Dynamics Trajectory Calculations Research Articles

Modeling titanium dioxide (TiO2) nanoclusters using a 2D sectional method with molecular dynamics (MD) determined coagulation rates

Accurate prediction of the particle size distribution (PSD) evolution of growing nanometer scale particles is important in designing gas-phase synthesis reactors for the production of nanomaterials. Towards improved predictions of growth, we model the evolution of the PSD of 1-4 nm TiO2 particles from the decomposition of titanium tetraisoproxide (TTIP) using a two-dimensional (2D) sectional method, uniquely with coagulation rates derived from molecular dynamics (MD) trajectory calculations which account for detailed particle–particle interactions. The PSDs predicted by the 2D sectional method are compared to recent experimental measurements of PSDs in the 1-3 nm range in a flow tube reactor. The nucleation of particles is modeled based on prior mobility measurements of ions attributed to TTIP and their decomposition, with the specific nucleation rate here fitted as a fraction of base nucleation rate (k) derived from these prior measurements. In the 2D sectional model, we examine the influence of the initial (nucleated) particle charge distribution on the PSD, with different coagulation rate coefficients for neutral-charged and charged-charged particle collisions. With the MD-derived coagulation rate coefficients, we find that using nucleation rate coefficients between 0.005k and 0.03k leads to strong agreement between modeled PSD and measured PSD for a wide variety of experimental residence times, initial TTIP concentrations and temperatures. Increasing the charge fraction from 0% (uncharged) to 80% (bipolar) does not result in a significant change in the PSD, because the particles rapidly self-neutralize through coagulation based on the simulation results. The results with MD-derived coagulation rate coefficients are compared to those of the sectional method with classical kinetic theory of gases (KTG) rates with a constant enhancement factor to account for potential interactions. Through comparison, we find that the predictions from the classical KTG model consistently exhibit weaker coagulation rates than the MD-derived model during the PSD evolution.

A neural network parametrized coagulation rate model for

Coagulation is a key factor governing the size distribution of nanoclusters during the high temperature synthesis of metal oxide nanomaterials. Population balance models are strongly influenced by the coagulation rate coefficient utilized. Although simplified coagulation models are often invoked, the coagulation process, particularly for nanoscale particles, is complex, affected by the coagulating nanocluster sizes, the surrounding temperature, and potential interactions. Toward developing improved models of nanocluster and nanoparticle growth, we have developed a neural network (NN) model to describe titanium dioxide (TiO2) nanocluster coagulation rate coefficients, trained with molecular dynamics (MD) trajectory calculations. Specifically, we first calculated TiO2 nanocluster coagulation probabilities via MD trajectory calculations varying the nanocluster diameters from 0.6 to 3.0nm, initial relative velocity from 20 to 700ms-1, and impact parameter from 0.0 to 8.0nm. Calculations consider dipole-dipole interactions, dispersion interactions, and short-range repulsive interactions. We trained a NN model to predict whether a given set of nanocluster diameters, impact parameter, and initial velocity would lead to the outcome of coagulation. The accuracy between the predicted outcomes from the NN model and the MD trajectory calculation results is >95%. We subsequently utilized both the NN model and MD trajectory calculations to examine coagulation rate coefficients at 300 and 1000K. The NN model predictions are largely within the range 0.65-1.54 of MD predictions, and importantly NN predictions capture the local minimum coagulation rate coefficients observed in MD trajectory calculations. The NN model can be directly implemented in population balances of TiO2 formation.

Noncanonical Isomers of Nucleoside Cation Radicals: An Ab Initio Study of the Dark Matter of DNA Ionization.

Cation radicals of DNA nucleosides, 2'-deoxyadenosine, 2'-deoxyguanosine, 2'-deoxycytidine, and 2'-deoxythymidine, can exist in standard canonical forms or as noncanonical isomers in which the charge is introduced by protonation of the nucleobase, whereas the radical predominantly resides in the deoxyribose moiety. Density functional theory as well as correlated ab initio calculations with coupled clusters (CCSD(T)) that were extrapolated to the complete basis set limit showed that noncanonical nucleoside ion isomers were thermodynamically more stable than their canonical forms in both the gas phase and as water-solvated ions. This indicated the possibility of exothermic conversion of canonical to noncanonical forms. The noncanonical isomers were calculated to have very low adiabatic ion-electron recombination energies (REad) for the lowest-energy isomers 2'-deoxy-(N-3H)adenos-1'-yl (4.74 eV), 2'-deoxy-(N-7H)guanos-1'-yl (4.66 eV), 2'-deoxy-(N-3H)cytid-1'-yl (5.12 eV), and 2'-deoxy-5-methylene-(O-2H)uridine (5.24 eV). These were substantially lower than the REad value calculated for the canonical 2'-deoxyadenosine, 2'-deoxy guanosine, 2'-deoxy cytidine, and 2'-deoxy thymidine cation radicals, which were 7.82, 7.46, 8.14, and 8.20 eV, respectively, for the lowest-energy ion conformers of each type. Charge and spin distributions in noncovalent cation-radical dA⊂dT and dG⊂dC nucleoside pairs and dAT, dCT, dTC, and dGC dinucleotides were analyzed to elucidate the electronic structure of the cation radicals. Born-Oppenheimer molecular dynamics trajectory calculations of the dinucleotides and nucleoside pairs indicated rapid exothermic proton transfer from noncanonical T+· to A in both dAT+· and dA⊂dT+·, leading to charge and radical separation. Noncanonical T+· in dCT+· and dTC+· initiated rapid proton transfer to cytosine, whereas the canonical dCT+· dinucleotide ion retained the cation radical structure without isomerization. No spontaneous proton transfer was found in dGC+· and dG⊂dC+· containing canonical neutral and noncanonical ionized deoxycytidine.

CARNOT: a Fragment-Based Direct Molecular Dynamics and Virtual-Reality Simulation Package for Reactive Systems.

Traditionally, the study of reaction mechanisms of complex reaction systems such as combustion has been performed on an individual basis by optimizations of transition structure and minimum energy path or by reaction dynamics trajectory calculations for one elementary reaction at a time. It is effective, but time-consuming, whereas important and unexpected processes could have been missed. In this article, we present a direct molecular dynamics (DMD) approach and a virtual-reality simulation program, CARNOT, in which plausible chemical reactions are simulated simultaneously at finite temperature and pressure conditions. A key concept of the present ab initio molecular dynamics method is to partition a large, chemically reactive system into molecular fragments that can be adjusted on the fly of a DMD simulation. The theory represents an extension of the explicit polarization method to reactive events, called ReX-Pol. We propose a highest-and-lowest adapted-spin approximation to define the local spins of individual fragments, rather than treating the entire system by a delocalized wave function. Consequently, the present ab initio DMD can be applied to reactive systems consisting of an arbitrarily varying number of closed and open-shell fragments such as free radicals, zwitterions, and separate ions found in combustion and other reactions. A graph-data structure algorithm was incorporated in CARNOT for the analysis of reaction networks, suitable for reaction mechanism reduction. Employing the PW91 density functional theory and the 6-31+G(d) basis set, the capabilities of the CARNOT program were illustrated by a combustion reaction, consisting of 28 650 atoms, and by reaction network analysis that revealed a range of mechanistic and dynamical events. The method may be useful for applications to other types of complex reactions.

Silica nanocluster binding rate coefficients from molecular dynamics trajectory calculations

Oxide nanoparticle growth from vapor phase precursors occurs in high temperature aerosol reactors first via the formation of nanoclusters, which are nanometer-scale condensed-phase species composed of 101-102 atoms. The binding rate for nanoclusters, defined as the rate at which two nanoclusters collide with and stick to one another, is hence of interest in predicting nanoparticle size distribution functions in an aerosol. We have utilized molecular dynamics (MD) trajectory calculations to determine the homogeneous (equal-sized) and heterogeneous (disparate-sized) binding rate coefficients of SiO2 (silica) nanoclusters composed of 18, 144, and 333 atoms. MD trajectory calculations incorporated all-atom models of nanoclusters using a combined Born–Huggins–Mayer-Lennard-Jones potential model, which accounts for both short range interactions and electrostatic interactions. MD calculations were utilized to determine the binding probability as a function of both initial relative velocity and impact parameter; integration of the binding probability across impact parameter and relative velocity space yields the binding rate coefficient. MD trajectory calculations reveal that the most common type of encounters between nanoclusters leading to binding are grazing collisions, i.e. instances where collision would not occur without induced dipole potential influences. The resulting binding rate coefficients are found to be extremely weakly dependent on system temperature, which is in contrast to the use of rate coefficient models which are the product of a hard-sphere collision rate coefficient and a constant enhancement factor (leading to a rate coefficient proportional to the square root of temperature). Enhancement factors defined from MD trajectory calculations fall in the range of 3–9 as system temperature decreases from 1500 K to 300 K. Such large values suggest that potential interactions need to be considered when modeling oxide nanocluster growth in the gas phase.

Photodissociative Cross-Linking of Non-covalent Peptide-Peptide Ion Complexes in the Gas Phase.

We report a gas-phase UV photodissociation study investigating non-covalent interactions between neutral hydrophobic pentapeptides and peptide ions incorporating a diazirine-tagged photoleucine residue. Phenylalanine (Phe) and proline (Pro) were chosen as the conformation-affecting residues that were incorporated into a small library of neutral pentapeptides. Gas-phase ion-molecule complexes of these peptides with photo-labeled pentapeptides were subjected to photodissociation. Selective photocleavage of the diazirine ring at 355nm formed short-lived carbene intermediates that underwent cross-linking by insertion into H-X bonds of the target peptide. The cross-link positions were established from collision-induced dissociation tandem mass spectra (CID-MS3) providing sequence information on the covalent adducts. Effects of the amino acid residue (Pro or Phe) and its position in the target peptide sequence were evaluated. For proline-containing peptides, interactions resulting in covalent cross-links in these complexes became more prominent as proline was moved towards the C-terminus of the target peptide sequence. The photocross-linking yields of phenylalanine-containing peptides depended on the position of both phenylalanine and photoleucine. Density functional theory calculations were used to assign structures of low-energy conformers of the (GLPMG + GLL*LK + H)+ complex. Born-Oppenheimer molecular dynamics trajectory calculations were used to capture the thermal motion in the complexes within 100ps and determine close contacts between the incipient carbene and the H-X bonds in the target peptide. This provided atomic-level resolution of potential cross-links that aided spectra interpretation and was in agreement with experimental data. Graphical Abstract ᅟ.

Condensation and dissociation rates for gas phase metal clusters from molecular dynamics trajectory calculations.

In gas phase synthesis systems, clusters form and grow via condensation, in which a monomer binds to an existing cluster. While a hard-sphere equation is frequently used to predict the condensation rate coefficient, this equation neglects the influences of potential interactions and cluster internal energy on the condensation process. Here, we present a collision rate theory-molecular dynamics simulation approach to calculate condensation probabilities and condensation rate coefficients. We use this approach to examine atomic condensation onto 6-56-atom Au and Mg clusters. The probability of condensation depends upon the initial relative velocity (v) between atom and cluster and the initial impact parameter (b). In all cases, there is a well-defined region of b-v space where condensation is highly probable, and outside of which the condensation probability drops to zero. For Au clusters with more than 10 atoms, we find that at gas temperatures in the 300-1200 K range, the condensation rate coefficient exceeds the hard-sphere rate coefficient by a factor of 1.5-2.0. Conversely, for Au clusters with 10 or fewer atoms and for 14- and 28-atom Mg clusters, as cluster equilibration temperature increases, the condensation rate coefficient drops to values below the hard-sphere rate coefficient. Calculations also yield the self-dissociation rate coefficient, which is found to vary considerably with gas temperature. Finally, calculations results reveal that grazing (high b) atom-cluster collisions at elevated velocity (>1000 m s-1) can result in the colliding atom rebounding (bounce) from the cluster surface or binding while another atom dissociates (replacement). The presented method can be applied in developing rate equations to predict material formation and growth rates in vapor phase systems.

Ab initio studies on the photodissociation dynamics of the 1,1-difluoroethyl radical.

Born-Oppenheimer molecular dynamics trajectory calculations at the HCTH147/6-31G** level of theory simulate the dissociation dynamics of photolytically excited 1,1-difluoroethyl radicals. EOMCCSD/AUG-cc-pVDZ calculations show that an excitation energy of 94.82 kcal/mol is necessary to initiate photodissociation reactions. In contrast to photodissociation dynamics of ethyl radicals where a large discrepancy between actual dissociation rates and rates that are predicted by statistical rate theories, we find reaction rates of 5.1 × 1011 s-1 for the dissociation of an H atom, which is in perfect accord with what is predicted by Rice-Ramsperger-Kassel-Marcus (RRKM) calculations and there is no indication of any nonstatistical effects. However, our trajectory calculations show a much larger fraction of C-C bond breakage reaction of 56% occurring than that expected by RRKM (only 16%).

Computational Prediction of Rate Constants for Reactions Involved in Al Clustering.

Aluminum (Al) clustering processes via three types of association reactions are herein studied using classical molecular dynamics trajectory calculations. The simulations were carried out under realistic experimental conditions. The dependence of rate constants on temperature and cluster size was obtained. The association reactions have a very small activation barrier, and the activation energy increases with increasing temperature. Our prediction of reaction rate constants can be of interest for the study of Al nanoparticle growth using kinetic models.

Nucleophilic Substitution in Reactions between Partially Hydrated Superoxide Anions and Alkyl Halides

The effect of solvation by water molecules on the nucleophilicity of the superoxide anion, O2(•-), has been investigated in detail by mass spectrometric experiments and quantum chemical calculations, including direct dynamics trajectory calculations. Specifically, the SN2 reactions of O2(•-)(H2O)n clusters (n = 0-5) with CH3Cl and CH3Br were studied. It was found that the reaction rate decreases when the number of water molecules in the cluster increases; furthermore, reaction with CH3Br is in general faster than reaction with CH3Cl for clusters of the same size. In addition, key transition-state geometries were identified and probed by Born-Oppenheimer molecular dynamics, showing how a water molecule may be transferred from the nucleophile to the leaving group during the reaction. The computational models are in good agreement with the experimental observations.

Diabatic Population Matrix Formalism for Performing Molecular Mechanics Style Simulations with Multiple Electronic States.

An accurate description of nonbonded interactions is important in investigating dynamics of molecular systems. In many situations, fixed point charge models are successfully applied to explaining various chemical phenomena. However, these models with conventional formulations will not be appropriate in elucidating the detailed dynamics during nonadiabatic events. This is mainly because the chemical properties of any molecule, especially its electronic populations, significantly change with respect to molecular distortions in the vicinity of the surface crossing. To overcome this issue in molecular simulations yet within the framework of the fixed point charge model, we define a diabatic electronic population matrix and substitute it for the conventional adiabatic partial charges. We show that this matrix can be readily utilized toward attaining more reliable descriptions of Coulombic interactions, in combination with the interpolation formalism for obtaining the intramolecular interaction potential. We demonstrate how the mixed formalism with the diabatic charges and the interpolation can be applied to molecular simulations by conducting adiabatic and nonadiabatic molecular dynamics trajectory calculations of the green fluorescent protein chromophore anion in aqueous environment.

Rovibrational coupling in molecular nitrogen at high temperature: An atomic-level study

This article contains an atomic-level numerical investigation of rovibrational relaxation in molecular nitrogen at high temperature (>4000 K), neglecting dissociation. We conduct our study with the use of pure Molecular Dynamics (MD) and Classical Trajectory Calculations (CTC) Direct Simulation Monte Carlo (DSMC), verified to produce statistically identical results at the conditions of interest here. MD and CTC DSMC solely rely on the specification of a potential energy surface: in this work, the site-site Ling-Rigby potential. Additionally, dissociation is prevented by modeling the N–N bond either as a harmonic or an anharmonic spring. The selected molecular model was shown to (i) recover the shear viscosity (obtained from equilibrium pure MD Green-Kubo calculations) of molecular nitrogen over a wide range of temperatures, up to dissociation; (ii) predict well the near-equilibrium rotational relaxation behavior of N2; (iii) reproduce vibrational relaxation times in excellent accordance with the Millikan-White correlation and previous semi-classical trajectory calculations in the low temperature range, i.e., between 4000 K and 10 000 K. By simulating isothermal relaxations in a periodic box, we found that the traditional two-temperature model assumptions become invalid at high temperatures (>10 000 K), due to a significant coupling between rotational and vibrational modes for bound states. This led us to add a modification to both the Jeans and the Landau-Teller equations to include a coupling term, essentially described by an additional relaxation time for internal energy equilibration. The degree of anharmonicity of the N2 bond determines the strength of the rovibrational coupling. Although neglecting N2 dissociation only provides a partial description of a nitrogen system at very high temperatures, high-energy trends for bound-bound transitions are essential to understand nonequilibrium gas flows, with possible implications on rovibration/chemistry interaction at the onset of N2 dissociation.

Chaos and ergodicity of two hard disks within a circular billiard

We investigate dynamical properties of the system of two interacting hard disks within a circular billiard numerically in the case of zero total angular momentum. Varying the radius of two identical disks, we examine chaotic irregularity and ergodicity of the system. Single-particle configuration and velocity distributions are obtained from dynamical trajectory calculations and compared with those in the microcanonical ensemble. We also analyze properties of trajectories by calculating the finite-time maximum Lyapunov exponent and clarify the existence of sticky motions around Kolmogorov-Arnold-Moser (KAM) tori even for small radii of disks. It is shown that the present system is almost ergodic in spite of the existence of tori for small radii of disks since the ratio of tori to the whole phase space is extremely small. On the other hand, a number of tori increase abruptly as the radius of disks increases beyond some value and tori prevent trajectories to run over the phase space uniformly, which makes the ergodicity of the system broken down.

Role of the cluster structure of 7Li in the dynamics of fragment capture

Exclusive measurements of prompt γ-rays from the heavy-residues with various light charged particles in the 7Li+198Pt system, at an energy near the Coulomb barrier (E/Vb∼1.6) are reported. Recent dynamic classical trajectory calculations, constrained by the measured fusion, α- and t-capture cross-sections have been used to explain the excitation energy dependence of the residue cross-sections. These calculations distinctly illustrate a two-step process, breakup followed by fusion, in case of the capture of t and α clusters; whereas for He6+p and He5+d configurations, massive transfer is inferred to be the dominant mechanism. The present work clearly demonstrates the role played by the cluster structures of 7Li in understanding the reaction dynamics at energies around the Coulomb barrier.

Lactate dehydrogenase from the tetraploid weatherfish Misgurnus fossilis during temperature adaptation: Determination of structural differences in two forms of the enzyme by molecular modeling methods

A structural analysis of two lactate dehydrogenase M4 protein forms has been performed. These structures are the protein products of two lactate dehydrogenase gene (LDH-A) copies in the weatherfish Misgurnus fossilis genome after thermal adaptation (acclimation) to 5 degrees C and 18 degrees C. The localization of three earlier identified amino acid substitutions (Gly214Val, Leu304Ile, Asp312Glu) has been determined, and the molecular dynamics simulation and computer modeling of two forms of the enzyme from skeletal muscles LDH-M4 have been carried out. After molecular dynamics trajectory calculations carried out at 5, 18, and 25 degrees C, the intersubunit distances for all structures used in calculations have been determined. It has been found that the Gly214Val substitution localized in the intersubunit region leads to a new intersubunit interaction, which plays a role in the stabilization of tetrameric enzyme structure after the adaptation to 18 degrees C.

Theoretical Unimolecular Kinetics for CH4 + M ⇄ CH3 + H + M in Eight Baths, M = He, Ne, Ar, Kr, H2, N2, CO, and CH4

Ensembles of classical trajectories are used to study collisional energy transfer in highly vibrationally excited CH(4) for eight bath gases. Several simplifying assumptions for the CH(4) + M interaction potential energy surface are tested against full dimensional direct dynamics trajectory calculations for M = He, Ne, and H(2). The calculated energy transfer averages are confirmed to be sensitive to the shape of the repulsive wall of the intermolecular potential, with an exponential repulsive wall required for quantitative predictions. For the diatomic baths, the usual "separable pairwise" approximation for the interaction potential is unable to describe the orientation dependence of the interaction potential accurately, and the ambiguity in the resulting parametrizations contributes an additional uncertainty to the predicted energy transfer averages of 20-40%. On the other hand, the energy transfer averages are shown to be insensitive to the level of theory used to describe the intramolecular CH(4) potential, with a computationally efficient semiempirical tight binding potential for hydrocarbons performing equally well as an MP2 potential. The relative collisional energy transfer efficiencies of the eight bath gases are discussed and shown to be a function of temperature. The ensemble-averaged energy transferred in deactivating collisions <ΔE(d)> for each bath is used to parametrize a single-exponential-down model for collisional energy transfer in master equation calculations. The predicted decomposition rate coefficients for CH(4) agree well with available experimental rate coefficients for M = He, Ar, Kr, and CH(4). The effect of vibrational anharmonicity on the predicted rate coefficients is considered briefly.

Mechanism and Kinetics of the Reaction NO3+ C2H4

The reaction of NO(3) radical with C(2)H(4) was characterized using the B3LYP, MP2, B97-1, CCSD(T), and CBS-QB3 methods in combination with various basis sets, followed by statistical kinetic analyses and direct dynamics trajectory calculations to predict product distributions and thermal rate constants. The results show that the first step of the reaction is electrophilic addition of an O atom from NO(3) to an olefinic C atom from C(2)H(4) to form an open-chain adduct. A concerted addition reaction mechanism forming a five-membered ring intermediate was investigated, but is not supported by the highly accurate CCSD(T) level of theory. Master-equation calculations for tropospheric conditions predict that the collisionally stabilized NO(3)-C(2)H(4) free-radical adduct constitutes 80-90% of the reaction yield and the remaining products consist mostly of NO(2) and oxirane; the other products are produced in very minor yields. By empirically reducing the barrier height for the initial addition step by 1 kcal mol(-1) from that predicted at the CBS-QB3 level of theory and treating the torsional modes explicitly as one-dimensional hindered internal rotations (instead of harmonic oscillators), the computed thermal rate constants (including quantum tunneling) can be brought into very good agreement with the experimental data for the overall reaction rate constant.

Development of a molecular dynamics-based coalescence model for DSMC simulations of ammonia condensate flows

A coalescence model for homogeneous condensation of ammonia in supersonic expansions to vacuum has been developed using molecular dynamics trajectory calculations. The MD calculations show that the sticking probability increases as the ammonia cluster size increases or the cluster temperature decreases. In addition, the sensitivity of the sticking probability to cluster size decreases as the temperature decreases. Comparison of the Ashgriz-Poo semiempirical coalescence model with MD simulations show that for cluster sizes larger than 100 the former model may be used. To model homogeneous nucleation in an ammonia jet, direct simulation Monte Carlo (DSMC) simulations were performed for different stagnation pressure conditions using the MD simulation outcomes for smaller cluster-cluster collisions and the Ashgriz-Poo model for cluster sizes larger than 100. We found that, by including the combined coalescence model, the average cluster sizes and size distributions predicted by DSMC agree reasonably well with experiment.

Kinematically complete chemical reaction dynamics

Kinematically complete studies of molecular reactions offer an unprecedented level of insight into the dynamics and the different mechanisms by which chemical reactions occur. We have developed a scheme to study ion-molecule reactions by velocity map imaging at very low collision energies. Results for the elementary nucleophilic substitution (SN2) reaction Cl- + CH3I → ClCH3 + I- are presented and compared to high-level direct dynamics trajectory calculations. Furthermore, an improved design of the crossed-beam imaging spectrometer with full three-dimensional measurement capabilities is discussed and characterization measurements using photoionization of NH3 and photodissociation of CH3I are presented.

Dissociative chemisorption of H2 on the Cu(110) surface: A quantum and quasiclassical dynamical study

Six-dimensional quantum dynamical and quasiclassical trajectory (QCT) calculations are reported for the reaction and vibrationally inelastic scattering of (v = 0,1,j = 0) H(2) scattering from Cu(110), and for the reaction and rovibrationally elastic and inelastic scattering of (v = 1,j = 1) H(2) scattering from Cu(110). The dynamics results were obtained using a potential energy surface obtained with density functional theory using the PW91 functional. The reaction probabilities computed with quantum dynamics for (v = 0,1,j = 0) were in excellent agreement with the QCT results obtained earlier for these states, thereby validating the QCT approach to sticking of hydrogen on Cu(110). The vibrational de-excitation probability P(v=1,j = 0 --> v = 0) computed with the QCT method is in remarkably good agreement with the quantum dynamical results for normal incidence energies E(n) between 0.2 and 0.6 eV. The QCT result for the vibrational excitation probability P(v = 0,j = 0 --> v = 1) is likewise accurate for E(n) between 0.8 and 1 eV, but the QCT method overestimates vibrational excitation for lower E(n). The QCT method gives probabilities for rovibrationally (in)elastic scattering, P(v = 1,j = 1 --> v('),j(')), which are in remarkably good agreement with quantum dynamical results. The rotationally averaged, initial vibrational state-selective reaction probability obtained with QCT agrees well with the initial vibrational state-selective reaction probability extracted from molecular beam experiments for v = 1, for the range of collision energies for which the v=1 contribution to the measured total sticking probability dominates. The quantum dynamical probabilities for rovibrationally elastic scattering of (v = 1,j = 1) H(2) from Cu(110) are in good agreement with experiment for E(n) between 0.08 and 0.25 eV.