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The rates and pathways of chemical reactions at metal surfaces can be strongly influenced by energy dissipation due to the nonadiabatic excitation of metallic conduction electrons. The introduction of frictional forces to account for this dissipation has been quite successful in situations for which the nonadiabatic coupling is weak. However, in cases where nonadiabatic coupling is strong, such as when electron transfer occurs, the friction model is likely to break down. Ryabinkin and Izmaylov have proposed 2-state and 3-state alternatives to the friction model for introducing electronic dissipation in molecular dynamics simulations. Here, we examine their 2-state model using some simple examples of atom-surface scattering. We find that, with the addition of decoherence, the 2-state model can produce quite promising results., (© 2024 Author(s). Published under an exclusive license by AIP Publishing.)

The recent development of the Ehrenfest dynamics approach in the nuclear-electronic orbital (NEO) framework provides a promising way to simulate coupled nuclear-electronic dynamics. Our previous study showed that the NEO-Ehrenfest approach with a semiclassical traveling proton basis method yields accurate predictions of molecular vibrational frequencies. In this work, we provide a more thorough analysis of the semiclassical traveling proton basis method to elucidate its validity and convergence behavior. We also conduct NEO-Ehrenfest dynamics simulations to study an excited state intramolecular proton transfer process. These simulations reveal that nuclear quantum effects influence the predictions of proton transfer reaction rates and kinetic isotope effects due to the intrinsic delocalized nature of the quantum nuclear wave function. This work illustrates the importance of nuclear quantum effects in coupled nuclear-electronic dynamical processes and shows that the NEO-Ehrenfest approach can be a powerful tool for providing insights and predictions for these processes.

Electronic friction and the ensuing nonadiabatic energy loss play an important role in chemical reaction dynamics at metal surfaces. Using molecular dynamics with electronic friction evaluated on the fly from density functional theory, we find strong mode dependence and a dominance of nonadiabatic energy loss along the bond stretch coordinate for scattering and dissociative chemisorption of H_{2} on the Ag(111) surface. Exemplary trajectories with varying initial conditions indicate that this mode specificity translates into modulated energy loss during a dissociative chemisorption event. Despite minor nonadiabatic energy loss of about 5%, the directionality of friction forces induces dynamical steering that affects individual reaction outcomes, specifically for low-incidence energies and vibrationally excited molecules. Mode-specific friction induces enhanced loss of rovibrational rather than translational energy and will be most visible in its effect on final energy distributions in molecular scattering experiments.

We recently reported a very unusual temperature dependence of the rate of thermal reaction of wild type bovine rhodopsin: the Arrhenius plot exhibits a sharp "elbow" at 47 °C and, in the upper temperature range, an unexpectedly large activation energy (114 ± 8 kcal/mol) and an enormous prefactor (10 72±5 s -1 ). In this report, we present new measurements and a theoretical model that establish convincingly that this behavior results from a collective, entropy-driven breakup of the rigid hydrogen bonding networks (HBNs) that hinder the reaction at lower temperatures. For E181Q and S186A, two rhodopsin mutants that disrupt the HBNs near the binding pocket of the 11-cis retinyl chromophore, we observe significant decreases in the activation energy (∼90 kcal/mol) and prefactor (∼10 60 s -1 ), consistent with the conclusion that the reaction rate is enhanced by breakup of the HBN. The results provide insights into the molecular mechanism of dim-light vision and eye diseases caused by inherited mutations in the rhodopsin gene that perturb the HBNs.

An accurate description of nonadiabatic energy relaxation is crucial for modeling atomistic dynamics at metal surfaces. Interfacial energy transfer due to electron-hole pair excitations coupled to motion of molecular adsorbates is often simulated by Langevin molecular dynamics with electronic friction. Here, we present calculations of the full electronic friction tensor by using first order time-dependent perturbation theory at the density functional theory level. We show that the friction tensor is generally anisotropic and nondiagonal, as found for hydrogen atom on Pd(100) and CO on Cu(100) surfaces. This implies that electron-hole pair induced nonadiabatic coupling at metal surfaces leads to friction-induced mode coupling, therefore, opening an additional channel for energy redistribution. We demonstrate the robustness and accuracy of our results by direct comparison to established methods and experimental data.

We introduce a system-independent method to derive effective atomic C6 coefficients and polarizabilities in molecules and materials purely from charge population analysis. This enables the use of dispersion-correction schemes in electronic structure calculations without recourse to electron-density partitioning schemes and expands their applicability to semi-empirical methods and tight-binding Hamiltonians. We show that the accuracy of our method is en par with established electron-density partitioning based approaches in describing intermolecular C6 coefficients as well as dispersion energies of weakly bound molecular dimers, organic crystals, and supramolecular complexes. We showcase the utility of our approach by incorporation of the recently developed many-body dispersion method [Tkatchenko et al., Phys. Rev. Lett. 108, 236402 (2012)] into the semi-empirical density functional tight-binding method and propose the latter as a viable technique to study hybridorganic-inorganic interfaces.

We present measurements of rate constants for thermal-induced reactions of the 11-cis retinyl chromophore in vertebrate visual pigment rhodopsin, a process that produces noise and limits the sensitivity of vision in dim light. At temperatures of 52.0-64.6 °C, the rate constants fit well to an Arrhenius straight line with, however, an unexpectedly large activation energy of 114 ± 8 kcal/mol, which is much larger than the 60-kcal/mol photoactivation energy at 500 nm. Moreover, we obtain an unprecedentedly large prefactor of 10(72±5) s(-1), which is roughly 60 orders of magnitude larger than typical frequencies of molecular motions! At lower temperatures, the measured Arrhenius parameters become more normal: Ea = 22 ± 2 kcal/mol and Apref = 10(9±1) s(-1) in the range of 37.0-44.5 °C. We present a theoretical framework and supporting calculations that attribute this unusual temperature-dependent kinetics of rhodopsin to a lowering of the reaction barrier at higher temperatures due to entropy-driven partial breakup of the rigid hydrogen-bonding network that hinders the reaction at lower temperatures.

We report a novel scheme for computing electronic excitation energies within the framework of density functional theory (DFT) based on a time-independent variational formulation of DFT. The excited state density functional is recast as a Kohn-Sham functional, which is further simplified by an adiabatic approximation of the exchange-correlation functional. Under the adiabatic approximation, the minimization of the excited state Kohn-Sham functional is shown to be equivalent to a ground state DFT computation augmented with orthogonality constraints with respect to the ground state Kohn-Sham determinant. An algorithm for the optimization of the energy subject to orthogonality constraints, which does not suffer from variational collapse, is described and implemented. A benchmark test set containing 28 organic molecules (Schreiber, M. J. Chem. Phys. 2008, 128, 134110) was used to assess the quality of the excitation energies obtained. Two novel approaches to spin-adapt the resulting excitation energies are discussed and found to provide results with error metrics similar to those of time-dependent DFT. Similarities and differences with respect to other time-independent DFT approaches are highlighted and some of the advantages of our scheme-including the ability to correctly describe charge-transfer excitations-are critically assessed.

We propose a ring polymer molecular dynamics method for the calculation of chemical rate constants that incorporates nonadiabatic effects by the surface-hopping approach. Two approximate ring polymer electronic Hamiltonians are formulated and the time-dependent Schrodinger equation for the electronic amplitudes is solved self-consistently with the ring polymer equations of motion. The beads of the ring polymer move on a single adiabatic potential energy surface at all times except for instantaneous surface hops. The probability for a hop is determined by the fewest-switches surface-hopping criterion. During a surface hop all beads switch simultaneously to the new potential energy surface with positions kept unchanged and momenta adjusted properly to conserve total energy. The approach allows the evaluation of total rate coefficients as well as electronic state-selected contributions. The method is tested against exact quantum mechanical calculations for a one-dimensional, two-state model system that mimics a prototypical nonadiabatic bimolecular chemical reaction. For this model system, the method reproduces quite accurately the tunneling contribution to the rate and the distribution of reactants between the electronic states.

Nonadiabatic dynamics--nuclear motion evolving on multiple potential energy surfaces--has captivated the interest of chemists for decades. Exciting advances in experimentation and theory have combined to greatly enhance our understanding of the rates and pathways of nonadiabatic chemical transformations. Nevertheless, there is a growing urgency for further development of theories that are practical and yet capable of reliable predictions, driven by fields such as solar energy, interstellar and atmospheric chemistry, photochemistry, vision, single molecule electronics, radiation damage, and many more. This Perspective examines the most significant theoretical and computational obstacles to achieving this goal, and suggests some possible strategies that may prove fruitful.

Surface phenomena: measurements of absolute probabilities are reported for the vibrational excitation of NO(v=0→1,2) molecules scattered from a Au(111) surface. These measurements were quantitatively compared to calculations based on ab initio theoretical approaches to electronically nonadiabatic molecule-surface interactions. Good agreement was found between theory and experiment (see picture; T(s) =surface temperature, P=excitation probability, and E=incidence energy of translation)., (Copyright © 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.)

This paper explores Fano resonances due to non-adiabatic coupling of vibrational modes and the electron continuum in dipole-bound anions. We adopt a simple one-electron model consisting of a point dipole and an auxiliary potential to represent the electron interaction with the neutral core. Nuclear motion is added by assuming that harmonic vibrations modulate the dipole moment. When the model is parameterized to simulate key features of the water tetramer anion, the resultant photodetachment lineshape closely resembles that observed experimentally and analyzed as a Fano resonance with a parameter q close to -1. Other parameterizations are explored for the model and it is found that large changes in the auxiliary potential are required to change the sign of q. This is consistent with the experimental finding that q is negative for all water cluster sizes studied.

Independent Electron Surface Hopping (IESH) is a computational method for accounting for nonadiabatic electronic transitions in simulations of molecular motion at metal surfaces. IESH is applicable in cases of strong coupling where the electronic friction model is suspect, and has been demonstrated to accurately reproduce the results of detailed molecular beam experiments on vibrationally inelastic scattering of nitric oxide from the (111) surface of gold. However, in its original form, IESH represents a closed system without energy flow outside the local region of explicitly included substrate atoms. In this paper we propose two "thermostats" for introducing energy flow to the bulk, one for phonons and the other for electronic excitations.

We consider photoinduced electronic transitions through conical intersections in large molecules. Starting from the linear vibronic model Hamiltonian and treating linear diabatic couplings within the second order cumulant expansion, we have developed a simple analytical expression for the time evolution of electronic populations at finite temperature. The derived expression can be seen as a nonequilibrium generalization of the Fermi golden rule due to a nonequilibrium character of the initial photoinduced nuclear distribution. All parameters in our model are obtained from electronic structure calculations followed by a diabatization procedure. The results of our model are found to agree well with those of quantum dynamics for a test set of systems: fulvene molecule, 2,6-bis(methylene) adamantyl cation, and its dimethyl derivative.

A "tiered" approach to Monte Carlo sampling of nuclear configurations is presented for ab initio, self-consistent field (SCF)-based potentials, including Hartree-Fock and density functional theory. Rather than Metropolis testing only the final SCF energy, individual cycle energies are tested in a tiered fashion, without approximation. Accordingly, rejected configurations are terminated early in the SCF procedure. The method is shown to properly obey detailed balance, and effective modifications are presented for cases in which the initial SCF guess is particularly poor. Demonstrations on simple systems are provided, including an assessment of the thermal properties of the neutral water dimer with B3LYP/6-31++G**. Cost analysis indicates a factor-of-two reduction in SCF cycles, which makes the method competitive with accelerated molecular dynamics sampling techniques, without the need for forces., (© 2011 American Institute of Physics)

A simple and efficient scheme is presented for using different time slices for different degrees of freedom in path integral calculations. This method bridges the gap between full quantization and the standard mixed quantum-classical (MQC) scheme and, therefore, still provides quantum mechanical effects in the less-quantized variables. Underlying the algorithm is the notion that time slices (beads) may be "collapsed" in a manner that preserves quantization in the less quantum mechanical degrees of freedom. The method is shown to be analogous to multiple-time step integration techniques in classical molecular dynamics. The algorithm and its associated error are demonstrated on model systems containing coupled high- and low-frequency modes; results indicate that convergence of quantum mechanical observables can be achieved with disparate bead numbers in the different modes. Cost estimates indicate that this procedure, much like the MQC method, is most efficient for only a relatively few quantum mechanical degrees of freedom, such as proton transfer. In this regime, however, the cost of a fully quantum mechanical simulation is determined by the quantization of the least quantum mechanical degrees of freedom.

On-the-fly, ab initio classical molecular dynamics are demonstrated with an underlying dual basis set potential energy surface. Dual-basis self-consistent field (Hartree-Fock and density functional theory) and resolution-of-the-identity second-order Møller-Plesset perturbation theory (RI-MP2) dynamics are tested for small systems, including the water dimer. The resulting dynamics are shown to be faithful representations of their single-basis analogues for individual trajectories, as well as vibrational spectra. Computational cost savings of 58% are demonstrated for SCF methods, even relative to Fock-extrapolated dynamics, and savings are further increased to 71% with RI-MP2. Notably, these timings outperform an idealized estimate of extended-Lagrangian molecular dynamics. The method is subsequently demonstrated on the vibrational absorption spectrum of two NO(+)(H₂O)₃ isomers and is shown to recover the significant width of the shared-proton bands observed experimentally.

Forming upon absorption of a UV photon, excited states of DNA are subject to nonadiabatic evolution, via either internal conversion (IC) back to the ground state or mutagenesis. Nonadiabatic processes following the formation of the first singlet excited states, S1, in 10 different small DNA fragments--4 single 4'H-nucleosides, 2 Watson-Crick base pairs, and 4 nucleotide quartets--have been investigated. Simulations were done via the nonadiabatic direct trajectory surface hopping semiclassical dynamics. The electronic wave function was obtained with configuration interaction, based on the semiempirical AM1 and PM3 Hamiltonians with fractional orbital occupation numbers. The evolution of the electronic wave function was governed by the time-dependent Schrödinger equation with a locally diabatic representation, intrinsically stable near surface crossings. The nuclei evolved on adiabatic potential energy surfaces, as prescribed by classical Newtonian dynamics, with sudden hops between potential energy surfaces to account for nonadiabatic transitions. The "fewest switches" surface hopping algorithm coupled the quantum and classical parts of the system. The dynamics simulations revealed several routes of nonadiabatic relaxation in these systems, which were not reported previously, and also recovered known routes of IC.

Nonadiabatic coupling of nuclear motion to electronic excitations at metal surfaces is believed to influence a host of important chemical processes and has generated a great deal of experimental and theoretical interest. We applied a recently developed theoretical framework to examine the nature and importance of nonadiabatic behavior in a system that has been extensively studied experimentally: the scattering of vibrationally excited nitric oxide molecules from a Au(111) surface. We conclude that the nonadiabatic transition rate depends strongly on both the N-O internuclear separation and the molecular orientation and, furthermore, that molecule-surface forces can steer the molecule into strong-coupling configurations. This mechanism elucidates key features of the experiments and provides several testable predictions regarding the dependence of vibrational energy transfer on the initial vibrational energy, molecular orientation, and incident angle.

Experimentally, it has been shown that magnetic field sensitivity in living organisms is connected to the presence of blue-light photoreceptor cryptochromes. Cryptochromes transduce a light signal through a chain of chemical reactions involving the formation of intermediate biradicals. It was proposed that an external magnetic field affects the interconversion between singlet and triplet states of biradicals and thus interferes with the signal transduction chain. Theoretical modeling of this process requires an accurate evaluation of all interactions important for singlet-triplet interconversion: electron-electron, spin-orbit, spin-spin, hyperfine, and Zeeman. In the current study we investigate these interactions at the CIS level of theory applied to representative fragments of the CRY-1 protein in the plant Arabidopsis thaliana. We find, in contrast to previous simplified modeling (O. Efimova, O.; Hore, P. J. Biophys. J. 2008, 94, 1565), that the spin-spin interaction is significantly larger than the "exchange" interaction. Thus it is not canceled by the latter but rather dies off with the inter-radical separation. Also, we find that the spin-orbit interaction can play a significant role in singlet-triplet interconversion for short inter-radical distances, and the hyperfine interaction becomes the only coupling interaction for long inter-radical distances.

Recent experiments have shown convincing evidence for nonadiabatic energy transfer from adsorbate degrees of freedom to surface electrons during the interaction of molecules with metal surfaces. In this paper, we propose an independent-electron surface hopping algorithm for the simulation of nonadiabatic gas-surface dynamics. The transfer of energy to electron-hole pair excitations of the metal is successfully captured by hops between electronic adiabats. The algorithm is able to account for the creation of multiple electron-hole pairs in the metal due to nonadiabatic transitions. Detailed simulations of the vibrational relaxation of nitric oxide on a gold surface, employing a multistate potential energy surface fit to density functional theory calculations, confirm that our algorithm can capture the underlying physics of the inelastic scattering process.

We have constructed a model Hamiltonian to describe the interaction of a nitric oxide (NO) molecule with a Au(111) surface. The diagonal elements of the 2x2 Hamiltonian matrix represent the diabatic potential energy surfaces corresponding to the neutral and negative-ion states of the molecule. A position-dependent off-diagonal element controls the extent of mixing of the two diabatic states. The parameters of the Hamiltonian matrix were determined from ground-state density functional theory calculations, both in the absence and presence of a small applied electric field to perturb the extent of charge transfer to the molecule. The resulting model Hamiltonian satisfactorily reproduces the ab initio results, and scattering simulations of the incident translational energy dependence of trapping probability and final rotational energy of NO agree quite well with experiment. The explicit incorporation of neutral and ionic configurations should serve as a realistic and practical platform for elucidating the importance of charge transfer and nonadiabatic effects at metal surfaces, as well as provide a useful testing ground for the development of theories of nonadiabatic dynamics.

Multidimensional Marcus theory is the extension of traditional Marcus theory to systems in which multiple particles are transferred. Rather than the intersecting parabolas of Marcus theory, multidimensional Marcus theory involves the intersection of paraboloids. In this paper, we examine the conditions under which a full multidimensional treatment of these paraboloids is necessary and when it is possible to use a simpler one-dimensional formalism. In particular, we examine transition state barrier energies, which are essential parameters in many reaction rate equations, and which depend on the formalism used. We find, based on both analytic calculations and numerical simulation, that the reduced one-dimensional treatment yields excellent agreement with the exact, multidimensional results over a wide variety of conditions for one particular choice of the single collective reaction coordinate. We also outline a procedure for calculating accurate multidimensional transition state barrier energies and apply it to a two-dimensional model of proton-coupled electron transfer.

We have extended the constrained density functional theory (DFT) approach to explicitly control the magnitude of spin contamination. Unlike a restricted or restricted open-shell approach, the present method allows finer granularity, not only constraining the magnitude of the spin contamination but also allowing for the possibility of applying the constraint to a subsystem of a much larger system. This allows for the description of spin polarization where physically meaningful, while simultaneously enabling the reduction of spurious overpolarization that is present in many DFT functionals. We utilize this constraint in two particular model applications: The calculation of isotropic and anisotropic hyperfine couplings of a transition metal complex, [Mn(CN)(5)NO](2-), and the calculation of the diabatic dissociation curves of OF radical. In both cases, the spin contamination constraint is essential for obtaining physically meaningful, qualitatively correct, results.

We re-examine the analysis of the equilibrium limits of the fewest switches surface hopping algorithm for mixed quantum-classical dynamics. In contrast with previously reported results, we show that surface hopping does not, in general, exactly yield Boltzmann equilibrium, but that in practice the observed deviations are quite small. We also demonstrate that surface hopping does approach the exact equilibrium distribution in both the limits of small adiabatic splitting and/or strong nonadiabatic coupling. We verify these analytical results with numerical simulations for a simple two-level quantum system connected to a bath of classical particles.

Within the adiabatic approximation, it is trivial to generalize existing imaginary time path-integral techniques to the case of multiple electronic surfaces. However, there are many times where nonadiabatic effects can play an important role. To this end, we reformulate the well-known path-integral expressions to incorporate multiple potential surfaces, without necessitating the adiabatic approximation. We show that the resulting expression, like its adiabatic counterpart, can be interpreted in terms of a simple classical isomorphic system and thus is amenable to simulation through Monte Carlo techniques. We derive simple expressions to compute expectation values of a general operator in both the nuclear coordinate and electronic state, and demonstrate the existence of a simple internal diagnostic that can be used to evaluate the magnitude of equilibrium nonadiabatic effects.

In this Letter, we demonstrate that nonadiabatic dynamics of molecular scattering from metal surfaces can be efficiently simulated by semiclassical Gaussian wave packet propagation on a local complex potential. The method relies on the wideband limit decoupling of the nuclear equations of motion on different electronic states. If the continuum diabatic potential surfaces are assumed to be parallel, the number of Gaussian wave packets spawned scales at most linearly with propagation time, allowing efficient propagation of nuclear dynamics.

An ab initio direct Ehrenfest dynamics method with time-dependent density functional theory is introduced and applied to collisions of 5 eV oxygen atoms and ions with graphite clusters. Collisions at three different sites are simulated. Kinetic energy transfer from the atomic oxygen to graphite local vibrations is observed and electron-nuclear coupling resulting in electronic excitation within the graphite surface as well as alteration of the atomic charge is first reported in this paper. The three oxygen species studied, O(3P), O-(2P), and O+(4S), deposit different amounts of energy to the surface, with the highest degree of damage to the pi conjugation of the cluster produced by the atomic oxygen cation. Memory of the initial charge state is not lost as the atom approaches, in contrast to the usual assumption.

We report density functional theory calculations of electron-hole pair induced vibrational lifetimes of diatomic molecules adsorbed on metal surfaces. For CO on Cu(100), Ni(100), Ni(111), Pt(100), and Pt(111), we find that the C-O internal stretch and the bending modes have lifetimes in the 1-6 ps range, and that the CO-surface stretch and the frustrated translational modes relax more slowly, with lifetimes >10 ps for all cases except CO on Ni(111). This strong mode selectivity confirms earlier calculations for CO on Cu(100) and demonstrates that the trends carry over to other metal substrates. In contrast, for NO adsorbed on Pt(111), whereas we still find that the bending mode has the shortest lifetime, about 1.3 ps, we predict the other three modes to have almost equal lifetimes of 8-10 ps. Similarly, for CN adsorbed on Pt(111), we calculate that the internal stretching and molecule-surface stretching modes have approximately equal lifetimes of about 15 ps. Our results are in reasonable agreement with experiment, where available. We discuss some of the underlying factors that may contribute to the observed mode selectivity with adsorbed CO and the altered selectivity with NO and CN.

We examine the equilibrium limits of self-consistent field (Ehrenfest) mixed quantum-classical dynamics. We derive an analytical expression for the equilibrium mean energy of a multistate quantum oscillator coupled to a classical bath. We show that, at long times, for an ergodic system, the mean energy of the quantum subsystem always exceeds the temperature of the classical bath that drives it. Furthermore, the energy becomes larger as the number of states increases and diverges as the number of quantum levels approaches infinity. We verify these results by simulations.

We present an ab initio direct Ehrenfest dynamics scheme using a three time-step integrator. The three different time steps are implemented with nuclear velocity Verlet, nuclear-position-coupled midpoint Fock integrator, and time-dependent Hartree-Fock with a modified midpoint and unitary transformation algorithm. The computational cost of the ab initio direct Ehrenfest dynamics presented here is found to be only a factor of 2-4 larger than that of Born-Oppenheimer (BO) dynamics. As an example, we compute the vibration of the NaCl molecule and the intramolecular torsional motion of H2C=NH2+ by Ehrenfest dynamics compared with BO dynamics. For the vibration of NaCl with an initial kinetic energy of 1.16 eV, Ehrenfest dynamics converges to BO dynamics with the same vibrational frequency. The intramolecular rotation of H2C=NH2+ produces significant electronic excitation in the Ehrenfest trajectory. The amount of nonadiabaticity, suggested by the amplitude of the coherent progression of the excited and ground electronic states, is observed to be directly related to the strength of the electron-nuclear coupling. Such nonadiabaticity is seen to have a significant effect on the dynamics compared with the adiabatic approximation.

We present an analysis of the equilibrium limits of the two most widely used approaches for simulating the dynamics of molecular systems that combine both quantum and classical degrees of freedom. For a two-level quantum system connected to an infinite number of classical particles, we derive a simple analytical expression for the equilibrium mean energy attained by the self-consistent-field (Ehrenfest) method and show that it deviates substantially from Boltzmann. By contrast, "fewest switches" surface hopping achieves Boltzmann quantum state populations. We verify these analytical results with simulations.

A washboard with moment of inertia (WBMI) model for gas atom scattering from a flexible surface is proposed and applied. This model is a direct extension of the washboard model [J. Chem. Phys. 92, 680 (1990)] proposed for gas atom scattering from relatively rigid, corrugated surfaces. In addition, a moment of inertia is incorporated in the original washboard model to describe the flexibility of softer, more highly corrugated surfaces such as polymer or liquid surfaces. The moment of inertia of the effective surface object introduces a dependence of the efficiency of energy transfer on the position and direction of impact, a feature that has been shown to be critical by molecular dynamics simulations. The WBMI model is solved numerically by Monte Carlo integration, which makes the implementation of multiple impacts between a colliding atom and the surface very efficient. The model is applied to Ne and Ar atoms scattering from an alkylthiolate self-assembled monolayer surface and reproduces the major results obtained by classical trajectory simulation of the same system, i.e., a bimodal translation energy distribution P(E(f)) with the low-energy component well-fit with a Boltzmann distribution, but with a temperature that may (Ar) or may not (Ne) be the same as the surface temperature. This indicates that the WBMI model, with well-motivated physical assumptions and simplified interaction, reveals many of the major aspects of the gas-surface collision dynamics, though it does not take into account the real-time dynamics explicitly., ((c) 2004 American Institute of Physics)

Theoretical aspects of dynamical processes at metal surfaces are reviewed. Experimental challenges to theory are presented and progress toward meeting these challenges is appraised. Topics include adsorbate vibrational energy flow, inelastic molecule-surface scattering, adsorption, transient mobility, dissociation, desorption, photochemistry, and electron-induced chemistry at metal surfaces. Experimental examples cited illustrate the richness of dynamical phenomena to be understood and the necessity of developing multidimensional, beyond Born-Oppenheimer, formulations of adsorbate dynamics. Classical mechanical and quantum mechanical treatments of dynamics are contrasted. The importance of including phonon and electron-hole pair dissipation in theories of adsorbate dynamics is emphasized, and strategies for doing this in classical and quantum treatments are presented.

The results of (13)C nuclear magnetic resonance (NMR) measurements on alkali fullerides KxC(60) are reported. The NMR spectra demonstrate that material with 0 < x < 3 is in fact a two-phase system at equilibrium, with x = 0 and x = 3. NMR lineshapes indicate that C(3-)(60) ions rotate rapidly in the K(3)C(60) phase at 300 K, while C(6)-(60) ions in the insulating K(6)C(60) phase are static on the time scale of the lineshape measurement. The temperature dependence of the (13)C spin-lattice relaxation rate in the normal state of K(3)C(60) is found to be characteristic of a metal, indicating the important role of the C(3-)(60) ions in the conductivity. From the relaxation measurements, an estimate of the density of electronic states at the Fermi level is derived.

Dramatic advances in our understanding of the motion of individual atoms and molecules at single-crystal surfaces have been made within the past 5 years. Recent experimental and theoretical studies of the interaction of nitric oxide with metal surfaces illustrate the depth of understanding now obtainable. General principles, applicable to a broader range of molecule-surface encounters, have begun to emerge out of the systematic and in-depth analyses of these and related studies.