Final Vibrational State Distributions Research Articles

Vibrational Relaxation of Highly Vibrationally Excited CO Scattered from Au(111): Evidence for CO- Formation.

Electronically nonadiabatic dynamics can be important in collisions of molecules at surfaces; for example, when vibrational degrees of freedom of molecules are coupled to electron-hole-pair (EHP) excitation of a metal. Such dynamics have been inferred from a host of observations involving multiquantum relaxation of NO molecules scattered from metal surfaces. Electron transfer forming transient NO- is thought to be essential to the nonadiabatic coupling. The question remains: is this behavior usual? Here, we present final vibrational state distributions resulting from the scattering of CO(vi = 17) from Au(111), which exhibits significantly less vibrational relaxation than NO(vi = 16). We explain this observation in terms of the lower electron affinity of CO compared to NO, a result that is consistent with the formation of a transient CO- ion being important to CO vibrational relaxation.

Dynamics of H2 Eley-Rideal abstraction from W(110): Sensitivity to the representation of the molecule-surface potential

Dynamics of the Eley-Rideal (ER) abstraction of H2 from W(110) is analyzed by means of quasi-classical trajectory calculations. Simulations are based on two different molecule-surface potential energy surfaces (PES) constructed from Density Functional Theory results. One PES is obtained by fitting, using a Flexible Periodic London-Eyring-Polanyi-Sato (FPLEPS) functional form, and the other by interpolation through the corrugation reducing procedure (CRP). Then, the present study allows us to elucidate the ER dynamics sensitivity on the PES representation. Despite some sizable discrepancies between both H+H/W(110) PESs, the obtained projectile-energy dependence of the total ER cross sections are qualitatively very similar ensuring that the main physical ingredients are captured in both PES models. The obtained distributions of the final energy among the different molecular degrees of freedom barely depend on the PES model, being most likely determined by the reaction exothermicity. Therefore, a reasonably good agreement with the measured final vibrational state distribution is observed in spite of the pressure and material gaps between theoretical and experimental conditions.

Quasiclassical predictions of final vibrational state distributions in reactive and nonreactive collisions

The validity of quasiclassical and semiclassical trajectory methods for predicting state-to-state vibrational transition probabilities in collisions of atoms with diatomic molecules is discussed with special emphasis on tests against accurate quantum calculations for He + H2, H + Cl2, and I + H2 collisions.

Mixed Quantum-Classical Reaction Path Dynamics of C2H5F → C2H4 + HF

A mixed quantum-classical method for calculating product energy partitioning based on a reaction path Hamiltonian is presented and applied to HF elimination from fluoroethane. The goal is to describe the effect of the potential energy release on the product energies using a simple model of quantized transverse vibrational modes coupled to a classical reaction path via the path curvature. Calculations of the minimum energy path were done at the B3LYP/6-311++G(2d,2p) and MP2/6-311++G** levels of theory, followed by energy-partitioning dynamics calculations. The results for the final HF vibrational state distribution were found to be in good qualitative agreement with both experimental studies and quasiclassical trajectory simulations.

Rovibrational resonance effects in collision-induced electronic energy transfer: I2(E,v=–2)+CF4

Collisions of I2 in the E(0(g)+) electronic state with CF4 molecules induce electronic energy transfer to the nearby D, beta, and D' ion-pair states. Simulations of dispersed fluorescence spectra reveal collision-induced electronic energy transfer rate constants and final vibrational state distributions within each final electronic state. In comparison with earlier reports on I2(upsilon(E)=0-2) collisions with He or Ar atoms, we find markedly different dynamics when I2, excited to the same rovibronic states, collides with CF4. Final vibrational state distributions agree with the associated Franck-Condon factors with the initially prepared state to a greater degree than those found with He or Ar collision partners and suggest that internal degrees of freedom in the CF4 molecule represent a substantial means for accepting the accompanying loss of I2 vibronic energy. Comparison of the E-->D transfer of I2 excited to the J=23 and J=55 levels of the upsilon(E)=0 state reveals the onset of specific, nonstatistical dynamics as the available energy is increased above the threshold for excitation of the low frequency nu2 bending mode of CF4.

Reduced dimensionality quantum reactive scattering calculations on the ab initio potential energy surface for the O( [formula omitted]) + N 2O→NO+NO reaction

Quantum reactive scattering calculations for the O( 1 D ) + N 2O→NO+NO reaction have been carried out with an emphasis on the effect of the initial orientation angle on final vibrational state distributions. The potential energy surface has been constructed on the basis of extensive ab initio molecular orbital calculations at multi-configurational second-order perturbation theory (CASPT2) with Dunning's correlation-consistent polarized valence double-zeta basis set. The reduced dimensionality model has been employed, in which the initial and final orientation angles are fixed during collision, while the other three stretching motions are fully treated quantum mechanically. The ab initio calculations show that a wide range of the O( 1 D )–N–N approach angle from collinear to nearly perpendicular configurations is attractive. The scattering calculations show that the reaction exothermicity is preferentially partitioned into the vibrational energy of the newly produced NO molecule while vibrational excitation of the `old' NO which already exists in the reactant N 2O molecule is less effective. However, it is found that this `old' NO bond is not a spectator since a part of the available energy is partitioned into the vibrational energy of this bond.

Vibrational predissociation of the I2⋯Ne2 cluster: A molecular dynamics with quantum transitions study

The MDQT (molecular dynamics with quantum transitions) method of Tully is applied to the vibrational predissociation of a Van der Waals cluster containing a diatomic molecule and two rare gas atoms, I2⋯Ne2. The vibrational degree of freedom of the diatomic is treated quantum mechanically using DVR (discrete variable representation) while all the other degrees of freedom are treated classically. The results are in very good agreement with the experimentally measured lifetimes and product state distributions. In particular, the final vibrational state distribution of I2, which could not be satisfactorily reproduced in quasiclassical studies, is well described. Based on these results a different kinetic scheme for interpreting the vibrational predissociation in this system is proposed. In addition, this work shows that the method is very promising for the study of clusters containing more rare gas atoms.

Single-collision caging of dissociating I 2: wave packet calculations and simulation of femtosecond spectra

Based on recent experimental results on caging of I 2 by collisions with rare gas atoms at room temperature [Wan et al, J. Chem. Phys. 106 (1997) 4353], wave packet simulations of Ar atoms colliding with I 2 excited above the B-state dissociation limit by an ultrashort laser pulse, are presented. With the dependence on the initial orientation and the collision partners of the final vibrational state distribution of caged I 2, full time-dependent simulations of the pump–probe experiments performed by Wan et al. for different Ar pressures were conducted. The excellent agreement between theory and experiment confirms the single-collision caging mechanism of Wan et al.

Final vibrational state resolved single-electron capture for impact of on and CO

By means of ion translational energy spectroscopy, single-electron capture (SEC) by ground state and metastable on and CO has been studied at impact energies . For SEC from the main channels involve transitions with the final vibrational state distributions being found in reasonably good agreement with multichannel Landau - Zener calculations.

A six dimensional quantum study for atom–triatom reactions: The H+H2O→H2+OH reaction

A time-dependent wave packet method has been developed to study atom–triatom ABC+D→AB+CD reactions in full six dimensions (6D). The approach employs a body-fixed coupled angular momentum basis for three angular coordinates, and three 1D bases for three radial coordinates. It permits the calculation of diatom AB vibrational state resolved total reaction probability for an initial rovibrational state of the triatom ABC. The approach is applied to study the H+H2O→H2+OH reaction on the modified Schatz–Elgersman potential energy surface. Initial state-selected total reaction probabilities are presented for initial ground and several vibrationally excited states of H2O for total angular momentum J=0, along with the final OH vibrational state distributions. We also report the cross sections for reaction from the initial ground vibrational and the first bending excited states of H2O. Comparisons are made between our results and those from other theoretical calculations and experiments.

Mean-lifetime calculations of the metastable doubly charged NeAr2+ rare-gas dimer.

The energies and mean lifetimes of the different vibrational states of the $^{1}\mathrm{\ensuremath{\Sigma}}^{+}$ electronic ground state of ${\mathrm{NeAr}}^{2+}$ have been calculated using the phase-shift technique. An efficient searching method for these narrow resonances was developed. The calculated lifetime of the v=12 vibrational state is in reasonable agreement with the experimental value of 275\ifmmode\pm\else\textpm\fi{}25 nsec, reported recently by Ben-Itzhak, Gertner, and Rosner [Phys. Rev. A 47, 289 (1993)], while the lifetimes of other states are more than three orders of magnitude off, thus determining the long-lived vibrational state detected unambiguously. From the difference between the calculated and measured mean lifetime, we have estimated that the potential curve of this 26-electron system is accurate to a few meV. We have also performed ab initio calculations of the $^{2}\mathrm{\ensuremath{\Sigma}}^{+}$ electronic ground state of ${\mathrm{NeAr}}^{+}$ and calculated the Franck-Condon factors for the final vibrational-state distribution of the ${\mathrm{NeAr}}^{2+}$ molecular ion produced in the ${\mathrm{NeAr}}^{+}$ charge-stripping collisions in order to estimate that high vibrational states are indeed produced in the experiment. We have also examined the validity of the WKB method for calculating the lifetimes of highly excited vibrational states.

Quantum calculations of mode specificity in reactions of H with HOD and H2O

We present approximate quantum calculations of cumulative reaction probabilities, rotationally averaged cross sections, and branching ratios for the reactions H+HOD and H+H2O, using the Walch–Dunning–Schatz–Elgersma potential. The calculations are done using the reduced dimensionality, adiabatic-bend approach in which the three internal bending degrees of freedom are treated adiabatically. The H+HOD calculations focus primarily on the effect of vibrationally exciting the OH or OD local modes of HOD on the reactivity, the branching ratios to form the products HD+OH and H2+OD, and their final vibrational state distributions. The calculations of the H+H2O reaction focus on two initial vibrational states, one with three quanta of vibrational excitation in the local mode stretch, and one with two quanta in one local mode and one quantum in the other local mode. The results are generally in good agreement with experiments and previous calculations.

The reaction Ne+H 2 + (v=0, 1, 2, 3, 4)?NeH++H: 3D potential energy surface and quasiclassical trajectory calculations

A three-dimensional potential energy surface for the endoergic reaction Ne+H2+→NeH++H in the2A′ ground state of the system NeH2+ has been calculated by quantum chemical ab initio methods (CEPA approximation). The calculated points on this surface were fitted to an analytic ansatz in terms of an extended LEPS functional form augmented by a correction function. The latter was expanded in polynomials in inverse powers of the internuclear distances. This analytic form was used for quasiclassical trajectory calculations of reactive cross sections. In agreement with experimental investigations a strong vibrational enhancement is observed, i.e. the reaction is markedly favored if the necessary reaction energy is supplied as vibrational energy of H2+ rather than as relative translational energy. Other properties of the reaction dynamics such as the backward to forward scattering ratio, the lifetime of the collision complex NeH2+, and final rotational and vibrational state distributions are also discussed on the basis of the quasiclassical trajectory calculations.

A new crossed beam approach to vibrationally inelastic scattering in neutral collision systems. State-to-state cross sections for He+I*2 (υ′=15, 25, 35) at Ec.m.=89 meV

Details are given of a new type of crossed beam experiment that is designed to study state-resolved vibrationally inelastic scattering of neutral atoms from neutral diatomics or polyatomics. The molecule is initially excited to a selected vibrational level in an excited electronic state by laser pumping. Dispersed fluorescence from molecules that have undergone inelastic scattering is used to observe the final vibrational state distributions. The technique is used here to characterize the vibrationally inelastic scattering of He from each of three initial levels υ′=15, 25 and 35 within the B0+u state of I2 . The center-of-mass collision energy is 89 meV (720 cm−1). Thirty cross sections (relative, not absolute) for vibrationally inelastic scattering are obtained. The cross sections characterize processes with vibrational quantum changes extending to Δυ=±3 for the initial level υ′=15, to Δυ=±5 for υ′=25, and to Δυ=±7 for υ′=35. Relative cross sections for pure rotationally inelastic scattering within the initially pumped υ′ levels are also reported. The data analysis incorporates much new information about I2 predissociation, spectroscopy, and Franck–Condon factors that has become available within the last ten years. An error analysis of the cross sections has been performed so that they are suitable benchmarks for theoretical calculation. Procedures are given for estimating fluorescence signal intensities in experiments of this type. The signal expectations are consistent with the I2 observations and suggest that extension to certain polyatomics is quite feasible.

Wave packet studies of predissociation in H3 Rydberg states

The predissociation of H3 Rydberg states by the two lowest electronic states of H3 is studied using time-dependent wave packet techniques. The final vibrational state distribution function and branching ratios between two- and three-body channels are calculated within a two-dimensional approximation. The effect of initial vibrational excitation on these distributions is studied, and comparison is made to recent experiments.

Diffuse vibrational structures in photoabsorption spectra: A comparison of CH3ONO and CH3SNO using two-dimensional a b i n i t i o potential energy surfaces

We investigated the photodissociation of methyl nitrite (CH3 ONO) and methyl thionitrite (CH3 SNO) within the first absorption band (S1 ←S0 ). The calculations were based on a two-dimensional model including the O–NO/S–NO and N=O bond distances as active coordinates. The S1 -potential energy surfaces were calculated with quantum chemical methods and the dynamical calculations were performed exactly within the time-independent approach. The main emphasis is on the origin of diffuse vibrational structure in the photoabsorption spectrum of both molecules. A low potential barrier of 0.086 eV along the O–NO dissociation coordinate in CH3 ONO prevents immediate dissociation and leads to an initial state dependent lifetime for the excited complex of 100–250 fs corresponding to 3–8 NO vibrational periods. CH3 ONO decays nonadiabatically via vibrational predissociation. The absorption spectrum of CH3 ONO is dominated by narrow Feshbach-like scattering resonances which can be characterized by two quantum numbers, m and n*: m=0 and 1 specifies the quanta of excitation in the O–NO bond and n*=0,1,2,... specifies the excited vibrational level of the N=O bond. The potential barrier is absent in CH3 SNO and the dissociation is direct on the time scale of about 10 fs corresponding to only one third of a NO vibrational period. Nevertheless, the absorption spectrum exhibits diffuse vibrational structures. The shape of the individual absorption peaks is determined by the classical Franck–Condon reflection principle. The dissociation of CH3 SNO is primarily adiabatic which leads to a pronounced energy dependence of the final NO vibrational state distribution. The diffuse structures originate in both cases from excitation of the NO stretching vibration. In order to make contact with time-dependent theory we calculated the autocorrelation function of the time-dependent wave function by inverse Fourier transformation of the energy-dependent spectra. The agreement with available experimental data for both molecules is quite satisfactory. This includes the energy spacing of the vibrational structure, the overall shape of the absorption spectrum, and the lifetime of the excited complex.

Photodissociation of CH3ONO in the first absorption band: A three-dimensional classical trajectory study

The photodissociation of cis-CH3 ONO following excitation into the first absorption band near 350 nm is investigated by means of classical trajectories and an ab initio potential energy surface. The calculations include the O–N coordinate, the N=O coordinate, and the ONO bending angle as variables whilst the internal degrees of freedom of the CH3 O moiety are kept fixed. The calculated lifetimes range from 120 to 410 femtoseconds for excitation of the n*=4 to n*=0 vibrational states of the terminal NO group in the intermediate complex. They agree well with the lifetimes estimated from the anisotropy parameter β. The ONO bending degree of freedom has only a small effect on the lifetime of the complex. The final vibrational state (n) distribution of the NO fragment exhibits a systematic energy dependence which manifests itself in a propensity for the excitation of level n=n*−1 that is in excellent agreement with the measurement. Two-dimensional calculations for a fixed ONO bending angle cannot satisfactorily reproduce these experimental findings. The rotational state distributions are highly inverted with maxima around j∼30–35 depending slightly on the initial state (n*) and the final state (n) of NO. The overall agreement with the measured distributions is satisfactory. The results of this study emphasize the importance of the bending degree of freedom in the dissociation of CH3 ONO and by revealing the interplay of the three active vibrational modes they provide a detailed picture of the predissociation mechanism in a polyatomic molecule.

The vibrational reflection principle in direct photodissociation of triatomic molecules: Test of classical models

The applicability of ordinary classical mechanics to treating vibrational excitation in direct photodissociation of triatomic molecules is tested. Simple classical calculations for a collinear model system agree very well with exact quantum mechanical calculations for the same potential energy surface. We find that the necessity to include non-zero initial momenta depends very much on the interaction potential in the transition region. The final vibrational state distributions are explained by the vibrational reflection principle which is completely analogous to the rotational reflection principle and to the well-known one-dimensional reflection principle for the energy dependence of the total absorption cross section in direct photodissociation. The vibrational distributions “reflect” in a direct way the intermolecular forces in the exit channel.

A quasiclassical trajectory study of final state distributions in collisions of fast H(D) atoms with HF(DF)

This paper presents a detailed theoretical study of the reactive and nonreactive final vibrational state distributions obtained in collisions of translationally hot H atoms with HF (and isotopic counterparts D+HF, H+DF, and D+DF). The potential surface used is surface No. 5 of Brown, Steckler, Schwenke, Truhlar, and Garrett, and it is characterized by a high barrier (1.9 eV) to F atom transfer. Cross sections and other dynamical information were generated using the quasiclassical trajectory (QCT) method, and we also did classical infinite-order-sudden (CIOS) calculations to characterize vibrational excitation mechanisms. Perhaps our most important results refer to the nonreactive final state distributions, where we find that collision of H with the F atom end of HF gives a broad vibrational distribution spread over many states while collision with the H atom end of HF gives a narrow distribution in which v′=1 is the only significant excited product. For D+HF, only the first collision mechanism is important, while for H+HF, H+DF, and D+DF, the second mechanism makes the dominant contribution to v′=1, and the first mechanism is the major contributor to v′>1. This leads to nonreactive vibrational distributions for H+HF, H+DF, and D+HF in which v′=1 is much larger relative to v′>1 than in D+HF. Comparison of these results with experiment for H+HF and D+HF indicates excellent agreement. Reactive distributions are also studied, and we find that the variation of these distributions with isotope can be explained in terms of a Franck–Condon overlap model. Comparison of the reactive final state distribution for D+HF with experiment indicates excellent agreement. Rotational excitation is examined for both reactive and nonreactive collisions, and we find that while the nonreactive rotational excitation is sensitive to which end of the molecule is struck, the reactive rotational distribution is controlled by kinematic propensities.

Energy transfer processes in linear triatomic molecule-solid surface collisions

Abstract The semiclassical stochastic trajectory method is extended to the study of rotational and vibrational transitions for linear triatomic molecules colliding with non-rigid solid surfaces. Rotational and vibrational motion are treated by quantum mechanics, translational motion by classical mechanics, and surface atom motion by the classical generalized Langevin equation. Self-consistent coupling of all motions is enforced via Ehrenfest's theorem. Calculations of the kinetic energy and gas temperature dependence of trapping probabilities, vibrational relaxation probabilities and final vibrational state distributions are presented for the CO2-Ag(111) system at surface temperatures of 0 and 600 K. The trapping probabilities are greatly enhanced by the rotational motion and also vary to some degree with the initial vibrational state of the CO2. Total vibrationally inelastic probabilities are on the order of 10−2 for a single collision event with an initial state (00°1). For the initial state (0110) these are much larger, ~ 10−1, due to the nature of bending mode motion. In conjunction with the large trapping probabilities, the mechanism of vibration to vibration, rotation, translation, phonon energy transfer can provide vibration relaxation probabilities in the range of those measured experimentally. A pseudo-selection rule for conservation of vibrational angular momentum is found.