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. It is therefore not at all obvious what should become of this exponential-gap-law phenomenology. We show in this paper how near exponential-gap-law behavior can still be derived for vibrational energy relaxation in liquids. To do so, we take advantage of the simple dynamics that the high-frequency relaxation has when it is launched from an individual instantaneous configuration. Interestingly, the physically relevant region turns out not to be true asymptotic limit of our formalism, but for realistic liquid parameters the behavior in the physical regime differs only slightly from an exact exponential-gap law and is strikingly independent of the details of the intermolecular spectra.     

Solvent-induced electronic spectral shifts: Benzene·Arn revisited

Just what can be learned about cluster dynamics (and, more generally, about solvation dynamics) from spectral studies of small clusters that have been doped with a chromophore is still an open question. In the present work we suggest a novel procedure for calculating the shift in the electronic absorption spectrum of a chromophore deriving from the attachment to or the incorporation in a cluster. The particular system of interest here is benzene·Ar _n , for which experimental results are readily available although their interpretation has been a point of controversy. In addition, since the present formalism is equally applicable to a chromophore isolated in a bulk phase (either liquid or solid), we are able to venture an explanation for the apparent observation that the spectral shift of cluster-isolated benzene does not approach the asymptotic values characteristic of the bulk-isolated species.     

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). Nonetheless, there are some clear examples of linear-response breakdowns seen in solute relaxation, including a recent theoretical and experimental study of rapidly rotating diatomics in liquids. In this paper we use this rotational relaxation example to carry out a theoretical exploration of the conditions that lead to linear-response failure. Some features common to all of the linear-response breakdowns studied to date, including our example, are that the initial solute preparation is far from equilibrium, that the subsequent relaxation promotes a significant rearrangement of the liquid structure, and that the nonequilibrium response is nonstationary. However, we show that none of these phenomena is enough to guarantee a nonlinear response. One also needs a sufficient separation between the solute time scale and that of the solvent geometry evolution. We illustrate these points by demonstrating precisely how our relaxation rate is tied to our liquid-structural evolution, how we can quantitatively account for the initial nonstationarity of our effective rotational friction, and how one can tune our rotational relaxation into and out of linear response.     

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. This paper is a theoretical attempt at understanding the kinds of molecular information that can be revealed by experiments of this sort. After developing the general classical statistical mechanical linear response theory for these spectra, we show that the experimentally interesting limit of long solute-pump/solvent-probe delays corresponds to measuring the differences in 4-wave-mixing spectra between solutions with equilibrated ground- and excited-state solutes-meaning that the spectra are essentially probes of how changing liquid structure affects intermolecular liquid vibrations and librations. We examine the spectra in this limit for the special case of an atomic solute dissolved in an atomic-liquid mixture, a preferential solvation problem, and show that, as with the experimental spectra, different solvents can lead to spectra with different magnitudes and even different signs. Our molecular-level analysis of these results points out that solvents can also differ in how local a portion of the solvent dynamics is accessed by this spectroscopy.     

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. The fact that even the lowest CCl(4) mode has a relatively high frequency compared to the intermolecular vibrational band of the solvent means that the only solute-solvent dynamics relevant to the vibrational energy transfer will be extraordinarily local, so much so that it is only the force between the instantaneously most prominent Cl and solvent atoms that will significantly contribute to the vibrational friction. We use this observation, within the context of a classical instantaneous-pair Landau-Teller calculation, to show that energy flows into CCl(4) primarily via one component of the nominally degenerate, lowest frequency, E mode and does so fast enough to make CCl(4) an excellent choice for monitoring methanol relaxation. Remarkably, within this theory, the different symmetries and appearances of the different CCl(4) modes have little bearing on how well they take up energy from their surroundings--it is only how high their vibrational frequencies are relative to the solvent intermolecular vibrational band edge that substantially favors one mode over another.     

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. The potential energy landscape ensemble, which we describe in the current paper, regards the maximum accessible potential energy, rather than the temperature, as a control variable. We show here that while this approach is thermodynamically equivalent to the canonical ensemble, it not only sidesteps the idea of barriers it allows us to be quantitative about the connectivity of a landscape. We illustrate these ideas with calculations on a simple atomic liquid and on the Kob-Andersen [Phys. Rev. E 51, 4626 (1995)] of a glass-forming liquid, showing, in the process, that the landscape of the Kob-Anderson model appears to have a connectivity transition at the landscape energy associated with its empirical mode-coupling transition. We turn to the problem of finding the most efficient pathways through potential energy landscapes in our companion paper.     

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. Although the most efficient path should be at its most dominant with the high-dimensional landscapes associated with many-body problems, it is useful to examine simpler, low-dimensional, constant-potential-energy problems such as these ones, both because the simpler models lend themselves to more accurate geodesic-path-finding approaches, and because they offer a significant contrast to many of the models used in the traditional energy-landscape literature. Neither the continuum nor the lattice percolation examples are adequately described by our geodesic-path formalism in the weakly disordered (relatively-fast-diffusion) limit, but in both cases the formalism successfully predicts the existence of the percolation transition and (to a certain extent) the slow diffusion characteristic of near-percolation behavior. The numerical results for these models are not nearly accurate enough near their transitions to describe critical exponents, but the models do showcase the qualitative validity of the geodesic perspective in that they allow us to see explicitly how tortuous and sparse the optimal pathways become as the diffusion constants begin to vanish.     

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. We suggest that the impressive level of quantitative agreement between these two liquids is largely a reflection of the fact that librations in these and other aromatic liquids act as torsional oscillations with oscillator frequencies selected from the liquid's librational bands. Since these bands are centered about the librational Einstein frequencies, the quantitative similarities between the liquids are essentially reflections of the near identities of their Einstein frequencies. Why then are the Einstein frequencies themselves so insensitive to molecular details? We show that, for nearly planar molecules, mean-square torques and moments of inertia tend to scale with molecular dimensions in much the same way. We demonstrate that this near cancellation provides both a quantitative explanation of the close relationship between benzene and biphenyl and a more general perspective on the similarities seen in the ultrafast dynamics of aromatic liquids.