Measuring order in disordered systems and disorder in ordered systems: Random matrix theory for isotropic and nematic liquid crystals and its perspective on pseudo-nematic domains.

Surprisingly long-ranged intermolecular correlations begin to appear in isotropic (orientationally disordered) phases of liquid crystal forming molecules when the temperature or density starts to close in on the boundary with the nematic (ordered) phase. Indeed, the presence of slowly relaxing, strongly orientationally correlated, sets of molecules under putatively disordered conditions ("pseudo-nematic domains") has been apparent for some time from light-scattering and optical-Kerr experiments. Still, a fully microscopic characterization of these domains has been lacking.

What is special about how roaming chemical reactions traverse their potential surfaces? Differences in geodesic paths between roaming and non-roaming events.

With the notable exception of some illustrative two-degree-of-freedom models whose surprising classical dynamics has been worked out in detail, theories of roaming have largely bypassed the issue of when and why the counterintuitive phenomenon of roaming occurs. We propose that a useful way to begin to address these issues is to look for the geodesic (most efficient) pathways through the potential surfaces of candidate systems. Although roaming manifests itself in an unusual behavior at asymptotic geometries, we found in the case of formaldehyde dissociation that it was the pathways traversing the parts of the potential surface corresponding to highly vibrationally excited reactants that were the most revealing.

The inherent dynamics of isotropic- and nematic-phase liquid crystals.

The geodesic (shortest) pathways through the potential energy landscape of a liquid can be thought of as defining what its dynamics would be if thermal noise were removed, revealing what we have called the "inherent dynamics" of the liquid. We show how these inherent paths can be located for a model liquid crystal former, showing, in the process, how the molecular mechanisms of translation and reorientation compare in the isotropic and nematic phases of these systems. These mechanisms turn out to favor the preservation of local orientational order even under macroscopically isotropic conditions (a finding consistent with the experimental observation of pseudonematic domains in these cases), but disfavor the maintenance of macroscopic orientational order, even in the nematic phase.

Potential energy landscape and inherent dynamics of a hard-sphere fluid.

Hard-sphere models exhibit many of the same kinds of supercooled-liquid behavior as more realistic models of liquids, but the highly nonanalytic character of their potentials makes it a challenge to think of that behavior in potential energy landscape terms. We show here that it is possible to calculate an important topological property of hard-sphere landscapes, the geodesic pathways through those landscapes, and to do so without artificially coarse-graining or softening the potential. We show, moreover, that the rapid growth of the lengths of those pathways with increasing packing fraction quantitatively predicts the precipitous decline in diffusion constants in a glass-forming hard-sphere mixture model.

Effects of Electronic-State-Dependent Solute Polarizability: Application to Solute-Pump/Solvent-Probe Spectra.

Experimental studies of solvation dynamics in liquids invariably ask how changing a solute from its electronic ground state to an electronically excited state affects a solution's dynamics. With traditional time-dependent-fluorescence experiments, that means looking for the dynamical consequences of the concomitant change in solute-solvent potential energy. But if one follows the shift in the dynamics through its effects on the macroscopic polarizability, as recent solute-pump/solvent-probe spectra do, there is another effect of the electronic excitation that should be considered: the jump in the solute's own polarizability.

The inherent dynamics of a molecular liquid: geodesic pathways through the potential energy landscape of a liquid of linear molecules.

Because the geodesic pathways that a liquid follows through its potential energy landscape govern its slow, diffusive motion, we suggest that these pathways are logical candidates for the title of a liquid's "inherent dynamics." Like their namesake "inherent structures," these objects are simply features of the system's potential energy surface and thus provide views of the system's structural evolution unobstructed by thermal kinetic energy. This paper shows how these geodesic pathways can be computed for a liquid of linear molecules, allowing us to see precisely how such molecular liquids mix rotational and translational degrees of freedom into their dynamics.

How a solute-pump∕solvent-probe spectroscopy can reveal structural dynamics: polarizability response spectra as a two-dimensional solvation spectroscopy.

The workhorse spectroscopy for studying liquid-state solvation dynamics, time-dependent fluorescence, provides a powerful, but strictly limited, perspective on the solvation process. It forces the evolution of the solute-solvent interaction energy to act as a proxy for what may be fairly involved changes in solvent structure. We suggest that an alternative, a recently demonstrated solute-pump∕solvent-probe experiment, can serve as a kind of two-dimensional solvation spectroscopy capable of separating out the structural and energetic aspects of solvation.

Vibrational energy relaxation of large-amplitude vibrations in liquids.

Given the limited intermolecular spaces available in dense liquids, the large amplitudes of highly excited, low frequency vibrational modes pose an interesting dilemma for large molecules in solution. We carry out molecular dynamics calculations of the lowest frequency ("warping") mode of perylene dissolved in liquid argon, and demonstrate that vibrational excitation of this mode should cause identifiable changes in local solvation shell structure. But while the same kinds of solvent structural rearrangements can cause the non-equilibrium relaxation dynamics of highly excited diatomic rotors in liquids to differ substantially from equilibrium dynamics, our simulations also indicate that the non-equilibrium vibrational energy relaxation of large-amplitude vibrational overtones in liquids should show no such deviations from linear response.

How dominant is the most efficient pathway through the potential energy landscape of a slowly diffusing disordered system?

It has been suggested that the most-efficient pathway taken by a slowly diffusing many-body system is its geodesic path through the parts of the potential energy landscape lying below a prescribed value of the potential energy. From this perspective, slow diffusion occurs just because these optimal paths become particularly long and convoluted. We test this idea here by applying it to diffusion in two kinds of well-studied low-dimensional percolation problems: the 2d overlapping Lorentz model, and square and simple-cubic bond-dilute lattices.

The molecular underpinnings of a solute-pump/solvent-probe spectroscopy: the theory of polarizability response spectra and an application to preferential solvation.

Recent ultrafast experiments on liquids have made clear that it is possible to go beyond light scattering techniques such as optical Kerr spectroscopy that look at the dynamics of a liquid as a whole. It is now possible to measure something far more conceptually manageable: how that liquid dynamics (and that light scattering) can be modified by electronically exciting a solute. Resonant-pump polarizability-response spectra (RP-PORS) in particular, seem to show that different solvents respond in noticeably distinct ways to such solute perturbations.

Preferential solvation dynamics in liquids: how geodesic pathways through the potential energy landscape reveal mechanistic details about solute relaxation in liquids.

It is not obvious that many-body phenomena as collective as solute energy relaxation in liquid solution should ever have identifiable molecular mechanisms, at least not in the sense of the well-defined sequence of molecular events one often attributes to chemical reactions. What can define such mechanisms, though, are the most efficient relaxation paths that solutions take through their potential energy landscapes. When liquid dynamics is dominated by slow diffusive processes, there are mathematically precise and computationally accessible routes to searching for such paths.

Anatomy of an energy transfer event in a liquid: the high-energy rotational relaxation of OH in solution.

The photochemical generation of highly rotationally excited diatomics affords us an intriguing way to study energy relaxation processes in solution. Because excited products involve only a single intramolecular degree of freedom and because their relaxations can lie well outside of the linear-response regime, it may be possible to infer detailed molecular mechanisms for these processes just from transient absorption measurements. In this paper we describe a theoretical study of the rotational relaxation of a new candidate for such measurements, OH radicals.

Global perspectives on the energy landscapes of liquids, supercooled liquids, and glassy systems: geodesic pathways through the potential energy landscape.

How useful it is to think about the potential energy landscape of a complex many-body system depends in large measure on how direct the connection is to the system's dynamics. In this paper we show that, within what we call the potential-energy-landscape ensemble, it is possible to make direct connections between the geometry of the landscape and the long-time dynamical behaviors of systems such as supercooled liquids. We show, in particular, that the onset of slow dynamics in such systems is governed directly by the lengths of their geodesics--the shortest paths through their landscapes within the special ensemble.

Global perspectives on the energy landscapes of liquids, supercooled liquids, and glassy systems: the potential energy landscape ensemble.

In principle, all of the dynamical complexities of many-body systems are encapsulated in the potential energy landscapes on which the atoms move--an observation that suggests that the essentials of the dynamics ought to be determined by the geometry of those landscapes. But what are the principal geometric features that control the long-time dynamics? We suggest that the key lies not in the local minima and saddles of the landscape, but in a more global property of the surface: its accessible pathways. In order to make this notion more precise we introduce two ideas: (1) a switch to a new ensemble that deemphasizes the concept of potential barriers, and (2) a way of finding optimum pathways within this new ensemble.

Anomalously slow solvent structural relaxation accompanying high-energy rotational relaxation.

Experimental and theoretical work on the relaxation of rapidly rotating solutes in liquids have pointed out a number of striking features. Even in rapidly relaxing solvents, the relaxation proceeds quite slowly, exhibiting a manifestly nonlinear response that depends explicitly on the initial rotational energy. In this paper, we show how the long-time behavior, in particular, stems from a strong coupling of solute orientation to local solvent geometry.

The molecular origins of nonlinear response in solute energy relaxation: the example of high-energy rotational relaxation.

A key step in solution-phase chemical reactions is often the removal of excess internal energy from the product. Yet, the way one typically studies this process is to follow the relaxation of a solute that has been excited into some distribution of excited states quite different from that produced by any reaction of interest. That the effects of these different excitations can frequently be ignored is a consequence of the near universality of linear-response behavior, the idea that relaxation dynamics is determined by the solvent fluctuations (which may not be all that different for different kinds of solute excitation).

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.

Why does the intermolecular dynamics of liquid biphenyl so closely resemble that of liquid benzene? Molecular dynamics simulation of the optical-Kerr-effect spectra.

The combination of optical-Kerr-effect (OKE) spectroscopy and molecular dynamics simulations has provided us with a newfound ability to delve into the librational dynamics of liquids, revealing, in the process, some surprising commonalities among aromatic liquids. Benzene and biphenyl, for example, have remarkably similar OKE spectra despite marked differences in their shapes, sizes, and moments of inertia--and even more chemically distinct aromatics tend to have noticeable similarities in their spectra. We explore this universality by using a molecular dynamics simulation to investigate the librational dynamics of molten biphenyl and to predict its OKE spectrum, comparing the results with our previous calculations for liquid benzene.

Multiphonon vibrational relaxation in liquids: should it lead to an exponential-gap law?

The profound differences between solids and liquids notwithstanding, high-frequency vibrational energy relaxation in liquids seems to be well described by assuming that the excess energy is being transferred into discrete overtones of some fundamental intermolecular vibrations-precisely the way it is in crystalline solids. In a solid-state context, this kind of analysis can be used to justify the observation that relaxation rates fall off exponentially with the energy being transferred. Liquids, however, have a substantial degree of disorder, causing their relevant intermolecular spectra to have correspondingly diffuse band edges and large bandwidths.

The workings of a molecular thermometer: the vibrational excitation of carbon tetrachloride by a solvent.

An intriguing energy-transfer experiment was recently carried out in methanol/carbon tetrachloride solutions. It turned out to be possible to watch vibrational energy accumulating in three of carbon tetrachloride's modes following initial excitation of O-H and C-H stretches in methanol, in effect making those CCl(4) modes "molecular thermometers" reporting on methanol's relaxation. In this paper, we use the example of a CCl(4) molecule dissolved in liquid argon to examine, on a microscopic level, just how this kind of thermal activation occurs in liquid solutions.