Chemical Physics

The vibrational excitations of ozone, including both bending and stretching vibrations, are studied in the framework of a symmetry-adapted algebraic approach. This method is based on the isomorphism between the U(2) algebra and the one-dimensional Morse oscillator, and the introduction of point group symmetry techniques. The use of symmetry-adapted interactions, which in the harmonic limit have a clear physical interpretation, makes it possible to systematically include higher order terms and anharmonicities. A least-square fit to all published experimental levels (up to ten quanta) of 16 O_3 and 18 O_3 yields a r.m.s. deviation of 2.5 and 1.0 1/cm, respectively.

We present an analysis of the temperature dependence of the optical response of small sodium clusters in a temperature range bracketing the melting phase transition. When the temperature increases, the mean excitation energy undergoes a red shift and the plasmon is significantly broadened, in agreement with recent experimental data. We show that the single--particle levels acquire a prominent width and the HOMO--LUMO gap as well as the width of the occupied band are reduced due to large thermal cluster size and shape fluctuations. This results in a sharp increase of the static polarizability with temperature.

A dielectric model of electrostatic solvation is applied to describe potentials of mean force in water along reaction paths for: a) formation of a sodium chloride ion pair; b) the symmetric SN2 exchange of chloride in methylchloride; and c) nucleophilic attack of formaldehyde by hydroxide anion. For these cases simulation and XRISM results are available for comparison. The accuracy of model predictions varies from spectacular to mediocre. It is argued that: a) dielectric models are physical models, even though simplistic and empirical; b) their successes suggest that second-order perturbation theory is a physically sound description of free energies of electrostatic solvation; and c) the most serious deficiency of the dielectric models lies in the definition of cavity volumes. Second-order perturbation theory should therefore be used to refine the dielectric models. These dielectric models make no attempt to assess the role of packing effects but for solvation of classical electrostatic interactions the dielectric models sometimes perform as well as the more detailed XRISM theory.

The calculation of the solvation properties of a single water molecule in liquid water is carried out in two ways. In the first, the water molecule is placed in a cavity and the solvent is treated as a dielectric continuum. This model is analyzed by numerically solving the Poisson equation using the DelPhi program. The resulting solvation properties depend sensitively on the shape and size of the cavity. In the second method, the solvent and solute molecules are treated explicitly in molecular dynamics simulations using Ewald boundary conditions. We find a 2 kcal/mole difference in solvation free energies predicted by these two methods when standard cavity radii are used. In addition, dielectric continuum theory assumes that the solvent reacts solely by realigning its electric moments linearly with the strength of the solute's electric field; the results of the molecular simulation show important non-linear effects. Non-linear solvent effects are generally of two types: dielectric saturation, due to solvent-solute hydrogen bonds, and electrostriction, a decrease in the solute cavity due to an increased electrostatic interaction. We find very good agreement between the two methods if the radii defining the solute cavity used in the continuum theory is decreased with the solute charges,

The structure of liquid N-methylformamide (NMF) has been investigated using synchrotron radiation at 77 and 95 keV. The use of high energy photons has several advantages, in this case especially the large accessible momentum transfer range, the low absorption and the direct comparability with neutron diffraction. The range of momentum transfer covered is 0.6 Å −1 < Q < 24.0 Å −1 . Neutron diffraction data on the same sample in the same momentum transfer range have been published previously. In that study two differently isotope - substituted species were investigated. In order to compare neutron and photon diffraction data properly Reverse Monte Carlo (RMC-) simulations have been performed. Some modifications had to be added to the standard RMC- code introducing different constraints for inter- and intramolecular distances as these distances partly overlap in liquid NMF. RMC- simulations having only the neutron data as input were carried out in order to test the quality of the X-ray data. The photon structure factor calculated from the RMC- configurations is found to agree well with the present experimental data, while it deviates considerably from earlier X-ray work using low energy photons (17 keV). Finally we discuss whether the different interaction mechanisms of neutrons and photons can be used to directly access the electronic structure in the liquid. Evidence is presented that the elastic self scattering part of liquid NMF is changed with respect to the independent atom approximation. This modification can be accounted for by a simple charged atoms model.

In the present paper we describe relaxation methods for constructing double-ended classical trajectories. We illustrate our approach with an application to a model anharmonic system, the Henon-Heiles problem. Trajectories for this model exhibit a number of interesting energy-time relationships that appear to be of general use in characterizing the dynamics.

We describe a new algorithm for simulating complex Markoff-processes. We have used a reaction-cell method in order to simulate arbitrary reactions. It can be used for any kind of RDS on arbitrary topologies, including fractal dimensions or configurations not being related to any spatial geometry. The events within a single cell are managed by an event handler which has been implemented independently of the system studied. The method is exact on the Markoff level including the correct treatment of finite numbers of molecules. To demonstrate its properties, we apply it on a very simple reaction-diffusion-systems (RDS). The chemical equations A+A -> inert and A+B -> inert in 1 to 4 dimensions serve as models for systems whose dynamics on an intermediate time scale are governed by fluctuations. We compare our results to the analytic approach by the scaling ansatz. The simulations confirm the exponents of the A+B system within statistical errors, including the logarithmic corrections in the dimension d=2. The method is capable to simulate the crossover from the reaction to diffusion limited regime, which is defined by a crossover time depending on the system size.

We study the chemical potential of water as a function of charge based on perturbation theory. By calculating the electrostatic-energy fluctuations of two states (fully charged and uncharged) we are able to determine accurate values for the dependence of the chemical potential on charge. We find identical results for the chemical-potential difference of fully charged and uncharged water from overlapping-histogram and acceptance-ratio methods and by smoothly connecting the curves of direct exponential averages. Our results agree with those of Rick and Berne (J. Am. Chem. Soc., 1994, 116, 3949) with respect to both the chemical-potential difference and its dependence on the charge coupling parameter. We observe significant deviations from simple Gaussian-fluctuation statistics. The dependence on the coupling parameter is not quadratic, as would be inferred from linear continuum models of electrostatics.

Calculations of time-resolved fluorescence anisotropy from a pair of chromophores coupled by an excitation transfer interaction are presented. For the purpose of investigating the effects of nuclear motion on the energy transfer and anisotropy, an illustrative model is developed that provides each chromophore with a single intramolecular vibrational mode. Account is taken of non-instantaneous excitation and time- and frequency-resolved detection. Effects of excitation pulse duration, detection window duration and frequency resolution, and excitation transfer coupling strength on the time-resolved anisotropy are examined in detail. Effects of vibrational relaxation and dephasing are also examined using a simplified Redfield description of the effects of coupling to a thermal bath.

A dielectric solvation model is applied to the prediction of the equilibrium ionization of liquid water over a wide range of density and temperature with the objective of calibrating that model for the study of ionization in water of organic acids, {\it e.g.\/}, proteins and nucleic acids. The model includes an approximate description of the polarizability of the dissociating water molecule. The calculated pK W are very sensitive to the value of the radii that parameterize the model. The radii required for the spherical molecular volumes of the water molecule in order to fit the experimental ion product are presented and discussed. These radii are larger than those commonly used. They decrease with increasing density as would be guessed but the rate of decrease is slight. They increase with increasing temperature, a variation opposite to what would be guessed if radii were strictly viewed as a distance of closest approach. The molecular theoretical principles that might provide an explanation of the thermodynamic state dependence of these radii are discussed.