or ‘‘natural’’ expansion and an expansion analogous to the Carlson–Keller expansion in terms of coordinate-density momentum-density products are considered, as is a method for separating the angular dependence of the momentum. There is a set of functions in phase space having the same overlap properties as the initial orbital basis in terms of which the charge density matrix is expressed. A Husimi matrix is defined and a scalar product in the space containing such matrices as elements is introduced. The connection with the vector space of density matrices is examined. The Husimi function is related to the Husimi matrix in a way analogous to the relationship between a density matrix and a density, but there is a major difference in that this map can always be inverted. For a harmonic oscillator basis the phase space basis functions, in terms of which the Husimi function is expressed, span a linear space but do not provide a complete set; their products provide a linearly independent set that is complete. It is suggested that similar behavior can be expected for other basis sets. [ABSTRACT FROM AUTHOR]

A careful semiclassical analysis of ‘‘above-barrier’’ localization is provided for the case of one-dimensional random analytic potentials. The result is a practical semiclassical formula for the localization length, which shows exponential unboundedness in the classical limit. The algebraic, h→0, asymptotic series for the density of states is also determined. In the process of deriving the latter result an interesting link between the density of states and the localization length (via the Lyapunov exponent) is revealed. In addition, the results of this paper provide some of the groundwork for the semiclassical analysis of ‘‘nonadiabatic transport’’ associated with time-varying potentials. [ABSTRACT FROM AUTHOR]

We describe a time-independent quantum theory for atom–diatom reactive scattering using a procedure based upon a division of configuration space into three distinct chemical channels. Within each chemical channel, coordinate systems defined as transformations of Jacobi coordinates are described which allow the use of R-matrix propagation in solving for the unbound motion along a scattering coordinate. The remaining five degrees of freedom are treated variationally, making use of the efficient discrete variable representation to describe the vibration–rotation interaction. The scattering information from the three chemical channels is matched on the common boundary, and the full S matrix is obtained at fixed total energy, angular momentum, and parity. In the second paper of this series, accurate results for the reactions of H+H2 and its isotopomers will be presented. [ABSTRACT FROM AUTHOR]

Studies the role of potential structure in classical, semiclassical and quantum mechanics. Difference between the ways classical and quantum dynamics react to features; Classical and quantum functional sensitivities.

Compares the sensitivity behavior between direct and long-lived classical trajectories and quantum wave packets in a H-H[sub 2] reaction. Response to perturbations; Sensitivities of trajectories to variations in the potential; Algorithm that accounts for the contributions to the sensitivities from the trajectories.

Presents a unitary time evolution method for quantum systems under the influence of time dependent Hamiltonians. Definition of a nonorthogonal basis; Integration of the evolution over an elementary time interval; Performance of the method on a triatomic molecule model under a monochromatic field.

Examines the classical, semiclassical and quantum mechanics of a chaotic Hamiltonian system. Adiabatic separation of the x and y motion; Connection between integrable approximation and the exact dynamics; Agreement between energy levels and energy spectrum.

Studies the quantization of the Meyer-Miller classical analog for the John-Teller system at intermediate couplings. Dynamics of the classical analog; Eigenvalues and eigenvectors of the Hamiltonian matrix obtained from the Liouville formulation; Quantum mechanics for the classical analog of a model.

Studies the analytical gradients for unrestricted Hartree-Fock wave functions and second order Moller-Plesset perturbation theory with single spin annihilation. Significant contamination from unwanted spin states; Distortion of the potential energy surface; Optimization of transition states.

In this paper, we present the results of coupled channel hyperspherical reactive scattering calculations on the reaction I+HI→IH+I using a semiempirical potential surface. Only the J=0 partial wave is considered. The bimolecular reaction probability is found to exhibit two sharp resonant peaks at energies below threshold for direct reaction. The resonances are associated with transition state quantum numbers (ν1ν2ν3)=(100) and (200), and their energies are in excellent agreement with the result of L2 calculations due to Clary and Connor, and to Bowman and Gazdy. At higher energy the reaction is dominated by rotational threshold effects, and then below the HI(ν=1) energetic threshold, additional resonances are found which correspond to quantum numbers (002), (102), (202), and (302). Franck–Condon factors associated with photodetachment of IHI- have also been calculated, and these show mainly direct scattering threshold behavior at low energies (E<0.30 eV), with the (100) and (200) resonances contributing only slightly. Resonant behavior is dominant at higher energies (0.3–0.4 eV) where the (002) resonance especially contributes. Agreement of our calculated photodetachment spectra with experimental results due to Neumark and co-workers is good provided that an 0.08 eV energy shift is made in the calculated spectra. This shift is probably due to an incorrect energy barrier on the semiempirical surface. [ABSTRACT FROM AUTHOR]

In Quantum Mechanics, Landau and Lifschitz derive a formula for the direct calculation of rovibronic statistical weights. If it were correct, this formula would dramatically reduce the effort necessary to calculate statistical weights in large molecules. Unfortunately, due to a common misapplication of the Pauli principle, the formula derived is incorrect, as are the subsequent examples and problem solutions. The correct fomula derived in this paper is used to calculate statistical weights for hydrogen, ethylene, and ammonia which agree with those of Herzberg, Townes and Schawlow, and Bunker. [ABSTRACT FROM AUTHOR]

In this paper, we examine classical–quantum correspondence in a system with strong vibration–rotation interaction. We study the quantum mechanics of a two degree of freedom rigid bender Hamiltonian, previously considered in the context of classical mechanics by Ezra [Chem. Phys. Lett. 127, 492 (1986)] and by Frederick and McClelland [J. Chem. Phys. 84, 4347 (1986)]. Eigenfunctions and eigenvalues of this system are calculated by matrix diagonalization in a harmonic oscillator–rigid rotor basis. The quantum mechanics are compared with the classical mechanics by visualizing the quantum eigenstates on a surface of section, defined in terms of the coherent states of the rotor and oscillator. We find clear connections between eigenstate structure on the quantum surface of section and features of the classical phase space, such as nonlinear resonance, period doubling, and chaos. [ABSTRACT FROM AUTHOR]

This paper presents a two degree of freedom model for describing the quantum dynamics of the insertion reaction O(1 D) + H2 in which bend motions are treated with a sudden approximation. Comparison of product state vibrational distributions from a classical version of this model with three dimensional trajectory results indicates that the model is realistic. Quantum/classical comparisons for the model Hamiltonian indicate that recrossing is more important in the quantum dynamics, and as a result, the quantum reaction probability from ground state reagents is lower by as much as 40%. In addition, the quantum vibrational state distribution shows higher excitation than its classical counterpart. This difference in excitation is due to trajectories that produce vibrationally cold products, and it is found that these trajectories always cross the deepest part of the H2O well. [ABSTRACT FROM AUTHOR]

The present paper clarifies a number of issues concerning the general problem of constructing improved short time quantum mechanical propagators. Cumulant methods are shown to be a particularly convenient tool for this task. Numerical results comparing methods based on partial averaging and on gradient approaches are presented for simple model problems and for many particle quantum fluids. [ABSTRACT FROM AUTHOR]

In this paper we present results of coupled channel quantum scattering calculations of the alignment selected j<3/2→ j=1/2 fine structure changing integral cross section for Na(2P)+He. This cross section has in the past been written in terms of a coherent sum of partial wave amplitudes, but we have found that it can be expressed in terms of an incoherent sum of partial cross sections, each labeled by the total angular momentum J and by parity. It is also possible to define an alignment selected wave function for each J such that the azimuthal average of the square of this wave function projected onto each final state is proportional to the magnitude of the partial cross section into that state. This J labeled wave function is thus clearly related to the physical measurables, and we have used it to determine propensities for preservation of asymptotically prepared alignment during collisions. Using a potential surface based on Pascale’s ab initio calculations, we find that the alignment ratio σ⊥/σ∥ is an increasing function of energy, with a value less than unity at low energy (<0.01 eV), but increasing quickly to a value of about 2.0 at 0.04 eV and then more slowly at higher energy, up to a value of 2.7 at 0.2 eV (the highest energy considered). Above 0.02 eV, both the alignment ratio and the alignment selected integral cross sections are in good agreement with values calculated in an accompanying semiclassical study (Kovalenko, Leone, and Delos).An examination of the J labeled alignment selected scattering wave functions and of the expectation values of 〈Ω〉, 〈Λ〉, and 〈Σ〉 indicates that at low J when the initial state is prepared with ∥ polarization, the dominant state at short range is Σ while with ⊥ polarization the dominant state is Π (i.e., asymptotic alignment is preserved). By way of contrast, this propensity for alignment preservation is not seen if fluxes or probability densities... [ABSTRACT FROM AUTHOR]

In this paper we investigate a new approach to reduced dimensionality descriptions of quantum mechanical systems resident in a bath. We study physical situations in which the coupling between the system and the bath is slowly varying. Our method involves an operator expansion of the Feynman propagator following the Zassenhaus theorem. From this general expansion we are able to derive an especially simple special case in which the coupling is a slowly varying function of the position operators of the system and the bath. From the approximate propagator after tracing over bath degrees, we are able to derive a short time propagator which yields both a form for efficient numerical calculation and an effective Schrödinger equation for the evolution of the system under the average influence of the bath. This theory is then applied to tunneling rearrangement in mixed crystals of benzoic acid. We find that independent of potential energy perturbations, dynamic system bath couplings increase the rate of tunneling. A central goal of this type of approach is to model the increasingly complex experimental data for large (often biological) systems. [ABSTRACT FROM AUTHOR]

A new approach for solving the time-dependent wave function in quantum scattering problem is presented. The conventional wave packet method, which directly solves the time-dependent Schrödinger equation, normally requires a large number of grid points since the Schrödinger picture wave function both travels and spreads in time. Also, since the Schrödinger picture wave function oscillates in time with frequency ω=E/h, a very small time increment is required to integrate the Schrödinger equation, especially for high energy collisions. The new method presented in this paper transforms the Schrödinger picture wave function into the interaction picture and carries out the integration in it. The new approach is superior to conventional one in that (1) a smaller numerical grid is required due to the localized nature of the interaction picture wave function, since it is not a traveling wave and does not spread appreciably in coordinate space, and thus behaves like a bound state wave function. (2) The interaction picture wave function varies slowly with time and is essentially independent of energy, permitting the use of a large time increment in the numerical integration. Because of these two features in this new approach, we are able to integrate the time dependent wave function once and obtain an accurate S matrix over a wide range of energy efficiently. [ABSTRACT FROM AUTHOR]

This paper provides the first explicit, general proof that the leading-order dispersion forces between two interacting molecules result from the attraction of nuclei in each molecule to the dispersion-induced change in the electronic charge density of the same molecule. The proof given here holds for molecules of any symmetry, provided that overlap between the charge distributions is small. New sum rules for the nonlinear response tensors are also obtained, after consideration of the long-range limit. A perturbation analysis gives the dispersion-induced polarization in each molecule in terms of nonlocal, nonlinear response tensors taken at imaginary frequencies. Forces on the nuclei are computed from a reaction-field expression for the dispersion energy, in terms of polarizability densities. Recent work has shown that the derivative of the polarizability density with respect to a nuclear coordinate is linked to an integral involving the nonlinear response tensor and the dipole propagator, and this link provides the key to the proof. [ABSTRACT FROM AUTHOR]

We report the details of a theory which predicts the freezing of quantum liquids, such as helium [J. Chem. Phys. 90, 4622 (1989)]. The freezing of a wide variety of classical liquids has been described by the density functional (DF) theory of statistical mechanics. By choosing a new ideal system, we construct a new DF theory which addresses directly many of the unusual features of the freezing of liquid helium, such as the weakly modulated liquid pair correlation function g(r) at freezing densities. The theory combines DF techniques with the Feynman path integral formulation of quantum mechanics, to include correctly dispersion effects. In classical DF theories, the density and external field of the ideal system are connected by a Boltzmann relation ρ(r)∝exp[-βV(r)]. In our quantum DF theory, we relate the density and external field of the ideal system through the Feynman path integral representation, in which the quantum particle is represented by a classical ‘‘ring polymer’’ of P beads. In practical applications, the DF perturbation expansion is truncated at second order, and classical DF theories fail for helium because they employ an ideal system which is too far removed from the interacting system. For a certain simplified problem, the density path integral of the ideal system can be performed in closed form, leading to a compact, physically descriptive theory. In a companion paper, the full theory is applied to the freezing of helium-4 and yields good results. [ABSTRACT FROM AUTHOR]

Time-dependent quantum mechanics has proved to be a useful conceptual and calculational tool for a wide range of femtosecond time scale processes. In this paper we develop a method of extending time-dependent methodology to processes taking many picoseconds, through use of the interaction representation of quantum mechanics. Two implementations are presented, one in the energy frame and one in the coordinate frame; both of these implementations scale as N2 with the number of basis functions, as opposed to N3 for a matrix diagonalization. The interaction representation approach allows the use of time steps much greater than those that can be used in the Schrödinger representation, and is expected to be useful for the broad class of problems where the Hamiltonian can be partitioned into H0+V, where V

The interpretation of the infrared and Raman spectra of pristine polypyrrole as 1-d lattice is presented as the result of lattice dynamical calculations. Geometries and vibrational force fields are derived from semiempirical quantum chemical calculations and/or from the optical spectra of oligomers. This paper lays the background information which are used in the second paper, which immediately follows, where the spectra of the conducting polymer are extensively discussed. [ABSTRACT FROM AUTHOR]

The low-temperature propagator of Mak and Andersen [J. Chem. Phys. 92, 2953 (1990)] allows for much more rapid convergence of Feynman path integral computer simulations of quantum systems. The effectiveness of this propagator is very sensitive to the choice of an effective frequency and the choice of this made by Mak and Andersen, although good, is not optimum. In this paper a harmonic reference system is used together with a variation principle to compute this effective frequency. Simulations show that when this is used in the low temperature propagator, the results converge much more rapidly than for other choices of the frequency. Moreover, an energy estimator is derived, which allows this effective potential to be used for the determination of the energy of the quantum system. In addition, using a cumulant expansion of the centroid density in the free particle reference system, an effective potential along with a corresponding energy estimator is derived and compared to the above. [ABSTRACT FROM AUTHOR]

A previous calculation for H+N2 [Walch, Duchovic, and Rohlfing, J. Chem. Phys. 90, 3230 (1989)] focused on the minimum energy path (MEP) region of the potential energy surface and on estimates of the lifetime of the HN2 species. In this paper, we report energies computed at geometries selected to permit a global representation of the potential energy surface (PES). As in the previous work, the calculations were performed using the complete active space self-consistent field/externally contracted configuration interaction (CASSCF/CCI) method. The surface was characterized using the same basis set as in the previous paper except that an improved contraction of the H s basis is used. Calculations with a larger basis set were carried out along an approximate MEP obtained with the smaller basis set. The new PES exhibits a sharp curvature, which was not present in the previous calculations, and has a slightly narrower and smaller barrier to dissociation. Saddle points for H atom exchange via collinear and T-shaped HN2 complexes are also reported. [ABSTRACT FROM AUTHOR]

The competition between desorption and relaxation of vibrationally excited CO adsorbed on a series of model surfaces is examined theoretically using a quantum mechanical description of the dynamics. This study complements that reported in the preceding paper which studied the classical mechanics of these processes. Quantitative differences between the quantal and classical results are seen in the rate constants for the various energy transfer processes. Moreover, qualitative differences are seen in the trend in the dynamics as the Debye frequency of the model surface is increased. The differences in the various rate constants in the quantal and classical calculations lead to an unusual ‘‘quantum effect’’ in which the trend in the energy flow with increasing Debye frequency is in different directions. Relaxation of the excited adsorbate is the dominant trend in the classical mechanics; thermal desorption of the excited adsorbate is the dominant trend in the quantal calculations. [ABSTRACT FROM AUTHOR]

The frame transformation concept, which is standardly used in discussions of atomic and molecular Rydberg spectra, is applied to heavy particle scattering theory. It is shown how this approach permits the use of an optimal reference frame in the various different ranges of the scattering coordinate. It is further argued that the accuracy of the coupled states or p-helicity decoupling approximations may be significantly improved without substantial additional computational effort especially for low energy scattering processes, through the use of frame transformation procedures. The method is then applied to the calculation of the photodissociation line shapes for the rotational predissociation of Ar–H2 within the framework of generalized multichannel quantum defect theory (MQDT). It is shown how the use of the frame transformation procedure yields reasonably correct product rotational state distributions in situations where the standard coupled states or body-fixed decoupling procedure fails even at the qualitative level. The paper also reviews the application of generalized MQDT to heavy particle scattering processes. [ABSTRACT FROM AUTHOR]

The tetrahedral (Td) form of the N4 molecule has been investigated via ab initio quantum mechanical methods. The lowest triplet state of N4 in the tetrahedral region of the potential energy surface, and the barrier separating TdN4 from two N2 molecules have also been examined. Both the transition state and 3A‘ state have Cs symmetry. The singlet state of tetrahedral N4 is predicted to lie 13 kcal/mol below the 3A‘ state. The energy difference between TdN4 and two N2 molecules is accurately determined to be 186 kcal/mol while the barrier separating these species is found to be about 61 kcal/mol. The possibility that TdN4 may be used as a high energy density fuel is investigated and discussed. In addition, a highly accurate determination of the equilibrium structure, harmonic vibrational frequencies, and infrared intensities of TdN4 has been performed using large atomic natural orbital (ANO) basis sets in conjunction with the coupled-cluster single and double (CCSD) excitation level of theory and the CCSD(T) extension. The largest ANO basis sets used for N4 contain f-type functions. Analogous studies of the N2 molecule are presented in order to judge the reliability of the theoretical predictions for the experimentally unknown TdN4. [ABSTRACT FROM AUTHOR]

Feynman’s path integral formulation of quantum mechanics, supplemented by an approximate projection operator (exact in the case of noninteracting particles), is used to study the 2D Hubbard model. The projection operator is designed to study Hamiltonians defined on a finite basis set, but extensions to continuous basis sets are suggested. The projection operator is shown to reduce the variance by a significant amount relative to straightforward Monte Carlo integration. Approximate calculations are usually within one standard deviation of exact results and virtually always within two to three standard deviations. In addition, the algorithm scales with the number of discretization points P as either P or P2 (depending on the method of implementation), rather than the P3 of the Hubbard–Stratonovich transformation. Accuracy to about 5%–10% in energies and spin–spin correlation functions are found using moderate amounts of computer time. [ABSTRACT FROM AUTHOR]

The cross sections for dissociative attachment in the chlorosilanes and chloromethanes for electrons in the energy range 0.2–5.0 eV have been measured. In addition, measurements of the total electron scattering cross sections of the chloromethanes in the 0.2–12.0 eV range are reported. It is observed that dissociative attachment is much more probable in the chloromethanes than the chlorosilanes. This is explained by quantum mechanical calculations which reveal qualitative differences in the nature of the electron–molecule complex for the silanes as compared to the methanes. [ABSTRACT FROM AUTHOR]

A quantum mechanical model for the fragment anisotropy parameter in the limit of a long dissociation lifetime with respect to parent rotation is derived. For excitation with light plane polarized along the Z axis, the anisotropy parameter can be expressed as β=A〈P2(cos θ’t)> +B〈sin2 θt cos 2[lowercase_phi_synonym]’t>, where A and B are functions of the excitation branch employed and the rotational level of the excited parent, and (θt,[lowercase_phi_synonym]’t) are the Euler angles of the final fragment recoil direction in the molecular frame, where the z axis is along the parent excitation transition dipole moment. For low J values, classically derived expressions for the anisotropy parameter of fragments produced from the photodissociation of a Boltzmann distribution of rotating parent molecules are shown to not be valid for H2 fragments produced from the photodissociation of H2CO excited to single rovibronic levels. This formula is applied to the measured anisotropies of the H2 (v=1,J=0) fragments produced from the fragmentation of H2CO excited to several different rotational levels of the 2141 band in S1. [ABSTRACT FROM AUTHOR]

The thermal rate coefficient for the prototype reaction H+H2→H2+H with zero total angular momentum is calculated by summing, averaging, and numerically integrating state-to-state reaction probabilities calculated by time-independent quantum-mechanical scattering theory. The results are very carefully converged with respect to all numerical parameters in order to provide high-precision benchmark results for confirming the accuracy of new methods and testing their efficiency. [ABSTRACT FROM AUTHOR]

The two degenerate components of the OH radical 2Π ground electronic state give rise to independent minima (of 2A‘ and 2A’ symmetries) upon interaction with the water molecule. These two minima have been investigated here for the first time using ab initio quantum mechanical methods. Minimum, double zeta, double zeta plus polarization, and triple zeta plus double polarization basis sets have been employed in conjunction with self-consistent-field, second-order perturbation, and configuration interaction methods. At all levels of theory, the 2A‘ state is predicted to be the global minimum, with a dissociation energy De of about 3.5 kcal/mol. The 2A’ state is predicted to lie about 1 kcal higher in energy. Both minima occur for structures with OH···O linkages close to linear and are reminiscent of the water dimer. However, the H···O distances (∼2.1 Å for 2A‘, ∼2.2 Å for 2A’) are significantly longer than observed for the water dimer. Preliminary estimates of the H2O·OH vibrational frequencies are made. [ABSTRACT FROM AUTHOR]