Volume 111, Issue 5, 01 August 1999
 CONDENSED PHASE DYNAMICS, STRUCTURE, AND THERMODYNAMICS: SPECTROSCOPY, REACTIONS, AND RELAXATION


Classical nucleation theory for the nucleation of the solid phase of spherical particles with a shortranged attraction
View Description Hide DescriptionClassical nucleation theory is used to estimate the freeenergy barrier to nucleation of the solid phase of particles interacting via a potential which has a shortranged attraction. Due to the high interfacial tension between the fluid and solid phases, this barrier is very large, much larger than in hard spheres. It is divergent in the limit that the range of the attraction tends to zero. We predict an upper limit on nucleation in good agreement with the results of experiments on the crystallization of proteins.

On the role of dielectric friction in vibrational energy relaxation
View Description Hide DescriptionThe phrase “dielectric friction” tends to bring to mind the drag force exerted by a polar liquid on some translating ion or rotating dipolar molecule, but the underlying idea is far more general. Any relaxation process taking place in a polar environment, including those involving solvation and vibrational relaxation, has the potential to be strongly affected by the special dynamics associated with Coulombic forces. Indeed, there is considerable evidence that vibrational energy relaxation is noticeably accelerated in hydrogenbonding solvents. What is less clear is precisely howelectrostatic forces achieve the accelerations they do and to what extent this phenomenon relies on specifically protic solvents. We explore this issue in this paper by using classical molecular dynamics to study the vibrational population relaxation of diatomic solutes with varying levels of polarity dissolved in both dipolar and nondipolar aprotic solvents. We find that the conventional analysis based on partitioning the force autocorrelation function can be usefully extended by adapting an instantaneous perspective; distinguishing between the purely equilibrium effects of the instantaneous liquid structure surrounding a solute and the solely nonequilibrium effects of the relaxation dynamics launched from those initial conditions. Once one removes the powerful influence of electrostatic forces on the liquid structure, either by simple normalization or by looking at the “forcevelocity” autocorrelation function, the subsequent dynamics (and therefore the mechanism) of the relaxation is revealed to be dominated by shortranged repulsive forces, even under the most polar circumstances. The main rateenhancing effect of Coulombic forces seems to be an equilibrium electrostriction: The solvent is simply ordered around the solute in such a way as to amplify the repulsive forces. At least in our examples, the slowly varying character of Colombic forces actually makes them quite ineffective at any kind of direct promotion of vibrational energy relaxation.

Liquiddrop formalism and freeenergy surfaces in binary homogeneous nucleation theory
View Description Hide DescriptionThree different derivations of the classical binary nucleationtheory are considered in detail. It is shown that the derivation originally presented by Wilemski [J. Chem. Phys. 80, 1370 (1984)] is consistent with more extensive derivations [Oxtoby and Kashchiev, J. Chem. Phys. 100, 7665 (1994)]; Debenedetti, Metastable Liquids: Concepts and Principles (Princeton University Press, Princeton, 1996) if and only if the assumption is made that the surface of tension of the binary nucleus coincides with the dividing surface specified by the surface condition where the denote surface excess numbers of molecules of species i, and the ’s are partial molecular volumes. From this condition, it follows that (1) the surface tension is curvature independent and (2) that the nucleus volume is where the are the numbers of molecules in the uniform liquid phase of the dropletmodel encompassed by the surface of tension, and the are the total molecular occupation numbers contained by the nucleus. We show, furthermore, that the above surface condition leads to explicit formulas for the surface excess numbers in the nucleus. Computations for the ethanol–water system show that the surface number for water molecules causes the negative occupation numbers obtained earlier using the classical nucleationtheory. The unphysical behavior produced by the classical theory for surface active systems is thus a direct consequence of the assumption of curvature independence of surface tension. Based on the explicit formulas for we calculate the full freeenergysurfaces for binary nucleation in the revised classical theory and compare these with the freeenergysurfaces in the Doyle (unrevised classical) theory. Significant differences in nucleus size and composition are found between these models and they are related to surface excess density. It is shown that only for the revised classical theory is the nucleus composition consistent with the Gibbs dividing surfacemodel.

Structure of molten systems from a polarizable ion simulation model
View Description Hide DescriptionComputer simulations of a range of molten salts of stoichiometry using a polarizable, formal charge ionic interaction model are described. The systems studied — and — span a range of cation sizes and the interaction model is a “generic” one, in the sense that the cation size is the only parameter in the interaction potential which distinguishes one system from another. The liquid structures predicted from the simulations are compared with recently obtained neutron diffraction data. Excellent agreement is found, except that the first coordination shell seems to be too tightly bound in the computer simulations. The cation in is found to be 7–8 fold coordinate, and the coordination number drops to 6 for the smallest cation considered so that the coordination number in these systems does not change substantially on melting, in contrast to earlier reports. The polarization effects promote a significant degree of edgesharing between these coordination polyhedra relative to predictions of a simple ionic pair potential. Associated with these changes is a shift to smaller scattering vectors of the prepeak in the structure factor and an increase in the fluidity.

Dipole and quadrupole polarization in ionic systems: Ab initio studies
View Description Hide DescriptionThe results of electronic structure calculations of the induced dipoles and quadrupoles on an anion in a locally distorted rocksalt crystal are described. Such information is of interest in the construction of ionic interaction potentials and for modeling the dielectric behavior of ionic materials. The systems included in the study are LiF, NaF, KF, LiCl, NaCl, KCl, LiBr, MgO and CaO. The results are used to characterize shortrange contributions to the induced multipoles— those not included in a pointcharge, pointpolarizable ionic model (the “asymptotic” model). It is shown that these shortrange effects are large, opposing and sometimes reversing the asymptotic contribution. The representation of the shortrange effects in a computationally tractable form, suitable for use in computer simulations, is examined. A pairwise additive form, containing a steplike function of the interionic separation, is found to provide a good representation of the ab initio data for both dipoles and quadrupoles. Furthermore, the parameters involved in the fitted functions transfer from one material to another in a physically transparent and predictable way.

A lattice model for fluids with directional interactions
View Description Hide DescriptionHere we analyze a lattice model for fluids with directional interactions in the framework of the Ono–Kondo theory. The free energy of the system is represented as an explicit function of the temperature and bulk density. It is shown that the model predicts both order–disorder and vapor–liquid phase transitions. This theory predicts a tricritical point where the vapor–liquid and order–disorder phase transitions both disappear. Also, it predicts retrograde condensation where the boundary of phase stability becomes a multivalued function of concentration. In addition, predictions of the theory are compared with Monte Carlo simulation data. It is shown that the partition function cannot be factored to predict separately the contributions of, for example, dispersion and hydrogen bonding interactions.

Dynamics on statistical samples of potential energy surfaces
View Description Hide DescriptionPrior work [K. D. Ball and R. S. Berry, J. Chem. Phys. 109, 8541 (1998); 109, 8557 (1998)] has demonstrated that master equations constructed from a complete set of minima and transition states can capture the essential features of the relaxation dynamics of small systems. The current study extends this work by examining robustness of master equations based only on statistical samples of the surfacetopography, to make it possible to work with larger systems for which a full topographical description is either impossible or infeasible. We ask whether such “statistical” master equations can predict relaxation on the entire potential energy surface. Our test cases are and for which we have extensive databases: 168 geometrically distinct minima and 1890 transition states for and 1478 minima and 17,357 saddles for which we assume represent complete set of stationary points. From these databases we construct statistical sample sets of transition sequences, and compare relaxation predictions based on these with those obtained from the master equations representing the full potential surfaces, and with results of molecular dynamics simulations. The slowest, ratecontrolling relaxation timescale converges at moderate temperatures as the number of sequences in a sample reaches ∼1000, approaching convergence for as few as 100 sequences. The asymptotic value of the slowest nonzero relaxation rate is essentially identical to that from the full potential energy surface. Equilibrium properties from the statistical samples match those of the full surface. To achieve convergence within a factor of 2 of fullsurface rates, the number of sequences required is approximately the same for as for Precise convergence, however, appears to scale as the number of stationary points. These results reveal how the reliability and precision of kinetic predictions from statistical master equations depends on the size of the statistical database.

Ab initio calculation of elastic constants of stishovite and αquartz
View Description Hide DescriptionWe present theoreticalab initio results for the elastic constants of two different phases of stishovite and αquartz using the planewavepseudopotential method. Our calculated values are in very good agreement with the experimental data as well as some of the existing model calculations. is one of the most abundant minerals in the earth’s mantle. Therefore, the knowledge of its elastic behavior will be very important from a seismology point of view. Our calculated sound velocities are presented and are accordingly also in good agreement with those derived from experiment.

Quantum consideration of electron transfer solvent control
View Description Hide DescriptionThe elementary act of the electron transfer process is considered within the quantum spinboson model. The expression for the coordinate dependent reaction flux correct to the second order in the intercenter coupling is obtained. It is shown that in the classical bath limit the flux is localized in a narrow nonadiabatic region in the vicinity of the crossing point of the potential surfaces. Thus, the wellknown pointtransition model describing solvent dynamical effect in the electron transfer kinetics is justified in this limit. The analysis of the Markovian kinetic equations for a quantum twostage electron system coupled to a classical bath used by a number of authors for the derivation of the pointtransition model is performed. It is demonstrated that this approach is often inappropriate for the description of the electron transfer process. Here we show that these equations may lead to unphysical predictions such as negative reaction rate and flux.

The dynamics of proton transfer in a water chain
View Description Hide DescriptionWe perform quantum molecular dynamics simulations to study proton transfer along small water aggregates, such as a chain of hydrogenbonded water molecules (protonwire) which is an important mechanism for charge species permeation. The electronic structure of the system is calculated concurrently with the nuclear motion using Born–Oppenheimer molecular dynamics within the framework of density functional theory. The simulations are performed on protonated linear chains of six water molecules, a linear water chain containing the water molecules, and an ammonia molecule. We discover that proton transfer along the chain is an extremely fast process, occurring in subpicosecond time scales. The translocation mechanism of the proton is neither a concerted mechanism in which the donoracceptor pattern would occur over the entire chain in a single step, nor a result of a single proton hopping along the chain. The process takes place through a series of semicollective motion during which rapid fluctuations of the hydrogenbond lengths along with reorganizations of water molecules are observed. The proton is translocated after a series of successive protonationdissociation steps along the chain where hydrogen ions hop from oxygen to oxygen. We also discover that and are the dominant species found during the course of the process. These simulations allow the study of dynamical properties of the systems at finite temperatures.

From molecular clusters to bulk matter. II. Crossover from icosahedral to crystalline structures in clusters
View Description Hide DescriptionThe change in structure with size in clusters has been investigated in the crossover regime from icosahedral to cubic morphology to 55) by molecular dynamics simulation. All the minima in the potential energy surface (PES) visited by the solid clusters at finite temperature have been characterized using a local structureanalysis method. A simple picture of the change in freeenergy minimum with size in solid clusters emerges from this work. It is based on the relative stability of two energy basins in the PES corresponding to the icosahedral and cubiclike structure, respectively. In addition, some evidence is provided for the existence of an icosahedral supercooled liquid in the size range near

Liquid vapor equilibria for an ab initio model for water
View Description Hide DescriptionThe vapor–liquid coexistence densities for water near the critical point were determined using a polarizable ab initio based model and grand canonical Monte Carlo simulations combined with the histogram reweighting technique. The predictions of the model used, which is found to give good agreement with experimental data at ambient conditions, are far below the experimental critical temperature and density. The saturation pressure is also overestimated. The source of this discrepancy may be related to the high pressure that the model exhibits even for liquid water. Since there is no fitting to experimental data, it is possible to refine the potential in a systematic way. In particular, an improvement in the sampling of the ab initio calculation for the repulsive part of the intermolecular potential is suggested in order to obtain better agreement with experiment at high temperatures and pressures.
