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).     

The effect of parity conservation on the spin-orbit conserving and spin-orbit changing differential cross sections for the inelastic scattering of NO(X) by Ar

The fully Λ-doublet resolved state-to-state differential cross sections (DCSs) for the collisions of NO(X, (2)Π, v = 0, j = 0.5) with Ar have been shown to depend sensitively on the conservation of the total parity of the NO molecular wavefunction. Parity changing collisions exhibit a single maximum only in the DCS, while parity conserving transitions exhibit multiple rainbow peaks. This behaviour is shown to arise directly from the constructive or destructive interference of collisions impacting on the two pointed ends and on the flatter middle of the NO molecule. A simple hard shell, four path model has been employed to determine the relative phase shifts of the paths contributing to the scattering amplitude. The model calculations using the V(sum) potential, together with the results of a quasi-quantum treatment, provide good qualitative agreement with the experimental spin-orbit conserving (Δ? = 0) DCSs, suggesting that the dynamics for all but the lowest Δj transitions are determined largely by the repulsive part of the potential. The collisions leading to spin-orbit changing transitions (Δ? = 1) have been also found to be dominated by repulsive forces, even for the lowest Δj values. However, they are less well reproduced by hard shell calculations, because of the crucial participation of the V(diff) potential in determining the outcome of these collisions.     

Fully Λ-doublet resolved state-to-state differential cross-sections for the inelastic scattering of NO(X) with Ar

Fully Λ-doublet resolved state-to-state differential cross-sections (DCSs) for the collisions of the open-shell NO(X, (2)Π(1/2), ν = 0, j = 0.5) molecule with Ar at a collision energy of 530 cm(-1) are presented. Initial state selection of NO(X, (2)Π(1/2), j = 0.5, f) was performed using a hexapole so that the (low field seeking) parity of ε = -1, corresponding to the f component of the Λ-doublet, could be selected uniquely. Although the Λ-doublet levels lie very close in energy to one another and differ only in their relative parities, they exhibit strikingly different DCSs. Both spin-orbit conserving and spin-orbit changing collisions have been studied, and the previously unobserved structures in the fully quantum state-to-state resolved DCSs are shown to depend sensitively on the change in parity of the wavefunction of the NO molecule on collision. In all cases, the experimental data are shown to be in excellent agreement with rigorous quantum mechanical scattering calculations.     

Doublet rotational energy transfer of the SH (X ²Π, v'=0) state by collisions with Ar

The rotational energy transfer (RET) by Ar collisions within the SH X?(2)Π (v' = 0, J' = 0.5-10.5) state is characterized. The integral cross sections as a function of collision energy for each rotational transition are calculated using a quantum scattering method in which the constructed potential energy functions are based on a ground state potential energy surface (PES) reported previously. On the other hand, a laser-induced excitation fluorescence technique is employed to monitor the relaxation of the rotational population as a function of photolysis-probe delay time following the photodissociation of H(2)S at 248 nm. The rotational population evolution is comparable to its theoretical counterpart based on calculated Λ-resolved RET rate constants. The propensity in Λ-resolved RET transitions is found to approximately resemble the case of OH(X?(2)Π, v' = 0) + Ar. The Λ-averaged RET collisions are also analyzed and result in several propensity rules in the transitions. Most propensity rules are similar to those observed in the collisions of SH(A?(2)Σ(+)) by Ar. However, the behavior of the conserving ratio, defined as rate constants for spin-orbit conserving transition divided by those for spin-orbit changing transition, shows distinct difference from those described by Hund's case (b).     

Inelastic state-to-state scattering of OH (2Pi3/2, J=3/2,f) by HCl

Parity resolved state-to-state cross sections for inelastic scattering of OH (X2Pi) by HCl were measured in a crossed molecular beam experiment at the collision energy of 920 cm(-1). The OH (X2Pi) radicals were prepared in a single quantum state, Omega=3/2, J=3/2, MJ=3/2, f, by means of electrostatic state selection in a hexapole field. The rotational distribution of the scattered OH radicals by HCl was probed by saturated LIF spectroscopy of the 0-0 band of the A 2Sigma+ - X 2Pi transition. Relative state-to-state cross sections were measured for rotational excitations up to J=9/2 within the Omega=3/2 spin-orbit manifold and up to J=7/2 within the Omega=1/2 spin-orbit manifold. A propensity for spin-orbit conserving transitions was found, but no propensity for excitation into a particular Lambda-doublet component of the same rotational state was evident. The data are presented and discussed in comparison with results previously obtained for collisions of OH with CO (Ecoll=450 cm(-1)) and N2 (Ecoll=410 cm(-1)) and with new data we have measured for the OH+CO system at a comparable collision energy (Ecoll=985 cm(-1)). This comparison suggests that the potential energy surface (PES) governing the interaction between OH and HCl is more anisotropic than the PES's governing the intermolecular interaction of OH with CO and N2.     

Differential cross sections for collisions of hexapole state-selected NO with He

The first measurements of differential inelastic collision cross sections of fully state-selected NO (j=12, Omega=12, epsilon= -1) with He are presented. Full state selection is achieved by a 2 m long hexapole, which allows for a systematic study of the effect of parity conservation and breaking on the differential cross section. The collisionally excited NO molecules are detected using a resonant (1+1') REMPI ionization scheme in combination with the velocity-mapped, ion-imaging technique. The current experimental configuration minimizes the contribution of noncolliding NO molecules in other rotational states j, Omega, epsilon--that contaminates images--and allows for study of the collision process at an unprecedented level of detail. A simple method to correct ion images for collision-induced alignment is presented as well and its performance is demonstrated. The present results show a significant difference between differential cross sections for scattering into the upper and lower component of the Lambda-doublet of NO. This result cannot be due to the energy splitting between these components.     

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.     

Differential cross sections for H + D2 → HD(v' = 2, j' = 0,3,6,9) + D at center-of-mass collision energies of 1.25, 1.61, and 1.97 eV

We have measured differential cross sections (DCSs) for the reaction H + D(2) → HD(v' = 2,j' = 0,3,6,9) + D at center-of-mass collision energies E(coll) of 1.25, 1.61, and 1.97 eV using the photoloc technique. The DCSs show a strong dependence on the product rotational quantum number. For the HD(v' = 2,j' = 0) product, the DCS is bimodal but becomes oscillatory as the collision energy is increased. For the other product states, they are dominated by a single peak, which shifts from back to sideward scattering as j' increases, and they are in general less sensitive to changes in the collision energy. The experimental results are compared to quantum mechanical calculations and show good, but not fully quantitative agreement.     

Three-vector correlation in statistical reactions: the role of the triatomic parity

This article presents a methodology for the determination of the k-j-k' three-vector correlation assuming a statistical model for atom-diatom reactions; k and k' are the reagent-approach and product-recoil directions, respectively, and j is the rotational angular momentum of the reagent diatomic. Although the polarization of reagent angular momentum is in most cases negligible, conservation of the triatomic parity imposes a certain polarization for some combinations involving low reagent and product rotational states. Statistical and quantum-mechanical polarization-dependent differential cross sections were calculated for the barrierless D(+) + H(2)(v = 0,j) → HD(v' = 0,j') + H(+) reaction. The agreement between the two is in most cases excellent, confirming the statistical character of the reaction at low and moderate collision energies.     

Vibrational and rotational cooling of NO+ in collisions with He

A quantum mechanical investigation of the vibrational and rotational deactivation of NO(+) in collisions with He atoms in the cold and ultracold regime is presented. Ab initio potential energy calculations are carried out at BCCD(T) level and a new global 3D potential energy surface (PES) is obtained by fitting ab initio points within the reproducing kernel Hilbert space method. As a first test of this PES the bound state energies of the (3)He-NO(+) and (4)He-NO(+) complexes are calculated and compared to previous rigid rotor calculations. The efficiency of the vibrational and the rotational cooling of this molecular ion using a buffer gas of helium is then investigated by performing close coupling scattering calculations for collision energy ranging from 10(-6) to 2000 cm(-1). The calculations are performed for the two isotopes (3)He and (4)He and the results are compared to the available experimental data.     

Measurements and quasi-quantum modeling of the steric asymmetry and parity propensities in state-to-state rotationally inelastic scattering of NO (2Pi1/2) with D2

Relative integrated cross sections are measured for spin-orbit-conserving, rotationally inelastic scattering of NO (2Pi1/2), hexapole-selected in the upper Lambda-doublet level of the ground rotational state (j = 0.5), in collisions with D2 at a nominal energy of 551 cm-1. The final state of the NO molecule is detected by laser-induced fluorescence (LIF). The state-selected NO molecule is oriented with either the N end or the O end toward the incoming D2 molecule by application of a static electric field E in the scattering region. This field is directed parallel or antiparallel to the relative velocity vector v. Comparison of signals taken for the different applied field directions gives the experimental steric asymmetry SA, defined by SA = (sigma v upward arrow downward arrow E - sigma v upward arrow upward arrow E)/(sigma v upward arrow downward arrow E + sigma v upward arrow upward arrow E), which is equal to within a factor of -1 to the molecular steric effect, Si-->f identical with (sigmaD2-->NO - sigmaD2-->ON)/(sigmaD2-->NO + sigmaD2-->ON). The dependence of the integral inelastic cross section on the incoming Lambda-doublet component is also measured as a function of the final rotational (jfinal) and Lambda-doublet (epsilonfinal) state. The measured steric asymmetries are similar to those previously observed for NO-He scattering. Spin-orbit manifold-conserving collisions exhibit a larger propensity for parity conservation than their NO-He counterparts. The results are interpreted in the context of the recently developed quasi-quantum treatment (QQT) of rotationally inelastic scattering [Gijsbertsen, A.; Linnartz, H.; Taatjes, C. A.; Stolte, S. J. Am. Chem. Soc. 2006, 128, 8777]. The QQT predictions can be inverted to obtain a fitted hard-shell potential that reproduces the experimental steric asymmetry; this fitted potential gives an empirical estimate of the anisotropy of the repulsive interaction between NO and D2. QQT computation of the differential cross section using this simple model potential shows reasonable agreement with the measured differential cross sections.     

Influence of collision energy and reagent rotation on the cross sections and product polarizations of the reaction F + HCl

Quasiclassical trajectory calculations have been carried out for the F+HCl reaction in three dimensions on a recent DHSN PES of the ground 1(2)A' electronic state [M. P. Deskevich, M. Y. Hayes, K. Takahashi, R. T. Skodje, and D. J. Nesbitt, J. Chem. Phys. 124, 224303 (2006)]. The effects of the collision energy and the reagent initial rotational excitation on the cross sections and product polarization are studied for the v = 0 and j ≤ 10 states of HCl over a wide collision energy range. It has been found that either the collision energy or the HCl rotational excitation increase remarkably reaction cross sections. The QCT-calculated integral cross sections are in good agreement with previous QM results. A detailed study on product polarization for the title reaction is also performed. The calculated results show that the product rotational angular momentum j' is not only aligned, but also oriented along the direction perpendicular to the scattering plane. The orientation of the HF product rotational angular momentum vector j' depends very sensitively on the collision energy and also affected by the reagent rotation. The theoretical findings and especially the roles of the collision energy and initial rotational momentum on the product polarization are discussed and reasonably explained by the HLH mass combination, the property of the PES, as well as the reactive mechanism.     

Resolution of angular rotational rainbows in Na2 + Ne,Ar collisions

State-to-state dfferential cross sections for rotational excitation in Na₂-Ne collisions have been measured and the characteristics of such processes involving repulsive surfaces demonstrated. The rotational rainbow maxima shift to larger scattering angles and broaden as the angular momentum transfer increases. Good agreement with IOS calculations is found. Results for Na₂-Ar are included.     

Spin-orbit relaxation of Cl(2P1/2) and F(2P1/2) in a gas of H2

The authors present quantum scattering calculations of rate coefficients for the spin-orbit relaxation of F(2P1/2) atoms in a gas of H2 molecules and Cl(2P1/2) atoms in a gas of H2 and D2 molecules. Their calculation of the thermally averaged rate coefficient for the electronic relaxation of chlorine in H2 agrees very well with an experimental measurement at room temperature. It is found that the spin-orbit relaxation of chlorine atoms in collisions with hydrogen molecules in the rotationally excited state j=2 is dominated by the near-resonant electronic-to-rotational energy transfer accompanied by rotational excitation of the molecules. The rate of the spin-orbit relaxation in collisions with D2 molecules increases to a great extent with the rotational excitation of the molecules. They have found that the H2/D2 isotope effect in the relaxation of Cl(2P1/2) is very sensitive to temperature due to the significant role of molecular rotations in the nonadiabatic transitions. Their calculation yields a rate ratio of 10 for the electronic relaxation in H2 and D2 at room temperature, in qualitative agreement with the experimental measurement of the isotope ratio of about 5. The isotope effect becomes less significant at higher temperatures.     

An investigation of nonadiabatic interactions in Cl(2Pj) + D2 via crossed-molecular-beam scattering

We have determined limits on the cross section for both electronically nonadiabatic excitation and quenching in the Cl((2)P(j)) + D(2) system. Our experiment incorporates crossed-molecular-beam scattering with state-selective Cl((2)P(12,32)) detection and velocity-mapped ion imaging. By colliding atomic chlorine with D(2), we address the propensity for collisions that result in a change of the spin-orbit level of atomic chlorine either through electronically nonadiabatic spin-orbit excitation Cl((2)P(32)) + D(2)-->Cl(*)((2)P(12)) + D(2) or through electronically nonadiabatic spin-orbit quenching Cl(*)((2)P(12)) + D(2)-->Cl((2)P(32)) + D(2). In the first part of this report, we estimate an upper limit for the electronically nonadiabatic spin-orbit excitation cross section at a collision energy of 5.3 kcal/mol, which lies above the energy of the reaction barrier (4.9 kcal/mol). Our analysis and simulation of the experimental data determine an upper limit for the excitation cross section as sigma(NA)< or =0.012 A(2). In the second part of this paper we investigate the propensity for electronically nonadiabatic spin-orbit quenching of Cl(*) following a collision with D(2) or He. We perform these experiments at collision energies above and below the energy of the reaction barrier. By comparing the amount of scattered Cl(*) in our images to the amount of Cl(*) lost from the atomic beam we obtain the maximum cross section for electronically nonadiabatic quenching as sigma(NA)< or =15(-15) (+44) A(2) for a collision energy of 7.6 kcal/mol. Our experiments show the probability for electronically nonadiabatic quenching in Cl(*) + D(2) to be indistinguishable to that for the kinematically identical system of Cl(*) + He.     

Rotational rainbow maxima: a time dependent study

The origin of rainbow-type maxima in the final rotational distribution of differential cross sections at fixed scattering angle is investigated in a time-dependent semiclassical (classical path) study. A maximum of fourty first-order, rotationally coupled differential equations are integrated numerically introducing the time dependence through an average trajectory determined by the spherically symmetric part of the potential surface. The rotational rainbow structures are explained by a simple mechanism coupling adjacent rotational states.     

The dynamics of reaction of Cl atoms with tetramethylsilane

Rotational state distributions and state-selected CM-frame angular distributions were measured for HCl (v' = 0, j') products from the reaction of Cl-atoms with tetramethylsilane (TMS) under single collision conditions at a collision energy, E(coll), of 8.2 +/- 2.0 kcal mol(-1). The internal excitation of these products was very low with only 2% of the total energy available partitioned into HCl rotation. A transition state with a quasi-linear C-H-Cl moiety structure was computed and used to explain this finding. A backward peaking differential cross section was also reported together with a product translational energy (T') distribution with a maximum at T' approximately E(coll). This scattering behaviour is accounted for by reactions proceeding through a tight transition state on a highly skewed potential energy surface, which favours collisions at low impact parameters with a strong kinematic constraint on the internal excitation of the products. The large Arrhenius pre-exponential factor previously reported for this reaction is reconciled with the tight differential scattering observed in our study by considering the large size of the TMS molecule.     

Rotational excitation by electron impact: a state selective study using laser-induced fluorescence

Angularly resolved pure rotational excitation of sodium dimers by intermediate energy electrons (150 to 300 eV) is studied using laser state selection technique, under nonresonant collision conditions. The experimental procedure, which is new to electron scattering, is described in detail. The experimental data show large rotational transitions and rotational rainbow structures. The relative cross sections agree well with the close coupling calculations and also with the spectator model predictions.     

Collision energy dependence of the HD(nu' = 2) product rotational distribution of the H + D2 reaction in the range 1.30-1.89 eV

An experimental and theoretical investigation of the collision energy dependence of the HD(nu' = 2,j') rotational product state distribution for the H + D2 reaction in the collision energy range of Ecol = 1.30-1.89 eV has been carried out. Theoretical results based on time-dependent and time-independent quantum mechanical methods agree nearly perfectly with each other, and the agreement with the experiment is good at low collision energies and very good at high collision energies. This behavior is in marked contrast to a previous report on the HD(nu' = 3,j') product state rotational distribution [Pomerantz et al., J. Chem. Phys. 120, 3244 (2004)] where a systematic difference between experiment and theory was observed, especially at the highest collision energies. The reason for this different behavior is not yet understood. In addition, this study employs Doppler-free spectroscopy to resolve an ambiguity in the E, F-X resonantly enhanced multiphoton ionization transition originating from the HD(nu' = 2,j' = 1) state, which is found to be caused by an accidental blending with the transition coming from the HD(nu' = 1,j' = 14) state.