Volume 110, Issue 23, 15 June 1999
 CONDENSED PHASE DYNAMICS, STRUCTURE, AND THERMODYNAMICS: SPECTROSCOPY, REACTIONS, AND RELAXATION


Exact solution for the singlet density distributions and secondorder correlations of normalmode coordinates for hard rods in one dimension
View Description Hide DescriptionWe examine the distribution of normalmode coordinates (defined via the eigenvectors of a chain of harmonic oscillators) for a system of purely repulsive hard rods in one dimension. We obtain an exact solution for the singlet density distribution, and separately for the covariances of the normalmode coordinates. The hardrod behavior is examined in terms of its deviation from the corresponding distributions for the system of harmonic oscillators. All offdiagonal covariances are zero in the hardrod system, and the (ondiagonal) variances vary with the normalmode wave number exactly as in the harmonic system. The detailed singlet normalmode density distributions are very smooth but nonanalytic, and they differ from the (Gaussian) distributions of the corresponding harmonic system. However, all of the normalmode coordinate distributions differ in roughly the same way when properly scaled by the distribution variance, and the differences vanish as in the thermodynamic limit of an infinite number of particles N.

Thermalization process after the relaxation of electronically excited states: Intramolecular proton transfer systems studied by the transient grating method
View Description Hide DescriptionPhotophysical and thermalization processes after photoexcitation of (HMPB) in cyclohexane and 2hydroxybenzophenone (HBP) in various solvents were investigated by the transient grating (TG) method. From the time profiles of the population grating (PG) signals, two distinct kinetics were observed for HMPB and HBP. For HMPB, the faster (600 fs) kinetics is attributed to the back proton transferreaction in the ground state, and the faster process of HBP (400 fs) is attributed to the vibrational cooling in the state. The slower one (∼30 ps) of both compounds is assigned to the vibrational cooling in the state. In ethanol (hydrogen bonding solvent), the PG signal originated from the state of HBP is apparent. However, the thermal energy from the state is negligibly small and the triplet quantum yield was found to be less than 0.05. The photoexcited HBP relaxes to the ground state by the internal conversion dominantly even in ethanol. The thermalization rates of these molecules were measured from a point of view of the translational energy of solvents by the acoustic peak delay method of the TG signal. The results show that in the early step of the thermalization, there is a very fast cooling process (less than a few ps) which is due to the energy transfer from the photoexcitedsolute to (several) effectively coupled solvent molecule(s), and then the heated solvent molecule becomes cool by the thermal diffusion to the bulk solvents. The thermalization processes depend on both of the solute and solvent properties. The time development of the temperature calculated based on this thermalization model explains the experimental observations.

Theory for electron transfer from a mixedvalence dimer with paramagnetic sites to a mononuclear acceptor
View Description Hide DescriptionPolynuclear transitionmetal complexes, such as Fe–S clusters, are the prosthetic groups in a large number of metalloproteins and serve as temporary electron storage units in a number of important redoxbased biological processes. Polynuclearity distinguishes clusters from mononuclear centers and confers upon them unique properties, such as spin ordering and the presence of thermally accessible excited spin states in clusters with paramagnetic sites, and fractional valencies in clusters of the mixedvalence type. In an earlier study we presented an effectivemode (EM) analysis of electron transfer from a binuclear mixedvalence donor with paramagnetic sites to a mononuclear acceptor which revealed that the clusterspecific attributes have an important impact on the kinetics of longrange electron transfer. In the present study, the validity of these results is tested in the framework of more detailed theories which we have termed the multimode semiclassical (SC) model and the quantummechanical (QM) model. It is found that the qualitative trends in the rate constant are the same in all treatments and that the semiclassical models provide a good approximation of the more rigorous quantummechanical description of electron transfer under physiologically relevant conditions. In particular, the present results corroborate the importance of electron transfer via excited spin states in reactions with a low driving force and justify the use of semiclassical theory in cases in which the QM model is computationally too demanding. We consider cases in which either one or two donor sites of a dimer are electronically coupled to the acceptor. In the case of multiconnectivity, the rate constant for electron transfer from a valencedelocalized (classIII) donor is nonadditive with respect to transfer from individual metal sites of the donor and undergoes an orderofmagnitude change by reversing the sign of the intradimer metal–metal resonance parameter (β). In the case of single connectivity, the rate constant for electron transfer from a valencelocalized (classII) donor can readily be tuned over several orders of magnitude by introducing differences in the electronic potentials at the two metal sites of the donor. These results indicate that theories of clusterbased electron transfer, in order to be realistic, need to consider both intrinsic electronic structure and extrinsic interactions of the cluster with the protein environment.

Solvation dynamics of benzonitrile excited state in polar solvents: A timedependent reference interaction site model selfconsistent field approach
View Description Hide DescriptionThe solvation dynamics of benzonitrile after the vertical transition in water methanol and acetonitrile solvents is studied with the reference interaction site model selfconsistent field (RISMSCF) method. The evolution of solute electronic states associated with the solvent relaxation is described by a timedependent RISMSCF method, incorporating the timedependent solute–solvent site–site radial distribution functions, which are derived from the surrogate linear response theory. Ab initio electronic structure calculations reveal that the state is of ionic nature whose dipole moment is larger by 2.41 D than that of the ground state. It is found that the excited statedipole moment is enhanced in the solutions, which provides the red shift of in the vertical excitation energy. The solvent relaxation further increases the charge polarization in solute, indicating the electronic state of excited is sensitive to the electrostatic field coming from the solvent. The dynamic Stokes shift is characterized by the solvation time correlation function (STCF). The calculated STCFs show that the solvent relaxation exhibits a nonexponential behavior and almost completes within 5 ps in and while a longtime tail is observed up to 20 ps in The slow component of the decay rate is consistent with other simulation calculations though the fast one is smaller. In order to analyze the solute charge polarization during the solvent relaxation, the solute charge time correlation function (CTCF) is calculated and the resultant CTCFs are discussed in terms of the solvent charge polarization in the vicinity of solute molecule.

Solid–liquid phase equilibrium for binary LennardJones mixtures
View Description Hide DescriptionSolid–liquidphase diagrams are calculated for binary mixtures of LennardJones spheres using Monte Carlo simulation and the Gibbs–Duhem integration technique of Kofke. We calculate solid–liquidphase diagrams for the model LennardJones mixtures: argon–methane, krypton–methane, and argon–krypton, and compare our simulation results with experimental data and with Cottin and Monson’s recent cell theory predictions. The LennardJones model simulation results and the cell theory predictions show qualitative agreement with the experimental phase diagrams. One of the mixtures, argon–krypton, has a different phase diagram than its hardsphere counterpart, suggesting that attractive interactions are an important consideration in determining solid–liquid phase behavior. We then systematically explore LennardJones parameter space to investigate how solid–liquidphase diagrams change as a function of the LennardJones diameter ratio, and welldepth ratio, This culminates in an estimate of the boundaries separating the regions of solid solution, azeotrope, and eutectic solid–liquid phase behavior in the space spanned by and for the case

Fluctuating charge model for polyatomic ionic systems: A test case with diatomic anions
View Description Hide DescriptionThe fluctuating charge (FQ) model proposed by Rick et al. [(J. Chem. Phys. 101, 6141 (1994)] for molecular dynamics (MD) simulation of water is applied to a test case for polyatomic ionic systems. A system resembling alkali cyanide crystals, with two partial charges on the atomic sites of the polarizable anions, is considered. The need for charge fluctuation considerations in such a simple system is demonstrated by ab initio calculations of the partial charges in the cyanide ion with different orientations within a fixed octahedral environment of sodium ions. It is shown that the charge distributions in the crystal obtained with the FQ model are sensitive to changes in the environment in such a way that the anions become more polarizable as the lattice parameter increases. Conversely, the charge distributions shrink with increasing repulsive shortrange interactions. Furthermore, a wellknown polarization effect, that is, the reduction in the frequencies of longitudinal optic modes of the crystal, is also obtained with the FQ model.

Equation of state of hard and Weeks–Chandler–Anderson hyperspheres in four and five dimensions
View Description Hide DescriptionThe fifth and sixth virial coefficient for hard hyperspheres in four and five dimensions has been computed using Monte Carlo techniques. It is found that has values and and that has values and in four and five dimensions, respectively. These values are used to investigate the equation of state of hard and Weeks–Chandler–Anderson (WCA) hyperspheres in four and five dimensions. Molecular dynamics simulations are performed for WCA hyperspheres. When compared to the molecular dynamics calculations, it is found that both the hard hypersphere and WCA equations of state are well described by a variety of theoretical approaches as long as the density is in the lowtomoderate regime. At the highest fluid densities studied, the Luban–Michels procedure provides the best accuracy for hard hyperspheres. The WCA prescription for the scaling of the reference system to a hard hypersphere one is a very good approximation in the fluid region.

Ultrafast intermolecular electron transfer from orthomethoxyaniline to excited coumarin dyes
View Description Hide DescriptionUltrafast intermolecular electron transfer(ET) from orthomethoxyaniline (orthoanisidine, ANS) to a number of excited 4trifluoromethyl1,2benzopyrones (coumarins) having differently substituted 7amino group has been investigated by femtosecondfluorescence upconversion technique. The ET dynamics in the present systems are nonsingleexponential and occur faster than the diffusive solvation dynamics. The ET rates are largely dependent on the nature of the substituents at the 7amino group of the coumarins. This dependence is well correlated with the free energy changes for the ETreactions. The ET dynamics become slower on using deuterated ANS as the donor, where the amino group hydrogens of ANS are substituted by deuterium. The deuterium isotope effect, however, gradually reduces as the ET dynamics becomes faster. Conventional ET theories can not explain all the observations. The results are explained on the basis of the twodimensional ET model, which considers the solvent coordinate and the intramolecular coordinate separately to depict the ET process. It is seen that in coumarinANS systems the ET occurs much faster than the coumarinaniline systems. It is indicated that the electronic coupling matrix element, a parameter which determines the extent of interaction between the reactant and the product states in the ET process, is much larger in the present systems than for the coumarinaniline systems. The deuterium isotope effect on the ET dynamics is explained in terms of the changes in the values on isotopic substitution of the solvent donors.

Improvement of integral equation theories for mixtures
View Description Hide DescriptionA comprehensive study of integral equationtheories for binary mixtures is presented. The mixture components differ primarily in size (the diameters differ by 10%, 20%, and 30%) and interact either via hard potentials or via LennardJones potentials. For the latter, variation with energy parameter (ε) is considered. This article focuses on improving the accuracy of the theories by systematic inclusion of bridge diagrams into the closure relationships. Specifically, the first two orders of bridge diagrams are exactly evaluated for these mixtures. A general Monte Carlo integration scheme for diagram evaluation is discussed and applied. Comparisons with diagrams obtained from a Legendre expansion technique are made in order to assess whether this approach is practical. The approximation of higher order diagrams has been considered. Specifically, techniques for approximation of all higher order diagrams, which were successful for single component fluids, were found to be problematic for mixtures. However, a simple algorithm for approximate third order diagrams is presented and found to lead to improvements. A detailed analysis of the bridge diagram variation with the nature of the mixture is presented and may be useful in extending the present results to related mixtures. The spatial dependence of the diagrams has also been examined and found to be extremely well reproduced by simple polynomial expansions. In addition, physical arguments have been applied to extract large separation limits of the diagrams. The accuracy of the integral equationtheories with order of bridge diagrams is assessed by comparing pressure estimates from the virial expansion and from the integration of compressibilities. With this measure, the quality of the integral equationtheories for each mixture is assessed at 18 state points. In all cases, the thermodynamic consistency improves smoothly and rapidly with the order of bridge diagram included in the theory. This result, together with the general Monte Carlo algorithm and the detailed structural and spatial analysis, shows that direct bridge diagram evaluation is practical and consistently improves the quality of the theory for these mixtures.
