We report a new method for calculating the Wigner transform of the Boltzmann operator in the canonical ensemble. The transform is accomplished by writing the Boltzmann operator in a semiharmonic form, utilizing the variational centroid effective frequencies introduced by Feynman and Kleinert (FK). The approximate many-body Wigner transformed Boltzmann operator is then utilized with a linearized path integral (LPI) representation for correlation functions. It is shown that this new FK-LPI method is capable of calculating quite accurately the short time behavior of linear and highly nonlinear correlation functions for low temperature Lennard-Jones model systems and that it is vastly superior to classical dynamics. The feasibility of the FK-LPI method for large systems is illustrated by considering a model liquid composed of 32 oxygen molecules with periodic boundary conditions. Initial conditions for molecular dynamics are obtained from its Boltzmann Wigner transform and the FK-LPI method is shown to describe correctly the zero-point motion of the liquid. The effective frequency representation of the Wigner transformed thermal density operator provides an efficient way of sampling nonclassical initial conditions for molecular-dynamics simulations more generally. Applications to vibrational energy relaxation and rate constant calculations in complex molecular systems are discussed.

Ultrafast time-resolved spectroscopic studies of complex chemical reactions in solution are frequently hindered by difficulties in recovering accurate structural models for transient photochemical species. Time-resolved x-ray and electron diffraction have recently emerged as techniques for probing the structural dynamics of short lived photointermediates. Here we determine the structure of a transient isomer of photoexcited CH 2 I 2 in solution and observe the downstream reactions of the initial photoproducts. Our results illustrate how geminate recombination proceeds via the formation of a transient covalent bond onto the iodine atom remaining with the parent molecule. Further intramolecular rearrangements are thus required for the CH 2 I-I isomer to return to CH 2 I 2 . The generation of I 3 ÿ from those iodine radicals escaping the solvent cage is also followed with time.

The photolysis of aqueous ClO2 has been studied with a new femtosecond transient absorption spectrometer, allowing absorbance changes as small as ΔA ≈ 1 × 10-4 to be recorded with a time resolution of 150 fs. ClO2 was photolyzed at 390 nm and the ultrafast formation and decay of photoproducts were monitored at 260, 390, and 780 nm. As expected from earlier studies, Cl atoms are formed with a quantum yield of Φ(Cl) = 0.1. However, the rate of formation is nearly 2 orders of magnitude higher than that reported. Moreover, Cl is the only photoproduct that survives 25 ps after the photolysis pulse. The main photolytic products, ClO + O, formed with a quantum yield of 0.9, disappear through fast geminate recombination, producing vibrational excited ClO2 in the electronic ground state. The vibrational relaxation of this species occurs with a time constant of 10 ps. The vanishing yield of cage escape for ClO + O, which contrasts with the reported result of the photolysis at 355 nm, indicates that the amount of excess energy imparted to these products at 390 nm is insufficient to enable them to separate. The decay of a photoinduced dichroism observed at 390 nm is interpreted as an orientational relaxation of ground-state ClO2 , the time constant (0.6 ps) agreeing with that calculated from the hydrodynamical slip model.

Operative correction of penile curvature is a reasonably safe procedure, but should not be performed solely for cosmetic reasons. In the present retrospective study the results were better after the Nesbit procedure compared with plication of the tunica albuginea. However, a review of the literature does not give support to one operative technique over the other. This can only be clarified by performing a prospective randomized trial.

Structure, transport properties, and IR spectra including quantum effects are calculated for a flexible simple point charge model of liquid water. A recently introduced combination of a variational local harmonic description of the liquid potential surface and the classical Wigner approximation for the dynamics is used. The potential energy and interatomic radial distribution functions are in good agreement with accurate results from the literature and are significantly closer to experiment than predictions found from classical theory. The oxygen and hydrogen velocity correlation functions are also calculated, and the corresponding molecular diffusion coefficient is in good accord with existing theoretical estimates including quantum effects. Of most interest, an ab initio quantum correction factor is obtained to correct the far IR spectrum of water. When corrected, a spectrum based on a classical simulation yields results that agree well with experiment. Combined with internal tests of consistency, these observations indicate that this quite flexible approach will be effective for a variety of molecular problems involving the dynamics of light nuclei.computer simulation ͉ liquid dynamics A lthough the molecular-level description of the structure and dynamics of disordered condensed phases, such as liquids, glasses, and globular proteins, is normally, and generally successfully, described by using classical mechanics, the underlying accurate description is, of course, quantum mechanical. It is simply that the quantum effects can be sufficiently small as to be unimportant in many contexts. Nevertheless, for lower temperatures and lighter masses, quantum effects will become increasingly important. For low-temperature (Ϸ30 K or less) simple liquids, such as liquid helium and molecular hydrogen with low masses, quantum effects associated with positional uncertainty are expected to substantially broaden features in the liquid structure, and the diffusion of these effectively larger but ''softer'' objects is expected to be significantly altered from the classical description, even in the absence of coherent quantum dynamics (1, 2). For a molecular hydrogen-bonded liquid, such as water, the low mass of the hydrogen atom causes the intramolecular vibrations to behave quantum mechanically to quite high temperatures, and the intermolecular vibrational modes, including the relatively high-frequency librational motions (Ϸ250-900 cm Ϫ1 ) resulting from the frustrated rotation of molecules, are significantly quantum mechanical at room temperature, where the available thermal energy, Ϸ200 cm Ϫ1 , is considerably smaller than the librational quantum spacing (3).In recent years, there has been a great deal of progress in our ability to accurately evaluate equilibrium, time-independent properties of liquids, and related materials with complete consideration of quantum mechanics. For the most part, these have been based on simulations implementing discretized path integral forms (3, 4). For dynamics, the problem is far more challe...

The photolysis of aqueous ICN is studied by transient absorption spectroscopy covering the spectral range from 227 to 714 nm with 0.5 ps time resolution. The experimental data show that when ICN(aq) is photolyzed at 266 nm, it dissociates into I and CN and both the I(2P3/2) and I(2P1/2) channels are populated. Approximately half the fragments escape the solvent cage while the remainder recombines within the solvent cage during the first picosecond. The majority of the recombinations form ICN while only a minor fraction produces the metastable INC isomer. INC and ICN relax to the vibrational ground state within 1 ps in good agreement with theoretical estimates based on the golden rule formalism as well as molecular dynamics simulations. Diffusive recombination involving fragments that have escaped the solvent cage further reduces the quantum yield of I and CN to 10% during the following 100 ps. This recombination produces exclusively ICN.

The spectrum of the Van Hove correlation function (CF) is calculated for liquid He(4) at 27 K and a density of 0.25 g/cm3 by utilizing a recently proposed approximation to quantum CFs derived by combining an effective-frequency Boltzmann−Wigner transform with a linearized path integral expression for CFs. For this anharmonic system and highly nonlinear CF, we obtain excellent agreement with available accurate results. In particular, the first, second, and third moments of the spectrum are in very good agreement with both experiment and earlier theoretical results. Also, the calculated kinetic energy is in excellent agreement with accurate path integral Monte Carlo results.

Quantum effects on diffusion in liquid para-hydrogen at temperatures of T ) 17 and 25 K and saturated vapor pressure is studied by calculating the diffusion coefficient from the standard Green-Kubo formula, using both the ordinary velocity correlation function (CF) and its Kubo-transformed counterpart. All CFs are calculated with a recently proposed linearized path integral expression for general CFs, using an approximate Wigner transformed Boltzmann operator based on Feynman-Kleinert variational path integral theory. Also, the ability of the approximate Wigner transform to predict the radial distribution function and kinetic energy of the liquid is investigated. The conclusions are as follows: (i) The predicted structure of liquid parahydrogen is in excellent agreement with accurate path integral Monte Carlo calculations at both temperatures. (ii) The calculated liquid kinetic energy is in very good agreement with the accurate value at T ) 25 K but deviates somewhat from the accurate value at T ) 17 K. (iii) The diffusion coefficients based on the Kubotransformed CF are in very good agreement with experiment, at both temperatures, whereas results from the ordinary velocity CF are not accurate at T ) 17 K. The reason for the better performance of the Kubo CF approach is attributed to the latter's robustness toward errors in the approximate Boltzmann operator Wigner transform. The kinetic energy derived from the Kubo-transformed CFs is in excellent agreement with accurate values at both temperatures. † Part of the special issue "Frank H. Stillinger Festschrift".