ALBERT

Notes: When the charge overlap between interacting molecules or ions A and B is weak or negligible, the first-order interaction energy depends only upon the molecular positions, orientations, and the unperturbed charge distributions of the molecules. In contrast, the first-order force on a nucleus in molecule A as computed from the Hellmann–Feynman theorem depends not only on the unperturbed charge distribution of molecule B, but also on the electronic polarization induced in A by the field from B. At second order, the interaction energy depends on the first-order, linear response of each molecule to its neighbor, while the Hellmann–Feynman force on a nucleus in A depends on second-order and nonlinear responses to B. One purpose of this work is to unify the physical interpretations of interaction energies and Hellmann–Feynman forces at each order, using nonlocal polarizability densities and connections that we have recently established among permanent moments, linear response, and nonlinear response tensors. Our theory also yields new information on the origin of terms in the long-range forces on molecules, through second order in the interaction.One set of terms in the force on molecule A is produced by the field due to the unperturbed charge distribution of B and by the static reaction field from B, acting on the nuclear moments of A. This set originates in the direct interactions between the nuclei in A and the charge distribution of B. A second set of terms results from the permanent field and the reaction field of B acting on the permanent electronic moments of A. This set results from the attraction of nuclei in A to the electronic charge in A itself, polarized by linear response to B. Finally, there are terms in the force on A due to the perturbation of B by the static reaction field from A; these terms stem from the attraction of nuclei in A to the electronic charge in A, hyperpolarized by the field from B. For neutral, dipolar molecules A and B at long range, the forces on individual nuclei vary as R−3 in the intermolecular separation R; but when the forces are summed over all of the nuclei, the vector sum varies as R−4. This result, an analogous conversion at second order (from R−6 forces on individual nuclei to an R−7 force when summed over the nuclei), and the long-range limiting forces on ions are all derived from new sum rules obtained in this work.

Notes: Analytic energy gradients for the coupled-cluster singles and doubles (CCSD) method have been implemented for closed-shell systems using restricted Hartree–Fock (RHF) and open-shell systems using unrestricted Hartree–Fock (UHF) reference functions. To achieve maximum computational efficiency, the basic theory has been reformulated in terms of intermediates, thus reducing the number of required floating-point operations, and all computational steps are given in terms of matrix products in order to exploit the vector capabilities of modern supercomputers. Furthermore, the implementation has been designed to take full advantage of Abelian symmetry operations. To illustrate the computational efficiency of our implementation and in particular to demonstrate the possible savings due to the exploitation of symmetry, computer timings and hardware requirements are given for several representative chemical systems. In addition, the newly developed analytic CCSD gradient methods are applied to calculate the equilibrium geometry and energy splitting of the lowest singlet and triplet states of the C4O2 molecule.

Notes: Temperature dependence of stretching modes are presented for two kinds of Rb2ZnCl4 crystals which exhibit different phase transition sequences. The comparison between both sets of results points out a special behavior of the line which appears below the normal–incommensurate phase transition. Appearance of the incommensurability is observed via the temperature dependence of certain stretching lines.

Notes: Recent theoretical developments have shown how such examples of excitation properties as the electronic band structure and the set of vibrational normal modes of a liquid can be studied by traditional classical-liquid-theory methods. In this paper, we add another example to this collection: the set of polarization modes of a liquid. The basic notion is that in any polarizable but nonpolar fluid, the dynamics of the instantaneous dipoles can be represented as a linear combination of harmonic contributions from independent, microscopically defined, polarization modes. We note first how many of the properties one would like to know about the liquid—its full dielectric behavior, its optical absorption spectrum, its effect on the absorption spectrum of a solute, and even how the net polarization of the liquid fluctuates with time—are available from these polarization modes. We then point out how the requisite information about the modes can be ascertained by the same liquid theory methods used to treat p-orbital-based electronic problems. These considerations allow us to show how the mean spherical approximation can be used to obtain more accurate versions of optical spectra than was possible heretofore. It also suggests how one might begin to look at the dynamics of polarization in polar liquids.

Notes: This work, which is purely methodological, demonstrates new applications of perturbation methods in computer simulations of simple liquids. Most applications are based on the calculation of bulk and local excess chemical potentials of one or several inserted test particles, using a Widom technique in the canonical ensemble. This gives a powerful tool for obtaining distribution functions, some of which are virtually impossible to determine with other techniques. Results are also presented for single-ion activity coefficients and Donnan potentials. A perturbation approach is used to calculate thermodynamic response functions with respect to particle number, temperature, and volume changes. The applicability is exemplified by studies of hard-sphere fluids, uniform and nonuniform electrolyte solutions within the primitive model, and screened Coulomb systems.

Notes: A study of phase angles of the electric birefringence including inertia is proposed in the case of the simultaneous action of two electric fields, namely a direct current (dc) bias field added to an alternating current (ac) field of angular frequency ω. The solution of the Fokker–Planck–Kramers (FPK) equation applied to the orientational motion of a polar (permanent moment μ) and anisotropically polarizable (induced moment Δα) molecule in two-dimensional (2D) space (disk model) leads to distinct phase angles θ1(ω) and θ2(ω), both of them corresponding to harmonic components in ω and 2ω of the birefringence. The evolution of the plots θj(ω), where j=1,2, for different values of the inertial parameter a2=τI/τ and given a value of P=(Δα/μ2)kT is presented. It is shown that in the high-frequency region, the phase angles may take up to twice the values they would have with zero inertia. τI and τ are the friction time and the Debye relaxation time, respectively, while kT stands for the usual thermal energy. Such variations must therefore be measurable by experiment and allow a new way of research in Kerr effect relaxation when inertia is taken into account.

Notes: Measurements of ion-velocity distributions of CO+ in a He buffer gas are presented as a function of an applied electric field. The distributions are obtained by single frequency, laser-induced fluorescence from various initial rotational states with the laser beam propagating parallel and perpendicular to the drift velocity vector. All distributions are well represented by a Maxwellian for the observed E/N range of 0–13 Td. The reduced mobilities, calculated from the shift of the mean velocity as a function of electric field, increase from 18.7±1.0 cm2 V−1 s−1 at very low fields to 26.4±0.7 cm2 V−1 s−1 at 13 Td. From the width of the Doppler profiles, translational "temperatures'' are calculated, which are compared to simple attractive and repulsive Maxwell models as a function of the field. The measured values disagree with the predictions, which are well established for atomic ion systems. The differences are discussed in terms of rotationally inelastic energy transfer in the collisions, which is predicted by kinetic theory models. This argument is strengthened by the fact that even though the rotational states rapidly equilibrate, measurements on different lines yield higher temperatures for higher rotational levels. Finally, the small influence of selective quenching of the electronically excited CO+ on the Doppler profiles is demonstrated by measuring effective lifetimes as a function of the applied drift field.

Notes: We present a simple classical model for understanding time-resolved absorption spectra of molecules that are in the process of dissociating. The model applies to absorption spectra that are obtained by measuring the spectral power density of an ultrafast, continuum probe pulse after transmission through the sample. We show that the classical model can yield results in good agreement with quantum-mechanical wave packet propagation calculations. In a close analogy with collisional line broadening, the time-resolved absorption spectra are shown to have an impact region near the separated-atom transition frequency and a far-wing region. The impact region is due to radiation emitted after the molecule has separated into atomic fragments, and the far-wing region is due to radiation emitted during the time of strong molecular interaction. The spectrum in the impact region depends upon an effective phase shift for a "partial'' collision, which begins at the time that the probe pulse sweeps through the molecular transition frequency. For narrow wave packets, this phase shift can be directly measured, and the molecular transition frequency can be recovered as a function of time along the path of dissociation. For very broad wave packets, the time-resolved absorption spectra approach a statistical limit, in which the absorption line shape becomes an image in frequency space of the probability density in configuration space at the time of excitation by the probe pulse. In all cases, the frequency-integrated absorption is proportional to the net population of molecules that are excited by the probe pulse. In principle, this result can be used to obtain the strength of the transition dipole moment as a function of internuclear separation. We also consider fluorescence induced by a short optical probe pulse, as in the experiments of Zewail and co-workers. Fluorescence measurements are shown to be fundamentally different from measurements of the transmitted spectral power density: fluorescence depends upon the net population excited by the probe pulse, whereas the transmitted spectral power density depends upon interference between the incident probe field and the polarization field. Thus these two experimental techniques are sensitive to different aspects of the dissociation process.

Notes: An investigation of the longitudinal acoustic mode (LAM) in a series perfluoro-n-alkanes under pressure has been carried out using Raman spectroscopy in conjunction with a diamond anvil cell. Perfluoro-n-alkanes are shown to undergo a phase transition from a helical to a planar zigzag structure at 5 kbar. This conformational change with pressure results in an abrupt increase in the LAM frequency. Since the chain axis elastic modulus of a planar zigzag molecule is larger than that of a helical one, such a conformational change leads to stiffening of the backbone giving rise to the observed change in the LAM frequency.

Notes: The oxygen adsorption site on the Ir{110}-c(2×2)-O surface has been studied by time-of-flight scattering and recoiling spectrometry (TOF-SARS) using 4 keV Ne+ for backscattering and Ar+ for recoiling. The oxygen site was analyzed from scans of (i) backscattering intensity versus incident angle, (ii) oxygen recoil intensity versus incident and azimuthal angle, and (iii) oxygen recoil energy versus azimuthal angle. Calibrated shadow cones and trajectory simulations were used to obtain the site coordinates. This TOF-SARS data is contrasted with that of Ni{110}-p(2×1)-O, in which it is well established that the adsorption site is in the long-bridge position along the 〈001〉 rows. Adsorption of oxygen in the short-bridge sites above the 〈11¯0〉 Ir rows is the only model consistent with all of the experimental data and simulations. The O–Ir bond length is estimated to be ≈1.8 A(ring).

Notes: We have calculated the evaporation rate for every cluster size of Ar+n and Xe+n in the microcanonical ensemble (as a function of its internal energy) up to n=37. This allows us to perform numerical experiments simulating the evolution of the size and energy distributions in a cluster beam up to arbitrary long times. We find that there is a time lag for the onset of magic numbers (especially abundant cluster sizes) of molecular clusters. This time is required for the clusters to cool down by evaporation and become solid-like and it may differ by several orders of magnitude for different species thus explaining apparently contradictory experiments. For longer times we find, in agreement with theoretical predictions but contrary to simple intuition, that the relative abundance of magic/nonmagic clusters decreases with time.

Notes: We explore the usefulness of the delta self-consistent-field (ΔSCF) approximation in connection with high-resolution x-ray photoelectron spectra for component and structural analysis of organic compounds. Results for core electron binding energy shifts for model molecules of the polymethylmethacrylate polymer are presented. A previously devised method for proper self-consistent-field solutions for core hole states in molecules is evaluated. The results indicate that chemical shifts can be obtained within a few tenths of an eV. A discussion is presented on the inherent errors in the ΔSCF approximation, the proper corrections for zero-point vibrational energies, and the role of relaxation of core orbitals.

Notes: We report the first observation of eliminative cationic polymerization within van der Waals (vdW) clusters following electron impact ionization at pressures of 10−8 Torr. The elimination reactions of C2H3Cl+ within the clusters terminate after three successive steps, each involving elimination of HCl or Cl. The results provide a mechanism for the early stages of gas phase cationic polymerization of vinyl chloride and demonstrate the feasibility of using vdW clusters as a means of studying gas phase cationic polymerization.

Notes: We present equations for generalized-normal-mode vibrational frequencies in reaction-path calculations based on various sets of coordinates for describing the internal motions of the system in the vicinity of a reaction path. We consider two special cases in detail as examples, in particular three-dimensional atom–diatom collisions with collinear steepest descent paths and reactions of the form CX3+YZ→CX3 Y+Z with reaction paths having C3v symmetry. We then present numerical comparisons of the differences in harmonic reaction-path frequencies for various coordinate choices for three such systems, namely, H+H2→H2+H, O+H2→OH+H, and CH3+H2→CH4+H. We test the importance of the differences in the harmonic frequencies for dynamics calculations by using them to compute thermal rate constants using variational transition state theory with semiclassical ground-state tunneling corrections. We present a new coordinate system for the reaction CH3+H2 that should allow for more accurate calculations than the Cartesian system used for previous reaction-path calculations on this and other polyatomic systems.

Notes: The NO γ emission is observed from the reaction of NO+(a)+NO. The emission provides a new detection method for studying the NO+(a) reaction kinetics at thermal energy without electric field. The NO+(a) is produced by photoionization of NO at 76.5 nm as well as by the reaction of Ar++NO, where Ar+ is also produced by photoionization of Ar. The vibrational population distributions of NO(A) resulted from the ion–molecule reactions are measured and used to discuss the mechanisms for the production of the emission. The reaction rate constants are determined from the decay rates of the emission intensity as a function of time. The reaction rate constants of NO+(a)+NO and Ar++NO at room temperature are measured to be (5.8±0.7)×10−10 and (2.1±1.0)×10−10 cm3/s, respectively. The reaction rate constant of NO+(a)+Ar at thermal energy is estimated to be about 10−12 cm3/s.

Notes: We present a new complex-scaling Fourier-grid Hamiltonian (CSFGH) method for accurate and efficient determination of laser-induced (multichannel) molecular resonance states without the use of basis set expansions. The method requires neither the computation of potential matrix elements nor the imposition of boundary conditions, and the eigenvectors provide directly the values of the resonance wave functions at the space grid points. The procedure is particularly valuable for excited-state problems where basis set expansion methods face the challenge. The simplicity and usefulness of the CSFGH method is demonstrated by a case study of the intensity-dependent complex quasivibrational energy eigenvalues (ER, −Γ/2) and eigenvectors associated with multiphoton and above-threshold dissociation of H+2 ions in the presence of intense laser fields (I=1012–1014 W/cm2 ).

Notes: Three-dimensional quantum theory of triatomic exchange reactions in strong laser fields is presented. Our theory consists of an exact partitioning technique for treating the effects of optical fields on reactive scattering, based on approximate hindered-rotor adiabatic wave functions describing the pure nonradiative events. The method enables computations to be performed for an arbitrary number of field intensities with very little effort beyond that required for a single-intensity computation. Differential and integral cross sections for the H+H2 exchange reaction, involving the ground and first excited electronic states, in the presence of laser fields, are computed. The dependence of reactive nonlinear optical effects, and especially that of "laser catalysis,'' on laser intensity; the way isolated and overlapping power-broadened resonances affect the optically induced reaction; the role of relative orientation of two incident molecular beams in crossed beams experiments are investigated. The three-dimensional computations confirm our previous expectations, based on a collinear model, that laser catalysis is achievable using only moderately high powered lasers. The above is expected to be true for all reactive systems (of which H+H2 is one) possessing optically allowed stable excited electronic states.

Notes: We investigate final rotational state distributions following the decay of long-lived resonance states with k*=0, 1, and 2 quanta of internal bending excitation. The calculations are related to the photodissociation of HONO on the S1 electronic state surface, truncated to two degrees of freedom namely the HO–NO dissociation bond and the ONO bending angle. The decay of the k*=0 resonance yields a smooth Gaussian-type distribution, in very good agreement with recent measurements. The distributions following the decay of the excited bending states show a bimodal behavior with the main maxima at high rotational states. The final angular momentum distributions reflect the coordinate-dependence of the dissociation wave function in the region of the transition state, mediated by the dynamics in the exit channel when the wave packet slides down the steep potential slope. A qualitative interpretation of the rotational state distributions is provided by a simple classical model which applies the transition-state wave function as a weighting for trajectories starting on a line that separates the intermediate complex from the product channel.

Notes: The deactivation processes of Cd(5 3P2) by H2 and D2 were studied by employing pulsed laser techniques. The cross sections for the intramultiplet relaxation to produce Cd(5 3P1) and Cd(5 3P0) were determined as follows: Cd(5 3P2)+H2→Cd(5 3P1)+H2; 6.3, Cd(5 3P2)+H2→Cd(5 3P0)+H2; 1.0, Cd(5 3P2)+D2→Cd(5 3P1)+D2; 4.4, Cd(5 3P2)+D2→Cd(5 3P0)+D2; 0.9, in units of 10−16 cm2 at 630 K. The cross sections for the overall deactivation of Cd(5 3P2) by H2 and D2 were determined to be 9.8×10−16 cm2 and 6.9×10−16 cm2, respectively. These values are compared with the calculated results based on a semiclassical curve crossing mechanism. It is suggested that electronic-to-rotational energy transfer without sharp resonances plays an important role in the deactivation of Cd(5 3P2).

Notes: Molecular dynamics simulations have been performed on a simple fluid in the non-Newtonian regime in order to study the nature of diffusion in the presence of shear stress. The nonequilibrium molecular dynamics (NEMD) sllod algorithm is used to generate a homogeneous boundary driven Couette flow. The elements of the tensor of diffusion coefficients have been evaluated by three different routes: through Einstein relations with the corresponding elements of the tensor of molecule displacements, through Green–Kubo expressions involving tensor of momentum autocorrelation functions and cross-correlation functions, and by utilizing an NEMD color field method. All three routes to the tensor of diffusion coefficients are shown to yield consistent results. A simple spherically symmetric Lennard-Jones fluid at its triple point was used in the simulation study. We find that in a Couette strain field of sufficiently large strain rate, diffusion in all directions is enhanced substantially. We propose and verify a new asymptotic relationship between the diagonal elements of the tensor of diffusion coefficients and the strain rate.

Notes: The angular distribution of light intensity scattered from a nonionic micellar solution of tetraethylene glycol n-decylether (C10E4) in water has been examined close to its critical point of mixing. Including multiple-scattering corrections to the light-scattering data, we have found the exponent γ=1.25±0.02 for the osmotic susceptibility χT and the exponent ν=0.63±0.01 for the long-range correlation length ξ in the temperature range of 1.03×10−4≤ε≤4.25×10−3, where ε=(Tc−T)/Tc. The values of the critical exponents obtained in this work are in good agreement with the theoretical and experimental ones for three-dimensional Ising systems.

Notes: We present an analysis of crystal growth of a pure material from its melt, using a phase field model. This model for a first-order phase transition couples nonconserved order parameter kinetics to thermal diffusion. It has been shown to give unique one-dimensional solutions, with velocity selection. We demonstrate that these steady-state solutions cease to exist for the thermal diffusivity above a critical value, which depends on the parameter coupling the kinetics to the temperature. We suggest a scaling which leads to agreement between numerical integration of the time-dependent equations and a perturbation analysis of the coupling. For small velocity, our model reduces to a standard model commonly applied to dendritic growth, which replaces the kinetic equation with one of interfacial equilibrium. Because the velocity vanishes at the critical point, the thermal diffusion length and dendritic wavelength diverge at this point. We relate this critical point to bifurcations in the phase space of a mechanical equivalent to the steady-state growth equations. We conclude that solutions cease because thermal diffusion drives the system to local kinetic equilibrium, and we discuss experimental accessibility and means of avoiding equilibrium.

Notes: We report the results of molecular dynamics simulations of the liquid–vapor interface of water. Two different water–water interactions were studied. The density profile of the interfacial transition region between liquid and vapor is monotone with a 10%–90% width of 3.45 A(ring), in good agreement with the value determined from x-ray reflectance measurements, namely 3.30 A(ring). The water molecules in the interface tend to lie with the HOH bisector in the plane of the surface and one OH bond pointing out of the surface. As the density falls in the transition region the tetrahedral structure of the bulk liquid breaks up and there is a tendency towards dimerization. The diffusion constant in the interfacial region is 58% larger than that in the bulk region.

Notes: The formation of C2H− is observed in two broad resonance bands when C2H2 is irradiated with vuv light. The higher-energy band has partially resolved structure, approximately linear pressure dependence, and a threshold at 16.335±0.021 eV. It is attributed to photoion-pair formation (C2H−+H+) consequent upon predissociation of one or more Rydberg states. This threshold, together with IP(H) and EA(C2H), gives D0(HCC–H)≤5.706±0.022 eV≡131.6±0.5 kcal/mol, or ΔH0f0 (C2H)≤134.5±0.5 kcal/mol. The lower-energy band has an approximately quadratic pressure dependence and curved step-like structure. It is attributed to photoelectron-induced dissociative attachment mediated by a πg shape resonance. The threshold, at 878.5±2.0 A(ring), corresponds to a photoelectron energy of 2.715±0.032 eV. This threshold combined with EA(C2H)=2.969±0.010 eV, yields D0(HCC–H)≤5.684±0.033 eV≡131.1±0.7 kcal/mol, or ΔH0f0 (C2H)=134.0±0.7 kcal/mol.

Notes: The time-dependent form of the Lippmann–Schwinger integral equation is used as the basis for a novel wave-packet propagation scheme. The method has the advantage over a previous integral equation treatment in that it does not require extensive matrix inversions involving the potential. This feature will be important when applications are made to systems where in some degrees of freedom the potential is expressed in a basis expansion. As was the case for the previous treatment, noniterated and iterated versions of the equations are given; the iterated equations, which are much simpler in the present new scheme than in the old, eliminate a matrix inversion that is required for solving the earlier noniterated equations. In the present noniterated equations, the matrix to be inverted is a function of the kinetic energy operator and thus is diagonal in a Bessel function basis set (or a sine basis set, if the centrifugal potential operator is incorporated into an effective potential). Transition amplitudes for various orbital angular momentum quantum numbers can be obtained from: (1) Fourier transform of the amplitude density from the time to the energy domain, and (2) direct analysis of the scattered wave packet. The approach is illustrated by an application to a standard potential scattering model problem.

Notes: Hydrogen adsorption on the (0001) beryllium surface is modeled using a Be45 cluster containing seven layers. The ab initio Hartree–Fock calculations employ effective core potentials and full D3h point group symmetry. Six low-lying electron configurations are investigated and the effect of electron spin coupling on the adsorption process is discussed. The adsorption of H on Be is calculated to be stable by 20 kcal/mol and lowers the work function by 1.3 eV.

Notes: The energy separation between the classical and nonclassical forms of protonated acetylene has been reinvestigated in light of the recent experimentally deduced lower bound to this value of 6.0 kcal/mol. The objective of the present study is to use state-of-the-art ab initio quantum mechanical methods to establish this energy difference to within chemical accuracy (i.e., about 1 kcal/mol). The one-particle basis sets include up to g-type functions and the electron correlation methods include single and double excitation coupled-cluster (CCSD), the CCSD(T) extension, multireference configuration interaction, and the averaged coupled-pair functional methods. A correction for zero-point vibrational energies has also been included, yielding a best estimate for the energy difference between the classical and nonclassical forms of 3.7±1.3 kcal/mol.

Notes: The electronic structure of small GaxAsy clusters (x+y≤10) are calculated using the local density method. The calculation shows that even-numbered clusters tend to be singlets, as opposed to odd-numbered clusters which are open shell systems. This is in agreement with the experimental observations of even/odd alternations of the electron affinity and ionization potential. In the larger clusters, the atoms prefer an alternating bond arrangement; charge transfers are observed from Ga sites to As sites. This observation is also in agreement with recent chemisorption studies of ammonia on GaAs clusters. The close agreement between theoretical calculations and experimental results, together with the rich variation of electronic properties of GaAs clusters with composition makes GaAs clusters an ideal prototype system for the study of how electronic structure influences chemical reactivity.

Notes: The recently formulated multiconfiguration-based unitary coupled electron pair approximation (UCEPA) is compared with multireference configuration interaction (MR-CISD) calculations, including all single and double excitations, for the molecules in this study. The electronic states of the molecules in this study are not only of experimental interest, but represent a challenge to any formalism to accurately predict the energy separations of the low-lying electronic states. The equilibrium geometries and fundamental vibrational frequencies of the three lowest electronic states (i.e., 1A1, 3A‘, and 1A‘) of aminonitrene H2N2, and phosphinonitrene, H2PN, have been determined using a split-valence basis with polarization functions on the heavy atoms and a small complete active space self-consistent-field (CASSCF) description of the active space. Both MR-CISD and UCEPA calculations have been performed at the equilibrium structures using larger basis sets to accurately determine the relative energetics of the electronic states. The equilibrium geometries and vibrational frequencies of the two lowest electronic states (i.e., 1A' and 3A‘) of phosphinocarbene, H2PCH, have been determined using a larger than double zeta basis set, augmented with polarization and diffuse functions, and a CASSCF description of the active space. Both MR-CISD and UCEPA calculations were performed on the equilibrium structures and predict that the singlet lies between 10.4 and 11.8 kcal/mol lower in energy than the triplet. The use of a generalized valence bond (GVB) reference function within UCEPA is introduced and is shown to be a useful approximation.

Notes: Complex oscillations and even aperiodicity can exist as transient phenomena in closed chemical systems. These effects are illustrated through the analysis of a simple, isothermal chemical model based on mass action kinetics for autocatalytic feedback, involving the conversion of a reactant to a final product via three intermediate species. The use of the so-called pool chemical approximation and of pseudo-steady-state analyses for such systems is indicated and discussed, particularly with relevance to "real'' chemical situations where small perturbations due to extraneous noise are inevitably present.

Notes: Vibrational and rotational distributions of CO excited by collisions with 2.3 eV H atoms have been obtained by monitoring the products with vacuum ultraviolet (VUV) laser induced fluorescence. Translational-to-vibrational (T→V) transfer is dominated by the dynamics of collisions occurring in the two wells on the H+CO potential energy surface, one characterizing the HCO radical and the other characterizing COH. The measured vibrational distributions agree well with the results of trajectory calculations performed on the ab initio potential energy surface of Bowman, Bittman, and Harding (BBH). The measured rotational distributions show two significant differences from the calculated ones. First, for v=0 the experiments find more population in J〈15 than predicted. This discrepancy may be due to errors in the repulsive part of the BBH surface that is outside the HCO and COH wells, but inside the van der Waals well. Second, for v=1, the experimental distribution is flat from J=0 to J=10, whereas the calculated one rises from near zero at J=0 to a peak at J=12. This discrepancy appears to be the result of an excessively high ab initio estimate (by a few tenths of an eV) of the barrier for H atom addition to CO to form COH.

Notes: The CH(A–X,B–X,C–X) emission systems have been observed from the Ar and Kr afterglow reactions of CH4. A significant attenuation of the CH(A–X,B–X,C–X) emissions by an addition of SF6 into the discharge flow suggested that the CH(A,B,C) radicals are excited via secondary electron–ion recombination processes. Since the CH(A–X,B–X,C–X) emissions disappeared by trapping ionic active species in the discharge flow, the responsible active species for the CH(A,B,C) production were found to be Ar+ and/or (Ar+)* in the Ar flow and Kr+ and/or (Kr+)* in the Kr flow. The contribution of Ar+ and Kr+ was examined in the He afterglow, where Ar+ or Kr+ and slow electrons were simultaneously produced by the He(23S)/Ar,Kr Penning ionization. Although intense CH(A–X,B–X,C–X) emissions were observed from Ar+/CH4 where CH+n(n=2–4) were formed, they were absent from Kr+/CH4 where only CH+4 was produced. It was, therefore, concluded that CH+2 and/or CH+3 are important precursor ions for the CH(A,B,C) production. The intensity distribution of CH(A,B,C) and the CH(A,B) rovibrational distributions obtained in the Ar afterglow agreed with those through Ar+/CH4, indicating that Ar+/CH4 plays a significant role for the production of precursor ions in the Ar afterglow or (Ar+)*/CH4 provides the same precursor ions. Since the relative intensity of CH(A,B) and the rovibrational distributions of CH(A) in the Kr afterglow were different from those in the Ar afterglow, different electron–ion recombination processes dominantly take part in the CH(A,B) production.

Notes: Guided ion-beam mass spectrometry is used to study the reactions of methane with O+2 in its ground electronic and vibrational state. In addition to the three previously reported reaction products, CH2OOH+, CH+3 , and CH+4 , we also observe three other products, CH2O+2 , H3O+, and CO+2 . Reactions of excited O+2 ions are also examined and are shown to be more efficient than those for ground-state ions. The thermochemistry and potential-energy surfaces for this reaction are discussed as well as the effects of vibrational, electronic, and translational energy on the reaction system. A heat of formation for CH2O+2 of 201.5±1.6 kcal/mol is measured and tentatively assigned to the methyne hydroperoxy ion structure, HC–O–OH+.

Notes: For the electronic ground state of CO+2 the three-dimensional potential energy, electric dipole, and transition moment functions have been calculated from highly correlated multireference configuration interaction electronic wave functions. Along the antisymmetric stretching displacements the shape of the potential energy functions is found to be very sensitive to the electron correlation effect. Using a modified theoretical potential energy function rovibronic energy levels have been calculated variationally by the method of Carter and Handy. In this approach, anharmonicity, rotation–vibration, electronic angular momenta, and electron spin coupling effects have been accounted for. The vibronic band origins agree to within about 10 to 20 cm−1 with the available experimental data, and the rotational levels agree to within 0.01 cm−1 for low J values. Additional vibrational band origins have been predicted for energies up to 3200 cm−1. The anomalously low frequency of the antisymmetric stretching mode and its inverse anharmonicity in the X 2Πg state of CO+2 have been reproduced with the potential energy functions for the adiabatic states. Previously, it has been assumed that this effect is due to the vibronic coupling. The molecular parameters of one-dimensional effective Hamiltonians obtained from fits of the spectral data are compared with those derived from the theoretical potential.

Notes: The double proton transfer reaction of the isolated formic acid dimer has been investigated within the reaction surface Hamiltonian framework, using a newly calculated three-dimensional ab initio potential energy surface. The symmetric (synchronous) proton movement, the asymmetric (asynchronous) proton movement and the relative motion of two formic acid molecules have been explicitly included in the calculation. The calculation gives a tunneling splitting of 0.004 cm−1, which is considerably smaller than a previous theoretical prediction (0.3 cm−1). An effective tunneling path has been calculated from the lowest vibrational eigenfunction of the reaction surface Hamiltonian, and the path deviates significantly from the minimum energy path on the potential energy surface. The new results are consistent with the conventional understanding of heavy–light–heavy mass combination reactions. The effective reaction path from this calculation reveals evidence of asymmetric proton movement. However, a synchronous double proton transfer is the major mode of reaction. Tunneling splittings for a few excited vibrational levels have also been calculated within the reaction surface Hamiltonian framework. Vibrational excitation of a large amplitude, heavy atom mode dramatically increases the tunneling splitting.

Notes: The deterministic kinetics of chemical reactions is compared with a stochastic description for the cubic Schlögl model with a single stable steady state, which has a nonlinear reaction mechanism. We solve numerically the birth-death master equation for this system for various numbers of particles (N=20–160). For small systems with tens of particles the deviation of the first moment of the stochastic distribution from the deterministic temporal variation of concentration can be substantial in the initial relaxation towards a stationary state. The relaxation of the master equation is faster than that of the deterministic equation. The maximum deviation in trajectories decreases as the parameters in the kinetic model are altered towards a linear mechanism. The maximum deviation differs from N1/2 as N decreases, but approaches N1/2 as N increases. Deviations from deterministic temporal evolution due to fluctuations depend on the extent of nonlinearity of the reaction. The variance of a stationary distribution of the master equation is shown to be significantly larger than the average for a nonlinear system.

Notes: The dissociation rates of energy-selected ethylchloride and deuterated ethylchloride ions were measured as a function of the parent-ion internal energy by the method of photoelectron photoion coincidence. Previously performed ab initio calculations indicated that the rate-determining step for this reaction is an H-atom transfer from the β carbon to the Cl atom via a substantial energy barrier of 92 kJ/mol (referenced to the zero-point energy). The ion internal energy range in which the experimental rates varied between 105 and 107 s−1 was found to lie well below the calculated barrier for H-atom transfer. The rates were modeled with the RRKM statistical theory which includes a tunneling step through an Eckart potential. The vibrational frequencies of both the normal and deuterated ethylchloride ions were determined by ab initio molecular-orbital methods. The theory accounted very well for the absolute rates including the strong deuterium isotope effect. The measured kinetic-energy release distribution appears nonstatistical. This indicates that the ion–dipole complex, which lies in between the transition state and the C2H+4+HCl products, is ineffective in randomizing the potential energy of the reverse activation barrier.

Notes: Frequency dependent second hyperpolarizabilities of N2 and the prototype organic molecule trans-butadiene are reported using generalized time dependent Hartree–Fock (TDHF) theory for several frequencies of applied fields. A monotonic increase of the values (positive dispersion) is observed for every nonlinear optical process in a range of frequencies for the applied field. Correlation effects are estimated using a second-order many body perturbation theory and coupled cluster singles and doubles relaxed density method for the analytical determination of the induced dipole moment. Such hybrid results for DC-induced second harmonic generation provide reasonable values in comparison with experiment for N2. However, dispersion and correlation effects in trans-butadiene are both found to be large and could be nonadditive.

Notes: A multireference coupled-cluster singles and doubles method utilizing two reference determinants which differ by a two electron excitation is proposed. One of these determinants is selected as the formal reference determinant. The proposed method includes single-reference coupled-cluster equations truncated after quadruples. These equations are graphically derived using Feynman diagrams. The appropriate restrictions are then placed on the triple and quadruple amplitudes to allow only those amplitudes which correspond to single and double excitations from the second reference determinant.

Notes: Collisional removal rate constants for the OH radical in v=12 of the ground electronic state are measured for the colliders CO2, O2, N2, H2, He, and Ar. OH molecules, generated in v=8 by the reaction of hydrogen atoms with ozone, are excited to v=12 by direct overtone excitation with pulsed infrared laser light. The temporal evolution of the v=12 radicals is probed as a function of collider gas pressure by a time-delayed pulsed ultraviolet probe laser. The probe laser is used to excite the molecules via the B 2Σ+–X 2Πi(0,12) electronic transition, and the resulting B 2Σ+–A 2Σ+ fluorescence is detected. We measure rate constants for CO2:(5.6±1.5)×10−11; O2:(1.6±0.2)×10−11; He:(3.6±0.6)×10−12; H2:(3.0±0.8)×10−12; Ar:(2.6±0.5)×10−12; N2:(2.5±0.7)×10−12 (all in units of cm3 s−1). These rate constants are over fifty times faster in all cases than the vibrational relaxation rate constants for the lower levels (v=1 and v=2) of the ground state.

Notes: We implement here the recursion method and its extensions to the case of nonorthogonal bases (Riedinger et al., 1989) for determining the electronic structure of molecules of intermediate size. The recursion method, which is a variant of the Lanczos method, has been introduced by Heine, Haydock, and Kelly in solid state physics during the 1970s. It provides an invaluable tool for studying the electronic structure of solids and amorphs in direct space, without explicit diagonalization, in the case of orthogonal bases. Applications with nonorthogonal bases are made on the decavanadate ion (V10O28)6−, described within the extended Hückel model. Our extension of the recursion method may even be applied to molecules of large size or to infinite systems, where the usual methods of quantum chemistry fail. It applies to crystals as well as to glasses and molecules, for which no translational symmetry exists.

Notes: In this paper we present the results of a theoretical study of the local geometry distortions produced by Cr+ and Cr3+ ions in fluorite, by means of the ab initio environment model potential method [J. Chem. Phys. 89, 5739 (1988)]. The valence energy and wave function of the (CrF8)q−(q=7,5) clusters embedded in the CaF2 lattice represented by 118 ab initio model potential ions plus 750 point-charge ions are calculated using a short CI, which includes all states related to the dn ionic configuration. A geometry optimization is performed for CaF2@B:(CrF8)7− within the cubic point symmetry and for CaF2@B:(CrF8)5− within the D3d point symmetry; the conclusions of analyses of the multimode Jahn–Teller coupling T1⊗(ε+τ2+τ'2) are used to address the geometry optimization, which is completed by a final unrestricted search. In an attempt to study all the structures proposed along previous experimental studies, the D3d structure corresponding to an octahedral cluster plus two axially displaced fluorines (octahedron+2) is investigated. Taking the ground state energy of the perfect cube as a reference, the results show that the most stable D3d distortion corresponds to an elongated cube in a 4A2g ground state, with an energy of about −1700 cm−1, while the compressed cube and the octahedron+2 structure energies are found to be −780 and +40 000 cm−1, respectively. A joint analysis of the available experimental data and the results of our calculations are presented.

Notes: Multireference configuration-interaction methods have been used to calculate equilibrium geometries for different C4 structures, using large basis sets of atomic natural orbitals. The ground state of C4 is found to be linear, cumulene-like with a 3∑−g electronic state and with an energy 4.1 kcal/mol below the rhombic structure. We show that the choice of basis set plays a crucial role in the determination of the ground-state conformation.

Notes: A scheme which may be considered "efficient'' has been evolved for the "exact'' determination of the free energy of classical fluids with arbitrary interparticle many-body interaction potentials. The judgment as to the extent of closeness of this scheme to an "ultimate'' approach (which up until now has been sought by researchers for the investigation of equilibrium properties of fluids) is one presently expected to be subjective. The versatility of the "recipe,'' however, is one that may be considered quite remarkable; and its "natural flavor'' seems to suggest the approach is one that is forced upon us rather than the approach being a tool that has been artifically fashioned and forced by us into the problem. Application of the scheme to a few simple realistic fluid models has proved quite successful. However, more elaborate applications are expected in the future to provide an ultimate test of the suitability of the scheme.

Notes: Because nearest-neighbor probability distributions have been found to be useful for an exact investigation of the statistical thermodynamics of classical fluids, their exact form (valid for fluids in which many-body interaction potentials may obtain) has therefore been developed in the present paper. For an introductory familiarization with nearest-neighbor probability density functions (NNPDF's) their connection with the commonly employed n-body distribution functions is first given. The usefulness of NNPDF's in the analysis of structure in classical systems is also briefly discussed. A notable development associated with the paper is the fact that while "useful'' exact expressions are not easily determined directly for n-body distribution functions (as evidenced by the several unsuccessful attempts to derive them in the literature), they are readily obtained directly for NNPDF's (which are closely related functions) even where the "most general'' interparticle interaction potentials may be said to obtain.

Notes: The solvent mediated force between the hard solutes mimicking liophobic colloids in Baxter's adhesive solvent is studied on the basis of the solution to the Percus–Yevick/Ornstein–Zernike equation for spatial correlations in an infinitely dilute solution. The contact value of the solute–solute potential of mean force remains the same as observed previously in hard sphere fluid but its range increases in the presence of the attractive interaction among the molecules of the solvent. At the critical conditions of the model fluid, the solvation force between the macroparticles tends to vanish in parallel with the increasing compressibility of the fluid. The size dependence of the intercolloidal interaction is similar but slightly more pronounced than found in fluids with pure hard core interaction.

Notes: We report exact results for the problem of diffusion over a barrier, for a piecewise linear potential. Full solution of the diffusion problem is obtained in the Laplace-transformed time variable. The "survival probability'' of a particle not to have escaped over the barrier at large times is studied in detail, and the results are compared with the asymptotic predictions of Kramers in the large-barrier limit.

Notes: Using the complete active space multiconfiguration self-consistent field (CAS-MCSCF) followed by full second-order configuration interaction (SOCI) calculations, 16 electronic states of LaH+ and 8 electronic states of LaH+2 are investigated. The potential energy surface of these electronic states of LaH+2 and LaH+ are computed. These calculations show that the 3F(5d2) ground state of La+ ion forms a weak complex with H2. The La+(1D) excited state inserts into H2 with a small barrier (〈8 kcal/mol) to form the 1A1 ground state of LaH+2 (re=2.057 A(ring), θe=106°). At the SOCI level of theory LaH+2 is found to be 11 kcal/mol more stable than La+(3F)+H2. Our calculations explain the experimental observations on La++H2→LaH++H reaction. The adiabatic ionization potential (IP) of LaH2 and LaH are calculated as 5.23 and 5.33 eV, respectively. The ground state of LaH+ was found to be a 2Δ state. We compute De(LaH+) and De(HLa–H+) as 2.54 eV in excellent agreement with the experimental De(LaH+)=2.57 eV measured by Armentrout and co-workers. The spin–orbit effects of LaH+ were also studied using the relativistic configuration interaction (RCI) method.

Notes: Using the unrestricted Hartree–Fock procedure, we have studied the numbers and locations of water molecules in the second hydration shells of the Mn+2–aquoion system. Two arrangements for the second hydration shell were considered, one involving 8 water molecules located along the body diagonals of a cube with Mn+2 ion at the body center and the other with 12 water molecules located in the directions of the lines joining the Mn+2 ion and the midpoints of the sides of the cube. Both these arrangements of the second hydration shells were considered in the presence of the octahedral arrangement of six water molecules in the first hydration shell. The total energies of the composite clusters were minimized with respect to the metal–oxygen distance for the second shell of water molecules to determine the equilibrium geometries in the two cases. From a consideration of the hydration energies, the eight-molecule configuration was found to be the more likely one for the second hydration shell, the metal–oxygen distance for the second shell being 3.75 A(ring) as compared to 2.19 A(ring) for the first. A physical reason associated with steric effects within the second shell water molecules and between the first and second shell molecules is suggested for the greater stability of the 8-member hydration shell as compared to the 12-member one. Using the calculated geometry, the contribution to the proton relaxivity in aqueous solution from the second hydration shell was determined to be 9.9% of that from the first hydration shell in the dipolar interaction regime, in magnetic fields of 0.25 T (corresponding to proton resonance frequency of about 10 MHz) and above and progressively smaller in importance as one went to lower fields corresponding to the contact interaction regime.

Notes: Here we present an ab initio study of the many-body expansion for the water–water interaction. Emphasis is made in the difference in convergence of the expansion for the different phases of water. It is shown that for the geometrical arrangements that appear in liquid water, the four-body nonadditivity is larger and the convergence slower than for the other two phases. Hence particular attention should be given for the proper description of the interactions in the aggregates that will arise in the numerical simulations of liquid water.

Notes: The moderation of subexcitation electrons in H2 and D2 is investigated by using the Spencer–Fano (SF) equation and the continuous-slowing-down approximation (CSDA). Cross-section data are adopted from the compilation by Buckman and Phelps [J. Chem. Phys. 82, 5001 (1985)]. Throughout, we focus on isotope effects, i.e., differences between H2 and D2, and consider electrons at energies appreciably higher than thermal energy. In summary, because vibrational and rotational excitation channels have lower thresholds in D2, subexcitation-electron behavior in D2 at energies below 0.6 eV shows different characteristics from that in H2. The moderation rate in H2 is larger than that in D2 by a factor of about 1.7. This difference is close to but not exactly the factor of 2 expected from an elementary estimate.

Notes: A new viewpoint on the kinetics of electrochemical nucleation of a new phase is presented by numerically solving the kinetic equations recently derived by one of the present authors (M.T.) to study the many-body effects on diffusion-controlled three-dimensional nucleus growth on a substrate. The static many-body (screening) effect is shown to cause the crossover of the growth exponent for the average nucleus radius from 1/2 to 1/6. Hence the electric current grows as t1/2 at short times and falls with t−1/2 at long times, according to the Cottrell equation. The dynamic many-body (correlation) effect is shown to give rise to a dispersion in the size of the nuclei and thus to cause appreciable corrections to the amplitudes for the radius and the current in the zero limit of volume fraction Q. The corrections go as Q1/2t1/3 and hence cause a large deviation of the average current from the Cottrell equation at long times. Nonthermal fluctuations around the mean motion generated by the correlation effect are also explicitly explored together with a comparison with thermal fluctuations existing at the beginning. A computer simulation is finally performed to confirm the validity of the kinetic equations. The theoretical results are shown to have excellent agreement with the simulation.

Notes: We introduce an operator formalism for random sequential adsorption on lattices and in continuous space. This provides a convenient framework for deriving series expansions for the deposition rate dθ/dt in powers of t. Several specific examples—the square lattice with nearest-neighbor exclusion, and with exclusion extended to next-nearest neighbors, and disks and oriented squares on the plane—are considered in detail. Precise estimates for θ(t) and the jamming coverage are obtained via Padé approximant analysis. These are found to be in excellent agreement with simulation results. A diagrammatic expansion for dθ/dt is derived, and its relation to the equilibrium Mayer series is elucidated.

Notes: Ab initio configuration-interaction (CI) calculations for the first electronic states and for the first six ionization potentials of trifluoromethane are reported. The UV spectrum is analyzed and the nature of the Rydberg transition is discussed in terms of the analysis of calculated charge transfer of each state. It is clearly seen that the distinction among type s, p, or d Rydberg states is difficult to establish and that the more intense broadband (B region) results from the overlapping of transition with different natures and intensities.

Notes: Ab initio molecular electronic structure methods have been used, in conjunction with large basis sets, to investigate the possible existence of isomers of the conventional C2v open-chain NO2 and its anion, NO−2. Equilibrium geometries have been optimized and harmonic vibrational frequencies obtained for both the "peroxy'' and cyclic isomers of these species at the self-consistent-field (SCF), single and double excitation configuration interaction (CISD), coupled cluster including all single and double substitutions (CCSD), and complete active space (CAS) SCF levels of theory utilizing both double-zeta plus polarization (DZ+P) and quadruple-zeta plus double polarization (QZ+2P) basis sets. For comparison, "normal'' (C2v open-chain) NO−2 was also studied. Diffuse functions were added to these basis sets to provide a better description of the electron densities of the anionic isomers. The four peroxy and cyclic structures investigated were predicted to be relatively high-lying (≥60 kcal mol−1) minima at most levels of theory considered. Moreover, interconversion between the C2v and Cs open-chain forms appears unlikely both for NO2 and NO−2.

Notes: This study utilizes a newly implemented method based on first-order perturbation theory for calculating the electronic magnetic circular dichroism (MCD) spectra in molecules. As an initial application, the MCD band maxima have been calculated for the B˜(1 1Bu)←X˜(1 1Ag) and 1 1B2←X˜(1 1A1) electronic transitions in the trans and cis bent conformations (respectively) of acetylene. The band intensity is assumed to come entirely from the B0 term in the MCD equations of Stephens, which explicitly includes a first-order perturbation correction to the two electronic states involved in the transition. The wave functions are determined using ab initio quantum chemical techniques including state averaged CASSCF and multireference CI. There has been speculation that the 1 1B2←X˜ band system might overlap the B˜←X˜, and be part of the reason for the diffuse nature of the spectrum in the 185–170 nm region. This study considers this claim. The current calculations predict MCD band maxima for the 0–0 and 1–0 vibrational bands in the B˜←X˜ to be Δεmax0=−3.48 and −5.82, respectively, while experiment gives −0.8 and −1.6. This is 103 times larger than the largest band maximum [Δεmax0(3–0)=−0.0037] calculated for the 1 1B2←X˜ transition. This study also finds the absorption oscillator strengths for the B˜←X˜ to be a factor of 60 larger than that found in the 1 1B2←X˜. Thus while these results do predict both the B˜←X˜ and 1 1B2←X˜ transitions to lie in the same spectral region, they do not support the hypothesis that the 1 1B2←X˜ is a major contributor to either the absorption or MCD intensity in the 185–170 nm region.

Notes: The electronic and dynamic properties of all-trans polyacetylene have been calculated on the basis of oligomer calculations on H–(CH)10–H and H–(CH)22–H at the ab initio 6-31G level. The calculated ir and Raman intensities are in good agreement with the experimental relative intensities.

Notes: We explore a mechanism for the remarkable charge isolation of the localized, or trapped, electrons found in the crystalline electrides Cs(18C6)2 and Cs(15C5)2. 133Cs NMR measurements show only ≈ 0.05% atomic character of the spin density at the Cs nucleus, consistent with many features of the structure and measured properties which indicate that the localized electron distribution is centered at the anion vacancies. The optical absorption data suggest that the localized electrons, which give rise to the Curie-law spin susceptibility, must penetrate appreciably into the crown ethers, (18C6) and (15C5), which encapsulate the Cs. We suggest that the large reduction of the spin density at the Cs nucleus is due to a Coulomb barrier resulting from negative charge on the oxygens. A crude model, one electron moving in two spherical charged shells surrounding the Cs core, illustrates the mechanism and accounts accurately for the ratio of spin densities at the Cs nucleus found in the 18C6 and the 15C5 electrides. Hartree–Fock calculations for an idealized model of an isolated Cs(18C6)2 molecule, namely Li(9C3)2, tend to support the mechanism.

Notes: The Belousov–Zhabotinskii reaction in an annular gel reactor [Z. Noszticzius et al., Nature 329, 619 (1987)] is modeled by the reduced two-variable Oregonator with radial gradients in the concentration of bromate and malonic acid. This model is found to produce a wave shape and dispersion relation that are in satisfactory agreement with the experimental data. The numerical studies also reveal that the pinwheel dynamics can be understood in terms of the local chemistry in the reactor.

Notes: The critical behavior of six polyisoprene/poly(ethylene–propylene) binary blends has been examined, primarily by dynamic light scattering. Specifically, the decay rate (Γ) of fluctuations in composition has been measured as a function of scattering vector (q) and temperature, above the stability limit. The results are interpreted in the context of mode-coupling corrections to the dynamics. Theoretically predicted crossovers between mean-field and nonclassical regimes, and between mode-coupled and mode-decoupled dynamics, are clearly seen. The mean-field to nonclassical crossover, or Ginzburg criterion, is localized, and the mode-coupled to mode-decoupled transition in the dynamics occurs well into the static mean-field regime. In addition, geometric crossovers between Γ∼q2 ("diffusive'') and Γ∼q3 or Γ∼q4 ("critical nondiffusive'') regimes are in quantitative agreement with theory. The applicability of the Kawasaki–Stokes relationship between Γ and the dynamic correlation length is also demonstrated.

Notes: The macroscopic properties of two-phase random heterogeneous media depend upon an infinite sequence of n-point functions S(i)n(x1,x2,...,xn) giving the joint probability of finding n points with positions x1,x2,...,xn all in phase i. This paper reports the first study and calculation of the two-point probability function S(i)2 for distributions of oriented, hard spheroids with eccentricity ε in a matrix. This is a useful model of statistically anisotropic two-phase media, enabling one to examine the special limiting cases of oriented disks (ε=0), spheres (ε=1), and oriented needles (ε=∞).

Notes: A modified dynamic reaction coordinate algorithm for tracing reaction paths is implemented in the framework of ab initio molecular orbital calculations. This method requires fewer energy and gradient evaluations than the traditional intrinsic reaction coordinate methodology and produces reaction pathways of acceptable accuracy. The approach is applied to the 1,5 hexadiene Cope rearrangement for which we trace the pathways passing through the chair and boat transition states. Analysis of the lowest energy pathway indicates that the rearrangement is concerted and synchronous.

Notes: Dynamic percolation theory is used to obtain the tracer diffusion coefficient in binary mixtures of "noninteracting'' lattice gas (with only the blocking interactions, i.e., double occupancy of a lattice site is forbidden) within the effective medium approximation (EMA). Our approach is based on regarding the background particles as a changing random environment. The result is expressed in terms of two fluctuation time parameters which we attempt to determine self-consistently. We compare two possible choices for these parameters which are consistent with our former results for the single component system. The resulting tracer diffusion coefficient for both choices compares well with numerical simulations whenever single bond EMA is expected to be reliable. Comparison is also made with the theoretical results of Sato and Kikuchi [Phys. Rev. B 28, 648 (1983)] and discrepancies between both theories are discussed.

Notes: The orientational properties of crystalline A–TCNB are calculated using a Monte Carlo procedure, based upon a previously reported site–site expression for the interactions between molecules. The nearly static TCNB complexes are orientationally quiescent. The A molecules respond to an orientational double well potential provided by the TCNB, and by their mutual interactions. As a consequence, the dominant part of the orientational Hamiltonian depends on only a single degree of freedom, from which the results are determined. Properties calculated include the orientational structures, internal energy, specific heat, and the phase transition temperature. Various order parameters are calculated to understand the microscopic nature of the transition, which seems to show features of both an order–disorder and displacive character, much like experimental interpretations.

Notes: We are able to reproduce the experimental volume and temperature dependence for quasiparticles of helium ii from the theoretical study reported here. We use the energy excitation spectrum together with a Hartree term as derived before [Physica Status Solidi A 159, 52 (1989)].

Notes: We present a new strong principle of corresponding states that reduces the entire pressure–volume–temperature (p–v–T) surface of a nonpolar fluid to a single curve; this curve corresponds to an effective pair distribution function at contact as a function of reduced density. This reduction of a surface to a curve is based on statistical-mechanical theory, which also furnishes the algorithms for calculating, from the intermolecular pair potential, the three temperature-dependent parameters needed for the reduction. If the pair potential is not known, data on the second virial coefficient as a function of temperature can be used instead. The principle is tested on a computer-simulated Lennard-Jones (12,6) fluid, on the noble-gas fluids (except He), on N2, CO2, CF4, SF6, and on the first four alkanes. A suitable reciprocal plot yields virtual straight lines for all the real fluids, which differ in shape from the expected Carnahan–Starling curve that describes the (12,6) fluid; we suggest that these shape differences are caused by many-body forces in the real fluids. By curve fitting straight lines to the empirical data for the real fluids, we obtain a simple analytic equation of state, cubic in the density, that can be characterized by three constants: the Boyle temperature, the Boyle volume, and a slope constant. This equation is not accurate in the nonanalytic critical and two-phase regions, but otherwise describes the volumetric behavior of nonpolar fluids very accurately over the entire range from the dilute gas to the dense liquid. It has considerable predictive power, since it permits the construction of the entire p–v–T surface from just the second virial coefficient plus a few liquid densities.

Notes: The kinetics of NH3 and ND3 desorption from Cu(001) surface have been measured by time-resolved electron energy loss spectroscopy. The desorption precess is observed to be characterized by pseudo-first-order kinetics. The desorption energy and the prefactor have been determined for both NH3 and ND3. The prefactors are unusually low as compared to those observed for simple diatomic molecules. Moreover, we observed an unusual behavior consistent with an isotope kinetic compensation effect. Both of these observations can be explained within the context of transition state theory by the interplay between isotopic masses and the shifts of frustrated vibrational modes of adsorbed molecules. Our results imply that the conventional Arrhenius form would not be precisely applicable to molecular desorption, if a large enough temperature range could be measured, particularly for hydrogen-containing molecules.

Notes: The Raman noncoincidence effect and line width of the symmetric C(large-closed-square)O stretching band have been measured in liquid propylene carbonate (PC), chloroethylene carbonate (CC), and dichloroethylene carbonate (DC) as a function of pressure up to 3 kbar and over the temperature range from −20 °C to 40 °C. The transition dipole moments of the C(large-closed-square)O mode for these liquids have also been determined by means of infrared spectroscopy at ambient conditions. The temperature, density, and transition dipole moment dependences of the experimental noncoincidence effect for these liquids are quantitatively interpreted in terms of Logan theory. An excellent agreement between the experimental results and theoretical predictions indicates that the observed noncoincidence effect is due to the transition dipole moment coupling and permanent dipole moment coupling. For the study of isotropic bandwidths, the band narrowing with increasing density is found for liquid CC and DC and quantitatively explained by means of intermolecular interactions, whereas band broadening is observed for PC. The latter broadening is unexpected since PC possesses the largest permanent dipole moment of these three liquids. A probable reason for difficulty in the interpretation of this result is given.

Notes: We have determined the angular distributions of H2, HD, and D2 desorbing from Cu(111) for surface temperatures in the range 370–800 K. These are found to be strongly peaked and symmetric about the surface normal in every case. Results for all three isotopes are found to be indistinguishable, being close to a cos 12θf distribution at 600 K, slightly narrower at 370 K, and slightly broader at 800 K. Results are discussed in terms of other previous desorption measurements and related to adsorption data via detailed balance.

Notes: A theory of homogeneous nucleation from the vapor phase is presented, which is based on an extension of Fisher's semiphenomenological droplet model for the Gibbs free energy of formation of a cluster. This droplet model allows translational, rotational, vibrational, and configurational degrees of freedom of the cluster as well as the variation of surface tension with cluster size. By suitable choice of the three free model parameters, known nucleation theories such as the classical Becker–Döring–Zeldovich theory and others are obtained as special cases. Since, however, an ansatz for the Gibbs free energy of formation allows the construction of an equation of state for real gases below the critical point, a new method of determining the model parameters is suggested, which is based on the idea of forcing the identity of the constructed equation of state with an experimentally verified one. Thus, all free model parameters can be determined purely from well-known handbook properties. It is shown that the new theory gives a better prediction of observed nucleation rates than the classical one.

Notes: We study bond-orientational order in liquid Si via Monte Carlo simulation in conjunction with empirical two- and three-body potentials of the form proposed by Stillinger and Weber. Bond-orientational order (BOO) is described in terms of combinations of spherical harmonic functions. Liquid Si is found to have pronounced short-range BOO corresponding to l=3, as expected for a structure with local tetrahedral order. No long-range BOO is found either in the equilibrium or the supercooled liquid. When the three-body potential is artificially removed, the tetrahedral bond-orientation order disappears and the liquid assumes a close-packed structure.

Notes: A semiempirical procedure was developed, within the framework of a modified electrostatic effective charge model, that links crystal field parameters with microscopic local structures of tetragonal symmetry centers in fluorite crystals doped with trivalent rare-earth ions. The procedure was used to study tetragonal centers in Er3+:CaF2, Dy3+:CaF2, and Eu3+:SrF2 systems. It is shown that satisfactory a priori predictions of experimentally observed energy level schemes of the spectra of interest, as well as reconstructions of local microscopic structures of the emitting centers in accord with other relevant information collected up to date, are thus obtained. An examination is also made of a spectrum that in the past was linked to a tetragonal center in the Eu3+:CdF2 system, and the results obtained indicate that it appears to be associated with a center (or centers) that is structurally different from the tetragonal centers present in the other rare-earth: fluorite systems.

Notes: The Monte Carlo method is applied to the study of disordered conformations of polymethylene chains confined in cylindrical mean-field potentials. It is assumed that the molecule, which is composed of 30 united atoms (methylene groups), has fixed bond length and bond angle, and makes quasicontinuous bond rotations. Various statistical properties of the molecule, such as dihedral angle distributions, dihedral angle pair correlations, transverse fluctuations, etc., are calculated vs strength of the mean-field potential. The dihedral angle distributions calculated exhibit the marked reduction of the gauche peaks with increasing potential; it implies the increasing inaccuracy of the usual rotational isomeric model. The dihedral angle pair correlations reveal novel characteristics of the dihedral angle fluctuation: the fluctuation has approximate period of four bonds with marked tendency for the next nearest bonds to counter-rotate. The characteristics are more conspicuous under weaker potential constraint. There are large transverse fluctuations of the chain, the average linear form of the chain being still maintained. These characteristic dihedral angle fluctuation and the transverse deviation of the chain are found to be well understood by a small scale kink model.

Notes: There has been a long standing disagreement between our flame experiments, which predict a very stable NaO2 molecule, and Na2O(c) vaporization/mass spectrometric studies of Hildenbrand et al., which imply a weak bond strength from an inability to detect such a species. We have now reanalyzed the vaporization experiments and have identified a possible explanation for this frustrating controversy. It appears that on becoming ionized, NaO+2 fragments to Na+ and O2. As a result, mass 23 reflects p(Na)+p(NaO2). This and the changes to the thermochemical data for NaO2 modifies the earlier ion intensity/vapor pressure calibration. As a result, the previously accepted thermochemical values for NaO and Na2O need to be reduced by 18 and 11 kJ mol−1, respectively. Recommended values now become ΔHf298K (NaO)=87±4, D0(NaO)=266±4, ΔHf298K(Na2O) =−36.0±8 and D0(Na–ONa)=228±8 kJ mol−1. It also appears that the I.P.(NaO2)≤739 kJ mol−1 (7.66 eV).The reported Clausius–Clapeyron vapor pressure curves are entirely consistent with this suggestion that the congruent vaporization of Na2O(c) is to Na and NaO2 rather than to Na and O2. A reinterpretation utilizing the previous slopes of the I(Na+) or I(O+2) signals leads to an independent measure of −90≥ΔHf298K(NaO2)≥−155 and 194≤D0(Na–O2)≤259 kJ mol−1. These are to be compared with the higher temperature flame determined values of −139±8 and 243±8 kJ mol−1, respectively. Earlier vaporization mass loss measurements of Brewer and Margrave were in approximate agreement with a vaporization to predominantly Na and O2. Analyses now show that the technique is insensitive and congruent vaporization to Na and NaO2 also fits their data. Hildenbrand and Murad measured Na+/O+2 ratios but these appeared to be a factor of 4 smaller than expected for congruency and remained unexplained. By invoking an alternate fragmentation of NaO+2 at higher energies to Na and O+2 (A.P.≈14.6 eV), with a branching ratio of ≥10%, this channel becomes the dominant source of O+2 and the observed Na+/O+2 signal ratios are consistent with congruency. These results have important implications for all mass spectrometric studies of alkali/oxygen mixtures including, for example, also carbonates and nitrates. A reappraisal for these is in order, particularly with reference to derived thermochemical values.

Notes: Deuteron magnetic resonance (2H-NMR) spectra have been obtained from a binary mixture of 2-fluorenyl-4'-tetradecyloxy benzoate-d9 (FLOC14) and para-xylene-d10 (p-xy) as a function of temperature [Hoatson et al. Mol. Cryst. Liq. Cryst. (to be published)]. The liquid crystal FLOC14 is selectively deuterated on the rigid fluorene moiety, while p-xy is perdeuterated. Nonlinear least-squares fits to the quadrupolar splittings νkQ allow unambiguous determination of the temperature dependence of the orientational order parameters Sizz and (Sixx−Siyy) of both species i=1,2. These results are the first to provide information on the degree and asymmetry of orientational order of both biaxial molecules in the uniaxial nematic phase of a binary mixture. The new approach introduced to analyze the experimental data allows for an arbitary orientation of the rigid core relative to the molecular axis. The results demonstrate that the splittings and derived order parameters are insensitive to this twist angle. The experimental results are interpreted using a new mean field theory of binary mixtures of biaxial molecules [Palffy-Muhoray and Hoatson (to be published)]. There is good agreement between the predictions of theory and the component order parameters determined from 2H-NMR experiments, over the entire temperature range studied. Thus this description is capable of predicting the temperature dependence and interrelation of the nematic orientational order parameters for both biaxial molecules in a binary mixture. The derived theoretical parameters are interpreted as the ratios of intermolecular interaction strengths.

Notes: Monte Carlo simulations employing the pivot algorithm are used to generate random and self-avoiding walks on two- and three-dimensional lattices. The moments of the end-to-end distance distribution function are calculated from the resulting configurations. It is found that the moments and the shape of the vector distribution function are in excellent agreement with the scaling form derived by des Cloizeaux.

Notes: Monte Carlo simulations are performed to determine the equation of state of star polymers which are modeled as a collection of freely- jointed hard spheres with a central bead that has arms of equal length protruding from it. Three- and four-arm stars are considered with three and five beads per arm, respectively. The generalized-Flory dimer theory is extended to star and branched molecules. The theory's predictions for the compressibility factor are in good agreement with the simulation data for the model star polymers.

Notes: The statistical principle of maximum entropy is applied to the analysis of dipolar couplings from 1H NMR of nonrigid molecules dissolved in liquid-crystalline phases. A distribution function for the orientational and inter-ring angles is so obtained. The most probable internal angle cursive-phi is determined for 4,4'-dichlorobiphenyl (cursive-phi=34°) in the nematic phase of I52, 4-pentyl-4'-cyanobiphenyl (cursive-phi=32°) and 4'-Br-4-Cl-2,6-difluorobiphenyl (cursive-phi=42°) in EBBA. The physical reliability of the distributions determined is discussed. The maximum-entropy treatment seems to indicate a limit for the information on the internal motion obtainable from the experimental data.

Notes: We have used pyridine and a number of related molecules to lower the workfunction of thin Ag films so as to compare the effects of various molecular properties on the photoemission process and on surface electronic modes. We find that a nitrogen lone pair electronic orbital is essential for a large threshold shift. Other molecular properties, such as dipole moment and polarizability have a very small effect. The films are rough, therefore we see strong photoyields at the energy of the surface plasma mode, 3.6 eV. There is also a peak in the photoyield at 3.85 eV, the energy of the bulk plasmon.

Notes: A lattice-gas model for the phase transitions of O monolayers on Mo(110) with interactions ranging up to fifth neighbors, and including a three-particle term, is studied by Bragg–Williams mean-field theory and finite-size scaling of data from Monte Carlo simulations and numerical transfer-matrix calculations. Attention is focused on the p(2×2) phase whose symmetry is that of an XY model with cubic anisotropy. The order–disorder transition lines are shown to exhibit the predicted nonuniversal behavior, and possess tricritical points. A phenomenological finite-size scaling theory for the Monte Carlo order-parameter data in the pertinent case of a third-order coupling in the Landau free energy is established. The order–order transition line between the p(2×2) and (2×1) phases is found to consist of two parts, a first-order line at low temperature, and a line at higher temperatures, along which the model has a pure Kosterlitz–Thouless phase. Good agreement is established with an experimental phase diagram based on low-energy electron diffraction (LEED) data.

Notes: Low energy helium diffraction has been used to study the packing and thermal motion of the terminal CH3 groups of monolayers of n-alkane thiols self-assembled on Au(111)/mica films and a Au(111) single crystal surface. At low temperatures (〈100 K), the terminal CH3 groups are arranged in domains containing a hexagonal lattice with a lattice constant of 5.01 A(ring). As the length of the carbon chain is shortened, an abrupt decrease in the diffraction peak intensities is observed for CH3(CH2)9SH/Au(111)/mica, and no diffraction is observed for CH3(CH2)5SH/Au(111)/mica. This is indicative of a sudden decrease in surface order at around ten carbon atoms per chain. A semi-quantitative estimation of the average domain size of each monolayer surface shows a maximum of 46 A(ring) at intermediate chain length [CH3(CH2)13SH/Au(111)/mica], decreasing to 26 A(ring) at longer [CH3(CH2)21SH/Au(111)/mica] and 41 A(ring) at shorter [CH3(CH2)9SH/Au(111)/mica] chain lengths. No phase transitions could be detected at the surfaces of these monolayers from 35 K to 100 K, but as expected for a soft material, the thermal motion of the n-alkane thiol molecules increases with increasing surface temperature and reduces the diffraction intensities to zero at around 100 K. The relative mean square displacements of the surface CH3 groups along the directions perpendicular and parallel to the surface have been calculated from the temperature dependence of the diffraction peak intensities using the standard Debye–Waller formalism. The measured values are in good agreement with the results from a recent molecular dynamics simulation. [J. Hautman and M. Klein, J. Chem. Phys. 93, 7483 (1990).]

Notes: We report two-dimensional Monte Carlo, mean-field, and exact one-dimensional studies of a statistical-mechanical model for the ripple (Pβ') phase of hydrated phosphatidylcholine lipid bilayers. The model is a p-state chiral clock model coupled to an Ising model through the chiral field. The microscopic parameters of the model are fixed by independently obtained values for pairwise molecular interactions. The one-dimensional model possesses a "floating fluid phase'' characterized by exponentially decaying, spatially modulated correlations. Solutions of the mean-field equations for the model include modulated phases but these are found to be metastable states, and the mean-field phase diagram is dominated by phases characteristic of the p-state chiral clock model. Monte Carlo simulations also reveal clock model phases. However, when unphysical effects due to mod p counting in the Hamiltonian are eliminated, the Monte Carlo simulations reveal a modulated phase, intermediate in temperature between a high-temperature disordered phase and a low-temperature ordered phase which is identified with the chain tilt (Lβ') phase.

Notes: It is demonstrated that the monoexcited configuration interaction matrix, constructed from the localized (or Wannier) orbitals for an one-dimensional extended system with translational symmetry can be used to define a series of finite-dimensional matrices whose lowest eigenvalues and eigenvectors converge to the lowest eigenvalues and eigenvectors of the infinite-dimensional full monoexcited configuration interaction problem. As an illustration, the developed monoexcited configuration interaction approach is applied to the π-electronic model of cyclic polyenes (annulenes) in the framework of the Pariser–Parr–Pople approximation. A standard parametrization scheme has been found to yield a value of ∼2.42 eV for the lowest singlet excitation energy of an infinite polyene, which is in good agreement with the experimental estimate of ∼2 eV.

Notes: The photochemistry of adsorbed CH3Cl on clean and potassium-dosed Pd(100) surfaces has been studied by illumination with low-intensity UV light from a high-pressure Hg lamp. The effects of illumination were established by post-irradiation thermal desorption, Auger and photoelectron spectroscopic measurements. Evidences are presented for photodissociation of the C–Cl bond to give surface bound methyl group coadsorbed with chlorine. The thermal decomposition of the surface methyl is accompanied by desorption of methane, and small amounts of ethane and ethylene. The presence of preadsorbed potassium greatly enhanced the extent of photodissociation of the C–Cl bond. The efficiency of potassium adatoms depended on its amount, i.e., on the work function of the coadsorbed systems. From the study of the wavelength dependence it is concluded that in the photodissociation of CH3–Cl the optical excitation of the substrate to produce photoelectrons plays a dominant role.

Notes: Recently developed methods for obtaining exact and approximate analytical solutions of the reference interaction site model-mean spherical approximation (RISM-MSA) integral equations for liquid mixtures composed of long, flexible polymers are applied to study the critical temperature Tc for phase separation of symmetric isotopic binary blends as a function of degree of polymerization N, spatial dimension D, and fractal dimension df of the individual macromolecules. For ideal random walk coils, the theory predicts a nonclassical behavior given by Tc∝N(D−2)/2 in two and three dimensions, and the classical Flory–Huggins mean field Tc∝N law is recovered in four and higher dimensions. For arbitrary interpenetrating polymeric fractals, the theory predicts Tc∝N(D−df)/df for spatial dimensions below 2df and Flory–Huggins behavior for D〉2df. These novel scaling laws for isotopic mixtures are a consequence of a consistent treatment of chain connectivity on all length scales, intermolecular excluded volume, and a short range unfavorable interaction between hydrogenated and deuterated polymers. A general, closure-independent physical argument based on a renormalization of the bare chi parameter by relatively long range correlated fluctuations in the blend is proposed which reproduces all the qualitative predictions of the RISM-MSA integral equation theory. Analogies with nonclassical critical fluctuation effects are established. Application of the analytical approach to purely athermal blends is also presented. The magnitude and composition dependence of the effective chi parameter is found to be a sensitive function of both spatial and fractal dimensions, and also local nonuniversal features. The various theoretical predictions are favorably compared with recent small angle neutron scattering measurements on binary polymer alloys.

Notes: Cluster size convergency of the chemisorption energy has been studied for the case of fluorine on Ni(100). Bond preparation of the cluster is found to be equally important for fluorine as for the previously studied hydrogen chemisorption. An estimate of the chemisorption energy for fluorine in the fourfold hollow site of Ni(100) is reached based on the average value for the bond-prepared clusters, a correction for the use of one-electron ECP's, an estimate of the basis set limit and finally adding the effect of 3d correlation. The chemisorption energy is in this way estimated to be about 120 kcal/mol. Even though the bonding between fluorine and the surface should be regarded as almost totally ionic, there is still no correspondence between the chemisorption energy for a cluster and the highest ionization energy (Fermi level) of that cluster. The critical feature of bond preparation is that it allows the fluorine lone-pair electrons pointing down towards the surface to be fitted into the electronic structure of the cluster.

Notes: Results from a set of minimum energy calculations performed for the Su Schrieffer Heeger Hamiltonian for trans-polyacetylene are presented. We fix the occupation numbers of the electronic states and look for the bond geometry which minimizes the total energy. The usual nonlinear solutions (polarons, solitons) are recovered for appropriate sets of occupation numbers of the electronic states. We study the spectrum of excited states and the properties of the model in the case of arbitrary doping. The situation where the original SSH Hamiltonian is modified in such a way as to account for the intrinsic periodicity of the monomeric units of conjugated polymers without a degenerate ground state is also examined.

Notes: Intramolecular reactions in entangled polymer systems are studied in the "reptation'' or "tube'' model. In the diffusion-controlled limit the reaction rates are strongly modified by the entanglement constraints and depend sensitively on the positioning of the reactive groups. For two internally positioned groups the fraction of polymers which have reacted after time t,R(t), scales as the volume explored by a group for times small compared to ts where ts is the relaxation time of the portion of polymer connecting the groups. This leads to R(t)∼t3/4 followed by R(t)∼t3/8 for t〈ts . For times larger than ts but less than the longest relaxation or reptation time τrep , R(t) scales as the distance moved by a group along its tube: R(t)∼t1/4 followed by R(t)∼t1/2. For the longest times, t〉τrep , the unreacted fraction [1−R(t)] decays exponentially with a reaction rate constant which is much less than τ −1rep. These results motivate new direct microscopic experimental tests of the reptation model.

Notes: The orientation, absolute coverage and core-electron binding energies of furan (C4H4O) and 2,5-dihydrofuran (C4H6O) on Ag(110) have been measured using near edge x-ray absorption fine structure and x-ray photoelectron spectroscopy. Both furan and 2,5-dihydrofuran (2,5-DHF) are tilted 22±7° from the plane of the surface for both submonolayer and monolayer coverages. The saturation monolayer coverages on the Ag(110) surface of 0.45±0.07 ML for furan and 0.41±0.06 ML for 2,5-DHF are consistent with expectations based on van der Waals radii. The C(1s) binding energies for a monolayer of furan on Ag(110) are 284.8 and 286.2 eV, while the C(1s) binding energies for 2,5-DHF are 285.1 and 286.6 eV. The O(1s) binding energies are 532.8 and 533.8 eV for furan and 2,5-DHF monolayers, respectively. The onset of excitations from C(1s) levels to the continuum lies well above the Fermi level due to the weak bonding interactions with the surface.

Notes: It is well established that when a hyperthermal atom collides with a solid surface, a large fraction of the atom's translational energy may be transferred to the solid in a single collision. The energy transferred to the solid may be channeled into two modes, which are electronic excitation and energy transfer to phonons. In the present work, electronic excitation in the solid was not considered. Thus, it was assumed that energy is transferred during the scattering event from the projectile to the solid vibrational modes only. Since the gas particle interacts with a limited small number of surface atoms, a "hot spot'' is formed on the surface. We found that the excitation of the vibrational modes of the solid decays initially with a decay constant of less than 0.5 ps and then more slowly with a decay constant of 2.5–3.5 ps. A discussion of which vibrational modes are excited is also given.

Notes: The distribution of condensing metal atoms over the two types of sites present on an atomically smooth Ir(111) has been measured in a field ion microscope. For Ir, Re, W, and Pd from a thermal source, condensing on Ir(111) at ≈20 K, the atoms are randomly distributed, as expected if they condense at the first site struck.

Notes: Polymer chains adsorbed on rough impenetrable surfaces have been investigated analytically and by simulations. The cases of physical and chemical roughness of surfaces are identified and their distinctive effects on the adsorption characteristics are studied. For the chemically rough surface the adsorption temperature is depressed by an amount proportional to the concentration of the impurities. A polymer adsorbed on a physically rough surface can be interpreted using the analogy to a one-dimensional electron in a periodic potential. It is shown that at low temperatures the chain is "localized'' in one of the wells. Between the localized regime and the unbinding transition point, there exists a "diffusive'' regime, where the chain is diffusing by being shared by several potential wells. This regime is equivalent to the conduction band in the electron analogy. In contrast to the case of a flat surface, the unbinding transition of a chain from a periodically rough surface is markedly sharp due to an effective anchoring of the chain in the wells.

Notes: The radical anions of alkynes have been first observed by electron spin resonance spectroscopy following alkene anions previously studied. Hexyne radical anions were formed in 1-, 2-, or 3-hexyne/n–hexane mixed crystals irradiated at 4.2 or 77 K. The characters of the anions were as follows; (a) the α-proton hyperfine coupling is very large (∼4.5 mT for the 1-hexyne anion), (b) the β-proton couplings are very small (∼1.0 mT for C–Hβ proton with the conformational angle of 0°), and (c) the radicals show a negative g shift (2.0014). From these observations, it was found that the anions have a nonlinear(bent) molecule structure in the anticonfiguration (trans C–C≡C–C) with the bend angle ∼60°, and that the unpaired electron orbital is approximately composed of the anticombination of the sp2 hybrid orbitals of the C≡C carbon atoms. A discussion based on complete neglect of differential overlap (CNDO) molecular orbital (MO) calculations was given for the observed negative g shift, which was shown to be characteristic of the alkyne anions which have a high-lying unpaired electron orbital and an antibonding 2p–2p π carbon orbital just above it on the upper energy side.

Notes: Thermal desorption of hydrogen from the Si(111)7×7 surface was investigated using optical second-harmonic generation to monitor the hydrogen coverage from 0.2 monolayer to below 0.01 monolayer. The results of isothermal desorption measurements are found to be compatible neither with simple first nor second-order kinetic behavior. It is suggested that different binding sites available for Si–H monohydride states on the Si(111)7×7 surface give rise to the apparent intermediate reaction order.

Notes: Photochemistry involving two types of molecules coadsorbed at monolayer coverage on a catalytically active single crystal metal surface at low temperatures has been observed with mass spectrometry and high resolution electron energy loss spectroscopy. Irradiation in the wavelength range 240–365 nm of H2S and CO coadsorbed on Cu(111) at 68 K leads to the desorption of H2, CO, H2S, HCO, H2CO, and the formation of HCO, H2CO, and OCS on the surface. The primary step of the photoreaction involves the selective photodissociation of H2S, generating a hot H atom (significantly more energetic than in thermal equilibrium) and HS fragment in ground and excited vibrational states. Subsequent collisions with coadsorbed species give rise to the observed photoproducts. The wavelength dependence for CO and HCO formation generally follows that of the H2 signal. The cross sections at 240 nm for photoinduced desorption of the two most abundant products, H2 and CO, are 2.4 ± 0.7 × 10−20 and 1.2 ± 0.6 × 10−20 cm2, respectively.

Notes: Microscopic theory of proton transfer in a symmetric and weakly asymmetric H-bond complex within some larger molecular system is formulated. The potential of the proton motion is assumed to be the double well one and a two-level approximation is used. The proton motion in the double well potential is taken to be strongly coupled to the end atom vibration of the H bond, which is subsequently coupled to other degrees of freedom forming a heat bath. The solution of the problem by means of Liouville equation and projection operator technique allows us to show (at least on this model) the connection between the rate constant formulation and the microscopic theory.

Notes: General expressions in terms of van Hove time correlation functions are given for the wave vector frequency-dependent dielectric function of multicomponent mixtures. The van Hove functions are obtained by applying the Kerr approximation and the dielectric relaxation at zero wave vector is considered in detail. At this level of theory, the frequency-dependent dielectric constant depends upon the self-reorientational correlation times of the various species involved and upon the equilibrium pair correlation functions. It is shown that if the self-correlation times are assumed to be given by the Stokes–Debye relationship, and if the equilibrium direct correlation functions obey certain relatively weak conditions, then for particles of equal size (i.e., the self-correlation times are the same for all species) the dielectric relaxation behavior can be described by a simple Debye formula with a single concentration-dependent relaxation time. This observation is independent of the number of components, of the concentration, and of the molecular dipole moments of the different species present. It may help explain why for some binary mixtures of polar molecules experimental measurements indicate only a single relaxation channel. The exact Kerr result for binary mixtures is expressed explicitly as the sum of two Lorentzians, and some numerical results are given for solutions of dipolar hard spheres of different diameter.

Notes: The dielectric relaxation theory of electrolyte solutions is formulated in terms of solvent–solvent, ion–ion, and ion–solvent van Hove time correlation functions. General wave vector frequency-dependent expressions are given for the longitudinal components of the relevant (i.e., polarization–polarization, current–current, current–polarization, polarization–current) time correlation functions and of the susceptibility, dielectric, and conductivity tensors. The Kerr theory relating the distinct and self parts of the van Hove functions is extended to mixtures of molecular fluids and solved explicitly in the k→0 limit for solutions of spherical ions (assuming that the self part of the van Hove functions is given by Fick's law) immersed in polar solvents. At this level of theory, the van Hove functions, the time correlation functions and the susceptibilities are all found to depend upon coupled ion–solvent motion. However, the dynamical coupling terms are shown to cancel exactly in the final expressions for the conductivity and dielectric constant yielding relatively simple results. Specifically, the conductivity obtained is independent of frequency and is related to the self diffusion constants of the ions by the Nernst–Einstein expression. If a spherical diffusor model is chosen for the solvent, then the frequency-dependent dielectric constant is given by a Debye-type formula with a concentration dependent relationship connecting the Debye and self reorientational relaxation times of the solvent.These results are discussed in the context of previous theories and experimental observations. It is shown that, although obviously oversimplified, the present theory does qualitatively predict the correct concentration dependence of the observed relaxation times for a number of salt solutions.

Notes: The symmetry breaking instability in the irreversible Oregonator model for sufficiently low and unequal diffusion coefficients of its three intermediate species has been investigated using the rate constants of Field and Försterling. The effects of diffusion and the control parameters on the shift of Hopf bifurcation points associated with the emergence of heterogeneous waves of short wavelengths are reported. The results are found to be in good agreement with those obtained by Prigogine et al. for Brusselator and Turing models.

Notes: A frequently encountered problem in molecular dynamics is how to treat the long times that are required to simulate condensed systems consisting of particles interacting through long range forces. Standard methods require the calculation of the forces at every time step. Because each particle interacts with all particles within the interaction range of the potential the longer the range of the potential the larger the number forces that must be calculated at each time step. In this note we present a variant of the RESPA (reference system propagator algorithm), which we developed for handling systems with multiple time scales like disparate mass mixtures. This version of RESPA greatly reduces the number of forces that must be computed at each time step and thereby leads to a dramatic acceleration of such simulations. The RESPA method uses ideas similar to NAPA, an algorithm we invented to treat high frequency oscillators interacting with low frequency bath. The method is based on a choice of a reference system in which the particles interact through short range forces. The reference system is numerically integrated for n time steps δt and the error incurred by using short range forces is corrected by solving a rigorous set of equations once every Δt=nδt. This method reduces the cpu time dramatically. It is shown that this approach and suitable generalizations should be very useful for future simulations of quantum and classical condensed matter systems.