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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. We illustrate in this paper how pseudo-nematic domains can be studied in even relatively small computer simulations by looking for order-parameter tensor fluctuations much larger than one would expect from random matrix theory. To develop this idea, we show that random matrix theory offers an exact description of how the probability distribution for liquid-crystal order parameter tensors converges to its macroscopic-system limit. We then illustrate how domain properties can be inferred from finite-size-induced deviations from these random matrix predictions. A straightforward generalization of time-independent random matrix theory also allows us to prove that the analogous random matrix predictions for the time dependence of the order-parameter tensor are similarly exact in the macroscopic limit, and that relaxation behavior of the domains can be seen in the breakdown of the finite-size scaling required by that random-matrix theory. [ABSTRACT FROM AUTHOR]

Experiments are conducted to show how the long-time behavior has obtained from a strong coupling of solute orientation to local solvent geometry. The slow dynamics is dynamically heterogeneous and the distribution of excited rotors is described by a distinct population of slowly relaxing hot rotational states.

A theoretical study of the electron diffraction patterns that from aligning a molecule, s-tetrazine (C2N4H2), in a high intensity laser field using the Friedrich-Herscbach approach is performed. It is suggested that alignment is very beneficial for extracting information from gas-phase diffraction patterns and where detrimental multiphoton processes do not yet compromise the interpretation of the molecular structure.

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. While the most efficient nematic pathways that maintain nematic order are indeed shorter than those that do not, it is apparently difficult for the system to locate these paths, suggesting that molecular motion in liquid-crystal formers is dynamically frustrated, and reinforcing the sense that there are strong analogies between liquid crystals and supercooled liquids. [ABSTRACT FROM AUTHOR]

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. The ratio of translational to rotational components of the geodesic path lengths, for example, is significantly larger than would be expected on equipartition grounds, with a value that scales with the molecular aspect ratio. These and other features of the geodesics are consistent with a picture in which molecular reorientation adiabatically follows translation—molecules largely thread their way through narrow channels available in the potential energy landscape. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. We apply this observation to the dynamics of preferential solvation, the relaxation around a newly excited solute by a solvent composed of different components with different solvating abilities. The slow solvation seen experimentally in these mixtures stems from the dual needs to compress the solvent and to do solvent-solvent exchanges near the solute. By studying the geodesic (most efficient) paths for this combined process in a simple atomic liquid mixture, we show that the mechanism for preferential solvation features a reasonably sharp onset for slow diffusion, and that this diffusion involves a sequential, rather than concerted, series of solvent exchanges. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. The more convoluted and labyrinthine these geodesics are, the slower that dynamics is. Geodesics in the landscape ensemble have sufficiently well-defined characteristics that it is straightforward to search for them numerically, a point we illustrate by computing the geodesic lengths for an ordinary atomic liquid and a binary glass-forming atomic mixture. We find that the temperature dependence of the diffusion constants of these systems, including the precipitous drop as the glass-forming system approaches its empirical mode-coupling transition, is predicted quantitatively by the growth of the geodesic path lengths. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

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 CCl4 modes “molecular thermometers” reporting on methanol’s relaxation. In this paper, we use the example of a CCl4 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 CCl4 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 CCl4 primarily via one component of the nominally degenerate, lowest frequency, E mode and does so fast enough to make CCl4 an excellent choice for monitoring methanol relaxation. Remarkably, within this theory, the different symmetries and appearances of the different CCl4 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. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The wealth of information carried by the two-dimensional Raman spectra of liquids comes with a price. The signal arises from a mixture of two entirely different mechanisms, each of which reveals its own perspective on intermolecular dynamics. In this paper we analyze the dynamical origins and consequences of both of these mechanisms. By applying an instantaneous-normal-mode formalism to the two-dimensional Raman spectrum of a solution of CS[sub 2] dissolved in Xe, we find discernable differences in the specific molecular degrees of freedom and basic symmetries that contribute to each mechanism. We then show how these differences can be exploited to separate these mechanisms experimentally. In particular, we point out how it should be possible to use two-dimensional Raman spectroscopy to measure the explicitly anharmonic contributions to liquid dynamics without obscuring the results by simultaneously measuring the nonlinear coupling of the polarizability to that dynamics. © 2003 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The basic solid-state perspective on energy relaxation—that a solute transfers large amounts of energy to its surroundings by exciting overtones of the solid’s phonons—is sufficiently beguiling that it is tempting to try to apply it to high-frequency vibrational energy relaxation in liquids. We suggest that when the phonon concept is suitably adapted this picture does provide a surprisingly realistic and quantitative portrait of vibrational energy dispersal in solution. Within the nonlinear instantaneous-normal-mode/instantaneous-pair theory of vibrational relaxation, relaxation rates can be formally written as a sum over the contributions of successively higher overtones of fundamental solvent frequencies. However the presence of a significant width to the band of fundamental frequencies in the liquid state means that there could, in principle, be complex interferences between multiple contributing overtones, rendering the overtone picture no more than a formal construct. What we find is that such interferences do not occur. Despite the fact the band shape is log normal—with a relatively long band tail—the relaxation is invariably dominated by a single overtone. This same perspective also helps us understand one of the failings of the common velocity-Verlet molecular dynamics algorithm in predicting high-frequency energy relaxation. © 2003 American Institute of Physics. [ABSTRACT FROM AUTHOR]

When the relevant frequencies get high enough, vibrational energy relaxation in liquids should, in principle, be governed by instantaneous-pair theory. The basic idea is that in any significantly contributing liquid configuration there is a single critical solvent molecule and that solute relaxation rates are determined by the time evolution of that molecule's distance from the solute. The theory posits, moreover, that dynamics can always be modeled as a simple one-dimensional, two-body, scattering process with the liquid playing a role only in determining the initial conditions for the scattering. In this article we reformulate this theory so that it can address both polyatomic solutes and molecular solvents and we show that fundamental assumptions and basic approach remain valid even with multiple solute and solvent sites and with long-ranged intermolecular forces. We further show that while the corrections are often not large, it is possible to make systematic improvements by allowing for the multidimensionality of the solute-solvent scattering. We then turn to the instantaneous-normal-mode (INM) interpretation and implementation of the theory. At the lowest level, INM analysis enables us to define the "high frequencies" relevant to the theory as being outside the INM band of the liquid's intermolecular vibrations and to think of the liquid as generating these frequencies from the overtones of a single INM mode. This kind of analysis predicts a temperature dependence to high-frequency vibrational relaxation remarkably similar to that of solid-state multiphonon models. However, by systematically improving this INM formulation we find that we can also explore the steps a liquid has to take to handle the relaxation of frequencies within its natural band. As the frequency decreases, a liquid evidently needs to invoke more and more of its band to drive the important solvent dynamics. Nonetheless, we continue to find that none of this important dynamics ever seems... [ABSTRACT FROM AUTHOR]

Vibrationally excited polyatomic molecules can relax in a variety of different ways in solution; the excess energy can be dissipated directly to the solvent, or it can be redistributed between any number of different intramolecular modes, with the liquid absorbing (or supplying) just enough energy to make the process work. What we consider here is how the solvent participates in these mechanistic choices. Using the prototypical example of a symmetric linear triatomic molecule, we compare the molecular origins of the vibrational friction for the direct vibrational cooling of the symmetric and antisymmetric stretching modes and contrast both of those with intramolecular vibrational energy transfer between these two modes. Instantaneous-normal-mode analysis reveals that a solid-statelike perspective is a plausible starting point for understanding these processes; the solvent does define a band of intermolecular vibrations, and it is only when the energy being transferred falls within that band that the solvent can easily accept energy from a solute. However, it is also possible to discern some more liquid-state-specific details. Despite their different symmetries and different kinematic requirements, all of the different relaxation pathways are apparently driven by the dynamics of the same instantaneously nearest solvents. [ABSTRACT FROM AUTHOR]

As complex as it may seem, a two-dimensional (fifth-order) nonresonant Raman spectrum may provide one of the simplest ways to get at the character of intermolecular dynamics in liquids. Its status as an echo spectroscopy means that it should not only permit us to survey the intermolecular vibrations, it should allow us to ascertain the extent of their coherence. Arriving at a microscopic interpretation of those spectra, however, poses some genuine theoretical challenges. We describe here the first complete molecular dynamics simulation of such a spectrum. By using classical dynamics and focusing on liquid Xe, we find that we are able to produce a spectrum strikingly similar to the experimentally reported (nonmagic-angle) spectra of liquid CS[sub 2]. We observe, in particular, that there is no discernable echo, suggesting that the dynamics is strongly homogeneously broadened. We turn, in a companion paper, to the implications of these results for instantaneousnormal-mode models of liquids. [ABSTRACT FROM AUTHOR]

One of the most direct outcomes one could have envisioned from the two-dimensional (fifth-order) nonresonant Raman spectroscopy of liquids would have been a verdict on usefulness of instantaneous normal modes (INMs) as a basis for describing ultrafast liquid dynamics. Seeing the echo predicted by standard INM theory would have been persuasive evidence that this dynamics could really be thought of in terms of independent harmonic intermolecular vibrations. However, molecular dynamics calculations on liquid Xe show that there is no echo, implying that dynamical anharmonicities can have qualitative consequences even on ultrafast time scales—a notion seemingly inimical to the entire INM concept. What we show in this paper is that the fifth-order Raman spectrum can be understood within the confines of INM ideas, and from a fully molecular perspective, simply by including the contributions of the pure dephasing undergone by each INM mode. We show, in particular, that this dephasing stems from the adiabatic variation of the INM frequencies and of the cubic anharmonicity along each mode, and that lack of an echo can be understood from the magnitudes of the instantaneous anharmonicities alone. The resulting detailed picture of fifth-order Raman spectroscopy allows us, at least for liquid Xe, to assign a definitive mechanism for the origin of the signal; the spectrum is largely a measure of the liquid's dynamical anharmonicities and not of any nonlinear coupling of the liquid dynamics to the polarizability. [ABSTRACT FROM AUTHOR]

Describes the individual rotational quantum states in liquids through analysis of the rotational Roman spectrum of solutions. Occurrence of dissolved hydrides on discrete rotational lines of the spectra; Causes of relaxation of the rotational quantum states; Rate of transition between rotational states of the liquid.

The combination of optical-Kerr-effect (OKE) spectroscopy and molecular dynamics simulations provided with an ability to delve into the librational dynamics of liquids, revealing, in the process, some surprising commonalities among aromic liquids. Benzene and biphenyl, 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.

The combination of molecular dynamics simulation and instantaneous-normal-mode analysis to take apart benzene's spectrum layer by layer by exploring the optical Kerr effect (OKE) spectra of an experimentally well-studied liquid is presented. The results reveals that the unusual shape of the experimental benzene OKE spectra arises from the presence of an especially large ratio of rotational to translational bandwidths, an explanation that may account for the similar spectra seen with numerous other planar molecules.

The electron diffraction patterns of s-tetrazine in specific electronic and vibrational states are calculated. The differences in diffraction patterns of isoenergetic vibrational states provide an opportunity for observing the flow of vibrational energy through the phase space by time-dependent three-dimensional mapping.

Describes an instantaneous pair theory for high-frequency vibrational energy relaxation in fluids. Indications that the crucial liquid motions are those that most rapidly modulate the force on the vibrating coordinate; Sufficiency of the instantaneous scattering dynamics of the solute-solvent pair in explaining high-frequency relaxation in the fluids.

Studies the role of dielectric friction in vibrational energy relaxation. Potential of relaxation processes to be affected by special dynamics associated with Coulombic forces; Evidence of acceleration of vibrational energy relaxation in hydrogen-bonding solvents; Use of classical molecular dynamics to study the vibrational population relaxation of diatomic solutes.

Investigates the mode evolution process and the role of anharmonic features in short-time dynamics of fluids. Formulation of analytical models for the instantaneous normal modes; Role of anharmonicity in mode frequency fluctuation; Implications of the interaction between two modes for temporary mixing of modes.

Discusses the treatment of vibrational friction and vibrational relaxation dynamics within an instantaneous normal mode (INM) formalism. Formulation of an INM generalized Langevin equation; INM predictions for vibrational friction kernels, line shapes and dynamics; Role of solute-solvent inhomogeneities in vibrational dynamics.

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, which is both exact (at least at short times) and has a completely transparent connection with solvent motion at the molecular level. We find, in particular, that under these conditions the instantaneous normal modes of the solution fill the role of the Zwanzig harmonic oscillators precisely, meaning that one can analyze friction in molecular terms by appealing to the explicitly microscopic definitions of the instantaneous modes. One of the implications of this perspective is that fluctuations of the solvent are automatically divided into configuration- to-configuration fluctuations and dynamics resulting from a given liquid configuration. It is the latter, instantaneous, friction that we shall want to decompose into molecular ingredients in subsequent papers. However, even here we note that it is the character of this instantaneous friction that leads to the fluctuating force on a solute having slightly, but measurably, non-Gaussian statistics. Our basic... [ABSTRACT FROM AUTHOR]

Although there has been considerable interest in solvation processes in small atomic and molecular clusters, uncertainties in the interpretation of spectral probes have made the experimental elucidation of the solvation, and in particular how it relates to bulk solvation, problematical. We demonstrate here that, through the application of a microscopic formalism which has the novel feature of accounting for the collective dielectric response of a cluster, the reported spectra of large benzene·(Ar)n clusters can be readily understood. Specifically, we show that the apparent lack of convergence of the benzene’s absorption spectrum to the corresponding bulk result derives from the dominance of nonwetting cluster structures for large n. Even observed peak multiplicities and individual linewidths may be understood within this formalism if the cluster structures upon which the calculations are based are generated in a nonequilibrium (rather than thermally equilibrated) simulation. Given this detailed understanding of the relationship between spectroscopy and structure, we also can clarify the experimental consequences of the so-called ‘‘melting’’ transition in benzene·(Ar)n clusters: The spectral signature of the melting is a change in the behavior of the linewidth of the absorption envelope which results from a subset, but not all, of the Ar atoms becoming fluid. This description of the melting behavior suggests an important refinement of the conventional picture of solid–fluid phase coexistence in clusters. © 1996 American Institute of Physics. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

At short enough times, the dynamics of a liquid can be resolved rigorously into independent simple harmonic motions called instantaneous normal modes. The spectrum of such modes is easily accessible via computer simulation, but, despite the existence of theories for other kinds of liquid modes, it has been difficult to come up with analytical approaches of power sufficient to explain the universal appearance of instantaneous normal-mode spectra—though Wu and Loring were recently able to arrive at a theory by exploiting the analogy between this problem and the master equation. In this paper we propose a hierarchy of liquid-theoretical treatments that do show the analogy between instantaneous normal modes and other collective excitations in liquids, but are nonetheless capable of leading to accurate predictions of instantaneous normal-mode spectra. The crucial ideas are that the theoretical treatment must respect the fact these modes conserve momentum and must also recognize the strongly local character of intermolecular force constants. We discuss two theories in detail—a renormalized mean-field theory, which turns out to be identical to the Wu–Loring theory, and a higher-order theory—and apply both to a simple atomic liquid. Both theories successfully predict the results of computer simulations, including the fact that the spectrum depends much more on density than on temperature in the normal liquid range. The higher-order theory, though, gives a slightly more accurate prediction of the fraction of imaginary modes. [ABSTRACT FROM AUTHOR]

Electron–electron interactions appear to play qualitatively vital roles in the behavior of expanded liquid metals; these systems display phenomena that simply do not occur in a single-electron picture. Motivated by a desire to understand such liquids, and to model electron interaction effects in liquids more generally, we show in this paper how one can formulate and solve a Hartree–Fock theory within a liquid by using liquid theory methods. The work generalizes the previous efforts of Logan and co-workers by removing the restrictions to model band shapes and Hubbard Hamiltonians. The Pariser–Parr–Pople Hamiltonian used here has the added feature of an interatomic Coulombic interaction and therefore allows us to assess the role of interaction-induced fluctuations in the local field at each atom. The model also requires a calculation of a quantity with the significance of a bond order, a concept of some possible utility in a wide variety of electronic-structure-in-liquids problems. [ABSTRACT FROM AUTHOR]

It is only relatively recently that it has become possible to use spectroscopy to track the solvation of a molecule as one proceeds from small solute-plus-solvent clusters, through bulk liquids, and into cryogenic matrices. One of the more surprising findings of such studies is that, in a number of noteworthy instances—such as with benzene dissolved in Ar—the solvent shifts of spectral lines in even apparently sizable clusters seem not to go smoothly into the bulk results. In this and the following paper we consider just what level of theoretical treatment is necessary in order to be able to account for the solvent shift of electronic spectra consistently in environments ranging from clusters to the bulk. As we discuss in some detail, neither continuum dielectric approaches nor sums of pair potentials can adequately describe the solvation. What we propose here, instead, is that the effects of nonpolar solvents can be treated fully microscopically by a model incorporating both local repulsive effects and longer-ranged dielectric effects. The latter contribution, resulting from the solvent’s polarizability, is formulated in terms of the so-called polarization modes of the solvent, which change with the detailed arrangement of the solute’s environment. We illustrate the ideas by showing that one can understand the optical spectroscopy of benzene in liquid Ar more or less quantitatively by using this model, and we point out some connections with analogous time-dependent solvation studies. The application of this same approach to clusters is described in the succeeding paper. [ABSTRACT FROM AUTHOR]

One of the most intriguing aspects of the behavior of small clusters is the extent to which their physical and chemical properties depend sensitively on the size of the clusters. But for clusters that are ‘‘large enough,’’ surely their properties must approach those of the corresponding bulk systems. The property of special interest in the present work is the shift in the electronic absorption of a chromophore (benzene) deriving from interaction with nonpolar solvent atoms (Ar), a shift that can be calculated using a microscopic formalism described in this and in the preceding paper which is equally well suited to the study of cluster and condensed phase environments. We are able to identify the evolution of the collective character of the dielectric response of the solvent atoms as being the key feature of the optical properties of these clusters that determines the degree to which their behavior is bulklike. Furthermore, we can associate specific spectral features with particular classes of cluster geometries, and in doing so we derive support for our previous speculations concerning the evidence for the contribution of metastable, nonwetting cluster structures to the experimental spectra. [ABSTRACT FROM AUTHOR]