Electron Transfer Past and Future (R Marcus) Electron Transfer Reactions in Solution: A Historical Perspective (N Sutin) Electron Transfer--From Isolated Molecules to Biomolecules (M Bixon & J Jortner) Charge Transfer in Bichromophoric Molecules in the Gas Phase (D Levy) Long--Range Charge Separation in Solvent--Free Donor--Bridge--Acceptor Systems (B Wegewijs & J Verhoeven) Electron Transfer and Charge Separation in Clusters (C Dessent, et al) Control of Electron Transfer Kinetics: Models for Medium Reorganization and Donor--Acceptor Coupling (M Newton) Theories of Structure--Function Relationships for Bridge--Mediated Electron Transfer Reactions (S Skourtis & D Beratan) Fluctuations and Coherence in Long--Range and Multicenter Electron Transfer (G Iversen, et al) Lanczos Algorithm for Electron Transfer Rates in Solvents with Complex Spectral Densities (A Okada, et al) Spectroscopic Determination of Electron Transfer Barriers and Rate Constants (K Omberg, et al) Photoinduced Electron Transfer Within Donor--Spacer--Acceptor Molecular Assemblies Studied by Time--Resolved Microwave Conductivity (J Warman, et al) From Close Contact to Long--Range Intramolecular Electron Transfer (J Verhoeven) Photoinduced Electron Transfers Through sigma Bonds in Solution (N--C Yang, et al) Indexes

Electron transfer : from isolated molecules to biomolecules

A new and convenient semiclassical method is proposed. It relies only upon classical trajectories and Gaussian integrals. It seems to work very well for the model molecular vibrational spectra investigated here. It should be applicable to a wide variety of processes and can be variationally improved if necessary.

Frozen Gaussians: A very simple semiclassical approximation

Two three-dimensional numerical schemes are presented for molecular integrands such as matrix alements of one-electron operators occuring in the Fock operator and expectation values of one-electron operators describing molecular properties. The schemes are based on a judicious partitioning of space so that product-Gauss integration rules can be used in each region. Convergence with the number of integration points is such that very high accuracy (8–10 digits) may be obtained with obtained with a modest number of points. The use of point group symmetry to reduce the required number of points is discussed. Examples are given for overlap, nuclear potential, and electric field gradient integrals.

Three-dimensional numerical integration for electronic structure calculations

In this paper the authors address the problem of internal consistency in trajectory surface hopping methods, i.e., the requirement that the fraction of trajectories running on each electronic state equals the probabilities computed by the electronic time-dependent Schrodinger equation, after averaging over all trajectories. They derive a formula for the hopping probability in Tully’s “fewest switches” spirit that would yield a rigorously consistent treatment. They show the relationship of Tully’s widely used surface hopping algorithm with the “exact” prescription that cannot be applied when running each trajectory independently. They also bring out the connection of the consistency problem with the coherent propagation of the electronic wave function and the artifacts caused by coherent Rabi-type oscillations of the state probabilities in weak coupling regimes. A real molecule (azobenzene) and two ad hoc models serve as examples to illustrate the above theoretical arguments. Following a proposal by Truhla...

Critical appraisal of the fewest switches algorithm for surface hopping

The Born–Oppenheimer approximation underlies much of chemical simulation and provides the framework defining the potential energy surfaces that are used for much of our pictorial understanding of chemical phenomena However, this approximation breaks down when the dynamics of molecules in excited electronic states are considered Describing dynamics when the Born–Oppenheimer approximation breaks down requires a quantum mechanical description of the nuclei Chemical reaction dynamics on excited electronic states is critical for many applications in renewable energy, chemical synthesis, and bioimaging Furthermore, it is necessary in order to connect with many ultrafast pump–probe spectroscopic experiments In this review, we provide an overview of methods that can describe nonadiabatic dynamics, with emphasis on those that are able to simultaneously address the quantum mechanics of both electrons and nuclei Such ab initio quantum molecular dynamics methods solve the electronic Schrodinger equation alongsi

/pdf/ab-initio-nonadiabatic-quantum-molecular-dynamics-2u9oif4pzs.pdf

Ab Initio Nonadiabatic Quantum Molecular Dynamics.

Rather general expressions are derived which represent the semiclassical time‐dependent propagator as an integral over initial conditions for classical trajectories. These allow one to propagate time‐dependent wave functions without searching for special trajectories that satisfy two‐time boundary conditions. In many circumstances, the integral expressions are free of singularities and provide globally valid uniform asymptotic approximations. In special cases, the expressions for the propagators are related to existing semiclassical wave function propagation techniques. More generally, the present expressions suggest a large class of other, potentially useful methods. The behavior of the integral expressions in certain limiting cases is analyzed to obtain simple formulas for the Maslov index that may be used to compute the Van Vleck propagator in a variety of representations.

Integral expressions for the semiclassical time‐dependent propagator

We present numerical tests of five related semiclassical techniques for computing time‐dependent wave functions. These methods are based on integral representations for the propagator and do not require searches for special trajectories satisfying double‐ended boundary conditions. In many respects, the computational techniques involved resemble those of conventional quasiclassical treatments. Three of these methods result in globally uniform asymptotic approximations to the wave function. One such method, the treatment of Herman and Kluk, is found to be capable of especially high accuracy and rapid convergence.

Numerical study of semiclassical initial value methods for dynamics

A semiclassical initial value technique for wave function propagation described by Herman and Kluk [Chem. Phys. 91, 27 (1984)] is tested for systems with two degrees of freedom. It is found that chaotic trajectories cause a serious deterioration in the accuracy and convergence of the technique. A simple procedure is developed to alleviate these difficulties, allowing one to propagate wave functions of a moderately chaotic system for relatively long times with good accuracy. This method is also applied to a very strongly chaotic system, the x2y2 or ‘‘quadric oscillator’’ model. The resulting energy spectra, obtained from the autocorrelation function of the wave function, are observed to be in good agreement with the corresponding quantal spectra. In addition, the density of states spectra, computed from the trace of the semiclassical propagator, are found to determine many individual energy levels of this system successfully.

Semiclassical propagation for multidimensional systems by an initial value method

This review describes some developments in the theory and application of the semiclassical initial representation for the treatment of the dynamical and static properties of atoms and molecules. The theoretical basis of initial value treatments for the propagator is discussed. A variety of useful alternative initial value expressions for the propagator and other quantities are presented as generalizations of the well-known Herman-Kluk approximation. Special emphasis is given to treatments that involve integration over only half the phase space variables. The recent development of semiclassical initial value expressions that are exact for specific, desired systems is reviewed and some of the implications are described.

Kenneth G. Kay

Papers

Integral expressions for the semiclassical time‐dependent propagator

Numerical study of semiclassical initial value methods for dynamics

Semiclassical propagation for multidimensional systems by an initial value method

Semiclassical initial value treatments of atoms and molecules

The Herman–Kluk approximation: Derivation and semiclassical corrections