ALBERT

Notizen: The deformation of the associative algebra of exterior forms is performed. This operation leads to a Yang–Baxter equation. Its relation with the braid group Bn−1 is analyzed. The correspondence of this deformation with the GLq(r,C) algebra is developed.

Notizen: The vacuum energy density (Casimir energy) corresponding to a massless scalar quantum field living in different universes (mainly no-boundary ones), in several dimensions, is calculated. Hawking's zeta function regularization procedure supplemented with binomial expansion is shown to be a rigorous and well suited method for performing the analysis. It is compared with other more involved techniques. The principal-part prescription is used to deal with the poles that eventually appear. Results of the analysis are the absence of poles at four dimensions (4D) (for a 4D Riemann sphere and for a 4D cylinder of 3D Riemann spherical section), the total coincidence of the results corresponding to a 3D and a 4D cylinder (the first after pole subtraction), and the fact that the vacuum energy density for cylinders is (in absolute value) over an order of magnitude smaller than for spheres of the same dimension.

Notizen: A type of field quantization is developed which, in some cases, leads directly from a field equation to a mass spectrum. The starting point is a field-Hamiltonian setup of the field equations. A Schrödinger-type wave function, a function of the field variables, is postulated and a Hamiltonian operator is inferred from the Hamiltonian function. A wave equation is suggested which has particle-type solutions only for special values of the rest mass. As examples, the spectra for the linear wave equation and for an equation with a sharply limited range of the field variable are discussed.

Notizen: Hierarchies of nonlinear Schrödinger equations were investigated for multiparticle systems, satisfying the separation property, i.e., where product wave functions evolve by the separate evolution of each factor. Such a hierarchy defines a nonlinear derivation on tensor products of the single-particle wave-function space, and satisfies a certain homogeneity property characterized by two new universal physical constants. A canonical construction of hierarchies is derived that allows the introduction, at any particular "threshold'' number of particles, of truly new physical effects absent in systems having fewer particles. In particular, if single quantum particles satisfy the usual (linear) Schrödinger equation, a system of two particles can evolve by means of a fairly simple nonlinear Schrödinger equation without violating the separation property. Examples of Galilean-invariant hierarchies are given.

Notizen: Systematic use of the infinite-dimensional spin representation simplifies and rigorizes several questions in quantum field theory. This representation permutes "Gaussian'' elements in the fermion Fock space, and is necessarily projective: its cocycle at the group level is computed, and Schwinger terms and anomalies from infinitesimal versions of this cocycle are obtained. Quantization, in this framework, depends on the choice of the "right'' complex structure on the space of solutions of the Dirac equation. We show how the spin representation allows one to compute exactly the S-matrix for fermions in an external field; the cocycle yields a causality condition needed to determine the phase.

Notizen: The interaction of various algebraic structures describing fusion, braiding, and group symmetries in quantum projective field theory is the object of investigation in this article. Structures of projective Zamolodchikov algebras, their representations, spherical correlation functions, correlation characters and enveloping quantum projective field theory (QPFT)-operator algebras, projective W¨-algebras, shift algebras, infinite-dimensional R matrices Rproj(u) and Rproj*(u) of the QPFT, braiding admissible QPFT-operator algebras, and projective G hypermultiplets are explored. It is proven (in the formalism of shift algebras) that sl(2,C)-primary fields are characterized by their projective weights and by the hidden additive weight, a hidden quantum number discovered in this article. Special attention is paid to various constructions of projective G hypermultiplets (QPFT-operator algebras with G symmetries).

Notizen: The moduli space of flat connections on a principal G-bundle over a compact oriented surface of genus g≥1 is considered herein. Using the holonomies around noncontractible loops, the moduli space is described as a quotient of a submanifold of G2g. An explicit expression is obtained for the symplectic form on the smooth part of moduli space, and several properties of this form are established.

Notizen: An overview of the integer quantum Hall effect is given. A mathematical framework using nonommutative geometry as defined by Connes is prepared. Within this framework, it is proved that the Hall conductivity is quantized and that plateaux occur when the Fermi energy varies in a region of localized states.

Notizen: The recent suggestion that a temporal form of quantum logic provides the natural mathematical framework within which to discuss the proposal by Gell-Mann and Hartle for a generalized form of quantum theory based on the ideas of histories and decoherence functionals is analyzed and developed herein. Particular stress is placed on properties of the space of decoherence functionals, including one way in which certain global and topological properties of a classical system are reflected in a quantum history theory.

Notizen: In (2+1)-dimensional general relativity, the path integral for a manifold M can be expressed in terms of a topological invariant, the Ray–Singer torsion of a flat bundle over M. For some manifolds, this makes an explicit computation of transition amplitudes possible. In this paper, the amplitude for a simple topology-changing process is evaluated. It is shown that certain amplitudes for spatial topology change are nonvanishing—in fact, they can be infrared divergent—but that they are infinitely suppressed relative to similar topology-preserving amplitudes.

Notizen: Given any space–time M without singularities and any event O, there is a natural continuous mapping f of a two-dimensional sphere into any spacelike slice T not containing O. The set of future null geodesics (or the set of past null geodesics) form a two-sphere S2 and the map f sends a point in S2 to the point in T which is the intersection of the corresponding geodesic with T. Considering the f for each point of a world-line W gives us a map F:S2×W→T. The local degree of F at a regular value y in T has the same parity as the number of null geodesics from W to y.

Notizen: The basic properties of q-vertex operators are formulated in the context of the Andrews–Baxter–Forrester (ABF) series, as an example of face interaction models, the q-difference equations satisfied by their correlation functions are derived, and their connection with representation theory established. The q-difference equations of the Kashiwara–Miwa (KM) series are discussed as an example of edge interaction models. Next, the Ising model, the simplest special case of both ABF and KM series, is studied in more detail using the Jordan–Wigner fermions. In particular, all matrix elements of vertex operators are calculated.

Notizen: It is shown how a constraint imposed by the physical relevance of the solutions reduces the dimension of space–time. The C(0) metric given by Nutku is used to describe gravitational shock waves and the trivial case is looked at. It is found that imposing triviality on the solutions reduces the dimension of space–time by one.

Notizen: The existence of the thermodynamic limit of the free energy for the ferromagnetic spin chain connected with the Riemann zeta function is proven.

Notizen: In this article symmetry reductions and exact solutions are presented for the (2+1)-dimensional Davey–Stewartson (DS) system which has the completely integrable DSI and DSII systems as special cases. These symmetry reductions are obtained using the direct method originally developed by Clarkson and Kruskal to study symmetry reductions of the Boussinesq equation which involves no group theoretic techniques. The DS system is reduced directly to ordinary differential equations, with no intermediate step. Using these reductions exact solutions of the DS system including some expressible in terms of the second and fourth Painlevé equations and elementary functions are obtained.

Notizen: A complete basis of nonlocal invariants in quantum gravity theory is built to third order in space–time curvature and matter-field strengths. The nonlocal identities are obtained which reduce this basis for manifolds with dimensionality 2ω〈6. The present results are used in heat-kernel theory, theory of gauge fields and serve as a basis for the model-independent approach to quantum gravity and, in particular, for the study of nonlocal vacuum effects in the gravitational collapse problem.

Notizen: The trace of the heat kernel is expanded in a basis of nonlocal curvature invariants of nth order. The coefficients of this expansion (the nonlocal form factors) are calculated to third order in the curvature inclusive. The early-time and late-time asymptotic behaviors of the trace of the heat kernel are presented with this accuracy. The late-time behavior gives the criterion of analyticity of the effective action in quantum field theory. The latter point is exemplified by deriving the effective action in two dimensions.

Notizen: Space–times admitting a similarity group are considered. Among them, special attention is given to the three-parameter ones. A classification of such space–times is given based on the Bianchi type of the similarity group H3, and the general form of the metric is provided in each case assuming the orbits are non-null.

Notizen: The purpose of this article is to study the unbounded Tomita–Takesaki theory by trace functionals on O*-algebras, and to apply the results to the algebras associated with the canonical commutation relation, pq−qp=−i1 (CCR-algebras).

Notizen: A square-integrable signal of positive energy is transformed into an analytic function in the upper half-plane, on which SL(2,R) acts. It is shown that this analytic function is determined by its scalar products with the discrete family of functions obtained by acting with SL(2,Z) on a cyclic vector, provided that the spin of the representation is less than 3.

Notizen: The relationship between the strength of a differential equation as introduced by Einstein, its Cartan characters, and its Hilbert polynomial is studied. Using the framework of formal theory previous results are extended to nonlinear equations of arbitrary order and to overdetermined systems. The problem of computing the number of arbitrary functions in the general solution is treated. Finally, the effect of gauge symmetries is considered.

Notizen: The high-order Virasoro algebra (HOVA) is deformed on a quantum plane C2||0 in a formalism reducible to the ordinary HOVA when q→1. After introducing the "associator,'' the Jacobi identity and central extensions are also investigated. The q-deformed HOVA possesses a Hopf algebra structure within the framework of q-product algebra. The W∞-algebra expressed in terms of linear combinations of HOVA can thus be q-deformed and possess a Hopf algebra structure.

Notizen: The generalized string-flip model for quantum scattering in a system of two N-body clusters is under consideration. The extra channel interpreted as the quark compound bag is considered which generates energy-dependent integral boundary conditions in the effective boundary problem. It is shown that the standard string-flip model can be generalized for N identical particles in a cluster. The effective Hamiltonian and effective integral equations for the partial s-wave S matrix are proven to be form invariant with respect to N. The effective configuration space is shown to be two-dimensional for every N and its geometry for different N is discussed. Results of the numerical calculations of s-wave scattering phases, inelasticity parameters, and scattering lengths for N=2 (meson–meson scattering) and N=3 (baryon–baryon scattering) are presented. The resonance influence of the extra channel is investigated. Generalizations including spin–spin interaction and quark color group SU(n) are also presented.

Notizen: A nonhomogeneous system of partial differential equations of first order involving two dependent and two independent variables is considered. The introduction of suitable differential constraint equations permits to develop an approach to determining exact solutions to the model in point based on the use of the hodograph transformation. Within the present theoretical framework the governing systems of rate-type materials and flows in fluid-filled elastic tubes are investigated.

Notizen: The explicit form of the Poisson kernel for the strip Tβ={z∈C:0〈Im z〈β} is used to derive some conditions for a state ω on a given C*-algebra dynamical system (A,αt) to be a Kubo–Martin–Schwinger (KMS) state. Reflection positivity and generalized periodicity of the Euclidean Green functions corresponding to ω are established and used for an analytic continuation to real time. Reflection positivity is also used for the construction of a cyclic and faithful representation of (A,αt) on some Hilbert space. A sufficient condition for the identification of the constructed dynamics with the modular group of a von Neumann algebra generated by the representation is formulated in terms of the Euclidean Green functions.

Notizen: Random walks are used to study diffusion on anyspace. Anyspace is characterized by coordinate ξ with ξN=0 and statistics ξξ'=e2πi/Nξ'ξ between independent copies. Anyonic integration and anyonic Dirac δ functions are introduced, and reduced to familiar results for supersymmetry when N=2. These ingredients are then used to formulate and solve the resulting anyonic diffusion equation.

Notizen: It is shown how the wavelet transform may be used to compute for a function s the symbol s(A) for any (not necessarily) self-adjoint operator A whose spectrum is contained in the upper half plane. For self-adjoint operators it is shown that this functional calculus coincides with the usual one. In particular it is shown how the exponential eitA can be written in terms of the resolvent Rz=(A−z)−1 of A as follows: eitA=(1/c) ∫0∞da an−2∫−∞+∞ dbgˆ¯ (at)eitbRb−ian(A), with c=−2iπ×∫0∞(dω/ω) (−iω)n−1gˆ¯(ω)e−ω, and n∈N, and the integral is understood as the Cesaro limit. This shows explicitly how the behavior for large t is determined by the behavior of Rz at @FIz(approximately-equal-to)1/t.

Notizen: The analysis of the Kac–Moody "like'' algebra Lˆ2( g) on the torus is performed. It will be seen that the root systems construction leading to a Cartan matrix is not possible. Different twists of Lˆ2λ( g) are discussed. Connections with known results are performed.

Notizen: Parastatistics are reformulated herein in terms of Lie-supertriple systems. In this way, various new kinds of parastatistics discovered recently by Palev in addition to the standard one are reproduced. Also, bosonic and fermionic operators may not necessarily commute with each other.

Notizen: In a previous article, it was shown that a soluble model can be constructed for the the description of a decaying system in analogy to the Lee–Friedrichs model of complex quantum theory. It is shown here that this model also provides a soluble scattering theory, and therefore constitutes a model for a decay-scattering system. Generalized second resolvent equations are obtained for quaternionic scattering theory. It is shown explicitly for this model, in accordance with a general theorem of Adler, that the scattering matrix is complex subalgebra valued. It is also shown that the method of Adler, using an effective optical potential in the complex sector to describe the effect of the quaternionic interactions, is equivalent to the general method of Green's functions described here.

Notizen: (2+1)-dimensional models of relativistic particles with the action depending arbitrarily on the world-trajectory curvature and torsion are investigated. A special class of models, described by the action with a maximal symmetry allowing only spin internal degrees of freedom, is singled out. A classical analysis of the systems from this special class is carried out, and the quantization procedure for them is described. Within this class, tachyon-free models are pointed out and the systems having classical and quantum spectra with only massive spin states (whose number in the quantum case may be both finite and infinite) are considered as concrete examples of such models.

Notizen: In the framework of symmetry scattering, SU(2,2)-invariant differential equations on the homogeneous space X=SU(2,2)/S(U(2)⊗U(2)) are studied. The radial Schrödinger equation for a family of one or two dimensional potentials or for two particles arise. From the asymptotic behavior of the solutions exact partial wave scattering amplitudes are derived.

Notizen: Analytical solutions of the Rankine–Hugoniot conditions for a radiating gas are presented both for shocks and subshocks. The case of Synge gas is studied in detail. In order to study subshocks, radiation is described by the moment equations closed with a variable Eddington factor.

Notizen: A general class of n-particle difference Calogero–Moser systems with elliptic potentials is introduced. Besides the step size and two periods, the Hamiltonian depends on nine coupling constants. We prove the quantum integrability of the model for n=2 and present partial results for n≥ 3. In degenerate cases (rational, hyperbolic, or trigonometric limit), the integrability follows for arbitrary particle number from previous work connected with the multivariable q-polynomials of Koornwinder and Macdonald. Liouville integrability of the corresponding classical systems follows as a corollary. Limit transitions lead to various well-known models such as the nonrelativistic Calogero–Moser systems associated with classical root systems and the relativistic Calogero–Moser system.

Notizen: In this article, a system of finite-dimensional involutive functions is presented and proven to be integrable in the Liouville sense. By using the nonlinearization method, the C. Neumann system associated with the modified Korteweg–de Vries (mKdV) hierarchy is obtained. Thus, the C. Neumann system is shown to be completely integrable via a gauge transformation between it and an integrable Hamiltonian system. Finally, the solution of a stationary mKdV equation and the involutive solutions of the mKdV hierarchy are secured. As two examples, the involutive solutions are given for the mKdV equation: vt+1/4vxxx−3/2v2vx=0 and the 5th mKdV equation vt−1/16vxxxxx+5/8v2vxxx +5/2vvxvxx +5/8v3x−3/40v4vx=0.

Notizen: It is conjectured that W gravity can be interpreted as the gauge theory of φ diffeomorphisms in the space of dimensionally reduced D=2+2 SU*(∞) Yang–Mills instantons. These φ diffeomorphisms preserve a volume-three form and are those that furnish the correspondence between the dimensionally reduced Plebanski equation and the KP equation in (1+2) dimensions. A supersymmetric extension furnishes super-W gravity. The super-Plebanski equation generates self-dual complexified super gravitational backgrounds (SDSG) in terms of the super-Plebanski second heavenly form. Since the latter equation yields N=1, D=4 SDSG complexified backgrounds associated with the complexified-cotangent space of the Riemannian surface, (T*Σ)c, required in the formulation of SU*(∞) complexified Self-Dual Yang-Mills theory, (SDYM); it naturally follows that the recently constructed D=2+2 N=4 SDSYM theory, as the consistent background of the open N=2 superstring, can be embedded into the N=1 SU*(∞) complexified self-dual-super-Yang–Mills (SDSYM) in D=3+3 dimensions. This is achieved after using a generalization of self-duality for D(approximately-greater-than)4. Finally, the plausible relationship between the geometry of N=2 strings and the moduli of SU*(∞) complexified SDSYM in 3+3 dimensions is indicated.

Notizen: An algebraically special solution of the Regge–Wheeler–Zerilli equation that has not been noticed is examined. This solution is proved to be related to Chandrasekhar's solution but has a simpler analytical expression.

Notizen: The vacuum fluctuations for an impulsive spherical gravitational wave due to the snapping of a "rotating'' cosmic string are calculated herein. This is complementary to the previous calculation due to a snapping string, which had the null result. Although the mathematical expressions are different at the intermediate steps, the same null result is found.

Notizen: Gravitational instantons are considered important in analyzing such quantum gravitational effects as the evaporation and condensation of black holes and the stability of the vacuum at finite temperature. Unfortunately, not every positive definite solution of the field equations is derivable from the Lorentzian regime by analytic continuation. As a first step in the investigation of these objects, it is proven that all Petrov-type D+D− spaces admit an Abelian, orthogonally transitive, two dimensional group of isometries. This is accomplished by using a Euclidean version of the Newman–Penrose formalism to classify the spaces according to the twist and expansion of their Debever–Penrose vectors. In each class one can then infer the existence of Killing spinors, vectors, and tensors required to yield the result.

Notizen: It is shown that in a type-D vacuum space–time with cosmological constant, the maximal spin weight components of the Weyl spinor perturbations, which obey separable decoupled equations, satisfy certain differential relations that are equivalent to the Teukolsky–Starobinsky identities fulfilled by the separated functions. It is also shown that the real and imaginary parts of the Starobinsky constants can be obtained from these relations.

Notizen: The duality that exists between the two subgroups SU(1,1) and O(5) of Sp(5,R) to construct basis states for the five-dimensional harmonic oscillator which simultaneously reduce the Sp(5,R)&supuline;U(5)&supuline;O(5)&supuline;SO(3) and Sp(5,R)&supuline; SU(1,1)&supuline;U(1) subgroup chains is used. It is shown that the vector-coherent-state wave functions of the fundamental five-dimensional SO(5) irrep [1,0] realize the traceless bosons introduced by Lohe and Hurst to classify the irreps of the orthogonal groups and employed in Chacon, Moshinsky, and Sharp's construction of a basis for the five-dimensional harmonic oscillator. Moreover, it is shown that VCS theory provides a simple mechanism for constructing matrix elements of the traceless boson operators. These matrix elements are used to extend the VCS representations of SO(5) in an SO(3) basis, given in a previous paper, to irreps of U(5) in an SO(5)&supuline; SO(3) basis. The extension to U(6)&supuline;U(5)&supuline;SO(5)&supuline;SO(3) is also given.

Notizen: A nonprincipal value prescription is used to define the spurious singularities of Yang–Mills theory in the temporal gauge. Typical one-loop dimensionally regularized temporal-gauge integrals in the prescription are explicitly calculated, and a regularization for the spurious gauge divergences is introduced. The divergent part of the one-loop self-energy is shown to be local and has the same form as that in the spatial axial gauge with the principal-value prescription. The renormalization of the theory is also briefly mentioned.

Notizen: The conformal group is added to the gauge group of a model of elementary particles based on the fiber bundle formalism. The inertial mass of a particle is interpreted as a manifestation of its interaction with the gauge bosons associated with the generators of the translation and special conformal subgroups. The generation of mass by this mechanism (together with the fact that the Higgs field is not necessarily required to effect bundle reduction) makes the Higgs and the Yukawa terms in the Lagrangian unnecessary: the Lagrangian then consists only of a Yang–Mills term and a covariantly free matter field term. A particular choice of gauge reproduces the usual mass terms for both fermions and gauge bosons. The "no-go theorem'' is not violated by the construction. The Poincaré generators commute with the internal symmetry generators after bundle reduction, and there is no mass splitting within symmetry multiplets. However, the left-handed/right-handed asymmetry allows the neutrino to remain massless; the definition of matter fields allows the up and down quarks to acquire different mass couplings; and the gauge bosons have different mass couplings determined by the inner product on the Lie algebra of the broken symmetry subgroup. The mass ratios of the gauge bosons—at tree level—are precisely those predicted by the Standard Model.

Notizen: In this paper the two parameter deformation of Virasoro algebra is derived. Two parameter deformation of central charge is also obtained. The operator product expansion for (p,q)-deformed Virasoro algebra is derived.

Notizen: In this paper the quantum Z3-graded space is discussed and its differential calculus is investigated and the quantum matrices in quantum Z3-graded space are obtained.

Notizen: The osp(1||2) algebra is first realized through one boson and two fermion pairs of creation annihilation operators and then both osp(1||2) and osp(3||2) are realized in terms of three boson and two fermion pairs. All these realizations are reducible, and the reduced states are labeled by the total occupation number.

Notizen: In this article Rosso's formula for the universal R matrix of Uqsl(n) algebras in case of Uqsl(n,m) quantum superalgebras is generalized.

Notizen: Coherent states on the m-sheeted complex plane are introduced and properties like overcompleteness and resolution of the identity are studied. Operators am+, am which create and annihilate clusters of m particles are considered and it is shown that the properties of our coherent states with respect to them are analogous to the properties of the ordinary (Glauber) coherent states with respect to a+, a. An extended Bargmann representation in the m-sheeted complex plane and P and Q representations with respect to our coherent states, are studied. Applications of this formalism in the study of Hamiltonians that describe m-particle clustering are also considered.

Notizen: Second harmonic generation, an important phenomenon in nonlinear optics, is modeled in this work. The model is derived from a nonlinear system of Maxwell's equations, which overcomes the known shortcomings of some commonly used models in the literature. Existence and uniqueness of solutions are established by a combination of a variational approach and the contraction mapping principle. Some numerical results are also presented.

Notizen: The eigenvalue problem for the radial Schrödinger equation with an "almost'' Coulomb potential is considered. This problem provides the simplest example of a system whose classical trajectories have singularities. Thus the standard semiclassical quantization procedure (in the sense of Einstein–Brillouin–Keller–Maslov) cannot be applied straightforwardly to this situation. The equation under consideration has two transition points on the half axis 0〈x〈∞: a regular singular point at the origin and a turning point for some x0(approximately-greater-than)0; these points coalesce at low energy levels. The well-known comparison equation method provides uniform asymptotics for equations of this kind, but has the following shortcomings: it does not appeal to the corresponding classical mechanical problem and the formulas for the eigenvalues and eigenfunctions contain phase integrals which are not analytic with respect to the parameter characterizing the closeness of the transition points. In the present article we derive new formulas for the eigenfunctions in the form of inverse Fourier transforms of rapidly oscillating exponentials multiplied by some powers of x, together with simple formulas for the eigenvalues. These formulas are directly connected with the classical trajectories and do not have the shortcomings of the comparison equation method, i.e., all the functions entering the asymptotic expansions are analytic in x and energy. As a by-product, an asymptotic expansion of integrals having two stationary phase points which coalesce for some value of the parameter and tend to infinity when the parameter tends to zero is obtained.

Notizen: A difficult and long-standing problem in mathematical physics concerns the determination of the value of f(∞) from the asymptotic series for f(x) about x=0. In the past the approach has been to convert the asymptotic series to a sequence of Padé approximants {Pnn(x)} and then to evaluate these approximants at x=∞. Unfortunately, for most physical applications the sequence {Pnn(∞)} is slowly converging and does not usually give very accurate results. In this paper the results of extensive numerical studies for a large class of functions f(x) associated with strong-coupling lattice approximations are reported. It is conjectured that for large n, Pnn(∞)∼f(∞)+B/ln n. A numerical fit to this asymptotic behavior gives an accurate extrapolation to the value of f(∞).

Notizen: The thermodynamics of vortices in the critically coupled Abelian Higgs model, defined on the plane, are investigated by placing N vortices in a region of the plane with periodic boundary conditions: a torus. It is noted that the moduli space for N vortices, which is the same as that of N indistinguishable points on a torus, fibrates into a CPN−1 bundle over the Jacobi manifold of the torus. The volume of the moduli space is a product of the area of the base of this bundle and the volume of the fiber. These two values are determined by considering two 2-surfaces in the bundle corresponding to a rigid motion of a vortex configuration, and a motion around a fixed center of mass. The partition function for the vortices is proportional to the volume of the moduli space, and the equation of state for the vortices is P(A−4π N)=NT in the thermodynamic limit, where P is the pressure, A the area of the region of the plane occupied by the vortices, and T the temperature. There is no phase transition.

Notizen: The time independent Bateman model which describes the damped harmonic oscillator coupled to its dual is studied using the path integral approach. The related propagator is calculated by means of the matrix representation.

Notizen: A formulation of the complete dynamics of electrons and nuclei is presented. The dynamical equations are derived using the time-dependent variational principle (TDVP). The approximate electronic state vectors are antisymmetrized geminal power (AGP) states parameterized as projected coherent states, while the nuclei are treated as classical point particles. This leads to a formulation of time-dependent AGP theory that generalizes time-dependent Hartree–Fock (TDHF) theory and explicitly includes the dynamics of the nuclei. The linear approximation to the evolution equations (the classical harmonic approximation) which corresponds to a generalized random phase approximation (RPA) based on an AGP electronic reference state and which explicitly includes the dynamics of the nuclei, is studied and presented in this paper. The equations are formulated in terms of the primitive nonorthogonal electronic atomic basis thus avoiding any transformation to orthonormal molecular orbitals during the evolution.

Notizen: An ansatz for elliptic Baker–Akhiezer functions is used to find new solutions for various spectral problems—the Sturm–Liouville problem with four and five-gap Lamé potentials and two third-order problems. One of the third-order problems is the classical Halphen equation with a spectral parameter. The eigenfunctions are used to construct elliptic solutions for integrable cases of a generalized Hènon–Heiles system.

Notizen: A study of the existence of some integrable systems with nonlinear constants of motion is presented using the approach of the theory of generalized (dynamical or hidden) symmetries. Two Lagrangians are considered, both obtained by modifying the Toda Lagrangian. First a two-particle system is studied and then the results are generalized to a three-particle system. It is shown that in both cases the Lagrangians possess nonlinear constants of motion in involution and, thus, they are integrable.

Notizen: Chaos in adiabatic Hamiltonian systems is a recent discovery and a pervasive phenomenon in physics. In this work, a geometric criterion is discussed based on the theory of action from classical mechanics to detect the existence of Smale horseshoe chaos in adiabatic systems. It is used to show that generic adiabatic planar Hamiltonian systems exhibit stochastic dynamics in large regions of phase space. To illustrate the method, results are obtained for three problems concerning relativistic particle dynamics, fluid mechanics, and passage through resonance, results which either could not be obtained with existing methods, or which were difficult and analytically impractical to obtain with them.

Notizen: The Lax formalism, as described by Oevel et al. and in an earlier and more fundamental form by Semenov, Kostant, Symes, and Adler, can easily be generalized to the case where anticommuting variables are involved, the so-called supercase. In this article this super-Lax formalism is applied to the well-known associative superalgebra G=Mat(m,n,Λ). Subspaces of G to which the super-Poisson structures can be restricted arise in a natural way. Taking L in one of these subspaces formally leads to superextensions of the hierarchy of nonrelativistic Toda lattices. In the simplest case, where only nearest-neighbor interaction is involved, the equations are explicitly solved. Furthermore, the relevant two super-Hamiltonian structures are explicitly calculated. Finally a superextension of the relativistic Toda lattice with a super-Hamiltonian structure is described herein.

Notizen: This paper constructs the geometrically natural objects which are associated with any projection tensor field on a manifold with any affine connection. The approaches to projection tensor fields which have been used in general relativity and related theories assume normal projection tensors of codimension one and connections which are metric compatible and torsion-free. These assumptions fail for projections onto lightlike curves or surfaces and other situations where degenerate metrics occur as well as projections onto two-surfaces and projections onto space–time in the higher dimensional manifolds of unified field theories. This paper removes these restrictive assumptions. One key idea is to define two different "extrinsic curvature tensors'' which become equal for normal projections. In addition, a new family of geometrical tensors is introduced: the cross-projected curvature tensors. In terms of these objects, projection decompositions of covariant derivatives, the full Riemann curvature tensor and the Bianchi identities are obtained and applied to perfect fluids, timelike curve congruences, string congruences, and the familiar 3+1 analysis of the spacelike initial value problem of general relativity.

Notizen: The far-infrared transmission of polycrystalline C60 and C70 compacts has been measured from 3 to 330 cm−1 as a function of temperature. Both intrinsic and impurity-induced absorption bands are identified in these samples. The low temperature phase of C60 is observed to have two infrared active translational modes at 40.9 and 54.7 cm−1. Samples of C60 exposed to air before cooling to low temperatures contain several additional infrared bands which have been identified with adsorbed H2O vapor. A large isotope shift is observed for some of the bands when H2O is replaced by D2O, consistent with rotational or librational behavior. For C70 one strong intrinsic band is centered at 21 cm−1 and four much weaker bands occur at 28, 32, 52, and 64 cm−1. When doped with H2O vapor, C70 also produces several strong H2O impurity bands, some of which show isotopic shifts. The temperature dependence of five intramolecular C70 modes in the frequency range from 200 to 330 cm−1 is also reported.

Notizen: The B KVV and Cl LVV normal and resonance Auger electron spectra in gaseous BCl3 have been observed with use of tunable photon beam from synchrotron radiation. The spectrum excited by photons with energy above the B K and the Cl L2,3 thresholds shows preferentially Cl LVV normal Auger bands. The pure B KVV normal Auger spectrum is obtained using the photons with energy between the B K threshold and the Cl L pre-edge excitation threshold. The spectator and participant Auger processes are observed at the B 1s→2a2‘(2pπB) and 1s→4e'(σBCl*) resonances. The spectator Auger processes are also observed in the Cl L2,3 excitation region, while the participant Auger processes are not significant in this region. The observed spectra are discussed with the aid of the one-electron properties of the valence orbitals.

Notizen: The absolute transition probabilities, more commonly known as absolute generalized oscillator strengths (GOSs), have been determined for selected electronic excitations from the C 1s or Cl 2p shell to the lowest-lying σ* orbitals for chlorofluoromethanes CF4−nCln (n=1–4) using angle-resolved electron energy loss spectroscopy at 2.5 keV impact energy. The GOS profiles of these inner-shell transitions were found to have shapes characteristic of predominant dipole-allowed transitions. Furthermore, the proportions of dipole-allowed components of these GOS profiles appeared to increase with successive chlorination for these molecules. In particular, the GOS profile of the C 1s→σC–Cl* [lowest unoccupied molecular orbital (LUMO)] transition of CF3Cl was found to contain relatively more intense higher momentum-transfer (K) components than those of the corresponding features in CF2Cl2 and CFCl3 (and CCl4). The GOS profiles for the Cl 2p3/2,1/2→σC–Cl* transitions of CF3Cl were found to contain a well-defined secondary maximum at K2∼1.2 a.u., characteristic of predominant nondipole interaction, in addition to the primary dipole-dominated peak at zero momentum transfer. Within the present statistics, our GOS measurements have not, however, revealed any discernible difference between the Cl 2p3/2→11a1 and Cl 2p1/2→11a1 features that could be attributed to spin effects. Furthermore, the dipole-dominated GOS profile was found to become more concentrated in the lower momentum transfer region for the Cl 2p3/2→σC–Cl* transition in CCl4 than that in CFCl3. The present work illustrates the possibilities of atomic-site-specific investigation of the excited states by means of GOS measurements of electronic excitations from localized inner-shell initial states.

Notizen: A strong IR fluorescence is observed following the excitation of O3 at the ν1+ν3 mode in xenon matrices. The emission frequency is characteristic of the 2ν3 to ν3 transition. The rise time and the decay time are both faster than a few nanoseconds. The excitation spectra are similar to the line profile of the ν1+ν3 absorption at 5 K. A spectral analysis of the fluorescence shows that no energy transfer occurs during the relaxation between molecules in the two trapping sites. The most perturbed molecules (high frequency component of the absorptions) seem to have a faster relaxation, exhibiting a stronger temperature dependence. The possible intramolecular vibrational cascades are discussed considering the literature data about vibrational relaxation of matrix isolated small polyatomic molecules in their ground electronic state.

Notizen: Direct connection between collisional Raman cross sections and state-to-state rotational ones permits, within the sudden approximation, to evidence drastic decouplings from isotropic to anisotropic lines. These decouplings are consistent with the results obtained by using the strong collision model. Convenient energy corrections to the sudden approximation are used for N2 to calculate the resulting effects on the isotropic and anisotropic Q-branch profiles in a large density range (several hundred bars). The comparison of the calculations with experimental coherent anti-Stokes Raman scattering (CARS) and stimulated Raman (SRS) spectra of nitrogen exhibits a good agreement. Such effects could have applications in optical diagnostics.

Notizen: The intensity distributions in the overtones of resonance Raman spectra for I2 in liquid CCl4 and Xe are presented for several excitation energies in the bound part of the B 3Π0u+ state. In liquid CCl4, the decrease in intensity with v‘ is monotonous and for all excitation energies similar to that of a free wave packet in the gas phase. A dephasing time shorter than the round trip time of 300 fs and a dephasing process which occurs beyond 3 A(ring) is inferred, in accordance with predissociation to the a or a' states earlier proposed. The intensity distributions in liquid Xe contain a fast decay and a plateau and the strength of both contributions varies with excitation energy. For low v' in the B state a predissociation to the B‘ 1Π1u state within 40 fs in the range of internuclear distances between 2.78 and 2.85 A(ring) is observed which is less pronounced for large v'. The wave packet moves undistorted beyond the crossing with the B‘ state up to 3 A(ring).

Notizen: The relaxation of an I=3/2 spin system in an anisotropic environment characterized by a finite residual quadrupolar splitting ωq is modeled by analytically solving for the density operator from Redfield's relaxation theory. The resulting equations are cast into the multipole basis in order to describe the tensorial components of the spin density matrix. Included in the relaxation matrix are off-diagonal elements J1 and J2, which account for anisotropic systems with ωq values less than the width of the resonant line. With the Wigner rotation matrices simulating hard pulses, the response to an arbitrary pulse sequence can be determined. An analytical expression for the response to the double quantum filtered (DQF) pulse sequence (π/2)−(τ/2)−π−(τ/2)−θ−δ−θ−AQ for θ=π/2 is presented, showing explicitly the formation of a second rank tensor owing only to the presence of a finite ωq. This second rank tensor displays asymptotic behavior when the (reduced) quadrupole splitting is equal to either of the off-diagonal spectral densities J2 and J1. Line shape simulations for ωq values of less than a linewidth reproduce the general features of some recently reported 23Na DQF line shapes from biological systems. Distinct relaxation dynamics govern each of the tensorial components of the resonant signal revealing the influence of the experimental variables on the line shape.

Notizen: We present a new direct ab initio dynamics methodology for calculating thermal rate constants from density functional theory (DFT). Dynamical theory is based on a full variational transition state theory plus multidimensional semiclassical tunneling approximations. We have applied this approach to the CH3+H2→CH4+H abstraction reaction using the BH&H-LYP method which is the combination of the hybrid Becke's half-and-half (BH&H) method for nonlocal exchange and Lee–Yang–Parr (LYP) functional for nonlocal correlation. The 6-311G(d,p) basis set was used in these calculations. To obtain quantitative results, the classical potential energy along the minimum energy path (MEP) was corrected either by scaling to match a more accurate ab initio results for the barrier heights or by carrying out single point calculations at selected points along the MEP at a more accurate level of ab initio molecular orbital (MO) theory. By comparing with our previous QCISD results and experimental rate constants, we found that DFT particular the BH&H-LYP method can provide sufficient accurate potential energy surface information for rate calculations for this system. The present direct DFT dynamics method can be used for reactive dynamics studies of reactions involving large polyatomic molecules from first principles. More work however is still needed to test the accuracy of DFT methods for such calculations.

Notizen: The collisional removal of O2 molecules prepared in selected vibrational levels of the A 3Σ+u state is studied using a two-laser double-resonance technique. The output of the first laser excites the O2 to A 3Σ+u, ν=6, 7, or 9, and the ultraviolet output of the second laser monitors these levels via resonance-enhanced ionization through either the ν=5 level of the C 3Πg Rydberg state, or the valence state or states tentatively associated with the 5 3Πg state. The temporal evolution of the A 3Σ+u state vibrational level is observed by scanning the time delay between the two pulsed lasers. Collisional removal rate constants are obtained for A 3Σ+u, ν=7 and 9 colliding with O2, N2, CO2, Ar, and He; and for ν=6 colliding with O2 and N2. We find the collisional removal of the A 3Σ+u state to be fast (k≥10−11 cm3 s−1) for all colliders studied. The rate constants vary by about an order of magnitude from the fastest collisional deactivator, CO2 to the slowest studied, the rare gases Ar and He. The rate constants for the atmospherically important colliders O2 and N2 are similar in magnitude and suggest that N2 collisions will dominate the removal rate in the Earth's atmosphere.

Notizen: Results of crossed-molecular beam inelastic scattering experiments from two levels of 1Au (S1) trans-glyoxal in collisions with H2 (Ec.m.=80 meV, 650 cm−1) and He (Ec.m.=95 meV, 770 cm−1) are reported. Relative inelastic scattering cross sections with quantitative error bars are obtained. S1←S0 laser excitation was used to prepare either the 00 level or the 72 level (εvib=466 cm−1) with the high rotational selection of K'=0 and J'=0–10. The final high levels populated by rotationally and rovibrationally inelastic scattering were monitored by dispersed fluorescence with K' state resolution. Fluorescence from only those molecules involved in inelastic scattering was obtained from the difference signal of spectra with the target gas beam (H2 or He) ON and OFF. Those dispersed fluorescence spectra were analyzed with a computer fitting procedure to extract 52 relative state-to-state cross sections for scattering from the (00, K'=0) level and 84 for the (72, K'=0) level. The cross sections have been compared quantitatively with the results of the three-dimensional quantal scattering calculations of Clary, Dateo, Kroes, and Rettschnick. The agreement between the experimental and theoretical cross sections is nearly quantitative for both target gases and both initial states. Disagreements between experiment and theory occur only in the details of K' distributions within the rovibrational channels. The vibrationally inelastic scattering is extremely selective among the many accessible channels. The cross sections for Δυ7=±1 changes in the lowest frequency mode ν7' = 233 cm−1, a CHO–CHO torsion, exceed those involving the other 11 modes by at least an order of magnitude. As judged by the relative magnitudes of rovibrational and rotational cross sections, rovibrational scattering is surprisingly efficient. In fact, when comparing cross sections for transferring energy by (T→R) vs (T→R,V) with similar ΔE, rovibrational cross sections are the greater in numerous examples.

Notizen: The Ne(3P00,2)+Xe+(5p5 2P01/2,3/2) excitation–transfer reaction has been studied by observing ultraviolet and visible emissions from Xe+* in a Ne flowing afterglow. The relative contribution of Xe+(2P03/2) and Xe+(2P01/2) to the excitation of Xe+* was examined by changing the [Xe+(2P01/2)]/[Xe+(2P03/2)] ratio with the addition of CH4 as a remover of the upper spin–orbit component. Since the intensity distribution of Xe+* lines was independent of the [Xe+(2P01/2)]/[Xe+(2P03/2)] ratio, it was concluded that the contribution of the Ne(3P00,2)+Xe+(2P01/2) reaction was insignificant. The Ne(3P00,2)+Xe+(2P03/2) reaction initially populates nine Xe+(6p,6p',7s,6) levels in the 13.86–16.60 eV range. The favored product levels are 6p' 2D03/2,5/2 and 7s 4P5/2 in the 16.36–16.43 eV range and 6p 4P05/2 at 13.88 eV, which are 0.2–0.3 and 2.7 eV below the entrance Ne(3P02)+Xe+(2P03/2) channel, respectively. The former near-resonant levels are excited by either direct curve crossings between attractive entrance potentials and flat exit ones or multiple curve crossings through a strongly attractive Ne−+Xe2+ ionic potential, while the latter nonresonant level is probably formed through the Ne−+Xe2+ ionic potential.

Notizen: The water molecule, rotationally state selected in the third and fourth OH stretching overtone (||04〉−, ||05〉−) and stretch–bend combination (||04−2〉) levels, has been photodissociated via the A˜ state at λ(approximately-equal-to)282 nm. The photofragment rotational state distributions, determined by OH(A–X) laser induced fluorescence (LIF), differ from those reported previously by Andresen and co-workers, in which water was initially prepared in the ||01〉− level and photodissociated at 193 nm, and from those by Crim and co-workers, in which H2O was photodissociated via the ||04〉− level at wavelengths shorter than 282 nm. These differences become more pronounced with increasing angular momentum in the parent water molecule and with an increasing number of quanta in the intermediate OH stretching overtone state. The Franck–Condon theory of Balint-Kurti, previously employed successfully to account for the product state distributions arising from the 193 nm photodissociation of H2O||01〉−, qualitatively reproduces the trends observed in the present study if it is assumed that dissociation occurs preferentially from extended RH-OH configurations of the ||04〉− and ||05〉− overtones. The product OH state distributions are thus shown to be sensitive indicators of the bending and rotational motions of H2O(X˜) in the wide amplitude stretching region of the ground state surface.

Notizen: Crossed molecular beam studies of rotationally and rovibrationally inelastic scattering of S1 glyoxal from H2 and He have been extended to one additional light gas, D2, and to two heavy gases of identical masses, Kr and cyclohexane, C6H12 (84 amu). Laser excitation was used to prepare glyoxal in its 00 level with K'=0 and 0≤J'≤10. Dispersed fluorescence detection was used to observe the final K' and vibrational states of the inelastic scattering. The relative scattering cross sections for D2 and He collisions are identical to within experimental error and differ substantially from those of H2. The Kr and C6H12 cross sections are also a matched set. These results show that the competition among the approximately 25 observable scattering channels is far more sensitive to the reduced mass of the collision than to variation in the intermolecular potential or even the internal structure of the target gas. An overview of rotational and rovibrational scattering in glyoxal from four vibrational levels (00, 72, 51, and 81) extending to εvib=735 cm−1 is used to uncover generalities and insights about the energy transfer. For all four initial levels the vibrational state changes are highly selective. The detectable channels are always limited to ±1 quantum change in only one of the 12 modes, specifically ν7' = 233 cm1, the lowest frequency mode. The cross sections for vibrational state change are surprisingly large relative to those for pure rotationally inelastic scattering.Many cases occur with the light target gases where the ΔK resolved cross sections for rovibrational interactions are nearly equal to those for pure rotationally inelastic scattering with equivalent energy transfer ΔE. Scattering from 72, K'=0 glyoxal contains examples with both H2 and He where the rovibrational cross sections actually exceed those for rotational scattering. Plots of the entire set of cross sections [rotational (ΔK) plus rovibrational (Δυ7=+1)] against ΔE are essentially superimposible for He scattering from 00, 51, and 81 glyoxal. In contrast, scattering from 72 glyoxal with the active mode initially excited is distinctive. For all initial levels, the distribution of cross sections for different ΔK within rotational channels differs from that within rovibrational channels. It is further seen in these comparisons that the change in angular momentum ΔK rather than ΔE controls the relative sizes of cross sections within these channels. The theoretical predictions of Clary, Kroes, and Rettschnick are in accord with these trends and distinctions, agreeing even on some rather subtle points.

Notizen: By saturating specific rovibrational transitions in (HF)2 using a high-resolution, single-mode color center laser, the vibrational transition moments for two F–H stretches have been measured regardless of the internal state distribution of the clusters in the molecular beam. Details of the experimental procedure and data analysis are presented. A slight enhancement (∼10%) of the transition moment over the noncomplexed monomer value was observed for the proton acceptor. The proton donor transition moment was substantially enhanced by ∼100% as a result of hydrogen bonding. These results are in excellent agreement with recent theoretical studies. This method is shown to serve as a useful gauge for estimating hydrogen bond interactions within molecular clusters.

Notizen: The optical potential method initially proposed by Jolicard and Austin in the context of the stabilization method is reviewed here and used with the accurate and the efficient discrete variable representation method to obtain the energies and the widths (respectively, the real and the imaginary part of the resonance energies) of rovibrational predissociated states of diatomic molecules. In this method the resonances for an n coupled states problem are obtained by a direct diagonalization of the Hamiltonian matrix in the diabatic representation. This Hamiltonian matrix is directly evaluated in the discrete variable representation using the Fourier grid Hamiltonian method proposed by Marston and Balint-Kurti. In this approach, two optical potentials are tested and used here to impose the asymptotic behaviors of the boundary conditions which are compatible with the resonance states. The method is exemplified for the B 1Σ+–D'1 Σ+ Rydberg–valence predissociating interaction in the CO molecule.

Notizen: The viscosity dependence of the photoisomerization of trans-stilbene in compressed liquid ethanol shows deviations from a simple power law description in the viscosity range from 1 to 4 mPa s. Corresponding deviations are observed in the solvents methanol, n-propanol, and n-butanol. This behavior is attributed to a competition between solvent relaxation and barrier crossing in the S1 state of trans-stilbene. The relative time scales of barrier crossing and solvent relaxation change as the pressure increases, because the dielectric relaxation rate of the solvent decreases more rapidly with increasing viscosity than the barrier crossing rate. Consequently, the reaction takes place in an increasingly retarded solvent environment which no longer relaxes completely around the changing charge distribution of the solute along its reaction path, giving rise to "dielectric friction.'' In contrast to trans-stilbene, the corresponding reaction of diphenylbutadiene in n-alkanols shows a much weaker sensitivity to solute-solvent interaction and, consequently, a simple inverse viscosity dependence of the photoisomerization rate is observed in all alkanols such as described by the Kramers–Smoluchowski theory. This significant difference is probably caused by smaller sudden polarization effects along the reaction path in diphenylbutadiene. The observed dependence of the trans-stilbene barrier crossing rate on pressure is compared either to a model with density dependent effective barrier height, or to a simple continuum model of the frequency dependence of the dielectric friction in the limit of weak coupling. Neither model works well unless a very strong viscosity dependence of the dielectric relaxation time of the solvent (τD∝η10) is employed to obtain agreement with the observed viscosity dependence of the barrier crossing rate.

Notizen: Experimental studies have shown that the steric effect in chemical reactions can decrease (e.g., for Ba+N2O→BaO*+N2) or increase [e.g., for Ca(1D2)+CH3F→CaF*+CH3] with increasing translational energy. Decreasing (negative) energy dependences have successfully been modeled with the angle dependent line of centers model. We present a classical model in which a positive energy dependence of the steric effect is explained by an isotropic, attractive long range potential. In this "trapping'' model we assume the reaction—apart from a cone of nonreaction at one side of the molecule—to be barrierless. This model shows that a positive energy dependence of the steric effect is not indicative of reorientation of the molecule, as has been suggested in the literature. Rather, the positive or negative energy dependence of the steric effect is shown to correlate with the absence or presence of a barrier to reaction and an attractive or repulsive long range potential. For the reorientation effects which occur in the case of anisotropic potentials, we consider the application of the standard quasiclassical trajectory (QCT) method and we introduce a modified QCT method. We argue that the latter is more suitable for the computation of the orientation dependent reactive cross section.

Notizen: Large basis set ab initio calculations have been carried out for a dense grid of points on the He3 potential energy surface. Three-body contributions were extracted at every point, and a number of concise functional representations for the three-body potential surface were then examined. Three-body multipolar dispersion terms and other radial and angular terms were used in the representations, and an assessment of relative importance of the different terms is presented. Combined with a two-body He–He potential, the results of this work should offer a high quality interaction potential for simulations of aggregated helium.

Notizen: The observed increase in the steric effect of the reaction Ca(1D)+CH3F(JKM=111) →CaF(2Π)+CH3 with increasing energy has been tentatively ascribed to a reorientation of the initially oriented CH3F axis, due to anisotropic long-range forces [M. H. M. Janssen, D. H. Parker, and S. Stolte, J. Phys. Chem. 95, 8142 (1991)]. Here we present ab initio calculations and use these to construct a long-range potential. To this potential we fit an isotropic model potential and two anisotropic model potentials. On the long-range potential and on the model potentials we perform classical trajectory calculations, and we compare the two methods presented in the preceding paper [G. C. Groenenboom and A. J. H. M. Meijer, J. Chem. Phys. 101, 7592 (1994)] for the extraction of the steric effect. We conclude that already the attractive isotropic model presented in this paper can account for the observed energy dependence of the steric effect for this reaction via a "trapping'' mechanism. We show that although reorientation is possible, it contributes little to the positive energy dependence of the steric effect.

Notizen: Six BH5 structures were examined in detail using the self-consistent field (SCF), configuration interaction including single and double excitations (CISD), and coupled cluster including single, double, and perturbatively included connected triple excitations [CCSD(T)] methods in conjunction with a double-ζ plus polarization (DZP), a triple-ζ plus polarization (TZ2P), and an augmented TZ(3d1f1g,2p1d) basis set. The C4v and the D3h isomers are high in energy [23 and 45 kcal mol−1, respectively, relative to the Cs(I) structure at DZP CCSD]. Although structure Cs(I) is the global minimum, both Cs structures, where BH5 is comprised of nearly planar monoborane (BH3) and a hydrogen molecule, are essentially equal in energy and allow virtually free rotation of the hydrogen moiety. The global minimum was characterized by vibrational frequency analyses at the TZ2P CCSD(T) level. Final energies were obtained with the TZ(3d1f1g,2p1d) basis set and the CCSD(T) method. At room temperature, the borane–hydrogen complex BH5 is unstable toward dissociation by 6.8 kcal mol−1. However, at the absolute zero (0 K), the complex forms exothermically (−1.4 kcal mol−1). The theoretical De value (6.3 kcal mol−1) appears to be effectively converged with respect to basis set and theoretical method. The inclusion of perturbative triple excitations accounts for 36% of the total binding energy, a remarkable effect. Hydrogen scrambling via a C2v structure seems unlikely since the activation barrier for this process is at least 2.8 kcal mol−1 higher than the dissociation barrier of BH5 into BH3 and H2.

Notizen: An error controlled finite element method (FEM) for solving stationary Schrödinger equations in three space dimensions is proposed. The method is based on an adaptive space discretization into tetrahedra and local polynomial basis functions of order p=1–5 defined on these tetrahedra. According to a local error estimator, the triangulation is automatically adapted to the solution. Numerical results for standard problems appearing in vibrational motion and molecular structure calculations are presented and discussed. Relative precisions better than 1e-8 are obtained. For equilateral H++3, the adaptive FEM turns out to be superior to global basis set expansions in the literature. Our precise FEM results exclude in a definite manner the stability or metastability of equilateral H++3 in its ground state.

Notizen: The density functional calculations using the Perdew nonlocal corrections to exchange and correlation have been carried out for a sequence of hydrated proton clusters. The optimized structures were obtained up to H13O+6. It is found that H3O+ is indeed the central unit in all the lowest energy structures we found. Our results support the argument that the structure with a four-coordinate first solvation shell is very unlikely in small hydrated proton clusters. The density functional calculations with the Perdew nonlocal corrections to exchange and correlation give somewhat shorter hydrogen bond lengths, but slightly longer chemical bond lengths as compared with the post-Hartree–Fock calculations. The harmonic vibrational frequencies and IR intensities of various vibrational modes have been generated for all the structures optimized. Results for small clusters are compared with the high resolution experimental spectroscopy studies of Yeh et al. and Begemann et al. Results for larger clusters are used to interpret the low resolution spectra of Schwartz. Very good accord with experimental results is obtained. The solvent effects on proton transfer energy barriers in clusters have been studied by designing a few model systems. The barrier is found to be very sensitive to the solvent configurations. When the solvent water is replaced by the classical partial charge model, a significant change of the barrier is observed, indicating that a quantitative treatment will ultimately require a good pseudopotential to properly account for the quantum nature of the solvent. A combined density functional and molecular dynamics simulation was used to calculate the proton transfer energy and free energy barrier in aqueous solution. The barrier is found to be 3 kcal/mol higher than in gas phase. Very large solvent fluctuation is observed which may have a significant influence on the reaction rate.

Notizen: The potential energy function for the electronic ground state of the water molecule has been obtained by fitting rotation-vibration term values involving J≤14 for 24 vibrational states of H216O together with 25 additional vibrational term values belonging to higher excited states. The fitting was carried out by means of an exact kinetic energy Hamiltonian. It was found that the differences between the exact kinetic energy calculations and calculations with the morbid program (i.e., calculations with an approximate kinetic energy operator) depend only very slightly on the parameters of the potential. This fact allowed us to make an inexpensive fitting using the morbid approach and still get the accuracy obtainable with the exact kinetic energy Hamiltonian. The standard deviation for 1600 term values was 0.36 cm−1. For 220 ground state energy levels the standard deviation was 0.03 cm−1. With the fitted potential, calculations of term values with J≤35 were carried out. This showed the excellent predictive power of the new potential. For the J=20 term values in the vibrational ground state, the deviations from experiment are typically below 0.2 cm−1. The discrepancy for the observed level with the highest Ka value, JKaKc = 20200, is only 0.008 cm−1. The calculated term value for the observed level with the highest J, 35035, deviates 0.1 cm−1 from experiment. Because of the level of accuracy achieved in these calculations, we can for the first time demonstrate the breakdown of the Born–Oppenheimer approximation for the water molecule. The high Ka level calculations allow us to show that the rotational energy level structure in water is at least of a very different nature than the fourfold cluster structures observed for H2Se and calculated for H2S, H2Se, and H2Te.

Notizen: The symmetry adapted cluster-configuration interaction (SAC-CI) method is briefly reviewed and applied to the excitation and ionization spectra of TiX4 (X=Br, I). The valence excited states of these molecules are investigated systematically and compared with the previous study on TiCl4. The experimental spectra are well reproduced and assigned by the SAC-CI calculation including spin–orbit interaction of the ligand p atomic orbital (AO) and Ti d AO. Nine A1, ten A2, 20 E, and 30 T1 and T2 states are calculated for the excited states, and the oscillator strengths are distributed among the transitions to 30 T2 states, which cause the excitation spectra to be very complicated, especially for the TiI4 molecule. The ordering of the ionized states in the outer valence region is (1t1)−1〈(3t2)−1〈(1e)−1〈(2t2)−1〈 (2a1)−1, which is the same as that of TiCl4. The spin–orbit splittings in the 2T2 states of TiBr4 and TiI4 are estimated to be smaller than those of the previous studies, and we propose a new assignment for the experimental photoelectron (PE) spectra.

Notizen: The impedance spectra are measured for protonated and deuterated clathrates, HClO4⋅5.5H2O and DClO4⋅5.5D2O, between 10 and 300 K. The conductance is investigated between 80 K and room temperature and the dielectric constant between 10 and 120 K. The data show deviation from the Arrhenius behavior of conductance in the low-temperature regime. A description of proton conductivity is developed on the basis of quantum theory of an elementary act of proton tunneling between donor–acceptor sites interacting with environmental fluctuations. Several models of the elementary act are considered. The mechanism, most consistent with the obtained data, incorporates—strong coupling of the proton with local vibrational modes of the closest environment and system diabatic transitions along these vibrational "coordinates''—fluctuations of the tunneling barrier for the proton. At low temperatures the motion along the vibrational coordinates is no longer purely classical and the slow mode tunneling takes place. The latter gives rise to a curvature in the Arrhenius plots apprehended as a decrease of the apparent activation energy at lower temperatures. The observed isotope effect is in line with the lower deuteron tunneling probability due to doubling the mass, though other parameters may also be affected by deuteration.

Notizen: The dependence of the magnetic coupling constant, J, with the pressure has been studied by an ab initio cluster model approach in a typical ionic solid such as KNiF3. By computing J at different values of the lattice parameter R, we predict a power law of the form ||J||≈R−n with 10.5〈n〈13.3 in good agreement with the suggested experimental value. This behavior is found even for the simplest Ni2F cluster model described by a complete active space configuration interaction wave function in which the active orbitals correspond to the open shell of each Ni2+ cation.

Notizen: The hyperfine structures of the isoelectronic molecules CCO, CNN, and NCN in their triplet ground states (X 3Σ−) are investigated by means of ab initio methods. The infrared frequencies and geometries are determined and compared with experiment. Configuration selected multireference configuration interaction calculations in combination with perturbation theory to correct the wave function (MRD-CI/BK) employing extended atomic orbital (AO) basis sets yielded very accurate hyperfine properties. The theoretical values for CCO are in excellent agreement with the experimental values determined by Smith and Weltner [J. Chem. Phys. 62, 4592 (1975)]. For CNN, the first assignment of Smith and Weltner for the two nitrogen atoms has to be changed. A qualitative discussion of the electronic structure discloses no simple relation between the structure of the singly occupied orbitals and the measured hyperfine coupling constants. Vibrational effects were found to be of little importance.

Notizen: The electronic structure, vibrational spectra, and thermodynamic stability of CCCN and HCCCN have been determined using ab initio molecular orbital theory. The heat of formation for HCCCN was determined using Gaussian-2 theory (G2) and was found to be 91.5±2 kcal mol−1. There is good agreement between the G2 value and that determined using an isodesmic reaction (i.e., one in which both the number and types of bonds are conserved), which yields 90.7±2 kcal mol−1. The heat of formation for the CCCN radical is 178.2±2 kcal mol−1. These data are used to compute the bond dissociation energies in HCCCN, D0(C–C) and D0(C–H), which are important in assessing the chemistry in Titan's atmosphere, as well as in other interstellar media.

Notizen: CC-R12—a combination of coupled cluster theory and the R12 method, is presented in which the correlation cusp is treated via inclusion of terms explicitly dependent on the interelectronic distance rij into the exponential expansion of the wave function. A diagrammatic derivation of the CC-R12 equations within the so-called "standard approximation B'' is given at the level of singles, doubles and triples (CCSDT-R12). MBPT(4)-R12 is derived as a byproduct of CCSDT-R12. Fifth order noniterative corrections are also discussed.

Notizen: We have developed an approach at the Hartree–Fock level by which it is possible to calculate the electronic structures of large polymers with or without periodic sequences systematically. This elongation method is based on the concept of a cluster-series calculation which means the successive connection of cluster molecules at the molecular orbital level in approximating a large polymer as a cluster molecule. It has already been reported that we can extract the periodic condition of the electronic states within the series of extended clusters by using the cluster-series model. Recently, we tried to introduce the elongation method into the program package of semiempirical molecular orbital methods mopac. In the present paper, we report results of applications to the calculations of three polymer systems by using AM1 parameters, that is, the first system is the periodic polymer, the second is the interface between two blocks in a polymer chain, and the third is the local defect within a periodic polymer. In calculations of periodic polymers, clusters of polyethylene, polytetrafluoroethylene, polyacetylene, or polydifluoroacetylene were elongated in one direction, and the interfaces between the above polymer blocks with ethylene- or acetylene-type chain were dealt with by the two-directional elongation method. Also, the solitonic structures with one plus or minus charge within polyacetylene chain were created in elongation calculations of the bidirectional extension as models for the local defect in a periodic polymer. Moreover, we discussed periodic states of electronic structures in these systems from cluster-series calculations.

Notizen: The semiclassical techniques developed in the previous paper are applied to the understanding of the hierarchical structure underlying the spectra. This organization, as analyzed by Davis with statistical models, is revealed by continuously changing the energy resolution of the spectra and noting the branching pattern of the peaks. We argue that the greater part of this hierarchical organization can be understood with classical events in the time domain.

Notizen: Conformational dynamics and relaxation of the torsional angle autocorrelation (ACF) function in bulk polybutadienes (PBD) have been studied over a wide temperature range via molecular dynamics simulations. All trans, all cis and 70 mol % trans were the configurations of the systems studied. Companion studies of these systems in the phantom state were also carried out to illuminate the effects of packing in the bulk. Conformational transitions at the –CH2–CH= bond alpha to the double bond and at the –CH2–CH2– beta bond were monitored. The activation energies for the overall transition rates for the α bond and for the β bond were found to correspond in both bulk and phantom states to one barrier height in their respective torsional potentials. A considerable degree of correlation was found between second neighbor bonds. At the α bond in trans-PBD correlated conformational changes across the double bond predominated but changes across the β bond when in the trans conformation were common also. In cis-PBD, due to steric hindrance at the α bond when in the cis conformation, correlated changes across the β bond were relatively more common although exchanges across the double bond were common also. In all of the above correlations, the direction of rotation in the two bonds are of opposite sign. In cis-PBD a correlated transition with same sign rotation was also found. The activation energies for relaxation times for the torsional ACF in phantom PBD were also found to correspond to single torsional barrier heights. In bulk PBD, however, the activation energies were significantly higher than single barrier. This behavior is the result of the conformational transitions becoming more heterogeneously distributed spatially over the bonds in the bulk as temperature is lowered. This phenomenon has also been found recently in simulations on polyethylene.

Notizen: We present a theoretical investigation by the sum-over-states formalism of the static first- and third-order polarizabilities of thienylenemethylidene oligomers; following the incorporation of a single conjugated carbon between the rings, these compounds present a partially quinoid geometry. We use a multireference determinant single–double configuration interaction approach to calculate excited-state energies, state dipole moments, and transition dipole moments which are introduced in the sum-over-states expressions. All the results are discussed in comparison to those obtained in thiophene oligomers of similar sizes; they indicate that the third-order polarizabilities are smaller for the methine-bridged compounds than for the corresponding thiophene oligomers. This feature is rationalized by analyzing the main optical (virtual excitation) channels that contribute to the nonlinear response.

Notizen: We have measured the unenhanced, nonresonant surface Raman spectra of one monolayer of hydrogen bound to flat and stepped Si(111) surfaces prepared using a novel, aqueous fluorine etch. The orientation and normal mode composition of adsorbate vibrations are obtained from polarized, angle-resolved Raman spectra using a 3-layer dielectric model. This approach requires the experimental determination of both the anisotropy in the dynamic polarizability of the adsorbate bond and the effective dielectric constant in the vicinity of the adsorbate. The measured Si–H bond anisotropy is 0.263±0.028 in good agreement with gas phase measurements. The adsorbate dielectric constant is measured to be 3.78±0.20; this response is clearly nonlocal and predominantly due to polarization of the underlying silicon lattice. Using this technique, we find that the step dihydride on a Si[6(111)-(1¯1¯2)] surface is rotated 37°±4° from the surface normal in good agreement with the 31° predicted by ab initio cluster techniques, but significantly larger than the 12.5° predicted by pseudopotential slab calculations. In contrast to both theoretical predictions, the normal modes of this step dihydride display little concerted motion indicating that subsurface relaxation near the step edge reduces steric interactions much further than predicted. The observed anisotropic etch rates, evidenced by the production of atomically straight steps, are explained in terms of the measured distortion at the step edge.

Notizen: In this paper we report on the ground and excited electronic states of localized excess electron surface states of (Ne)−N (N=1.1×104–6×1023) and (H2)−N (N=4.6×103–6×1023) clusters. We used an electron-cluster model potential, which consists of a short-range repulsive interaction with a strength V¯0 [with a lower limit V¯0 ((approximately-greater-than)0) corresponding to the energy of the quasifree electron in the macroscopic condensed material], and a long-range attractive polarization potential, to explore cluster size effects on the energetics and on the charge distribution of these excess electron clusters. The onset of the cluster size for excess electron localization in the ground (n=1, l=0) electronic state was inferred from a near-threshold scaling analysis, being characterized by a "critical'' cluster radius R(1,0)c(approximately-equal-to)2(1−Q)a0/Q, where Q=(ε−1)/4(ε+1) is the effective cluster charge (for the cluster dielectric constant ε), R(1,0)c=39 A(ring) for Ne(s), R(1,0)c=46 A(ring) for Ne(l), R(1,0)c=35 A(ring) for H2(s) and R(1,0)c=41 A(ring) for H2(l), where (s) and (l) denote rigid and nonrigid cluster structures, respectively. With a further increase in the cluster radius R(approximately-greater-than)R(1,0)c, higher nl electronic states become localized.Moving up in the cluster size above the localization threshold, the energy levels Enl can be expressed (for low values of ε≤1.5) in terms of a "universal'' scaling relation Enl/Ef=Φnl(rf/R), where Ef=(e2/2a0)Q2, rf=a0/Q and the scaling function Φnl is independent of ε. This scaling relation allows for the determination of isotope effects and the state of aggregation of the cluster on the energetics of electron localization. In order to make contact with experiment, we have studied electric field-induced ionization and the electronic spectroscopy of these excess electron clusters. The threshold dc electric field F(nl)c for field-induced ionization from the n,l state (over a broad range of R, i.e., R〈320 A(ring) for the 1s and 1p states and R〈900 A(ring) for the 2p state) is of the form F(nl)c∝||Enl||5/4 (ε−1)−1/4R−3. Information on electronic spectroscopy was inferred from the cluster size dependence of the transition energies and oscillator strengths for the 1s(n=1,l=0)→n'p(n'=1,2,...,l=1) transitions. The cluster size dependence of the spectroscopic data for the 1s→1p transition reveals that both the transition energy ΔE(1s→1p) and the oscillator strength f(1s→1p) are proportional to (1/R)2, with ΔE(1s→1p)→0 and f(1s→1p)→0 for R→∞, exhibiting the l degeneracy of the flat surface. On the other hand, for the 1s→2p transition, the energy ΔE(1s→2p) and the oscillator strength f(1s→2p) increase with increasing R, reaching the flat macrosurface value for R→∞.

Notizen: In this investigation, the growth, structure, and electronic properties of Pt films on the polar surfaces of ZnO were examined using high-resolution electron energy-loss spectroscopy (HREELS) and low-energy, electron diffraction (LEED). The growth mode of vapor-deposited Pt films on ZnO(0001¯) and ZnO(0001) at 300 K was found to be nearly layer-by-layer. The surfaces of Pt films produced in this manner exhibited hexagonal symmetry and were stable up to 600 K. At higher temperatures, the Pt agglomerated into particles which remained oriented with respect to the ZnO substrate. HREELS results indicate that there are only weak interactions at the Pt/ZnO(0001¯) interface, while charge transfer and Schottky barrier formation occurs at the Pt/ZnO(0001) interface.

Notizen: Smalley and co-workers discovered that chemisorption reactivities of silicon clusters vary over three orders of magnitude as a function of cluster size. In particular, they found that Si33, Si39, and Si45 clusters are least reactive towards various reagents compared to their immediate neighbors in size. We explain these observations based on our stuffed fullerene model. This structural model consists of bulk-like core of five atoms surrounded by fullerene-like surface. Reconstruction of the ideal fullerene geometry gives rise to fourfold coordinated crown atoms and π-bonded dimer pairs. This model yields unique structures for Si33, Si39, and Si45 clusters without any dangling bonds and thus explains their lowest reactivity towards chemisorption of closed shell reagents. This model is also consistent with the experimental finding of Jarrold and Constant that silicon clusters undergo a transition from prolate to spherical shapes at Si27. We justify our model based on an in depth analysis of the differences between carbon and silicon chemistry and bonding characteristics. Using our model, we further explain why dissociative chemisorption occurs on bulk surfaces while molecular chemisorption occurs on cluster surfaces. We also explain reagent specific chemisorption reactivities observed experimentally based on the electronic structures of the reagents. Finally, experiments on SixXy (X = B, Al, Ga, P, As, AlP, GaAs) are suggested as a means of verifying the proposed model. We predict that Six(AlP)y and Six(GaAs)y (x=25,31,37;y=4) clusters will be highly inert and it may be possible to prepare macroscopic samples of these alloy clusters through high temperature reactions.

Notizen: The vibrational frequency shift of physisorbed diatomic molecules is related to the interaction with the adsorbent expressed in terms of the internuclear distance ρ. It is calculated by the Schrödinger equation, the perturbation theory, and a simplified method. We show that it is sufficient to calculate the interaction potential for the values of ρ in the ground and first vibrational states in order to get a precision of 10% on the frequency shift. The comparison between the theoretical and experimental frequency shift of H2 adsorbed in NaA zeolite is used to adjust the interaction potential, especially in terms of the ionicity of the crystal.

Notizen: The partition functions of discrete as well as continuous stiff molecular chains are calculated using the maximum entropy principle. The chain is described by mass points, and their connectivity is taken into account by harmonic constraints (flexible segments) in addition to the bending restrictions. For comparison and as a test of the formalism the freely rotating chain as well as the Kratky–Porod wormlike chain (rigid segments) are reexamined treating the bending restrictions as constraints. It is shown that the second moments for the chain of flexible segments agree exactly with those known from the freely rotating chain for the discrete as well as the continuous chain and for all stiffnesses. Moreover, the Green's function for the continuous chain is determined, which allows to obtain any desired two point distribution function. The influence of various bending restrictions on equilibrium properties is discussed. Furthermore, a comparison to other existing models, especially the Harris and Hearst model, is given and the validity of the various models is examined.