Richard M. Stratt

Instantaneous normal mode analysis of liquid water

We present an instantaneous‐normal‐mode analysis of liquid water at room temperature based on a computer simulated set of liquid configurations and we compare the results to analogous inherent‐structure calculations. The separate translational and rotational contributions to each instantaneous normal mode are first obtained by computing the appropriate projectors from the eigenvectors. The extent of localization of the different kinds of modes is then quantified with the aid of the inverse participation ratio—roughly the reciprocal of the number of degrees of freedom involved in each mode. The instantaneous normal modes also carry along with them an implicit picture of how the topography of the potential surface changes as one moves from point to point in the very‐high dimensional configuration space of a liquid. To help us understand this topography, we use the instantaneous normal modes to compute the predicted heights and locations of the nearest extrema of the potential. The net result is that in liquid water, at least, it is the low frequency modes that seem to reflect the largest‐scale structural transitions. The detailed dynamics of such transitions are probably outside of the instantaneous‐normal‐mode formalism, but we do find that short‐time dynamical quantities, such as the angular velocity autocorrelation functions, are described extraordinarily well by the instantaneous modes.

The short‐time dynamics of molecular liquids. Instantaneous‐normal‐mode theory

Since the sharply varying forces that control the arrangement of molecules in liquids are themselves intrinsically anharmonic, the natural assumption would be that any picture that regarded molecular motion as harmonic would be at best a rough phenomenological guide. This expectation is, in fact, not a correct one. While the packing forces that determine liquid structure are indeed strongly anharmonic, the short‐time displacements and librations that molecules execute are actually quite harmonic. It is possible to show rigorously that, for short enough (subpicosecond) time intervals, the dynamics of liquids is governed by a set of independent, collective, harmonic modes—the instantaneous normal modes of the liquid. In this paper we illustrate this fact by predicting the translational and rotational dynamics of a model diatomic liquid using the instantaneous normal modes computed by simulation. When compared to the exact molecular‐dynamics results for the same autocorrelation functions, we find that perfec...

Convenient and accurate discretized path integral methods for equilibrium quantum mechanical calculations

In the path integral representation of quantum theory, a few body quantum problem becomes a classical many body problem. To exploit this isomorphism, it becomes necessary to develop methods by which degrees of freedom can be explicitly removed from consideration. The interactions among the remaining relevant variables are described by effective interactions. In this paper, we present a general methodology to carry out the reduction in numbers of degrees of freedom. Certain path integral algorithms are shown to correspond to reference systems for the full isomorphic classical many body problem. The correspondence allows one to determine systematic corrections to the algorithms by low order perturbation approximations familiar in the theory of simple classical fluids. We show how to use discretized path integrals to compute rigorous upper and lower bounds to the free energy for nontrivial quantum systems, and we discuss how to optimize the upper bounds with variational theories. Several illustrative example...

The short‐time dynamics of solvation

At long enough times, the idiosyncratic motions of individual solvent molecules have long since ceased to matter to the process of solvation; the fact that a real solvent is not a featureless continuum just has no bearing on the dynamics. However, at short times, typically times well under a picosecond, the situation is quite different. We show here that at least within the realm of classical mechanics, one can indeed talk about how specific molecular motions contribute to short‐time solvation. Precisely how one should think about these motions depends on just how short a time interval one is considering. At the very shortest times, we use the fact that it is possible to express solvation time correlation functions rigorously as power series in time to confirm that the onset of solvation is unequivocally a matter of inertial (free‐streaming) motion of individual solvent molecules. We allow for somewhat longer, but still short, time intervals by writing these same correlation functions in terms of the instanteous normal modes of the solvent. The instantaneous‐normal‐mode expressions allow us to decompose the solvent dynamics into separate, well‐defined collective motions, each with its own characteristic abilities to foster solvation. As distinctive as they appear, these two complimentary short‐time views are, in fact, equally correct in the inertial regime, a point we establish by proving that two are simply different mathematical representations of the same underlying behavior.

Instantaneous normal mode analysis as a probe of cluster dynamics

We report an analysis of dynamical transitions in small argon clusters based on a study of the vibrational frequencies (photon spectra) of these systems. Even in the liquidlike regime such an analysis can be shown to provide an exact description of the short‐time cluster dynamics and represents an alternative to more conventional strategies which concentrate on an enumeration of minimum energy structures. The overall picture of ‘‘melting’’ transitions emerging from this study is one of a series of isomerizations which preserve the short‐range structures of the clusters, with the structures linked by these isomerizations sometimes being far from any of the local minima on the potential energy hypersurface. As a part of the analysis, we describe a general method for estimating cluster atom self‐diffusion constants from system configurations obtained via either isothermal or isoergic Monte Carlo calculations.

A theory of percolation in liquids

Problems involving percolation in liquids (i.e., involving connectivity of some sort) range from the metal–insulator transition in liquid metals to the properties of supercooled water. A common theme, however, is that connectivity can be distinguished from interaction and that one should not be slighted in order to describe the other. In this paper we suggest a model for percolation in liquids—the model of extended spheres—which permits connectivity to be studied in the context of, but independently from, liquid structure. This model is solved exactly in the Percus–Yevick approximation, revealing the existence of an optimum liquid structure for percolation. We analyze this behavior by first deriving an explicit diagrammatic representation of the Percus–Yevick theory for connectivity and then studying how the various diagrams contribute. The predictions are in excellent qualitative agreement with recent Monte Carlo calculations.

Liquid theory for band structure in a liquid. II. p orbitals and phonons

Surprisingly, the ground‐state quantum mechanical problem of calculating the set of single‐electron states available to a liquid (its electronic band structure) can be turned into an exercise in ordinary classical liquid theory. We generalize our previous findings by showing that this statement continues to hold for bands constructed from a basis of atomic p orbitals and we use this idea to provide a simple mean field theory useful for p bands in liquids. In addition, there is a natural way of thinking about the normal modes of vibration of a liquid (its phonons) that is accessible through virtually the same formalism. We discuss the significance of these ‘‘instantaneous normal modes’’ and show that the same kind of mean field theory is helpful in understanding both this phonon spectrum and its implications for liquid‐state dynamics.

Rotational coherence and a sudden breakdown in linear response seen in room-temperature liquids

Highly energized molecules normally are rapidly equilibrated by a solvent; this finding is central to the conventional (linear-response) view of how chemical reactions occur in solution. However, when a reaction initiated by 33-femtosecond deep ultraviolet laser pulses is used to eject highly rotationally excited diatomic molecules into alcohols and water, rotational coherence persists for many rotational periods despite the solvent. Molecular dynamics simulations trace this slow development of molecular-scale friction to a clearly identifiable molecular event: an abrupt liquid-structure change triggered by the rapid rotation. This example shows that molecular relaxation can sometimes switch from linear to nonlinear response.

New insight into experimental probes of cluster melting

Experiments are now appearing which attempt to probe melting in small clusters, a notable example of these being the recent studies of benzene–Arn clusters by Hahn and Whetten [Phys. Rev. Lett. 61, 1190 (1988)]. We report a study of the dynamics of these same benzene–Arn clusters which seeks to clarify further the nature of ‘‘phase transitions’’ in small systems. The techniques used here, involving an instantaneous normal mode analysis based on the results of Monte Carlo calculations, have been shown previously to yield a picture of argon cluster melting which is more complete than the one which emerges from a mere enumeration of low‐energy structures. Although the bare argon clusters are found to undergo dynamical transitions as the cluster temperature is increased, these transitions are inhibited by the presence of an embedded benzene molecule, which provides a template for ordering of the argon atoms. The calculations also suggest a possible explanation for the doubly peaked spectra observed in the exp...

The short‐time intramolecular dynamics of solutes in liquids. I. An instantaneous‐normal‐mode theory for friction

It is sometimes useful to be able to think of the energy relaxation of a solute dissolved in a liquid as being caused by some sort of solvent‐inspired friction. This intuitive association can, in fact, be made literal and quantitative in classical mechanics by casting the dynamics into a solute‐centered equation of motion, a generalized Langevin equation, in which the dissipative character of the solvent is embodied in a (generally time delayed) friction force. An exact prescription is available for finding this friction, but the process is formal and the connection with microscopic degrees of freedom is rather indirect. An alternate approach due to Zwanzig, which portrays the solvent as a harmonic bath, makes explicit use of a set of solvent coordinates, but these coordinates have no immediate relationship with any of the real solvent degrees of freedom. We show here that by taking a short‐time perspective on solute relaxation we can derive a generalized Langevin equation, and hence a friction kernel, wh...