The different roles the attractive and repulsive forces play in forming the equilibrium structure of a Lennard‐Jones liquid are discussed. It is found that the effects of these forces are most easily separated by considering the structure factor (or equivalently, the Fourier transform of the pair‐correlation function) rather than the pair‐correlation function itself. At intermediate and large wave vectors, the repulsive forces dominate the quantitative behavior of the liquid structure factor. The attractions are manifested primarily in the small wave vector part of the structure factor; but this effect decreases as the density increases and is almost negligible at reduced densities higher than 0.65. These conclusions are established by considering the structure factor of a hypothetical reference system in which the intermolecular forces are entirely repulsive and identical to the repulsive forces in a Lennard‐Jones fluid. This reference system structure factor is calculated with the aid of a simple but accurate approximation described herein. The conclusions lead to a very simple prescription for calculating the radial distribution function of dense liquids which is more accurate than that obtained by any previously reported theory. The thermodynamic ramifications of the conclusions are presented in the form of calculations of the free energy, the internal energy (from the energy equation), and the pressure (from the virial equation). The implications of our conclusions to perturbation theories for liquids and to the interpretation of x‐ray scattering experiments are discussed.

Role of Repulsive Forces in Determining the Equilibrium Structure of Simple Liquids

For more than 70 years, researchers in several areas of science have been intrigued by the physical and chemical properties of the lowest excited states of molecular oxygen. With two singlet states lying close above its triplet ground state, the O2 molecule possesses a very unique configuration, which gives rise to a very rich and easily accessible chemistry, and also to a number of important photophysical interactions. In particular, photosensitized reactions of the first excited state, O2(∆g), play a key role in many natural photochemical and photobiological processes, such as photodegradation and aging processes including even photocarcinogenesis. Reactions of O2(∆g) are associated with significant applications in several fields, including organic synthesis, bleaching processes, and, most importantly, the photodynamic therapy of cancer, which has now obtained regulatory approval in most countries for the treatment of several types of tumors. The development of both applications and novel observation techniques has strongly accelerated during the past few years. Significant recent advances include, for example, the development of novel luminescent singlet oxygen probes,1-4 the time-resolved detection of O2(∆g) in a transmission microscope,5 the first time-resolved measurements of singlet oxygen luminescence in vivo,6 and the observation of oxygen quenching of triplet-excited single molecules.7 Experimental and theoretical studies on the mechanisms of photosensitized formation of excited O2 states and of their deactivation have been performed for almost 40 years. While most early liquid-phase studies were exclusively concerned with O2(∆g), recent technological advances also made possible time-resolved investigations of the second excited state, O2(Σg), which can be formed in competition with O2(∆g) in many cases. A significant number of * Corresponding author. Tel.: ++49 69 79829448. Fax: ++49 69 79829445. E-mail: R.Schmidt@chemie.uni-frankfurt.de. 1685 Chem. Rev. 2003, 103, 1685−1757

Physical mechanisms of generation and deactivation of singlet oxygen.

On vibrational relaxation in liquids

An approach is presented for the theoretical calculation of self‐diffusion coefficients of liquid metals. The basic assumption is that the self‐diffusion coefficient of a liquid metal is equal to that of an appropriate hard sphere fluid. The hard sphere diameter is dependent upon temperature, and a method is developed for estimating this temperature dependence by exploring the relationship between the diameter and the interatomic potential energy function of the liquid metal. The theory gives accurate results for the magnitude and temperature dependence of the self‐diffusion coefficient for many liquid metals. In addition, the physical basis for the theory is consistent with what has been learned about the liquid state from molecular dynamics calculations.

Theory of transport in liquid metals. I. Calculation of self‐diffusion coefficients

The effects of short range solvent structure and short range dynamical correlations are investigated for the steady state rate constant k for solution reactions influenced by diffusion. The description is in terms of a Smoluchowski equation describing relative motion of two molecules in an outer spatial translational region, supplemented by a sink term that accounts for dynamics in an inner reaction zone. In the outer region, solvent structural effects are included by a potential of mean force, which exhibits a short range well and barrier combination leading to ’’potential caging.’’ Outer region short range dynamical correlations are included via a separation‐dependent diffusion coefficient, leading to ’’dynamical caging’’ as relative motion is showed at small separations. These two short range effects are neglected in standard diffusion treatments. We find that k is only modestly influenced by the above short range effects. In order to expose short range structure and correlation influence in a more sen...

Short range caging effects for reactions in solution. I. Reaction rate constants and short range caging picture

Free‐path distributions and collision rates for systems of hard‐sphere and square‐well molecules are computed and compared to simple models. Mean free paths for solids and dense fluids are found to be within 2% of those predicted by dividing the kinetic‐theory mean free path by the relative probability of two molecules in contact. These mean free paths are much smaller than a mean intermolecular spacing or even the diameter of a free volume. For hard‐sphere and hard‐disk fluids, free‐path distributions are found to be monotone decreasing, nearly exponential, and when scaled by the mean free path, nearly density independent for all fluid densities. This density independence precludes any essential difference in transport mechanisms between dilute and dense fluids based on independent free paths. Scaled free‐path distributions for hard‐sphere and hard‐disk solids are found to agree with those of their fluid counterparts except for long free paths where the smaller free‐path distribution for solids reflects their increased molecular localization. The free‐volume theory and its simple extensions are shown to be qualitatively inconsistent with the shape of observed free‐path distributions in solids. For fluids of square‐well molecules, the rate of hard‐core collisions is found to be insensitive to the presence of the square well, and so is the free‐path distribution as well as selected values of the pair‐distribution function. These features are in good agreement with the van der Waals hypothesis, which neglects soft collisions. For dense liquids, hard‐core collisions are in the majority, invalidating the hypothesis that soft‐core collisions cause a Brownian motion between successive hard‐core collisions.

T. Einwohner

Papers

Molecular Dynamics. VI. Free‐Path Distributions and Collision Rates for Hard‐Sphere and Square‐Well Molecules