Steric asymmetry and lambda-doublet propensities in state-to-state rotationally inelastic scattering of NO(2Pi(1/2)) with He

Relative integrated cross sections are measured for rotationally inelastic scattering of NO(2Pi(1/2)),hexapole selected in the upper lambda-doublet level of the ground rotational state (j = 0.5), in collisions with He at a nominal energy of 514 cm(-1). Application of a static electric field E in the scattering region, directed parallel or antiparallel to the relative velocity vector v, allows the state-selected NO molecule to be oriented with either the N end or the O end towards the incoming He atom. Laser-induced fluorescence detection of the final state of the NO molecule is used to determine the experimental steric asymmetry, [formula: see text], which is equal to within a factor of (- 1) to the molecular steric effect, S(i-->f) is identical with (sigma(He-->NO) - (sigma(He-->ON))/(sigma(He-->NO) + sigma(He-->ON)). The dependence of the integral inelastic cross section on the incoming lambda-doublet component is also observed as a function of the final rotational (j'), spin-orbit (omega'), and lambda-doublet (epsilon') state. The measured steric asymmetries are significantly larger than previously observed for NO-Ar scattering, supporting earlier proposals that the repulsive part of the interaction potential is responsible for the steric asymmetry. In contrast to the case of scattering with Ar, the steric asymmetry of NO-He collisions is not very sensitive to the value of omega'. However, the lambda-doublet propensities are very different for [omega=0.5(F1)-->omega'= 1.5(F2)] and [omega=0.5(F1)-->omega'=0.5(F1)] transitions. Spin-orbit manifold conserving collisions exhibit a propensity for parity conservation at low deltaj, but spin-orbit manifold changing collisions do not show this propensity. In conjunction with the experiments, state-to-state cross sections for scattering of oriented NO(2Pi) molecules with He atoms are predicted from close-coupling calculations on restricted coupled-cluster methods including single, double, and noniterated triple excitations [J. Klos, G. Chalasinski, M. T. Berry, R.Bukowski, and S. M. Cybulski, J. Chem. Phys. 112, 2195 (2000)] and correlated electron-pair approximation [M. Yang and M. H. Alexander, J. Chem. Phys. 103, 6973 (1995)] potential energy surfaces. The calculated steric asymmetry S(i-->f) of the inelastic cross sections at Etr= 514 cm(-1) is in reasonable agreement with that derived from the present experimental measurements for both spin-manifold conserving (F1-->Fl) and spin-manifold changing (F1 --F2) collisions, except that the overall sign of the effect is opposite. Additionally, calculated field-free integral cross sections for collisions at Etr = 508 cm(-1) are compared to the experimental data of Joswig et al. [J. Chem. Phys.85, 1904 (1986)]. Finally, the calculated differential cross section for collision energy Etr= 491 cm(-1) is compared to experimental data of Westley et al. [J. Chem. Phys. 114, 2669 (2001)] for the spin-orbit conserving transition F1 (j = 0.5) -F1f (j' = 3.5).     

Fully quantum state-resolved inelastic scattering between He and NO(X (2)Pi)

Quantum mechanical close-coupling calculations have been used to obtain fully quantum state-resolved differential cross sections and opacity functions for the rotationally inelastic collisions of NO(X (2)Pi) with He at collision energies of 63 and 147 meV using the most recent ab initio potential energy surfaces of K?os et al. [J. Chem. Phys. 112, 2195 (2000)]. Double peaks observed in the Lambda-doublet resolved differential cross sections are shown to be related to the presence of analogous peaks in the corresponding opacity functions. These structures can be linked directly to a specific expansion term in the potential, and reflect the fact that NO is not quite homonuclear.     

Steric effects in state-to-state scattering of OH (2pi(3/2),J=3/2,f) by HCl

In this paper we address stereo-dynamical issues in the inelastic encounters between OH (chi2pi) radicals and HCl (chi1sigma+). The experiments were performed in a crossed molecular-beam machine at the nominal collision energy of 920 cm(-1). Prior to the collisions, the OH molecules were selected using a hexapole in a well-defined rotational state v=0, omega=32, J=32, M(J)=32, f, and subsequently oriented in a homogeneous electrical field. We have measured rotationally resolved relative cross sections for collisions in which OH is oriented with either the O side or the H side towards HCl, from which we have calculated the corresponding steric asymmetry factors S. The results are presented in comparison with data previously obtained by our group for the inelastic scattering of OH by CO (E(coll)=985 cm(-1)) and N2 (E(coll)=985 cm(-1)) studied under similar experimental conditions. The dissimilarity in the behavior of the OH+HCl system revealed by this comparison is explained on the basis of the difference in the anisotropy of the interaction potential governing the collisions. The interpretation of the data takes into account the specific features of both nonreactive and reactive parts of the potential-energy surface. The results indicate that the scattering dynamics at this collision energy may be influenced by the HO-HCl van der Waals well and by reorientation effects determined by the long-range electrostatic forces and, furthermore, may involve reactive collisions.     

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.     

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.     

Rotational transitions and diffraction in D2 scattering from the LiF(001) surface: theory and experiment

High probabilities of energy transfer from translation to molecular rotations are observed in the scattering of n-D(2) from LiF(001) at an incident beam energy of 85.3 meV. For the 100 incidence direction, close-coupling calculations yield ratios of the rotationally inelastic (j=0-->2) and (j=1-->3) peaks to the rotationally elastic specular peaks (G=0) that are in reasonable agreement with experiment, as are the ratios of the rotationally elastic diffraction peak intensities to the specular peak intensities. The agreement between theory and experiment is also quite good for the rotationally inelastic diffractive (-1-1) transitions for (j=1-->3), but rather poor for (j=0-->2). The calculations show that the interaction between the electrostatic field of the surface ions and the quadrupole moment of the D(2) molecule efficiently promotes the (j=0-->2) and (j=1-->3) transitions. If this electrostatic interaction is excluded from the potential model, the ratios of the (j=0-->2) and (j=1-->3) rotationally inelastic peaks to the corresponding specular peaks show a large discrepancy with experiment, underlining the importance of this interaction. The close-coupling calculations show a somewhat worse agreement with experiment for the 110 incidence direction. In particular, the sharp peaks observed experimentally in the ratios of the peak intensities of the rotationally inelastic G=0 (j=0-->2) and (j=1-->3) to the rotationally elastic G=0 transitions as a function of incident angle are not reproduced by the calculations. The theoretical ratios of the peak intensities of the rotationally elastic diffraction to G=0 transitions are shifted to lower incidence angles with respect to experiment. The rotationally inelastic diffractive (-10) transitions present an interesting resonance phenomenon for the (j=0-->2) rotational transition. This resonance is predicted by both theory and experiment, although at rather different incident angles.     

The effect of kinematic parameters on inelastic scattering of glyoxal

The effect of kinematic parameters (relative velocity v(rel), relative momentum p(rel), and relative energy E(rel)) on the rotational and rovibrational inelastic scatterings of 0(0)K(0)S(1) trans-glyoxal has been investigated by colliding glyoxal seeded in He or Ar with target gases D2, He, or Ne at different scattering angles in crossed supersonic beams. The inelastic spectra for target gases He and D2 acquired with two different sets of kinematic parameters revealed no significant differences. This result shows that kinematic factors have the major influence in the inelastic scattering channel competition whereas the intermolecular potential energy surface plays only a secondary role. The well-defined exponential dependence of relative cross sections on exchanged angular momentum identifies angular momentum as the dominant kinematic factor in collision-induced rotationally and rovibrationally inelastic scatterings. This is supported by the behavior of the relative inelastic cross sections data in a "slope-p(rel)" representation. In this form, the data show a trend nearly independent of the target gas identity. Representations involving E(rel) and v(rel) show trends specific to the target gas.     

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.     

The effect of vibrational bond stretching on rotational inelastic electron-molecule scattering

Differential cross sections for state-to-state rotationally inelastic electron-Na₂ scattering, with the molecule being in the vibrational levelv′'=31, are measured at a collision energy of 150 eV. Angular momentum transfer of up to Δj=26 is observed, which is even more than previously obtained for the vibrational ground statev′'=0. Good agreement is found with theoretical results from a spectator scattering model. This work, in general, elucidates the role of vibrational excitation in collision dynamics under vibrationally sudden conditions.     

Absolute level-resolved reactive and inelastic rate constants in Li+Li2*

We have used nuclear parity-changing collisions to obtain absolute level-to-level rate constants for reactive scattering in a triatomic system with identical nuclei. We have determined rate constants for the system (7)Li(2) (*)(A (1)Sigma(u) (+))(v(i)=2,j(i)=19)+(7)Li-->(7)Li+(7)Li(2) (*)(A (1)Sigma(u) (+))(v(f),j(f)), from laser-induced fluorescence spectra of lithium vapor in a heat pipe oven. Parity-preserving collisions yielded measurements of absolute rotationally and vibrationally inelastic rate constants as well. We compare the reactive rate constants with statistical prior distributions and the inelastic results with previously measured results on the Ne+(7)Li(2) (*) system.     

Rotationally inelastic molecule–surface scattering: dynamical lie algebraic method

The rotationally inelastic molecule–surface scattering is analyzed using dynamical Lie algebraic method. We treat, by example, the simple model of the scattering of NO from a rigid, flat Ag(111) surface. The explicit expressions of transition probability and the probability current density are obtained. It is proved that dynamical Lie algebraic method can be useful for describing the scattering problems. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 76: 500–510, 2000     

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.     

State-to-state inelastic scattering of OH by HI: a comparison with OH-HCl and OH-HBr

Relative state-to-state cross sections and steric asymmetries have been measured for the scattering process: OH (X (2)Pi(32),v=0,J=32,M(J)=32,f)+HI ((1)Sigma,v=0,J<4)-->OH (X (2)Pi,v=0,Omega=12,J=12-52 and Omega=32,J=32-92,ef)+HI, at 690 cm(-1) collision energy. Comparison with the previously studied systems OH-HCl and OH-HBr reveals relevant features of the potential energy surfaces of these molecular systems. Some measured differences concerning the internal energy distribution after collision and the propensities for the impact with one or the other side of the OH molecule in scattering by HCl, HBr, and HI molecules are discussed.     

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.     

Application of the Lie algebraic approach to diffractionally and rotationally inelastic molecule–surface scattering

The Lie algebraic approach of Alhassid and Levine [Phys. Rev. A 18 , 89 (1978)] is applied to the molecule–surface scattering. Specially, the diffractionally and rotationally inelastic scattering of a diatomic molecule from a solid surface is dealt with. Within the framework of the close-coupling method, we construct a Hamiltonian for the scattering system and use it to generate a dynamical algebra h₆. By solving equations of motion for the group parameters, the scattering wave functions near the surface are obtained. Computed transition probabilities of diffractively and rotationally inelastic scattering of H₂ from LiF(001) surface with the use of Lie algebraic method are seen to agree well with the coupled-channel calculations. The Lie algebraic method thus appears to have a wide range of validity for describing the dynamics of gas–surface scattering. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 981–989, 1997     

State-to-state differential and relative integral cross sections for rotationally inelastic scattering of H2O by hydrogen

State-to-state differential cross sections (DCSs) for rotationally inelastic scattering of H(2)O by H(2) have been measured at 71.2 meV (574 cm(-1)) and 44.8 meV (361 cm(-1)) collision energy using crossed molecular beams combined with velocity map imaging. A molecular beam containing variable compositions of the (J = 0, 1, 2) rotational states of hydrogen collides with a molecular beam of argon seeded with water vapor that is cooled by supersonic expansion to its lowest para or ortho rotational levels (J(KaKc) = 0(00) and 1(01), respectively). Angular speed distributions of fully specified rotationally excited final states are obtained using velocity map imaging. Relative integral cross sections are obtained by integrating the DCSs taken with the same experimental conditions. Experimental state-specific DCSs are compared with predictions from fully quantum scattering calculations on the most complete H(2)O-H(2) potential energy surface. Comparison of relative total cross sections and state-specific DCSs show excellent agreement with theory in almost all details.     

The effect of a nonresonant radiative field on low-energy rotationally inelastic collisions

We examine the effects of a linearly polarized nonresonant radiative field on the dynamics of rotationally inelastic Na⁺+N₂ collisions at eV collision energies. Our treatment is based on the Fraunhofer model of matter wave scattering and its recent extension to collisions in electric fields [M. Lemeshko, B. Friedrich, J. Chem. Phys. 129 (2008) 024301]. The nonresonant radiative field changes the effective shape of the target molecule by aligning it in the space-fixed frame. This markedly alters the differential and integral scattering cross-sections. As the cross-sections can be evaluated for a polarization of the radiative field collinear or perpendicular to the relative velocity vector, the model also offers predictions about steric asymmetry of the collisions.     

An analytic model of rotationally inelastic collisions of polar molecules in electric fields

We present an analytic model of thermal state-to-state rotationally inelastic collisions of polar molecules in electric fields. The model is based on the Fraunhofer scattering of matter waves and requires Legendre moments characterizing the "shape" of the target in the body-fixed frame as its input. The electric field orients the target in the space-fixed frame and thereby effects a striking alteration of the dynamical observables: both the phase and amplitude of the oscillations in the partial differential cross sections undergo characteristic field-dependent changes that transgress into the partial integral cross sections. As the cross sections can be evaluated for a field applied parallel or perpendicular to the relative velocity, the model also offers predictions about steric asymmetry. We exemplify the field-dependent quantum collision dynamics with the behavior of the Ne-OCS((1)Sigma) and Ar-NO((2)Pi) systems. A comparison with the close-coupling calculations available for the latter system [Chem. Phys. Lett. 313, 491 (1999)] demonstrates the model's ability to qualitatively explain the field dependence of all the scattering features observed.     

A further test of the shape and anisotropy of the F---H2 interaction potential

A recently proposed anisotropic potential model for the interaction of a fluorine atom with a hydrogen molecule treated as a rigid rotor analysed by carrying out exact quantum calculations of elastic and rotationally inelastic differential cross sections for comparison with previoully reported F---H₂ and newly measured F---D₂ state selected measurements. The sensitivity of the cross sections to changes of the potential anisotropy and to isotopic substitution is examined. The results provide specific indications on the features of the best potential energy surface in terms of its average ‘size’ and its most likely anisotropy responsible for inelastic rotational excitations occuring at collision energies of about 85 meV.