Search

We derive a closed form analytical expression for the non-adiabatic transition probability for a distribution of trajectories passing through a generic conical intersection (CI), based on the Landau-Zener equation for the non-adiabatic transition probability for a single straight-line trajectory in the CI's vicinity. We investigate the non-adiabatic transition probability's variation with topographical features and find, for the same crossing velocity, no intrinsic difference in efficiency at promoting non-adiabatic decay between peaked and sloped CIs, a result in contrast to the commonly held view. Any increased efficiency of peaked over sloped CIs is thus due to dynamical effects rather than to any increased transition probability of topographical origin. It is also shown that the transition probability depends in general on the direction of approach to the CI, and that the coordinates' reduced mass can affect the transition probability via its influence on the CI topography in mass-scaled coordinates. The resulting predictions compare well with surface hopping simulation results. [ABSTRACT FROM AUTHOR]

The connection between diffusion and solvent exchanges between first and second solvation shells is studied by means of molecular dynamics simulations and analytic calculations, with detailed illustrations for water exchange for the Li+ and Na+ ions, and for liquid argon. First, two methods are proposed which allow, by means of simulation, to extract the quantitative speed-up in diffusion induced by the exchange events. Second, it is shown by simple kinematic considerations that the instantaneous velocity of the solute conditions to a considerable extent the character of the exchanges. Analytic formulas are derived which quantitatively estimate this effect, and which are of general applicability to molecular diffusion in any thermal fluid. Despite the simplicity of the kinematic considerations, they are shown to well describe many aspects of solvent exchange/diffusion coupling features for nontrivial systems. [ABSTRACT FROM AUTHOR]

Constrained molecular dynamics simulations are carried out to compare the adsorption/incorporation mechanism of two (nonionizable) hydrogen halide acid molecules HF and HCl on/in ice at typical stratospheric temperatures (190 and 235 K). From the determination of the free energy profiles, it is shown that the free energy barrier to molecular HF incorporation is higher than that for molecular HCl. This difference is interpreted as resulting from the formation of two strong H bonds between HF and its water neighbors, while a single, more flexible, H bond with water favors the penetration for HCl. [ABSTRACT FROM AUTHOR]

Molecular Dynamics simulation is used to study the vibrational relaxation of the first excited state of the O–H stretch for HOD dissolved in D2O. The technique applied is based on a Landau–Teller type formula, in which the solvent contribution is computed classically, while the quantum nature of the solute enters through the transition moments of the molecular normal modes. The experimental result for the relaxation time (≊8 ps) is accounted for, and the pathway to the ground state is determined. The relaxation proceeds through a sequence of intramolecular transitions initially facilitated by the solute internal anharmonicities. In particular, the anharmonicity allows an initial and rate-determining transfer to the first overtone of the HOD bend; a corresponding harmonic force field calculation in which this step is precluded yields a relaxation time that is three orders of magnitude larger. The excess energy is removed by the bath modes, which include rotations and translations of all molecules, including the solute. Relaxation by Coriolis coupling plays a minor but non-negligible role, while the centrifugal coupling contribution to the relaxation is negligible. © 1996 American Institute of Physics. [ABSTRACT FROM AUTHOR]

A theory for the description of electronic structure in solution for solution phase chemical reactions is formulated in the framework of a dielectric continuum solvent model which takes solute boundary effects into account. This latter feature represents a generalization of the Kim–Hynes theory, in which the solute boundary was treated in the dielectric image approximation. The electronic structure of the molecular solute, embedded in a cavity of the dielectric, is described by a manifold of orthogonalized diabatic—e.g., valence bond (VB)—states. The polarization of the dielectric solvent is partitioned into an electronic (fast) and an orientational (slow) component. The formulation encompasses both nonequilibrium and equilibrium regimes of the orientational polarization with respect to the solute charge distribution. The analysis is carried out in the general case of quantized solvent electronic polarization, but with reference to two limits in terms of which the general results can be most readily comprehended: with the electronic polarization much slower than the solute electronic motions and equilibrated to a delocalized solute charge distribution—the self-consistent limit; with the electronic polarization fast enough to equilibrate to components of the solute electronic distribution rather than to the average distribution—the Born–Oppenheimer limit. The general results depend on the relative time scales of the resonant interconversion between the VB states and the solvent electronic polarization. With the ansatz that the nonequilibrium orientational polarization is a linear combination of equilibrium terms with nonequilibrium coefficients, the solute–solvent system free energy is obtained together with a nonlinear Schrödinger equation for the solute electronic structure. A procedure is given for the natural definition of the set of solvent coordinates which describe the nonequilibrium regime necessary... [ABSTRACT FROM AUTHOR]

The electronic structure in solution theory developed in the preceding article is applied to the molecular ion I2-[larger_closed_square]I+I- reaction system in the dipolar, aprotic solvent acetonitrile, which illustrates in detail the implementation of the general theory. A two-dimensional, nonequilibrium free energy surface in the nuclear separation and a difference solvent coordinate is constructed via solution of a nonequilibrium solvation, nonlinear Schrödinger equation. The reduction to a single important solvent coordinate—from a manifold of three solvent coordinates—is motivated by an examination of the equilibrium solvation path and an analysis of the harmonic nonequilibrium fluctuations around this path. The evolving solute electronic structure over the basis of two orthogonal valence bond diabatic states—approximately corresponding to -II and II-—is discussed. Comparisons with the limiting Born–Oppenheimer and self-consistent approximations for the solvent electronic polarization are made, with the former proving to be more accurate, and the latter giving a qualitatively inaccurate picture of the electronic structure near the equilibrium geometry. The validity of the dielectric image approximation is also examined. The polarization force associated with the charge shift in the reaction system and important for the system vibrational relaxation is also calculated. © 1995 American Institute of Physics. [ABSTRACT FROM AUTHOR]

A theory is presented for the rate constant k for electron transfer between a metal electrode and a redox couple solute in solution, in or near the electronically adiabatic regime. The departure of k from its electronically adiabatic transition state theory limit kTST is described via Grote–Hynes theory, and includes two sources of friction. The electronic friction arises from excitation of electron hole pairs in the metal, i.e., electronic nonadiabaticity effects. The solvent friction arises from solvent dynamical effects. Both features can result in significant reduction of k below kTST, and their interplay can lead to interesting nonmonotonic variations with reaction overpotential. [ABSTRACT FROM AUTHOR]

The electronic structure of a solute in a polar and polarizable solvent depends on the nonequilibrium (or equilibrium) state of the solvent. Here we present a theory for this phenomenon, at the level of a dielectric continuum description of the solvent, characterized by an orientational polarization Por and an electronic polarization Pel. The entire range of electronic coupling between solute electronic states is considered. The present theory supersedes, in important respects, our earlier work [H. J. Kim and J. T. Hynes, J. Phys. Chem. 94, 2737 (1990); J. Chem. Phys. 93, 5194 (1990); 93, 5211 (1990)] by including a full quantization of Pel; this is a feature recently shown in a model study for weak electronic coupling [J. N. Gehlen, D. Chandler, H. J. Kim, and J. T. Hynes, J. Phys. Chem. (to be published)] to be necessary for, e.g., a correct description of electron transfer activation free energies and transition states. The quantization of Pel is effected via a coherent state formulation, coupled with a multiconfiguration self-consistent representation of the solute-Pel wave function. Nonequilibrium free energies and solute electronic structure are found and depend explicitly on the comparative time scales of a transferring electron in the solute and of Pel. The corresponding equilibrium relations are also found.For activated electron transfer, the current theory recovers (and generalizes) the conventional expression for the activation free energy, in both the electronically nonadiabatic and adiabatic regimes, for small electronic coupling. For larger electronic coupling—but still within the regime of activated electron transfer—the theory predicts an increased activation free energy compared to conventional results, associated with the (partial) solvation by the electronic polarization of delocalized solute electronic structure of the transition state. This trend is the same as that previously reported by us, but is smaller in magnitude due... [ABSTRACT FROM AUTHOR]

The results of a molecular dynamics (MD) computer simulation are presented for the solvation dynamics of an ion pair instanteously produced from a neutral pair, in a model polar aprotic solvent. These time-dependent fluorescence dynamics are analyzed theoretically to examine the validity of several linear response theory approaches, as well as of various theoretical descriptions (e.g., Langevin equation) for the solvent dynamics per se. It is found that these dynamics are dominated for short times by a simple inertial Gaussian behavior, a feature which is absent in many current theoretical treatments, and which is related to the approximate validity of linear response theory. Nonlinear aspects, such as an overall spectral narrowing, but a transient initial spectral broadening, are also discussed. A model photochemical charge transfer process is also briefly considered to elucidate aspects of the connection between solvation dynamics and chemical kinetic population evolution. [ABSTRACT FROM AUTHOR]

It is shown how a dynamical theory for proton transfer rates in solution can be implemented in a molecular-dynamics simulation for a model reaction system. The reaction is in the nonadiabatic limit, in which the transfer occurs via quantum tunneling of the proton. The importance of the coupling of the proton to the solvent and to an intramolecular vibration is illustrated, and the simulation results are successfully compared with analytic rate-constant expressions in several limiting regimes. [ABSTRACT FROM AUTHOR]

A theoretical formulation is developed to describe the electronic structure of an immersed solute, electrostatically coupled to a polar and polarizable solvent. The solvent is characterized, in the dielectric continuum approximation, by electronic and orientational polarizations. Starting from a general free-energy expression for the quantum solute–solvent system, a time-independent nonlinear Schrödinger equation is derived. The nonlinearity arises from the assumed equilibration of the solvent electronic polarization Peqe, to the solute electronic wave function Ψ and the solvent orientational polarization Por. When Por is arbitrary, there is nonequilibrium solvation. When Por is equilibrated to Peqe and Ψ, equilibrium solvation obtains. The theory is illustrated for a model symmetric electron donor–acceptor solute system in a two state basis set description. Solution of the nonlinear Schrödinger equation in the presence of arbitrary Por yields nonequilibrium solvation stationary states (NSS) for the solute–solvent system, including the solvent-dependent solute electronic structure, and the associated free energies. When Por=Peqor, the corresponding equilibrium solvation states (ESS) and their characteristics are obtained. The NSS are classified into three distinct regimes, according to the relative strengths of the electronic coupling, which tends to delocalize the solute electronic distribution, and the solvent polarization, which tends to localize it. The ESS stability characteristics are also important in this classification. Two of the regimes correspond to activated electron transfer processes, and differ according to whether there is or is not a continuous free-energy path leading from localized reactants to localized products. The third regime, in which the electronic coupling dominates the solvent polarization, corresponds to stable delocalized states between which spectroscopic transitions are of interest.... [ABSTRACT FROM AUTHOR]

The formulation developed in the preceding paper [H. J. Kim and J. T. Hynes, J. Chem. Phys. 93, 5194 (1990)] is applied to describe the electronic structure and spectroscopic features of a model symmetric electron–donor–acceptor solute system D-A⇋DA- in solution in the strong coupling limit. In this limit, the electronic coupling is sufficiently strong to overcome the localizing influence of the solvent polarization, and two stable delocalized solute electronic states are found in the presence of either nonequilibrium or equilibrium solvation. The nonlinear influence of the equilibrated solvent electronic polarization and of exchange contributions to the solute electronic distribution incorporated in the theory lead to several consequences absent in standard descriptions. Among these are the necessity of two solvent coordinates to describe the system, and the prediction of solvent-dependent spectral shifts and the appearance of solvent relaxation dynamics after a Franck–Condon transition between the delocalized electronic states. Estimates of the magnitude of these new effects are provided, and the possibility for their experimental observation is briefly discussed. [ABSTRACT FROM AUTHOR]

The atom–atom encounter model developed in the accompanying paper [M. G. Sceats, J. Chem. Phys. 91, 0000 (1989)] is applied to the collisional deactivation of highly vibrationally excited triatomic molecules CS2 and SO2 by the monatomic colliders He, Ne, Ar, Kr, and Xe at 300 K. The molecular inputs are a crude normal mode analysis, vibrational frequencies and effective anharmonicities, while the collisional inputs are parameters of the atom–atom potentials. The results for CS2 are compared with the simulations of Bruehl and Schatz and the experiments of Dove, Hippler, and Troe, while those for SO2 are compared with the simulations of Schranz and Troe and the experimental results of Heymann, Hippler, and Troe. Excellent agreement is found with experiment, and the superlinear energy dependence of the average energy transfer is attributed to anharmonicity of the triatomic molecule. [ABSTRACT FROM AUTHOR]

The resonance Raman spectrum of the chlorine molecular anion Cl-2 has been obtained using pulsed laser photolysis as a radical production method. The fundamental and nine overtone transitions are observed. Analysis of the vibrational progression gives the vibrational constants ωe =277.0±0.3 cm-1 and ωeχe =1.83±0.05 cm-1; these constants give an upper limit dissociation energy of 1.3±0.1 eV (all errors are 1σ). Time-resolved resonance Raman spectroscopy has been employed to study the kinetics of Cl-2 disproportionation. A disproportionation rate coefficient of (11±7)×109 M-1 s-1 is obtained where the reported error includes 1σ precision and estimates of systematic errors. A resonance Raman detection limit for Cl-2 of 5×10-6 M has been obtained. [ABSTRACT FROM AUTHOR]

A solution reaction path Hamiltonian (SRPH) is constructed for heavy particle charge transfer reactions in a nondissipative polar solvent. This formulation includes anharmonicities arising from, e.g., potential anharmonicity and reaction path curvature. The SRPH is used in conjunction with variational transition state theory (VTST) to obtain an expression for the reaction rate constant. This expression generalizes the van der Zwan–Hynes rate theory to include the influence of anharmonic effects as well as nonequilibrium solvation. A discussion of the reaction path in solution and its departure from an equilibrium solvation perspective is given. [ABSTRACT FROM AUTHOR]

The solution reaction path Hamiltonian (SRPH) developed in the previous paper is applied to model SN2 and ionic dissociation reactions in water solvent. The solution reaction paths are determined and show marked deviations from a standard equilibrium solvation picture. The impact of potential anharmonicities, reaction path curvature, and varying solvent mass on the rate constant is calculated via the variational transition state theory approach of I, and the deviations from harmonic van der Zwan–Hynes (ZH) theory are calculated. Typically only minor deviations from ZH theory are found. The reasons for this are discussed. [ABSTRACT FROM AUTHOR]

A dynamical theory for the rates of unimolecular dissociations in polar solvents is constructed. Two classes of dissociation reactions, with dipolar and ionic transition states, are considered, and the theory is illustrated for a generalized continuum model water solvent. The rate of charge variation along the reaction coordinate is found to play a central role. Deviations from equilibrium solvation transition state theory predictions are found and discussed. Two nonequilibrium solvation regimes—nonadiabatic solvation and polarization caging—occur, and their appearance is connected to whether the solvated transition state has a reactant-like or product-like charge distribution. [ABSTRACT FROM AUTHOR]

A detailed classical trajectory study of the overtone-induced dissociation of hydrogen peroxide HO2H and its isotopic variant HO2D is presented. The factors affecting intramolecular energy flow, such as nonlinear resonances and the various couplings, are examined in detail. The dissociation lifetimes are found to be on the order of picoseconds and comparable with statistical lifetimes, although the intramolecular energy redistribution is not complete within the lifetime of the molecules. Lifetime broadening contributes very little to the rather large width of the overtone excitation feature, which we conclude is in the main inhomogeneously broadened by rotational structure instead. The implications of our results are discussed. [ABSTRACT FROM AUTHOR]

Examines the vibrational phase and energy relaxation of cyanide ion in liquid water. Adoption of molecular dynamics simulations and semiclassical perturbation theory; Role of Coulomb and non-Coulomb forces; Relevance of intermolecular terms in the vibration-solvent coupling on frequency shift.

We consider dynamical curve crossing behavior for one dimensional intermolecular potentials of arbitrary curvature. Our focus is threefold. (1) A semiclassical WKB formalism yields simple analytic expressions for time dependent transition probabilities throughout the crossing region. For low velocities v, our results reduce to the required quasistatic unitary transformation between diabatic and adiabatic representations. At higher v, the WKB solutions exhibit time dependent oscillations (‘‘beating’’ between the stationary adiabatic states) in excellent quantitative agreement with exact numerical solutions. (2) The WKB analysis indicates that an oscillatory dependence of curve crossing probability Pcr on v occurs for potential crossings of sufficient curvature, in qualitative disagreement with the extensively used Landau–Zener expression. These probability oscillations can be understood and predicted from simple considerations of potential curvature and coupling strengths. (3) We explore this oscillatory behavior for realistic curve crossing geometries. The results indicate that a nonmonotonic dependence of Pcr on velocity may occur in real molecular systems and could be experimentally observed in favorable albeit special circumstances. Even in the absence of oscillations, however, pronounced departure from Landau–Zener predictions can be anticipated. [ABSTRACT FROM AUTHOR]