Evidence for excited spin-orbit state reaction dynamics in F+H2: theory and experiment

We describe fully quantum, time-independent scattering calculations of the F+H2-->HF+H reaction, concentrating on the HF product rotational distributions in v'=3. The calculations involved two new sets of ab initio potential energy surfaces, based on large basis set, multireference configuration-interaction calculations, which are further scaled to reproduce the experimental exoergicity of the reaction. In addition, the spin-orbit, Coriolis, and electrostatic couplings between the three quasidiabatic F+H2 electronic states are included. The calculated integral cross sections are compared with the results of molecular beam experiments. At low collision energies, a significant fraction of the reaction is due to Born-Oppenheimer forbidden, but energetically allowed reaction of F in its excited (2P 1/2) spin-orbit state. As the collision energy increases, the Born-Oppenheimer allowed reaction of F in its ground (2P 3/2) spin-orbit state rapidly dominates. Overall, the calculations agree reasonably well with the experiment, although there remains some disagreement with respect to the degree of rotational excitation of the HF(v'=3) products as well as with the energy dependence of the reactive cross sections at the lowest collision energies.     

Role of the F spin-orbit excited state in the F+HD reaction: contributions to the dynamical resonance

We report quantum mechanical calculations of excitation functions (relative reaction cross sections) for the F+HD reaction. We include three potential energy surfaces and an accurate treatment of all couplings (non-adiabatic, spin-orbit, and Coriolis). Comparison with experimental results [Dong, Lee, and Liu, J. Chem. Phys., 113, 3633 (2000)] show excellent agreement for the DF product channel and an improved but not perfect agreement for the HF product channel. In the former case, when weighted by the (16%) fractional population of the spin-orbit excited state (F(*)) in the beam, the overall reactivity of the F(*) is small (approximately 5%). For the HF product channel and with the same (16%) fractional weight, F(*) reactivity makes a contribution of approximately 12% in the high-energy tail of the resonance peak. As a result, averaging over the population of F spin-orbit states in the beam changes the shape of the resonance. The greater the fraction of F(*) in the beam, the less pronounced will be the resonance modulation of the reaction excitation function.     

Communication: non-adiabatic coupling and resonances in the F + H2 reaction at low energies

Quantum reactive scattering calculations on accurate potential energy surfaces predict that at energies below ～5 meV, the reaction of F atoms with H(2) is dominated by the Born-Oppenheimer (BO) forbidden reaction of the spin-orbit excited F((2)P(1∕2)) atom. This non-BO dominance is amplified by low-energy resonances corresponding to quasi-bound states of the HF(v = 3, j = 3) + H product channel. Neglect of non-adiabatic coupling between the electronic states of the F atom leads to a qualitatively incorrect picture of the reaction dynamics at low energy.     

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.     

Time-dependent quantum study of the kinetics of the H(2S) + FO(2II) OH(2II) + F(2P) reaction

Quantum mechanical wave packet calculations are carried out for the H((2)S) + FO((2)II) --> OH((2)II) + F((2)P) reaction on the adiabatic potential energy surface of the ground (3)A' triplet state. The state-to-state and state-to-all reaction probabilities for total angular momentum J = 0 have been calculated. The probabilities for J > 0 have been estimated from the J = 0 results by using J-shifting approximation based on a capture model. Then, the integral cross sections and initial state-selected rate constants have been calculated. The calculations show that the initial state-selected reaction probabilities are dominated by many sharp peaks. The reaction cross section does not manifest any sharp oscillations and the initial state-selected rate constants are sensitive to the temperature.     

A crossed molecular beam imaging study of the O(1D2)+HCl-->OH+Cl(2P J=3/2, 1/2) reaction.

A crossed molecular beam study is presented for the O((1)D(2))+HCl-->OH+Cl((2)P(J)) reaction at the collision energy of 6 kcal mol(-1). State-resolved doubly differential cross sections are obtained for the Cl((2)P(J=3/2) ) and Cl*((2)P(J=1/2) ) products by velocity-map ion imaging. Both products are slightly more forward scattered, which suggests a reaction mechanism without a long-lived intermediate in the ground electronic state. A small fraction (23 %) of the energy release into the translational degree of freedom indicates strong internal excitation of the counterpart OH radical. The contribution of the electronic excited states of O--HCl to the overall reaction is also examined from the doubly differential cross sections.     

Relativistic calculations of ground and excited states of LiYb molecule for ultracold photoassociation spectroscopy studies

We report a series of quantum-chemical calculations for the ground and some of the low-lying excited states of an isolated LiYb molecule by the spin-orbit multistate complete active space second-order perturbation theory (SO-MS-CASPT2). Potential energy curves, spectroscopic constants, and transition dipole moments (TDMs) at both spin-free and spin-orbit levels are obtained. Large spin-orbit effects especially in the TDMs of the molecular states dissociating to Yb((3)P(0,1,2)) excited states are found. To ensure the reliability of our calculations, we test five types of incremental basis sets and study their effect on the equilibrium distance and dissociation energy of the ground state. We also compare CASPT2 and CCSD(T) results for the ground state spectroscopic constants at the spin-free relativistic level. The discrepancies between the CASPT2 and CCSD(T) results are only 0.01 ? in equilibrium bond distance (R(e)) and 200 cm(-1) in dissociation energy (D(e)). Our CASPT2 calculation in the supermolecular state (R=100 a.u.) with the largest basis set reproduces experimental atomic excitation energies within 3% error. Transition dipole moments of the super molecular state (R=100 a.u.) dissociating to Li((2)P) excited states are quite close to experimental atomic TDMs as compared to the Yb((3)P) and Yb((1)P) excited states. The information obtained from this work would be useful for ultracold photoassociation experiments on LiYb.     

Stereodynamics of the F + HD(v = 0, j = 1) reaction: direct vs. resonant mechanisms

The stereodynamics and mechanism of the F + HD(v = 0, j = 1) → HF (DF) + D (H) reactions have been thoroughly analysed at collision energies in the 0-160 meV range. Specifically, this study is focused on (i) the comparison between the stereodynamics of the collisions leading to HF and DF formation, and (ii) the stereodynamical fingerprints of the resonance that occurs at low collision energies in the HF channel and whose manifestation in the total cross section is greatly diminished for initial j > 0. While previous studies were limited to the analysis of integral cross sections (ICS), differential cross sections (DCS) and reaction probabilities, in the present work we have included the analysis of vectorial quantities such as the direction of the initial rotational angular momentum and internuclear axis, and their effect on reactivity. In particular, polarisation parameters (PP) and polarisation dependent differential cross sections (PDDCS), quantities that describe how the intrinsic HD rotational angular momentum and molecular axis polarisations contribute to reaction, are calculated and examined. The evolution of the PPs with the collision energy differs markedly between the two reaction channels. For the DF channel, the PP values are small and change very little in the energy range in which DF formation is appreciable. In contrast, rapid fluctuations in the magnitude and sign of the PPs are observed in the HF channel at low collision energies in and around the resonance. As the collision energy increases, direct (non-resonant) scattering prevails, and the various quantities are reasonably well accounted for by the QCT calculations, as in the case of the DF channel. The intrinsic directional information has been used to access the extent of control that can be achieved through polarisation of the HD molecule prior to collision. It was found that the same extrinsic preparation leads to very different outcomes on the HF channel DCS when the collision energy is close to the resonance. It is also shown that polarisation of the HD internuclear axis along the initial relative velocity enhances the effect of the resonance and allows its clear identification. Finally, the effect of different extrinsic preparations on the angle-velocity DCS is found to be strong, thus allowing considerable control of product angular distributions.     

Real wave packet and flux analysis studies of the H + F2 → HF + F reaction

The H + F₂ → HF + F reaction on ground state potential energy surface is investigated using the quantum mechanical real wave packet and Flux analysis method based on centrifugal sudden approximation. The initial state selected reaction probabilities for total angular momentum J = 0 have been calculated by both methods while the probabilities for J > 0 have been calculated by Flux analysis method. The initial state selected reaction probabilities, integral cross sections and rate coefficients have been calculated for a broad range of collision energy. The results show a large rotational enhancement of the reaction probability. Some resonances were seen in the state‐to‐state reaction probabilities while state‐to‐all reaction probabilities and the reaction cross section do not manifest any oscillations and the initial state selected reaction rate constants are sensitive to the temperature. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

Nonadiabatic reactant-product decoupling calculation for the F(2P(1/2)) + H2 reaction

In this paper we present a theoretical study using time-dependent nonadiabatic reactant-product decoupling method for the state-to-state reactive scattering calculation of F((2)P(1/2))+H(2) (nu=j=0) reaction on the Alexander-Stark-Werner potential energy surface. In this nonadiabatic state-to-state calculation, the full wave function is partitioned into reactant component and a sum of all product components. The reactant and product components of the wave function are solved independently. For the excited state reaction, the state-to-state reaction probabilities for J=0.5 are calculated. Comparing the state-to-state reaction probabilities, it is found that the vibrational population of the HF product is dominated by vibrational levels nu=2 and 3. The rotation specific reaction probabilities of HF product in j=1 and 2 are larger than those in other rotational levels. As the rotation quantum number j increases, the positions of the peak in the rotational reaction probability of HF product in nu=3 shift to higher collision energy.     

Reduced dimensionality spin-orbit dynamics of CH3 + HCl ⇌ CH4 + Cl on ab initio surfaces

A reduced dimensionality quantum scattering method is extended to the study of spin-orbit nonadiabatic transitions in the CH(3) + HCl ? CH(4) + Cl((2)P(J)) reaction. Three two-dimensional potential energy surfaces are developed by fitting a 29 parameter double-Morse function to CCSD(T)/IB//MP2/cc-pV(T+d)Z-dk ab initio data; interaction between surfaces is described by geometry-dependent spin-orbit coupling functions fit to MCSCF/cc-pV(T+d)Z-dk ab initio data. Spectator modes are treated adiabatically via inclusion of curvilinear projected frequencies. The total scattering wave function is expanded in a vibronic basis set and close-coupled equations are solved via R-matrix propagation. Ground state thermal rate constants for forward and reverse reactions agree well with experiment. Multi-surface reaction probabilities, integral cross sections, and initial-state selected branching ratios all highlight the importance of vibrational energy in mediating nonadiabatic transition. Electronically excited state dynamics are seen to play a small but significant role as consistent with experimental conclusions.     

Differential Cross Sections for the H+D2O→HD+OD Reaction: a Full Dimensional State-to-State Quantum Dynamics Study

The time-dependent wave-packet method was employed to calculate the first full-dimensional state-to-state differential cross sections (DCS) for the title reaction with D₂O in the ground and the first symmetric (100) and asymmetric stretching (001) excited states. The calculated DCSs for these three initial states are strongly backward peaked at low collision energies. With the increase of collision energy, these DCSs become increasingly broader with the peak position shifting gradually to a smaller angle, consistent with the fact that the title reaction is a direct reaction via an abstraction mechanism. It is found that the (100) and (001) states not only have roughly the same integral cross sections, but also have essentially identical DCS, which are very close to that for the ground state at the same total energy of reaction. The reaction produces a small fraction of OD in the v=1 state, with the population close to the relative reactivity between the ground and vibrationally excited states, therefore confirming the experimental result of Zare et al. and the local mode picture[J. Phys. Chem. 97 , 2204 (1993)]. Unexpectedly, the stretching excitation reduces the rotation excitation of product HD at the same total energy.     

C-Cl bond fission dynamics and angular momentum recoupling in the 235 nm photodissociation of allyl chloride

The photodissociation dynamics of allyl chloride at 235 nm producing atomic Cl((2)P(J);J=1/2,3/2) fragments is investigated using a two-dimensional photofragment velocity ion imaging technique. Detection of the Cl((2)P(1/2)) and Cl((2)P(3/2)) products by [2+1] resonance enhanced multiphoton ionization shows that primary C-Cl bond fission of allyl chloride generates 66.8% Cl((2)P(3/2)) and 33.2% Cl((2)P(1/2)). The Cl((2)P(3/2)) fragments evidenced a bimodal translational energy distribution with a relative weight of low kinetic energy Cl((2)P(3/2))/high kinetic energy Cl((2)P(3/2)) of 0.097/0.903. The minor dissociation channel for C-Cl bond fission, producing low kinetic energy chlorine atoms, formed only chlorine atoms in the Cl((2)P(3/2)) spin-orbit state. The dominant C-Cl bond fission channel, attributed to an electronic predissociation that results in high kinetic energy Cl atoms, produced both Cl((2)P(1/2)) and Cl((2)P(3/2)) atomic fragments. The relative branching for this dissociation channel is Cl((2)P(1/2))/[Cl((2)P(1/2))+Cl((2)P(3/2))]=35.5%. The average fraction of available energy imparted into product recoil for the high kinetic energy products was found to be 59%, in qualitative agreement with that predicted by a rigid radical impulsive model. Both the spin-orbit ground and excited chlorine atom angular distributions were close to isotropic. We compare the observed Cl((2)P(1/2))/[Cl((2)P(1/2))+Cl((2)P(3/2))] ratio produced in the electronic predissociation channel of allyl chloride with a prior study of the chlorine atom spin-orbit states produced from HCl photodissociation, concluding that angular momentum recoupling in the exit channel at long interatomic distance determines the chlorine atom spin-orbit branching.     

Quantum Dynamics of Li+HF/DF Reaction Investigated by a State-to-State Time-dependent Wave Packet Approach

Using the reactant coordinate based time-dependent wave packet method, on the APW potential energy surface, the differential and integral cross sections of the Li+DF/HF(v=0, j=0, 1) reactions were calculated over the collision energy range from the threshold to 0.25 eV. The initial state-specified reaction rate constants of the title reaction were also calculated. The results indicate that, compared with the Li+DF reaction, the product LiF of Li+HF reaction is a little more rotationally excited but essentially similar. The initial rotational excitation from j=0 to 1 has little effect on the Li+DF reaction. However, the rotational excitation of DF does result in a little more rotationally excited product LiF. The different cross section of both reactions is forward biased in the studied collision energy range, especially at relatively high collision energy. The resonances in the Li+HF reaction may be identifiable as the oscillations in the product ro-vibrational state-resolved integral cross sections and backward scattering as a function of collusion energy. For the Li+HF reaction, the rate constant is not sensitive to the temperature and almost has no change in the temperature range considered. For the Li+DF reaction, the rate constant increase by a factor of about 10 in the temperature range of 100?300 K. Brief comparison for the total reaction probabilities and integral cross section of the Li+HF reaction has been carried out between ours and the values reported previously. The agreement is good, and the difference should come from the better convergence of our present calculations.     

Quantum dynamics study of Li + HF reaction

We report rigorous quantum dynamics studies of the Li + HF reaction using the time-dependent wavepacket approach. The dynamics study is carried out on a recent ab initio potential energy surface, and state-selected reaction probabilities and cross sections are calculated up to 0.4 eV of collision energy. Many long-lived resonances (as long as 10 ps) at low collision energies (below 0.1 eV) are uncovered from the dynamics calculation. These long-lived resonances play a dominant role in the title reaction at low collision energies (below 0.1 eV). At higher energies, the direct reaction process becomes very important. The reaction probabilities from even rotational states exhibit a different energy dependence than those from odd rotational states. Our calculated integral cross section exhibits a broad maximum near the collision energy of 0.26 eV with small oscillations superimposed on the broad envelope which is reminiscent of the underlying resonance structures in reaction probabilities. The energy dependence of the present CS cross section is qualitatively different from the simple J-shifting approximation, in which a monotonic increase of cross section with collision energy was obtained. Received: 8 January 1997 / Accepted: 14 January 1997     

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.     

Direct evidence for nonadiabatic dynamics in atom+polyatom reactions: crossed-jet laser studies of F+D2O-->DF+OD

Quantum-state-resolved reactive-scattering dynamics of F+D(2)O-->DF+OD have been studied at E(c.m.)=5(1) kcal/mol in low-density crossed supersonic jets, exploiting pulsed discharge sources of F atom and laser-induced fluorescence to detect the nascent OD product under single-collision conditions. The product OD is formed exclusively in the v(OD)=0 state with only modest rotational excitation ( =0.50(1) kcal/mol), consistent with the relatively weak coupling of the 18.1(1) kcal/mol reaction exothermicity into "spectator" bond degrees of freedom. The majority of OD products [68(1)%] are found in the ground ((2)Pi(32) (+/-)) spin-orbit state, which adiabatically correlates with reaction over the lowest and only energetically accessible barrier (DeltaE( not equal) approximately 4 kcal/mol). However, 32(1)% of molecules are produced in the excited spin-orbit state ((2)Pi(12) (+/-)), although from a purely adiabatic perspective, this requires passage over a DeltaE( not equal) approximately 25 kcal/mol barrier energetically inaccessible at these collision energies. This provides unambiguous evidence for nonadiabatic surface hopping in F+D(2)O atom abstraction reactions, indicating that reactive-scattering dynamics even in simple atom+polyatom systems is not always isolated on the ground electronic surface. Additionally, the nascent OD rotational states are well fitted by a two-temperature Boltzmann distribution, suggesting correlated branching of the reaction products into the DF(v=2,3) vibrational manifold.     

Reactions of C(1D) with H2 and its deuterated isotopomers, a wave packet study

Using a Chebyshev wave packet method, total and state-resolved reaction probabilities (J=0) were calculated for the reactions of C(1D) with various hydrogen isotopomers (H2, D2, and HD, nu i=0, j i=0) on a recent ab initio potential energy surface. For all the isotopic variants, it was found that the initial state specified reaction probabilities have no energy threshold and are strongly oscillatory, indicative of the involvement of long-lived resonances in this barrierless reaction. The J=0 product vibrational and rotational distributions for all three isotopic reactions, and the CH/CD branching ratio for the C+HD reaction, show strong dependence on the collision energy, further underscoring the important role played by the resonances. The generally decaying vibrational distributions and highly excited rotational distributions, which corroborate an insertion mechanism, and the dominance of the CD+H channel in the C+HD reaction are consistent with existing experimental observations. Initial state specified integral cross sections and rate constants were estimated using a capture model. The estimated rate constants were found to be close and in the order kHD>kH2>kD2. Finally, a method to calculate branching ratio in the C+HD reaction is proposed.     

Seven-dimensional quantum dynamics study of the H+NH3-->H2+NH2 reaction

Initial state-selected time-dependent wave packet dynamics calculations have been performed for the H+NH3-->H2+NH2 reaction using a seven-dimensional model and an analytical potential energy surface based on the one developed by Corchado and Espinosa-Garcia [J. Chem. Phys. 106, 4013 (1997)]. The model assumes that the two spectator NH bonds are fixed at their equilibrium values. The total reaction probabilities are calculated for the initial ground and seven excited states of NH3 with total angular momentum J=0. The converged cross sections for the reaction are also reported for these initial states. Thermal rate constants are calculated for the temperature range 200-2000 K and compared with transition state theory results and the available experimental data. The study shows that (a) the total reaction probabilities are overall very small, (b) the symmetric and asymmetric NH stretch excitations enhance the reaction significantly and almost all of the excited energy deposited was used to reduce the reaction threshold, (c) the excitation of the umbrella and bending motion have a smaller contribution to the enhancement of reactivity, (d) the main contribution to the thermal rate constants is thought to come from the ground state at low temperatures and from the stretch excited states at high temperatures, and (e) the calculated thermal rate constants are three to ten times smaller than the experimental data and transition state theory results.