Showing papers in "Journal of Chemical Physics in 1983"

Comparison of simple potential functions for simulating liquid water

Abstract: Classical Monte Carlo simulations have been carried out for liquid water in the NPT ensemble at 25 °C and 1 atm using six of the simpler intermolecular potential functions for the water dimer: Bernal–Fowler (BF), SPC, ST2, TIPS2, TIP3P, and TIP4P. Comparisons are made with experimental thermodynamic and structural data including the recent neutron diffraction results of Thiessen and Narten. The computed densities and potential energies are in reasonable accord with experiment except for the original BF model, which yields an 18% overestimate of the density and poor structural results. The TIPS2 and TIP4P potentials yield oxygen–oxygen partial structure functions in good agreement with the neutron diffraction results. The accord with the experimental OH and HH partial structure functions is poorer; however, the computed results for these functions are similar for all the potential functions. Consequently, the discrepancy may be due to the correction terms needed in processing the neutron data or to an effect uniformly neglected in the computations. Comparisons are also made for self‐diffusion coefficients obtained from molecular dynamics simulations. Overall, the SPC, ST2, TIPS2, and TIP4P models give reasonable structural and thermodynamic descriptions of liquid water and they should be useful in simulations of aqueous solutions. The simplicity of the SPC, TIPS2, and TIP4P functions is also attractive from a computational standpoint.

Natural bond orbital analysis of near‐Hartree–Fock water dimer

Abstract: We have carried out a natural bond orbital analysis of hydrogen bonding in the water dimer for the near‐Hartree–Fock wave function of Popkie, Kistenmacher, and Clementi, extending previous studies based on smaller basis sets and less realistic geometry. We find that interactions which may properly be described as ‘‘charge transfer’’ (particularly the n‐σ*OH interaction along the H‐bond axis) play a critical role in the formation of the hydrogen bond, and without these interactions the water dimer would be 3–5 kcal/mol repulsive at the observed equilibrium distance. We discuss this result in relationship to Klemperer’s general picture of the bonding in van der Waals molecules, and to previous theoretical analyses of hydrogen bonding by the method of Kitaura and Morokuma.

A simple model for the ionization potential, electron affinity, and aqueous redox potentials of small semiconductor crystallites

Abstract: Large semiconductor crystals have intrinsic electronic properties dependent upon the bulk band structure. As the crystal becomes small, a new regime is entered in which the electronic properties (excited states, ionization potential, electron affinity) should be strongly dependent upon the electron and hole in a confined space. We address the possibility of a shift in the photochemical redox potential of one carrier, as a function of crystallite size. As a semiquantitative guide, one might expect a shift on the order of h2/8em*R2 due to the kinetic energy of localization in the small crystallite. We model the elementary quantum mechanics of a charged crystallite using (a) the effective mass approximation, (b) an electrostatic potential for dielectric polarization, and (c) penetration of the carrier outside the crystallite in a cases of small effective mass. Shifts of several tenths of an eV appear possible in crystallites of diameter 50 A. The carrier charge density reside near the crystallite surface if ...

Chemistry in noninteger dimensions between two and three. I. Fractal theory of heterogeneous surfaces

Abstract: In this, the first of a series of papers, we lay the foundations for appreciation of chemical surfaces as D‐dimensional objects where 2≤D<3. Being a global measure of surface irregularity, this dimension labels an extremely heterogeneous surface by a value far from two. It implies, e.g., that any monolayer on such a surface resembles three‐dimensional bulk rather than a two‐dimensional film because the number of adsorption sites within distance l from any fixed site, grows as lD. Generally, a particular value of D means that any typical piece of the surface unfolds into mD similar pieces upon m‐fold magnification (self‐similarity). The underlying concept of fractal dimension D is reviewed and illustrated in a form adapted to surface‐chemical problems. From this, we derive three major methods to determine D of a given solid surface which establish powerful connections between several surface properties: (1) The surface area A depends on the cross‐section area σ of different molecules used for monolayer cov...

Analysis of small angle neutron scattering spectra from polydisperse interacting colloids

Abstract: In this paper, we outline a simple procedure for analyzing small angle neutron scattering (SANS) spectra from interacting colloids containing a continuous distribution of particle sizes. In particular, the effects of polydispersity on the apparent interparticle structure factor S′(Q) observed by SANS is investigated. We find that the oscillations in S′(Q) are significantly damped in comparison to those of the true structure factor S(Q). When our procedure is extended to the analysis of SANS spectra from nonspherical particles, we find that orientational averaging affects S′(Q) in a qualitatively similar way. The applicability of the procedure to the analysis of real data is demonstrated with spectra taken from water‐in‐oil microemulsions, ionic micelles, and interacting proteins.

Quantum mechanical rate constants for bimolecular reactions

Abstract: Several formally exact expressions for quantum mechanical rate constants (i.e., bimolecular reactive cross sections suitably averaged and summed over initial and final states) are derived and their relation to one another analyzed. It is suggested that they may provide a useful means for calculating quantum mechanical rate constants accurately without having to solve the complete state‐to‐state quantum mechanical reactive scattering problem. Several ways are discussed for evaluating the quantum mechanical traces involved in these expressions, including a path integral evaluation of the Boltzmann operator/time propagator and a discrete basis set approximation. Both these methods are applied to a one‐dimensional test problem (the Eckart barrier).

Solution of the Schrödinger equation by a spectral method II: Vibrational energy levels of triatomic molecules

Abstract: The spectral method utilizes numerical solutions to the time‐dependent Schrodinger equation to generate the energy eigenvalues and eigenfunctions of the time‐independent Schrodinger equation. Accurate time‐dependent wave functions ψ(r, t) are generated by the split operator FFT method, and the correlation function 〈ψ(r, 0) ‖ ψ(r, t)〉 is computed by numerical integration. Fourier analysis of this correlation function reveals a set of resonant peaks that correspond to the stationary states of the system. Analysis of the location of these peaks reveals the eigenvalues with high accuracy. Additional Fourier transforms of ψ(r, t) with respect to time generate the eigenfunctions. Previous applications of the method were to two‐dimensional potentials. In this paper energy eigenvalues and wave functions obtained with the spectral method are presented for vibrational states of three‐dimensional Born–Oppenheimer potentials applicable to SO2, O3, and H2O. The energy eigenvalues are compared with results obtained with the variational method. It is concluded that the spectral method is an accurate tool for treating a variety of practical three‐dimensional potentials.

Collective diffusion, nucleation, and spinodal decomposition in polymer mixtures

Abstract: The dynamics of concentration fluctuations in binary polymer mixtures AB, A and B being long and flexible chains, is studied near the critical point of unmixing. A ‘‘hydrodynamic’’ theory in close analogy to the treatments of Cahn–Hilliard and Cook for the dynamics of unmixing alloys is developed, and its validity is carefully analyzed. It is shown that homogeneous nucleation for long chains is negligible except in a narrow region of volume fraction φ0 near the spinodal curve φs0 of width (φs0−φ0)/φ0∝N−1, where N is the number of subunits of the chains. For N→∞ the spinodal curve hence is well defined, in contrast to mixtures with short‐range forces, and also the linearized theory of spinodal decomposition is predicted to have wider validity. The collective relaxation in the one‐phase region is described by a characteristic time involving the collective diffusion constant Dcoll τq=(Dcoll q2)−1, if the wave vector q is smaller than the inverse correlation length ξ−1coll, while in the range ξ−1coll≪q≪R−1 (R...

Particle–antiparticle annihilation in diffusive motion

Abstract: We study both numerically and analytically the time development of a system of particles and antiparticles moving diffusively and annihilating irreversibly The asymptotic behavior is found to depend dramatically on whether the initial fluctuations are localized or entirely random Physical examples of each kind are identified

Collisional deactivation of vibrationally highly excited polyatomic molecules. II. Direct observations for excited toluene

Abstract: Vibrationally highly excited toluene molecules with 52 000 cm−1 of vibrational energy have been prepared by UV laser excitation of the isomer cycloheptatriene and subsequent isomerization. The collisional loss of energy from the excited toluene molecules has been observed directly by monitoring hot UV absorption spectra. Direct measurements of the average energies 〈ΔE〉 transferred per collision have been made for about 60 different bath gases. For complex bath gases, 〈ΔE〉 values appear to be considerably smaller than those derived from earlier indirect measurements. 〈ΔE〉 was found not (or only slightly) to depend on the excitation energy.

Chemistry in noninteger dimensions between two and three. II: Fractal surfaces of adsorbents

Abstract: The concept of fractal dimension D of surfaces, advanced as natural measure of surface irregularity in part I of this series, is shown to apply to a remarkable variety of adsorbents: graphites, fume silica, faujasite, crushed glass, charcoals, and silica gel. The D values found for these examples vary from two to almost three (for smooth and very irregular surfaces, respectively), thus covering the whole possible range. They quantify the intuitive picture that surface inhomogeneities are minor, e.g., in graphites, but dominant, e.g., in charcoal. The analysis is based on adsorption data, with main focus on adsorbates of varying molecular cross section. They include N2, alkanes, polycyclic aromatics, a quaternary ammonium salt, and polymers. The straight‐line plots so obtained confirm also a number of reported on‐surface conformations of specific adsorbates. The converse method to get D from varying the size of adsorbent particles is exemplified for fume silica and crushed glass.

The enhancement of Raman scattering, resonance Raman scattering, and fluorescence from molecules adsorbed on a rough silver surface

Abstract: The enhancements of normal Raman scattering, resonance Raman scattering, and fluorescence from molecules adsorbed on identical, well‐characterized, silver‐island films are reported. The enhancement arises from the electromagnetic interaction between the molecules and the electronic plasma resonance of the silver islands. A hierarchy of enhancement ratios is found, with typical values of 105 for RS, 103 for RRS and 10−1 to 10 for fluorescence, depending on the quantum yield of the molecular fluorescence. A model, developed on heuristic grounds and substantiated using the density matrix formalism, describes the light scattering processes and the effects of the plasma resonance. This model presents a unified picture of the surface‐induced enhancement effects and is consistent with the experimental values. The comparison of all the forms of optical scattering leads to a complete determination of the role of the plasma resonances in the various portions of the scattering process. The excitation of the electronic plasma resonance results in an increased local field at the molecules leading to an increased excitation or absorption rate. Similarly, the excitation of the plasma resonance by the molecular emission dipole results in an increase in the radiative decay rate. However, the electromagnetic coupling of the molecule to the plasma resonance also adds an additional damping channel which can result in a reduction of the absorption or excitation rate as well as the emission yield. The resultant balance of these processes leads to the hierarchy in the measured enhancements. The hierarchy of enhancements is also shown to have important spectroscopic consequences.

Deformable stochastic boundaries in molecular dynamics

Abstract: A new approach to studying localized chemical events in condensed phases is developed. The approach provides a simple and convenient method for reducing the total number of solvent particles explicitly included in simulations of localized processes while decreasing spurious edge effects. Both energy flow across the boundary and density fluctuations in the simulation region are included; this makes it possible to treat nonequilibrium processes, such as thermal gradients and endothermic or exothermic chemical reactions. The essential element of the approach is the introduction of a soft boundary force and a stochastic buffer region. For simple liquids, the boundary force is determined from the solvent equilibrium structure (radial distribution function) and is readily incorporated into conventional molecular dynamics algorithms. The methodology is illustrated by application to liquid argon in spherical and cubical simulation regions; comparison with standard molceular dynamics results show excellent agreeme...

Transient nucleation in condensed systems

Abstract: Using classical nucleation theory we consider transient nucleation occurring in a one‐component, condensed system under isothermal conditions. We obtain an exact closed‐form expression for the time dependent cluster populations. In addition, a more versatile approach is developed: a numerical simulation technique which models directly the reactions by which clusters are produced. This simulation demonstrates the evolution of cluster populations and nucleation rate in the transient regime. Results from the simulation are verified by comparison with exact analytical solutions for the steady state. Experimental methods for measuring transient nucleation are assessed, and it is demonstrated that the observed behavior depends on the method used. The effect of preexisting cluster distributions is studied. Previous analytical and numerical treatments of transient nucleation are compared to the solutions obtained from the simulation. The simple expressions of Kashchiev are shown to give good descriptions of the nucleation behavior.

On the nonradiative and radiative decay rates and a modified exponential energy gap law for 4f-4f transitions in rare-earth ions

Abstract: A modified exponential energy gap law for nonradiative decay has been derived for 4f–4f transitions where only a few phonons participate in the transition. Its preexponential factor varies by only a factor of 10 for different host materials and is purely electronic in nature. The modified law is the usual law (giving a factor of 105 variation) modified by using an energy gap which is effectively two (maximum) phonon energies smaller than the energy difference between the initial and the final electronic state. A general relation between the radiative and nonradiative decay rates has been constructed. For 4f–4f transitions this relation enables one to predict the nonradiative decay rate from a knowledge of the radiative decay rate to within one order of magnitude accuracy.

Theory of critical micelle concentration for solutions of block copolymers

Abstract: A simple microscopic model for micellar formation in mixtures of block copolymers and homopolymers is presented. The size, number of chains, and energy of formation of micelle are calculated. The fraction of copolymer chains aggregating into micelles is computed as a function of the overall copolymer content. A critical micelle concentration behavior is found for low copolymer contents even for weak incompatibilities of species. The similarity with an aborted phase transition is underlined.

The role of long ranged forces in determining the structure and properties of liquid water

Abstract: We have performed molecular dynamics calculations for liquid water using the revised central force model potential truncated at various distances and using two sizes of system, in order to study the effect of system size and range of the potential on the calculated thermodynamic and structural properties and to compare the results with those obtained by Ewald summation. All calculations were performed for a cubic system using periodic boundary conditions. Provided the side of the cube is equal to or greater than twice the range of the potential, the thermodynamic properties and distribution functions, including an orientational distribution function, are insensitive to the size of the system, for fixed range. Provided the range of the potential is equal to or greater than 6 A, the thermodynamic energy and pressure are only slightly dependent on the range of the potential, to an extent that is, however, larger than that observed for dipolar hard spheres and the Stockmayer potential which do not have the tetrahedral structure similar to water. For potentials with ranges of 6 A or greater, the atom–atom distribution functions are very insensitive to the range, but the orientational correlations are very sensitive to the range, as had been observed many times in studies of dielectric properties of simulated fluids. A potential with a range of 6 A has thermodynamic and structural properties very similar to those of a longer ranged potential and similar to those obtained by Ewald summation. Use of such a model, which correctly describes interactions between nearest neighbors and next nearest neighbors but has no longer ranged forces, lead to significant increases in the speed of simulations.

Anisotropic orientation in molecular monolayers by infrared spectroscopy

Abstract: Fourier transform IR measurements of Langmuir–Blodgett monolayers have been made with both grazing incidence reflection and transmission techniques. The reflection arrangement at incident angles from 85° to 88° has the electric field component perpendicular to the substrate surface while the standard transmission arrangement has the electric field component in the plane of the film. These techniques were used to explore the anisotropic arrangement of cadmium arachidate molecules perpendicular and parallel to the monolayer plane. The implication of these results for characterizing the orientational anisotropy of chemical groups in thin polymer films is also discussed. In addition, the question of uniaxial and biaxial orientation in the monolayer plane was addressed because of the importance of intermolecular packing on both the extent and rate of polymerization in unsaturated fatty acid monolayer components which form synthetic membranes.

Noncrystalline structure of argon clusters. I. Polyicosahedral structure of ArN clusters, 20<N<50

Abstract: Small argon clusters are produced in a free jet expansion and studied by electron diffraction. Due to their very low proportion in the beam sample in comparison to the monomers, the smallest detectable clusters contain about 20 atoms. When they grow up to some 50 atoms, they present the same noncrystalline structure. This structure is identical to that of solid models constructed during a molecular dynamics calculation by cooling a liquid drop of atoms interacting through a Lennard‐Jones potential. Because it is composed of icosahedra of 13 atoms, either joined one to the other either interpenetrating each other, this structure may be called polyicosahedral. The comparison between theoretical and experimental diffraction functions leads to an estimate of the cluster temperature 27±3 K and of the proportion of monomers in the beam. We discuss the similarity in the radial distribution functions of both PIC models and bulk amorphous materials, and give arguments for the stability of the clusters.

Determination of product population and alignment using laser‐induced fluorescence

Abstract: For collision systems having axial symmetry, the anisotropy of the laser‐induced fluorescence is given explicitly in terms of the zeroth, second, and fourth rank moments of the angular momentum distribution, which, respectively, are proportional to the population, the quadrupole alignment, and hexadecapole alignment of the product internal state under study. Expressions are presented for determining these three quantities from the dependence of the fluorescence intensity on the polarizations of the absorbed and detected photons. Results are presented for an arbitrary excitation‐detection geometry which is then specialized to the commonly occurring cases where the direction of fluorescence detection is at right angles to the axis of cylindrical symmetry and the direction of the incoming light beam is either along the axis of cylindrical symmetry or at right angles to it and to the fluorescence detection direction. The approach of these expressions to the high‐J limit is considered. The effect of nuclear spin on the fluorescence intensity is analyzed and the extent of depolarization is shown to be unimportant for large J. The use of angular momentum recoupling algebra permits the geometrical and dynamical aspects of this problem to be completely disentangled.

Computer ‘‘experiment’’ for nonlinear thermodynamics of Couette flow

Abstract: Nonequilibrium computer simulations reveal that the equation of state of fluids undergoing shear flow, varies with strain rate. This observation prompted the development of a nonlinear generalization of irreversible thermodynamics to describe steady planar Couette flow, very far from equilibrium. In this paper we use computer simulation to perform a quantitative test of a prediction of this thermodynamics. The prediction tested is: fluids which exhibit positive shear dilatancy for isothermal shear flow should also cool as the strain rate is increased while keeping the internal energy constant. To perform calculations of this effect a new nonequilibrium molecular dynamics algorithm was developed to simulate Couette flow at constant internal energy.

Transient kinetics of chemical reactions with bounded diffusion perpendicular to the reaction coordinate: Intramolecular processes with slow conformational changes

Abstract: Intramolecular reactions inside macromolecules (e.g., binding of ligands to iron inside heme proteins) may often be coupled to slow random fluctuations in the reaction center geometry. This motion is ‘‘perpendicular’’ to the reaction coordinate. It can be described as bounded diffusion in the presence of a binding potential field and an intramolecular rate constant which depends on the perpendicular degree of freedom. The diffusion equation is solved under the appropriate reflective boundary conditions. The transient decay of the total population is multiexponential (power law) for small diffusivity, changing to monoexponential kinetics for large diffusivity. For large times or large diffusivity, direct integration is very tedious, but an eigenvalue expansion converges rapidly. It also allows the calculation of the ‘‘average survival time’’ (an extension of the ‘‘first passage time’’) a natural candidate for replacing the reciprocal rate constant in multiexponential kinetics. An example is given for electron transfer between two loosely bound sites in a macromolecule. The average survival time shows a non‐Kramers dependence on diffusivity, of the type found in the binding kinetics in heme proteins.

CO binding to heme proteins: A model for barrier height distributions and slow conformational changes

Abstract: A model for the dependence of the potential energy barrier on a ‘‘protein coordinate’’ is constructed. It is based on a two dimensional potential energy surface having as variables the CO–iron distance and a conceptual protein coordinate. The distribution of barrier heights observed in kinetics follows from an initial Boltzmann distribution for the protein coordinate. The experimental nonexponential rebinding kinetics at low temperatures or large viscosities (when the protein coordinates can be assumed ‘‘frozen’’) can be fit with a simply parametrized energy surface. Using the same energy surfaces and the theory of bounded diffusion perpendicular to the reaction coordinate, we generate (in qualitative agreement with experiment) the survival probability curves for larger diffusivity, when the constraint on the protein coordinate is relaxed. On the basis of our results, the outcomes of new experiments which examine the concepts underlying the theory can be predicted.

Theory of electronic relaxation in solution in the absence of an activation barrier

Abstract: We present a theory which describes the effects of viscosity on those electronic relaxation processes in solution in which the intramolecular potential surface does not present a barrier to the motion leading to the decay of the initially formed excited state. We model the reactive motion as the motion of a solute particle on the excited state potential surface with a position dependent sink which gives rise to the decay of the excited state population. Three different types of sinks are considered: (A) a pinhole sink at the minimum of the potential surface; this models the situation when the molecule decays to ground state as soon as it reaches the potential minimum; (B) a Gaussian sink with probability of decay maximum at the potential minimum; (C) a Lorentzian sink with maximum decay at the potential minimum. For case (A) an explicit analytic solution is obtained for the decay rate, but for cases (B) and (C) we obtained the decay rate numerically. Model (A) predicts nonexponential decay at all viscosities except at long times when the decay is single exponential. For cases (B) and (C) the decay is single exponential at low viscosities but becomes multiexponential at high viscosities. We show that the experimentally observed fractional viscosity dependence of fluorescence quantum yield arises naturally in this theory due to the position dependence of the sink as well as due to the competition between radiative and nonradiative relaxation. Our model also predicts a crossover from an apparent negative (constant viscosity) activation energy at low viscosities to a positive activation energy at high viscosity. The physical significance of these results is discussed in light of the available experimental results on TPM dye relaxation. Some possible generalizations of our theory to more realistic cases are indicated.

Supersonic metal cluster beams of refractory metals: Spectral investigations of ultracold Mo2

Abstract: A novel technique involving pulsed laser vaporization of the bulk metal within a pulsed supersonic nozzle has been shown to successfully produce ultracold bare metal clusters of even the most refractory of metals, tungsten and molybdenum. Clusters of up to 25 atoms may be readily prepared using this technique. Mass‐selective resonant two‐photon ionization spectra of Mo2 produced in this fashion show that the dimer is efficiently cooled in the expansion Ttrans<6 K, Trot∼5 K, and Tvib∼325 K. We have rotationally resolved the A 1Σ+u←X 1Σ+g (0–0) band for 92Mo2 and determined the bond length in the ground and excited states to be 1.940±0.009 and 1.937±0.008 A, respectively. This confirms and extends the analysis of Efremov et al. [J. Mol. Spectrosc. 73, 40 (1970)] who prepared 98Mo2 by flash photolysis of isotopically pure Mo(CO)6. We have also observed the (1–1), (2–2), and (3–3) sequence bands which together with the ground state data of Efremov et al. determine vibrational constants ω′e=449.0±0.2 cm−1 and ...

The influence of adsorbate interactions on kinetics and equilibrium for CO on Ru(001). II. Desorption kinetics and equilibrium

Abstract: A variety of methods [temperature programmed desorption via pressure rise and via work function changes (Δφ); isothermal desorption via Δφ: quasiequilibrium measurements via isobars monitored by Δφ, in combination with sticking coefficients] has been used to obtain detailed data on the coverage dependence of the adsorption equilibrium and desorption kinetics for CO on the basal Ru(001) face. While the deviation from reversibility varies strongly over these methods, no significant influence of the degree of irreversibility on the results has been found. Desorption energies and isosteric heats are constant at 160 kJ/mol for 0<Θ<0.2, then rise slowly up to 175 kJ/mol at Θ=0.33, where they fall abruptly to 120 kJ/mol and more gradually at higher coverage. The ‘‘first order’’ frequency factor (Arrhenius preexponential normalized by the coverage) is 1016 s−1 at Θ=0, rises precipitously, especially in the range 0.2<Θ<0.33, to 1019 s−1 at Θ≊0.33, where it drops abruptly to ≊1014 s−1. The main conclusions drawn ar...

Critical point shifts in films

Abstract: Critical behavior in thin films is discussed with attention to the example of phase separation in binary fluid mixtures between parallel plates. The analyses focus on the dependence of the shift in critical temperature ΔTc, critical field, etc., on the film thickness D, and on the nature of the walls as modeled by a surface field or chemical potential h1 which acts near the walls and leads to preferential adsorption of one of the bulk phases. Mean field theory for an Ising/lattice‐gas model is utilized and the resulting asymptotic scaling functions for the shifts ΔTc etc. are computed within Landau theory by analytic and numerical methods. Series analyses for simple cubic lattice Ising model films with h1=0 are used to estimate universal features of three‐dimensional systems: specifically, if ξ(ΔT) is the bulk correlation length, determined, say, via scattering experiments, at ΔT=T−T∞c≳0 then the shift ratio D/ξ(‖ΔTc‖) is about 2.89 for h1=0 but 4.61 for h1→∞, compared with mean field values π and 5.0699....

Evidence for ‘‘subsurface’’ hydrogen on Pd(110): An intermediate between chemisorbed and dissolved species

Abstract: We report experimental evidence for the formation of a ‘‘subsurface’’ hydrogen species at 130 K on a Pd(110) single crystal surface. This is well separated by distinct activation energy barriers from species which are chemisorbed or which are dissolved in the Pd bulk, thereby confirming a model of H absorption in Pd in which a subsurface state acts as a reaction intermediate.