Cold and ultracold chemical reactions of F+HCl and F+DCl

We report quantum dynamics calculations of F((2)P)+HCl(v,j)-->HF(v('),j('))+Cl((2)P) and F+DCl(v,j)-->DF(v('),j('))+Cl reactions at cold and ultracold temperatures. The effect of rotational and vibrational excitations of the HCl molecule on the reactivity is investigated. It is found that, in the ultracold regime, vibrational excitation of the HCl molecule from v=0 to v=2 enhances the reactivity by four orders of magnitude. The rotational excitation from j=0 to j=1 decreases the reactivity while the rotational excitation from j=0 to j=2 increases the reactivity. The overall effect of rotational excitation was found to be much smaller than vibrational excitation. The reactivity of the F+DCl system is significantly lower than that of the F+HCl case indicating the importance of quantum tunneling at low energies. For both reactions, Feshbach resonances corresponding to Fcdots, three dots, centered HCl or Fcdots, three dots, centeredDCl triatomic states occur at low energies. We also explored the validity of the coupled-states approximation for cold collisions taking the F+HCl(v=0,j=0) reaction as an illustrative example. It is found that the coupled-states approximation is generally valid for the background scattering even at low energies but it is inadequate to accurately describe the rich resonances in the energy dependence of the cross section resulting from the decay of van der Waals complexes. It is further shown that the coupled-states approximation cannot be used for scattering in the Wigner threshold regime when the molecule is initially in a rotationally excited level.     

CH4+O(3P)→CH3+OH反应的准经典轨线研究

用准经典轨线方法研究了O（3P）与CH4的反应，计算结果表明，CH4（υ＝0，j＝0）与O（3P）的反应在低及高的碰撞参数下都是直接反应，无短寿命的碰撞复合物生成，产物OH以向后散射为主，基本上处于振转基态.CH4（υ＝1，j＝1）与O（3P）的反应在低及高的碰撞参数下反应机理不一样。在低碰撞参数下是直接反应，无短寿命的碰撞复合物生成，产物OH以向后散射为主，主要处于振动基态，转动基本上是冷的，但比高碰撞参数下的热.在高的碰撞参数下则生成短寿命的碰撞复合物，产物OH以向前散射为主，表现出明显的周边动力学反应的特征，主要处于振动激发态（υ＝1），但转动仍然是较冷的。     

Study of the H+O2 reaction by means of quantum mechanical and statistical approaches: the dynamics on two different potential energy surfaces

The possible existence of a complex-forming pathway for the H+O(2) reaction has been investigated by means of both quantum mechanical and statistical techniques. Reaction probabilities, integral cross sections, and differential cross sections have been obtained with a statistical quantum method and the mean potential phase space theory. The statistical predictions are compared to exact results calculated by means of time dependent wave packet methods and a previously reported time independent exact quantum mechanical approach using the double many-body expansion (DMBE IV) potential energy surface (PES) [Pastrana et al., J. Phys. Chem. 94, 8073 (1990)] and the recently developed surface (denoted XXZLG) by Xu et al. [J. Chem. Phys. 122, 244305 (2005)]. The statistical approaches are found to reproduce only some of the exact total reaction probabilities for low total angular momenta obtained with the DMBE IV PES and some of the cross sections calculated at energy values close to the reaction threshold for the XXZLG surface. Serious discrepancies with the exact integral cross sections at higher energy put into question the possible statistical nature of the title reaction. However, at a collision energy of 1.6 eV, statistical rotationally resolved cross sections managed to reproduce the experimental cross sections for the H+O(2)(v=0,j=1)-->OH(v(')=1,j('))+O process reasonably well.     

Acceleration of the reaction OH + CO → H + CO2 by vibrational excitation of OH

The collision complex formed from a vibrationally excited reactant undergoes redissociation to the reactant, intramolecular vibrational relaxation (randomization of vibrational energy), or chemical reaction to the products. If attractive interaction between the reactants is large, efficient vibrational relaxation in the complex prevents redissociation to the reactants with the initial vibrational energy, and the complex decomposes to the reactants with low vibrational energy or converts to the products. In this paper, we have studied the branching ratios between the intramolecular vibrational relaxation and chemical reaction of an adduct HO(v)-CO formed from OH(X(2)Π(i)) in different vibrational levels v = 0-4 and CO. OH(v = 0-4) generated in a gaseous mixture of O(3)/H(2)/CO/He irradiated at 266 nm was detected with laser-induced fluorescence (LIF) via the A(2)Σ(+)-X(2)Π(i) transition, and H atoms were probed by the two-photon excited LIF technique. From the kinetic analysis of the time-resolved LIF intensities of OH(v) and H, we have found that the intramolecular vibrational relaxation is mainly governed by a single quantum change, HO(v)-CO → HO(v-1)-CO, followed by redissociation to OH(v-1) and CO. With the vibrational quantum number v, chemical process from the adduct to H + CO(2) is accelerated, and vibrational relaxation is decelerated. The countertrend is elucidated by the competition between chemical reaction and vibrational relaxation in the adduct HOCO.     

Rate constant for OH(2 Pi)+O(3P)-->H(2S)+O2(3 Sigma g-) reaction on an improved ab initio potential energy surface and implications for the interstellar oxygen problem

The authors report a global potential energy surface for the ground electronic state of HO(2)(X (2)A(")), which improves upon the XXZLG potential [Xu and et al., J. Chem. Phys. 122, 244305 (2005)] with additional high-level ab initio points for the long-range interaction potential in the O+OH channel. Exact J=0 quantum mechanical reaction probabilities were calculated on the new potential and the rate constant for the title reaction was obtained using a J-shifting method. The calculated rate constant is in good agreement with available experimental values and our results predict a significantly lower rate at temperature range below 30 K, offering a possible explanation for the "interstellar oxygen problem."     

Bimolecular reactions of vibrationally excited molecules. Roaming atom mechanism at low kinetic energies

Quasiclassical trajectory calculations have been performed for the H + H'X(v) → X + HH' abstraction and H + H'X(v) → XH + H' (X = Cl, F) exchange reactions of the vibrationally excited diatomic reactant at a wide collision energy range extending to ultracold temperatures. Vibrational excitation of the reactant increases the abstraction cross sections significantly. If the vibrational excitation is larger than the height of the potential barrier for reaction, the reactive cross sections diverge at very low collision energies, similarly to capture reactions. The divergence is quenched by rotational excitation but returns if the reactant rotates fast. The thermal rate coefficients for vibrationally excited reactants are very large, approach or exceed the gas kinetic limit because of the capture-type divergence at low collision energies. The Arrhenius activation energies assume small negative values at and below room temperature, if the vibrational quantum number is larger than 1 for HCl and larger than 3 for HF. The exchange reaction also exhibits capture-type divergence, but the rate coefficients are larger. Comparisons are presented between classical and quantum mechanical results at low collision energies. At low collision energies the importance of the exchange reaction is enhanced by a roaming atom mechanism, namely, collisions leading to H atom exchange but bypassing the exchange barrier. Such collisions probably have a large role under ultracold conditions. The calculations indicate that for roaming to occur, long-range attractive interaction and small relative kinetic energy in the chemical reaction at the first encounter are necessary, which ensures that the partners can not leave the attractive well. Large orbital angular momentum of the primary products (equivalent to large rotational excitation in a unimolecular reaction) is favorable for roaming.     

State-to-state reaction probabilities for the H+O2(v,j)-->O+OH(v',j') reaction on three potential energy surfaces

We report state-to-state and total reaction probabilities for J=0 and total reaction probabilities for J=2 and 4 for the title reaction, both for ground-state and initially rovibrationally excited reactants. The results for three different potential energy surfaces are compared and contrasted. The potential energy surfaces employed are the DMBE IV surface by Pastrana et al. [J. Phys. Chem. 94, 8073 (1990)], the surface by Troe and Ushakov (TU) [J. Chem. Phys. 115, 3621 (2001)], and the new XXZLG ab initio surface by Xu et al. [J. Chem. Phys. 122, 244305 (2005)]. Our results show that the total reaction probabilities from both the TU and XXZLG surfaces are much smaller in magnitude for collision energies above 1.2 eV compared to the DMBE IV surface. The three surfaces also show different behavior with regards to the effect of initial state excitation. The reactivity is increased on the XXZLG and the TU surfaces and decreased on the DMBE IV surface. Vibrational and rotational product state distributions for the XXZLG and the DMBE IV surface show different behaviors for both types of distributions. Our results show that for energies above 1.25 eV the dynamics on the DMBE IV surface are not statistical. However, there is also evidence that the dynamics on the XXZLG surface are not purely statistical for energies above the onset of the first excited product vibrational state v'=1. The magnitude of the total reaction probability is decreased for J>0 for the DMBE IV and the XXZLG surfaces for ground-state reactants. However, for initially rovibrationally excited reactants, the total reaction probability does not decrease as expected for both surfaces. As a result the total cross section averaged over all Boltzmann accessible rotational states may well be larger than the cross section reported in the literature for j=1.     

A case study in ultracold reactive scattering: D + H2

We report theoretical results for reaction and vibrational quenching of the ultracold collision D + H(2) (v, j = 0) for a wide range of initial vibrationally excited states v. The v-dependence of the zero-temperature limit of the reaction rate coefficient shows two distinct regimes: a barrier dominated regime for 0 ≤ v ≤ 4, and a barrierless regime for v ≥ 5. We also present detailed distributions over the rovibrational states of the products. We find an approximate conservation of the internal vibrational energy; namely, the branching ratios always favor the highly excited final states, which have vibrational energies similar to that of the entrance channel.     

Quantum and classical studies of the O(3P) + H2(v = 0-3,j = 0) --> OH + H reaction using benchmark potential surfaces

We present results of time-dependent quantum mechanics (TDQM) and quasiclassical trajectory (QCT) studies of the excitation function for O(3P) + H2(v = 0-3,j = 0) --> OH + H from threshold to 30 kcal/mol collision energy using benchmark potential energy surfaces [Rogers et al., J. Phys. Chem. A 104, 2308 (2000)]. For H2(v = 0) there is excellent agreement between quantum and classical results. The TDQM results show that the reactive threshold drops from 10 kcal/mol for v = 0 to 6 for v = 1, 5 for v = 2 and 4 for v = 3, suggesting a much slower increase in rate constant with vibrational excitation above v = 1 than below. For H2(v > 0), the classical results are larger than the quantum results by a factor approximately 2 near threshold, but the agreement monotonically improves until they are within approximately 10% near 30 kcal/mol collision energy. We believe these differences arise from stronger vibrational adiabaticity in the quantum dynamics, an effect examined before for this system at lower energies. We have also computed QCT OH(v',j') state-resolved cross sections and angular distributions. The QCT state-resolved OH(v') cross sections peak at the same vibrational quantum number as the H2 reagent. The OH rotational distributions are also quite hot and tend to cluster around high rotational quantum numbers. However, the dynamics seem to dictate a cutoff in the energy going into OH rotation indicating an angular momentum constraint. The state-resolved OH distributions were fit to probability functions based on conventional information theory extended to include an energy gap law for product vibrations.     

Quasiclassical trajectory study of the vibrational quenching of hydroxyl radicals through collision with O atoms

The collisional removal of vibrationally excited OH radicals by O atoms is studied by the quasiclassical trajectory method. To evaluate the effect of different topological features on the scattering processes two different global potential energy surfaces, DMBE IV and TU, are used. Results for reactive, exchange, and inelastic scattering probabilities are reported for central collisions (with zero total angular momentum) with a fixed relative translational energy for vibrational levels of OH ranging from nu=1 to v=8. Vibrational state distributions of product molecules are also compared on the two potential energy surfaces. Both surfaces predict higher probabilities for reaction than for exchange or inelastic scattering. The vibrational state distributions of the product diatomic molecules are different on the two surfaces. In particular, the two surfaces give substantially different probabilities for multiquantum OH vibrational relaxation transitions OH(v)+O-->OH(v')+O.     

Experimental and master equation study of the kinetics of OH + C2H2: temperature dependence of the limiting high pressure and pressure dependent rate coefficients

The kinetics of the reaction OH + C2H2 have been studied using laser flash photolysis at 248 nm to generate OH radicals and laser-induced fluorescence to monitor OH removal. An attempt was made to use the rate coefficients OH (v = 1,2) + C2H2 to determine the limiting high-pressure rate coefficient, k(1a)(infinity), over the temperature range of 195-823 K. This method is usually applicable if the reaction samples the potential energy well of the adduct, HOC2H2, and if intramolecular vibrational relaxation is fast. In the present case, however, the rate coefficients for loss of the vibrationally excited states by reaction with C2H2 also contain a substantial contribution from nonreactive vibrational relaxation, which occurs via a mechanism that does not sample the adduct potential energy well but involves, at least at low temperatures, collisions that access a shallower, longer range van der Waals well. The data were analyzed using a composite mechanism that incorporates both reactive and nonreactive energy transfer mechanisms, which allows the determination of k(1a)(infinity)(T) for OH + C2H2 with satisfactory accuracy over the temperature range 195-823 K. The kinetics of the reaction OH (v = 0) + C2H2 were also studied in He over the range of conditions: 210-373 K and 5-760 Torr. A one-dimensional master equation (ME) analysis of the experimental data provided a further determination of k(1a)(infinity)(T) and also (down) for He. Combining the two sets of results gives a consistent dataset for k(1a)(infinity) and the Arrhenius parameters A1ainfinity = 7.3 x 10(-12) cm(3) molecule(-1) s(-1) and E(1a)(infinity) = 5.3 kJ mol(-1), with (down) = 150(T/300 K) cm(-1). Additional experiments were conducted at room temperature in N(2) and SF(6) by laser flash photolysis with cavity ring down spectroscopy, and ME calculations were then optimized for the pressure falloff in N(2) by varying the average downward energy transfer parameter ((down)). The output from the best fit ME was parametrized using a modified Troe expression to provide rate data for use in atmospheric modeling.     

Coupled-states statistical investigation of vibrational and rotational relaxation of OH(2pi) by collisions with atomic hydrogen

We report state-to-state cross sections and thermal rate constants for vibrational and rotational relaxation of OH(2pi) by collision with H atoms. The cross sections are calculated by the coupled-states (CS) statistical method including the full open-shell character of the OH + H system. Four potential energy surfaces (PESs) ((1,3)A' and (1,3)A') describe the interaction of OH(X2pi) with H atoms. Of these, three are repulsive, and one (1A') correlates with the deep H2O well. Consequently, rotationally and ro-vibrationally inelastic scattering of OH in collisions with H can occur by scattering on the repulsive PESs, in a manner similar to the inelastic scattering of OH by noble gas atoms, or by collisions which enter the H2O well and then reemerge. At 300 K, we predict large (approximately 1 x 10(-10) cm3 molecule(-1) s(-1)) vibrational relaxation rates out of both v = 2 and v = 1, comparable to earlier experimental observations. This anomalously fast relaxation results from capture into the H2O complex. There exists a significant propensity toward formation of OH in the pi(A') lambda-doublet level. We also report state-resolved cross sections and rate constants for rotational excitation within the OH v = 0 manifold. Collisional excitation from the F1 to the F2 spin-orbit manifold leads to an inverted lambda-doublet population.     

A quasiclassical trajectory study of the reaction H + O2 <==> OH + O with the O2 reagent vibrationally excited

Quasiclassical trajectories have been computed on the Melius-Blint (MB) Potential Energy Surface (PES) and on the Double Many-Body Expansion (DMBE) IV PES of Pastrana et al. describing the H + O(2) <==> OH + O reaction with the nonrotating (J = 0) O(2) reagent vibrationally excited to levels v = 6, 7, 8, 9, and 10 at four temperatures: 1000, 2000, 3000, and 4000 K. The vibrational energy levels were selected by using a semiclassical Einstein-Brillouin-Keller (EBK) quantization procedure while the relative translational energy was sampled from a Boltzmann weighted distribution. The rate coefficient for the formation of the OH + O products is seen to increase monotonically with quantum number and nearly monotonically with temperature. On the MB PES, at T = 1000 K, the total rate coefficient increases by a factor of 5.2 as the initial vibrational quantum number of the O(2) diatom increases from v = 6 to v = 10. For T = 2000 K, this factor drops to 3.3, to 2.9 for T = 3000 K, and to 2.5 for T = 4000 K. On the DMBE IV PES, at T = 1000 K the total rate coefficient increases by a factor of 4.1 as the initial vibrational quantum number of the O(2) diatom increases from v = 6 to v = 10. For T = 2000 K, this factor drops to 3.5, to 2.1 for T = 3000 K, and to 2.0 for T = 4000 K. The less-direct group (defined below) of trajectories is sensitive to the initial O(2) vibrational excitation in several different temperature ranges, apparently retaining the effect of reagent vibrational excitation. The more-direct group (defined below) of trajectories does not exhibit this behavior. Reagent vibrational excitation does not increase the total rate coefficients for the title reaction more than the increase due to a simple temperature increase. The less-direct and more-direct groups of trajectories differ in their contribution to the rate coefficient for the title reaction. In particular, at T = 4000 K, the two PESs used in this work differ dramatically in the roles of the less-direct and more-direct trajectories. The behavior of the more-direct and less-direct groups of trajectories can be understood in terms of the efficiency of intramolecular vibrational energy transfer. This work utilizes the recently introduced PES Library, POTLIB 2001, which made the comparisons between the two PESs discussed in this work possible in a very straightforward way.     

Quantum dynamics study of the K+HF(v=0-2,j=0)-->KF+H reaction and comparison with quasiclassical trajectory results

Extensive quantum real wave packet calculations within the helicity decoupling approximation are used to analyze the influence of the HF vibrational excitation on the K+HF(v=0-2,j=0)-->KF+H reaction. Quantum reaction probabilities P and reaction cross sections sigma are compared with corresponding quasiclassical trajectory (QCT) results. Disregarding threshold regions for v=0 and 1 (v=2 has no threshold), both approaches lead to remarkably similar results, particularly for sigma, validating the use of the QCT method for this system. When moving from v=0 to v=1 there is a large increase in P and sigma, as expected for a late barrier system. For v=2 the reaction becomes exoergic and P approximately 0.95 (with the exception of large total angular momenta where centrifugal barriers play a role). While substantial vibrational enhancement of the reactivity is thus seen, it is still quite less than that inferred from experimental data in the intermediate and high collision energy ranges. The origin of this discrepancy is unclear.     

Quasiclassical trajectory calculations for Li(2(2)P(J)) + H2 → LiH(X(1)Σ+) + H: influence by vibrational excitation and translational energy

Ab initio potential energy surfaces and the corresponding analytical energy functions of the ground 1A' and excited 2A' states for the Li(2(2)P) plus H(2) reaction are constructed. Quasiclassical trajectory calculations on the fitted energy functions are performed to characterize the reactions of Li(2(2)P) with H(2)(v = 0, j = 1) and H(2)(v = 1, j = 1) as well as the reaction when the vibrational energy is replaced by collision energy. For simplicity, the transition probability is assumed to be unity when the trajectories go through the crossing seam region and change to the lower surface. The calculated rotational distributions of LiH(v = 0) for both H(2)(v = 0, j = 1) and H(2)(v = 1, j = 1) reactions are single-peaked with the maximum population at j' = 7, consistent with the previous observation. The vibrational excitation of H(2)(v = 1) may enhance the reaction cross section of LiH(v' = 0) by about 200 times, as compared to a result of 93-107 reported in the experimental measurements. In contrast, the enhancement is 3.1, if the same amount of energy is deposited in the translational states. This endothermic reaction can be considered as an analog of late barrier. According to the trajectory analysis, the vibrational excitation enlarges the H-H distance in the entrance channel to facilitate the reaction, but the excess energy may not open up additional reaction configuration.     

Quantum and quasiclassical studies of the O(3P)+HCl-->OH+Cl(2P) reaction using benchmark potential surfaces

We have performed quantum mechanical (QM) dynamics calculations within the independent-state approximation with new benchmark triplet A" and A' surfaces [B. Ramachandran et al., J. Chem. Phys. 119, 9590 (2003)] for the rovibronic state-to-state measurements of the reaction O(3P)+HCl(v=2,j=1,6,9)-->OH(v'j')+Cl(2P) [Zhang et al., J. Chem. Phys. 94, 2704 (1991)]. The QM and experimental rotational distributions peak at similar OH(j') levels, but the QM distributions are significantly narrower than the measurements and previous quasiclassical dynamics studies. The OH(low j) populations observed in the measurements are nearly absent in the QM results. We have also performed quasiclassical trajectory with histogram binning (QCT-HB) calculations on these same benchmark surfaces. The QCT-HB rotational distributions, which are qualitatively consistent with measurements and classical dynamics studies using other surfaces, are much broader than the QM results. Application of a Gaussian binning correction (QCT-GB) dramatically narrows and shifts the QCT-HB rotational distributions to be in very good agreement with the QM results. The large QCT-GB correction stems from the special shape of the joint distribution of the classical rotational/vibrational action of OH products. We have also performed QM and QCT calculations for the transition, O+HCl(v=0,T=300 K)-->OH(v'j')+Cl from threshold to approximately 130 kcal mol(-1) collision energy as a guide for possible future hyperthermal O-atom measurements. We find in general a mixed energy release into translation and rotation consistent with a late barrier to reaction. Angular distributions at high collision energy are forward peaked, consistent with a stripping mechanism. Direct collisional excitation channel cross sections, O+HCl(v=0,T=300 K)-->O+HCl(v'=1), in the same energy range are large, comparable in magnitude to the reactive channel cross sections. Although the (3)A" state dominates most collision processes, above approximately 48 kcal mol(-1), the (3)A' state plays the major role in collisional excitation.     

The relaxation of OH (v=1) and OD (v=1) by H2O and D2O at temperatures from 251 to 390 K

We report rate coefficients for the relaxation of OH(v=1) and OD(v=1) by H2O and D2O as a function of temperature between 251 and 390 K. All four rate coefficients exhibit a negative dependence on temperature. In Arrhenius form, the rate coefficients for relaxation (in units of 10(-12) cm3 molecule-1 s-1) can be expressed as: for OH(v=1)+H2O between 263 and 390 K: k=(2.4+/-0.9) exp((460+/-115)/T); for OH(v=1)+D2O between 256 and 371 K: k=(0.49+/-0.16) exp((610+/-90)/T); for OD(v=1)+H2O between 251 and 371 K: k=(0.92+/-0.16) exp((485+/-48)/T); for OD(v=1)+D2O between 253 and 366 K: k=(2.57+/-0.09) exp((342+/-10)/T). Rate coefficients at (297+/-1 K) are also reported for the relaxation of OH(v=2) by D2O and the relaxation of OD(v=2) by H2O and D2O. The results are discussed in terms of a mechanism involving the formation of hydrogen-bonded complexes in which intramolecular vibrational energy redistribution can occur at rates competitive with re-dissociation to the initial collision partners in their original vibrational states. New ab initio calculations on the H2O-HO system have been performed which, inter alia, yield vibrational frequencies for all four complexes: H2O-HO, D2O-HO, H2O-DO and D2O-DO. These data are then employed, adapting a formalism due to Troe (J. Troe, J. Chem. Phys., 1977, 66, 4758), in order to estimate the rates of intramolecular energy transfer from the OH (OD) vibration to other modes in the complexes in order to explain the measured relaxation rates-assuming that relaxation proceeds via the hydrogen-bonded complexes.     

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.