On the determination of absolute vibrational excitation probabilities in molecule-surface scattering: Case study of NO on Au(111)

We describe a method to obtain absolute vibrational excitation probabilities of molecules scattering from a surface based on measurements of the rotational state, scattering angle, and temporal distributions of the scattered molecules and apply this method to the vibrational excitation of NO scattering from Au(111). We report the absolute excitation probabilities to the v = 1 and v = 2 vibrational states, rotational excitation distributions, and final scattering angle distributions for a wide range of incidence energies and surface temperatures. In addition to demonstrating the methodology for obtaining absolute scattering probabilities, these results provide an excellent benchmark for theoretical calculations of molecule-surface scattering.     

Quantum stereodynamics of Li + HF reactive collisions: the role of reactants polarization on the differential cross section

A complete quantum study for the state-to-state Li + HF(v,j,m) → LiF(v',j',Ω') + H reactive collisions has been performed using a wave packet method, for different initial rotational states and helicity states of the reactants. The state-to-state differential cross section has been simulated, and the polarization of products extracted. It is found that the reactivity is enhanced for nearly collinear collisions, which produces a vibrational excitation of HF, needed to overcome the late barrier. It is also found that LiF(v' = 0) products are preferentially forward scattered, while vibrationally excited LiF(v' = 1 and 2) are backward scattered. These results are interpreted with a simple reaction mechanism, based on the late character and bent geometry of the transition state, originating from a covalent/ionic crossing, which consists of two steps: the arrival at the transition state and the dissociation. In the first step, in order to get to the saddle point some HF vibrational excitation is required, which favors head-on collisions and therefore low values of m. In the second step a fast dissociation of H atom takes place, which is explained by the ionic Li(+)F(-)H character of the bent transition state: the FH(-) is repulsive making that H depart rapidly leaving a highly rotating LiF molecule. For the higher energy analyzed, where resonances slightly contribute, the orientation and alignment of product rotational states, referred to as reactants frame (with the z-axis parallel to k), are approximately constant with the scattering angle. The alignment is close to -1, showing that j' is perpendicular to k, while starting from initial states with well defined rotational orientation, as states with pure m values, the final rotational are also oriented. It is also found that when using products frame (with the z'-axis parallel to k') the rotational alignment and orientation of products varies a lot with the scattering angle just because the z' axis changes from being parallel to anti-parallel to k when varying from θ = 0 to π.     

Quantum interference as the source of steric asymmetry and parity propensity rules in NO-rare gas inelastic scattering

Rotationally inelastic scattering of rare gas atoms and oriented NO molecules exhibits a remarkable alternation in the sign of steric asymmetry between even and odd changes in rotational quantum number. This effect has also been found in full quantum-mechanical scattering calculations. However, until now no physical picture has been given for the alternation. In this work, a newly developed quasi-quantum treatment (QQT) provides the first demonstration that quantum interferences between different orientations of the repulsive potential (that are present in the oriented wave function) are the source of this alternation. Further, from application of the treatment to collisions of nonoriented molecules, a previously unrecognized propensity rule is derived. The angular dependence of the cross sections for excitation to neighboring rotational states with the same parity is shown to be similar, except for a prefactor. Experimental results are presented to support this rule. Unlike conventional quantum-mechanical (or semiclassical) treatments, QQT requires no summation over the orbital angular momentum quantum number l or integration over the impact parameter b. This eliminates the need to solve large sets of coupled differential equations that couple l and rotational state channels among which interference can occur. The QQT provides a physical interpretation of the scattering amplitude that can be represented by a Legendre moment. Application of the QQT on a simple hard-shell potential leads to near-quantitative agreement with experimental observations.     

Communication: direct angle-resolved measurements of collision dynamics with electronically excited molecules: NO(A2Σ+) + Ar

We report direct doubly differential (quantum state and angle-resolved) scattering measurements involving short-lived electronically excited molecules using crossed molecular beams. In our experiment, supersonic beams of nitric oxide and argon atoms collide at 90°. In the crossing region, NO molecules are excited to the A(2)Σ(+)state by a pulsed nanosecond laser, undergo rotationally inelastic collisions with Ar atoms, and are then detected 400 ns later (approximately twice the radiative lifetime of the A(2)Σ(+)state) by 1 + 1(') multiphoton ionization via the E(2)Σ(+) state. The velocity distributions of the scattered molecules are recorded using velocity-mapped ion imaging. The resulting images provide a direct measurement of the state-to-state differential scattering cross sections. These results demonstrate that sufficient scattering events occur during the short lifetimes typical of molecular excited states (～200 ns, in this case) to allow spectroscopically detected quantum-state-resolved measurements of products of excited-state collisions.     

Ambiguities in the semiclassical assignment of the asymmetric rotor rotational quantum numbers

The semiclassical quantization of the rigid asymmetric rotor is revisited in the context of classical inelastic collisions. It is shown that the standard bin histogram method, widely used in quasiclassical trajectory calculations involving linear target molecules, cannot be generalized to the case of asymmetric top molecules owing to ambiguities in the assignment of the final classical action to a particular rotational quantum state. These ambiguities result from pairs of states which are indistinguishable within the bin histogram approach at all the common levels of semiclassical theory. A single value of the classical action can thus correspond to two different quantum states, preventing the distinction between these states in the calculation of rotational cross sections. Our results are illustrated for the rotational states J=1-4 of the water molecule at its equilibrium geometry.     

Quantum Switching of π-Electron Rotations in a Nonplanar Chiral Molecule by Using Linearly Polarized UV Laser Pulses

Nonplanar chiral aromatic molecules are candidates for use as building blocks of multidimensional switching devices because the π electrons can generate ring currents with a variety of directions. We employed (P)-2,2'-biphenol because four patterns of π-electron rotations along the two phenol rings are possible and theoretically determine how quantum switching of the π-electron rotations can be realized. We found that each rotational pattern can be driven by a coherent excitation of two electronic states under two conditions: one is the symmetry of the electronic states and the other is their relative phase. On the basis of the results of quantum dynamics simulations, we propose a quantum control method for sequential switching among the four rotational patterns that can be performed by using ultrashort overlapped pump and dump pulses with properly selected relative phases and photon polarization directions. The results serve as a theoretical basis for the design of confined ultrafast switching of ring currents of nonplanar molecules and further current-induced magnetic fluxes of more sophisticated systems.     

Parity-dependent rotational rainbows in D2-NO and He-NO differential collision cross sections

The (j', Omega', epsilon') dependent differential collision cross sections of D2 with fully state selected (j = 12, Omega = 12, epsilon = -1) NO have been determined at a collision energy of about 550 cm(-1). The collisionally excited NO molecules are detected by (1+1') resonance enhanced multiphoton ionization combined using velocity-mapped ion-imaging. The results are compared to He-NO scattering results and tend to be more forward scattered for the same final rotational state. Both for collisions of the atomic He and the molecular D2 with NO, scattering into pairs of rotational states with the same value of n = j' - epsilon epsilon'2 yields the same angular dependence of the cross section. This "parity propensity rule" remains present both for spin-orbit conserving and spin-orbit changing transitions. The maxima in the differential cross sections-that reflect rotational rainbows-have been extracted from the D2-NO and the He-NO differential cross sections. These maxima are found to be distinct for odd and even parity pair number n. Rainbow positions of parity changing transitions (n is odd) occur at larger scattering angles than those of parity conserving transitions (n is even). Parity conserving transitions exhibit-from a classical point of view-a larger effective eccentricity of the shell. No rainbow doubling due to collisions onto either the N-end or the O-end was observed. From a classical point of view the presence of a double rainbow is expected. Rotational excitation of the D2 molecules has not been observed.     

Frequency distribution of radiation emitted from excited atomic systems

General expressions for the time-dependent probability amplitudes of the quantum states of two arbitrary, interacting atoms are calculated when one atom is initially in an excited p state and the other atom is in an s ground state. The lifetimes of the excited states and the line shape of the emitted radiation are obtained as functions of both the atomic separation and the energy difference between the excited states of the two atoms. The emission line shape is shown to be doubly peaked and to agree with the line shape of the radiation scattered by a system of two interacting atoms. The expressions for the lifetimes of the excited states are found to be identical to those obtained for the radiation scattering situation.     

Rotation of molecules around specific axes: Axes reorientation under rotational excitation

Rotational energy levels of nearly spherical molecules in an isolated vibrational state are studied. It is shown that, in the limit of high rotational quantum number J, the rotational states may be interpreted as those of a stable rotation around axes properly oriented in the molecular frame. The orientation of the axes depends on J. Simple analytical solutions are given for the problem considered in the asymptotic and harmonic approximations. The results obtained possess a clear quantitative interpretation of the phenomena considered and, at the same time, agree quantitatively with the results of numerical diagonalization. The analogy between the effects of rearrangement of the rotational levels under the variation of J and the critical phenomena in macroscopic systems is discussed. The intensities of rovibrational transitions between totally symmetric vibrational states are calculated. A new selection rule is introduced which is due to a overlap of the rotational functions corresponding to the rotation around differently oriented axes.     

Molecular beam scattering of NO+Ne: a joint theoretical and experimental study

The collision dynamics of the NO+Ne system is investigated in a molecular beam scattering experiment at a collision energy of 1055 cm(-1). Employing resonance enhanced multiphoton ionization of NO, we measured state-resolved integral and differential cross sections for the excitation to various levels of both spin-orbit manifolds. The dependence of the scattered intensity on the laser polarization is used to extract differential quadrupole moments for the collision induced angular momentum alignment. The set of cross section data is compared with results of a full quantum mechanical close coupling calculation using the set of ab initio potential energy surfaces of Alexander et al. [J. Chem. Phys. 114, 5588 (2001)]. In previous work, it was found that the positions and rotational substructures for the lowest bend-stretch vibrational states derived from these surfaces agree very well with the observed spectrum of the NO-Ne complex. For the same potential, we find that the calculated cross sections show a less satisfactory agreement with the experimental data. While the overall Jf dependence and magnitude of the integral and differential cross sections are in good agreement, noticeable discrepancies exist for the angle dependence of the differential cross sections. In general, the calculated rotational rainbow structures are shifted towards larger scattering angles indicating that the anisotropy of the potential is overestimated in the fit to the ab initio points or in the ab initio calculation itself. For most states, we find the measured alignment moments to be in excellent agreement with the results of the calculation as well as with predictions of sudden models. Significant deviations from the sudden models are observed only for those fine-structure changing collisions which are dominated by forward scattering. Results of the full quantum calculation confirm the deviations for these states.     

Translational to rotational energy transfer in molecule-surface collisions

A theoretical approach that combines classical mechanics for treating translational and rotational degrees of freedom and quantum mechanics for describing the excitation of internal molecular modes is applied to the scattering of diatomic molecules from metal surfaces. Calculations are carried out for determining the extent of energy transfer to the rotational degrees of freedom of the projectile molecule. For the case of observed spectra of intensity versus final rotational energy, quantitative agreement with available experimental data for the scattering of NO and N(2) from close packed metal surfaces is obtained. It is shown that such measurements can be used to determine the average rotational energy of the incident molecular beam. Measurements of the exchange of energy between translational and rotational degrees of freedom upon collision are also described by calculations for these same systems.     

Differential reaction cross sections from rotationally resolved quantum scattering calculations: application to gas-phase S(N)2 reactions

Differential reaction cross sections have been computed based on previous rotationally resolved time-independent quantum-mechanical scattering calculations for the complex-forming S(N)2 reaction Cl(-) + CH(3)Br → ClCH(3) + Br(-). The results show almost isotropic cross sections for reactant molecules with high rotational quantum numbers. Backward scattering is disfavoured for reaction out of states with small rotational excitation, in particular the rovibrational ground state. This is a quantum-mechanical effect (interference of partial waves) that can partly be rationalized by simple classical arguments. In particular for higher vibrational excitations, an umbrella effect can be observed that favours the backward direction. It can be explained by the strong enhancement of the reactivity by opening a direct mechanism. The ion-dipole interaction exerts a torque onto the molecule which carries out a rotation by about 90° and then completes the reaction.     

Comparison of experimental time-of-flight spectra of the HF products from the F+H2 reaction with exact quantum mechanical calculations

High resolution HF product time-of-flight spectra measured for the reactive scattering of F atoms from n-H2(p-H2) molecules at collision energies between 69 and 81 meV are compared with exact coupled-channel quantum mechanical calculations based on the Stark-Werner ab initio ground state potential energy surface. Excellent agreement between the experimental and computed rotational distributions is found for the HF product vibrational states v'=1 and v'=2. For the v'=3 vibrational state the agreement, however, is less satisfactory, especially for the reaction with p-H2. The results for v'=1 and v'=2 confirm that the reaction dynamics for these product states is accurately described by the ground electronic state 1 (2)A' potential energy surface. The deviations for HF(v'=3, j' > or =2) are attributed to an enhancement of the reaction resulting from the 25% fraction of excited ((2)P(12)) fluorine atoms in the reactant beam.     

Three-dimensional quantum dynamics study of vibrational predissociation of HeI2 van der Waals molecule for low vibrational excitation using the time-dependent wave packet method

Three-dimensional quantum mechanical calculations for vibrational predissociation of He1₂(B) van der Waals molecules are presented using the time-dependent wave packet technique within the golden rule approximation. The total and partial decay widths, lifetimes, rates and their dependence on initial vibrational states were obtained for HeI₂ at low initial vibrational excited levels. Our calculations show that the calculated total decay widths, lifetimes and rates agree well with those extrapolated from experimental data available. The predicted total decay widths as a function of initial vibrational states exhibit highly nonlinear behavior. The very short propagation time (less than 1 ps) required in the golden rule wave packet calculation is determined by the duration time of the final state interaction between the fragments on the vibrationally deexcited adiabatic potential surface. The final state interaction between the fragments is shown to play an important role in determining the final rotational distribution. This interpretation clearly explains the dynamical effect that the final rotational distribution shifts to the lower rotational energy levels as the initial vibrational quantum numberu increases.     

Rotational state populations and angular distributions on surface scattered molecules: No on graphite

Rotational state populations and angular distributions of NO molecules were determined after the scattering of a supersonic beam from a graphite surface at different surface temperatures. The angular distributions exhibit an isotropic and a specular part. The rotational population of the scattered molecules can be described by Boltzmann distributions with identical temperatures for both electronic ground states²Π_½ and²Π_3/2 and both scattering components. The rotational temperature agrees with the surface temperature below 170 K and converges to a constant value of 250 K for surface temperatures higher than 350 K.     

Steric effects and quantum interference in the inelastic scattering of NO(X) + Ar

Rotationally inelastic collisions of NO(X) with Ar are investigated in unprecedented detail using state-to-state, crossed molecular beam experiments. The NO(X) molecules are selected in the Ω = 0.5, j = 0.5, f state and then oriented such that either the ‘N’ or ‘O’ end of the molecule is directed towards the incoming Ar atom. Velocity map ion imaging is then used to probe the scattered NO molecules in well-defined quantum states. We show that the fully quantum state-resolved differential steric asymmetry, which quantifies how the relative efficiency for scattering off the ‘O’ and the ‘N’ ends of the molecule varies with scattering angle, is strongly affected by quantum interference. Significant changes in both integral and differential cross sections are found depending on whether collisions occur with the N or O ends of the molecule. The results are well accounted for by rigorous quantum mechanical calculations, in contrast to both classical trajectory calculations and more simplistic models that provide, at best, an incomplete picture of the dynamics.     

Rotational relaxation measurements on OCS using a beam maser

Rotational relaxation cross sections are reported for J = 0, 1 and 2 rotational states of OCS using a variety of polar and non-polar scattering gases. Cross sections are reported for pure states, superposition states and total beam attenuation. Inelastic cross sections for symmetric top scattering molecules are much larger than corresponding cross sections for linear scattering molecules. Upper and lower states for both J = 0 → 1 and J = 1 → 2 transitions were selected using quadrupole or co-axial focusers. These preliminary results show differences in cross sections for different rotational states.     

Electric quadrupole state selectors for measurements of rotational state distributions of reactively scattered molecules

The analysts of internal quantum state distributions of product molecules formed in molecular beam scattering studies of chemical reactions provides a sensitive test of reaction theories. The electrostatic quadrupole state selector can be used to measure directly the rotational state distribution of polar molecules. The method has the advantage over all others in that the rotational state distribution can be measured at a given arbitrary scattering angle and final velocity. The method has already been used to study the reaction Rb + Br₂ → RbBr + Br and Rb + HBr → RbBr + H. It has also been used to characterize a Xe seeded C-F nozzle beam. The present paper describes in detail the apparatus used, us theory of operation, the methods for evaluating the experimental data and some results from the above mentioned experiments.     

Planar study of H2O+Cl<-->HO+HCl reactions

The first four dimensional (4D) quantum scattering calculations on the tetra-atomic H2O+Cl<-->HO+HCl reactions are reported. With respect to a full (6D) treatment, only the planar constraint and a fixed length for the HO spectator bond are imposed. This work explicitly accounts for the bending and local HO stretching vibrations in H2O, for the vibration of HCl and for the in-plane rotation of the H2O, HO and HCl molecules. The calculations are performed with the potential energy surface of Clary et al. and use a Born-Oppenheimer type separation between the motions of the light and the heavy nuclei. State-to-state cross sections are reported for a collision energy range 0-1.8 eV measured with respect to H2O+Cl. For the H2O+Cl reaction, present results agree with previous (3D) non planar calculations and confirm that excitation of the H2O stretching promotes more reactivity than excitation of the bending. New results are related to the rotation of the H2O molecule: the cross sections are maximal for planar rotational states corresponding to 10相似文献