Reactive scattering of F+HD→HF(v,J)+D: HF(v,J) nascent product state distributions and evidence for quantum transition state resonances

Non-equilibrium dynamics at the gas-liquid interface: State-resolved studies of NO evaporation from a benzyl alcohol liquid microjet

First measurements of internal quantum-state distributions for nitric oxide (NO) evaporating from liquid benzyl alcohol are presented over a broad range of temperatures, performed by liquid-microjet techniques in an essentially collision-free regime, with rotational/spin-orbit populations in the ²Π_1/2,3/2 manifolds measured by laser-induced fluorescence. The observed rotational distributions exhibit highly linear (i.e., thermal) Boltzmann plots but notably reflect rotational temperatures (T_rot) as much as 30 K lower than the liquid temperature (T_jet). A comparable lack of equilibrium behavior is also noted in the electronic degrees of freedom but with populations corresponding to spin-orbit temperatures (T_SO) consistently higher than T_rot by ∼15 K. These results unambiguously demonstrate evaporation into a non-equilibrium distribution, which, by detailed-balance considerations, predict quantum-state-dependent sticking coefficients for incident collisions of NO at the gas-liquid interface. Comparison and parallels with previous experimental studies of NO thermal desorption and molecular-beam scattering in other systems are discussed, which suggests the emergence of a self-consistent picture for the non-equilibrium dynamics.

Crossed Molecular Beam Study of the H + HD → H2 + D Reaction at 0.60 and 1.26 eV Using the Near-Threshold Ionization Velocity Map Ion Imaging

By using the 1 + 1' near-threshold ionization velocity map ion imaging technique, state-to-state reactive differential cross sections have been measured for the H + HD → H₂ + D reaction. High-resolution images of the D products, with the rotational states of the H₂ co-products clearly resolved, were acquired at the collision energies of 0.60 and 1.26 eV, respectively. It is found that the angular distribution is predominantly backward-scattering at the collision energy of 0.60 eV. However, at 1.26 eV, where the collision energy is higher, the angular distribution becomes forward-backward-scattering. Notably, at both collision energies, the main peaks of backward-scattered products gradually shift from backward toward sideways direction as the rotational quantum number of H₂ increases. Moreover, in the forward direction, fast angular oscillations, which are induced by specific partial waves have also been observed at 1.26 eV. These features show a strong correlation between the product states and angular distributions and also indicate the unique role of partial waves in quantum reactive scattering.

Photodissociation transition states characterized by chirped pulse millimeter wave spectroscopy

The 193-nm photolysis of CH₂CHCN illustrates the capability of chirped-pulse Fourier transform millimeter-wave spectroscopy to characterize transition states. We investigate the HCN, HNC photofragments in highly excited vibrational states using both frequency and intensity information. Measured relative intensities of J = 1-0 rotational transition lines yield vibrational-level population distributions (VPD). These VPDs encode the properties of the parent molecule transition state at which the fragment molecule was born. A Poisson distribution formalism, based on the generalized Franck-Condon principle, is proposed as a framework for extracting information about the transition-state structure from the observed VPD. We employ the isotopologue CH₂CDCN to disentangle the unimolecular 3-center DCN elimination mechanism from other pathways to HCN. Our experimental results reveal a previously unknown transition state that we tentatively associate with the HCN eliminated via a secondary, bimolecular reaction.

The effect of nonadiabaticity on the C+ + HF reaction

The chemistry of fluorine in the interstellar medium is particularly simple, with only a few key species and important reactions. Of the latter, the rate of the reaction of C⁺ ions with HF is not well established but is one of the key reactions that sets the relative abundance of HF and the CF⁺ ion, the two fluorine-bearing species that have been observed in interstellar clouds. The C⁺ + HF → CF⁺ + H reaction proceeds through a deeply bound HCF⁺ well. In this work, statistical methods, namely, the statistical adiabatic channel method originally developed by Quack and Troe and the quantum statistical method of Manolopoulos and co-workers, are applied to compute the total cross section as a function of energy for this reaction. This reaction proceeds on the ground 1² A' potential energy surface (PES), and there are also two non-reactive PES's, 1² A″ and 2² A', correlating with the C⁺(² P _1/2,3/2) + HF reactants. Two sets of scattering calculations were carried out, namely, a single-surface calculation on the 1² A' PES and the one in which all three PES's and the spin-orbit splitting of C⁺ are included in the description of the entrance channel. In the latter, reactivity of the spin-orbit excited ² P _3/2 level can be computed, and not just assumed to be zero, as in the single-state adiabatic approximation.

Complex angular momentum theory of state-to-state integral cross sections: resonance effects in the F + HD → HF(v′ = 3) + D reaction

State-to-state reactive integral cross sections (ICSs) are often affected by quantum mechanical resonances, especially in the neighborhood of a reactive threshold.

Quantum state resolved scattering dynamics of F+HCl→HF(v,J)+Cl

State-to-state reaction dynamics of the reaction F+HCl-->HF(v,J)+Cl have been studied under single-collision conditions using an intense discharge F atom source in crossed supersonic molecular beams at Ecom=4.3(1.3) kcal/mol. Nascent HF product is monitored by shot-noise limited direct infrared laser absorption, providing quantum state distributions as well as additional information on kinetic energy release from high resolution Dopplerimetry. The vibrational distributions are highly inverted, with 34(4)%, 44(2)%, and 8(1)% of the total population in vHF=1, 2, and 3, respectively, consistent with predominant energy release into the newly formed bond. However, there is a small [14(1)%] but significant formation channel into the vHF=0 ground state, which is directly detectable for the first time via direct absorption methods. Of particular dynamical interest, both the HF(v=2,J) and HF(v=1,J) populations exhibit strongly bimodal J distributions. These results differ significantly from previous flow and arrested-relaxation studies and may signal the presence of microscopic branching in the reaction dynamics.

Breakdown of the Born-Oppenheimer Approximation in the F+ o -D 2 → DF + D Reaction

The reaction of F with H2 and its isotopomers is the paradigm for an exothermic triatomic abstraction reaction. In a crossed-beam scattering experiment, we determined relative integral and differential cross sections for reaction of the ground F(2P(3/2)) and excited F*(2P(1/2)) spin-orbit states with D2 for collision energies of 0.25 to 1.2 kilocalorie/mole. At the lowest collision energy, F* is approximately 1.6 times more reactive than F, although reaction of F* is forbidden within the Born-Oppenheimer (BO) approximation. As the collision energy increases, the BO-allowed reaction rapidly dominates. We found excellent agreement between multistate, quantum reactive scattering calculations and both the measured energy dependence of the F*/F reactivity ratio and the differential cross sections. This agreement confirms the fundamental understanding of the factors controlling electronic nonadiabaticity in abstraction reactions.

Exact quantum calculations of the kinetic isotope effect: cross sections and rate constants for the F+HD reaction and role of tunneling

In this paper we present integral cross sections (in the 5-220 meV collision energy range) and rate constants (in the 100-300 K range of temperature) for the F+HD reaction leading to HF+D and DF+H. The exact quantum reactive scattering calculations were carried out using the hyperquantization algorithm on an improved potential energy surface which incorporates the effects of open shell and fine structure of the fluorine atom in the entrance channel. The results reproduce satisfactorily molecular beam scattering experiments as well as chemical kinetics data for both the HF and DF channels. In particular, the agreement of the rate coefficients and the vibrational branching ratios with experimental measurements is improved with respect to previous studies. At thermal and subthermal energies, the rates are greatly influenced by tunneling through the reaction barrier. Therefore exchange of deuterium is shown to be penalized with respect to exchange of hydrogen, and the isotopic branching exhibits a strong dependence on translational energy. Also, it is found that rotational excitation of the reactant HD molecule enhances the production of HF and decreases the reactivity at the D end, obtaining insight on the reaction stereodynamics.

Theories of reactive scattering

This paper is an overview of the theory of reactive scattering, with emphasis on fully quantum mechanical theories that have been developed to describe simple chemical reactions, especially atom-diatom reactions. We also describe related quasiclassical trajectory applications, and in all of this review the emphasis is on methods and applications concerned with state-resolved reaction dynamics. The review first provides an overview of the development of the theory, including a discussion of computational methods based on coupled channel calculations, variational methods, and wave packet methods. Choices of coordinates, including the use of hyperspherical coordinates are discussed, as are basis set and discrete variational representations. The review also summarizes a number of applications that have been performed, especially the two most comprehensively studied systems, H+H2 and F+H2, along with brief discussions of a large number of other systems, including other hydrogen atom transfer reactions, insertion reactions, electronically nonadiabatic reactions, and reactions involving four or more atoms. For each reaction we describe the method used and important new physical insight extracted from the results.

A crossed-beam study of the F+HD→HF+D reaction: The resonance-mediated channel

This is the last report of our extensive studies on the title reaction. Presented here are the state-to-state differential cross section determinations at 11 collision energies, ranging from 1.30 to 4.53 kcal/mol. Together with previously reported results at six lower energies (0.4-1.18 kcal/mol), this perhaps represents one of the most comprehensive set of data from a single investigation for any chemical reaction. The information contents of this set of data are examined in detail, from which the dynamical consequences of reactive resonances are elucidated. Qualitative interpretations of some of the major findings are proposed. Observations that need further theoretical investigations for better physical understanding are pointed out.

Recent advances in crossed-beam studies of bimolecular reactions

A critical overview of the recent progress in crossed-beam reactive scattering is presented. This review is not intended to be an exhaustive nor a comprehensive one, but rather a critical assessment of what we have been learning about bimolecular reaction dynamics using crossed molecular beams since year 2000. Particular emphasis is placed on the information content encoded in the product angular distribution-the trait of a typical molecular beam scattering experiment-and how the information can help in answering fundamental questions about chemical reactivity. We will start with simple reactions by highlighting a few benchmark three-atom reactions, and then move on progressively to the more complex chemical systems and with more sophisticated types of measurements. Understanding what cause the experimental observations is more than computationally simulating the results. The give and take between experiment and theory in unraveling the physical picture of the underlying dynamics is illustrated throughout this review.

A crossed-beam study of the F+HD→DF+H reaction: The direct scattering channel

State-to-state differential cross sections of the title reaction are presented at four collision energies, ranging from 1.18 to 4.0 kcal /mol. Product angular distributions are predominantly backscattered at low energies and shift toward sideways (peaking near 150 degrees ) at higher energies. Experimental evidence for contributions from migratory trajectories was found in the more detailed angle-specific internal state distributions. The dynamics of this reaction is mostly governed by classical mechanics, and several major findings can qualitatively be rationalized. These "classical" behaviors serve as "references" and are to be contrasted to the attributes observed for the other isotopic product channel, HF+D, in a forthcoming paper.

Multireference configuration interaction calculations for the F(P2)+HCl→HF+Cl(P2) reaction: A correlation scaled ground state (1A′2) potential energy surface

This paper presents a new ground state (1 (2)A(')) electronic potential energy surface for the F((2)P)+HCl-->HF+Cl((2)P) reaction. The ab initio calculations are done at the multireference configuration interaction+Davidson correction (MRCI+Q) level of theory by complete basis set extrapolation of the aug-cc-pVnZ (n=2,3,4) energies. Due to low-lying charge transfer states in the transition state region, the molecular orbitals are obtained by six-state dynamically weighted multichannel self-consistent field methods. Additional perturbative refinement of the energies is achieved by implementing simple one-parameter correlation energy scaling to reproduce the experimental exothermicity (DeltaE=-33.06 kcalmol) for the reaction. Ab initio points are fitted to an analytical function based on sum of two- and three-body contributions, yielding a rms deviation of <0.3 kcalmol for all geometries below 10 kcalmol above the barrier. Of particular relevance to nonadiabatic dynamics, the calculations show significant multireference character in the transition state region, which is located 3.8 kcalmol with respect to F+HCl reactants and features a strongly bent F-H-Cl transition state geometry (theta approximately 123.5 degrees ). Finally, the surface also exhibits two conical intersection seams that are energetically accessible at low collision energies. These seams arise naturally from allowed crossings in the C(infinityv) linear configuration that become avoided in C(s) bent configurations of both the reactant and product, and should be a hallmark of all X-H-Y atom transfer reaction dynamics between ((2)P) halogen atoms.

Reactive scattering dynamics in atom+polyatomic systems: F+C2H6-->HF(v,J)+C2H5

State-to-state scattering dynamics of F+C2H6-->HF(v,J)+C2H5 have been investigated at Ecom=3.2(6) kcalmol under single-collision conditions, via detection of nascent rovibrationally resolved HF(v,J) product states with high-resolution infrared laser absorption methods. State-resolved Doppler absorption profiles are recorded for multiple HF(v,J) transitions originating in the v=0,1,2,3 manifold, analyzed to yield absolute column-integrated densities via known HF transition moments, and converted into nascent probabilities via density-to-flux analysis. The spectral resolution of the probe laser also permits Doppler study of translational energy release into quantum-state-resolved HF fragments, which reveals a remarkable linear correlation between (i) HF(v,J) translational recoil and (ii) the remaining energy available, Eavail=Etot-E(HF(v,J)). The dynamics are interpreted in the context of a simple impulsive model based on conservation of linearangular momentum that yields predictions in good agreement with experiment. Deviations from the model indicate only minor excitation of ethyl vibrations, in contrast with a picture of extensive intramolecular vibrational energy flow but consistent with Franck-Condon excitation of the methylene CH2 bending mode. The results suggest a relatively simple dynamical picture for exothermic atom+polyatomic scattering, i.e., that of early barrier dynamics in atom+diatom systems but modified by impulsive recoil coupling at the transition state between translationalrotational degrees of freedom.

Nonadiabatic reactant-product decoupling calculation for the F(P1∕22)+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.

Direct evaluation of the lifetime matrix by the hyperquantization algorithm: Narrow resonances in the F+H2 reaction dynamics and their splitting for nonzero angular momentum

We propose a new method for the direct and efficient evaluation of the Felix Smith's lifetime Q matrix for reactive scattering problems. Simultaneous propagation of the solution to a set of close-coupled equations together with its energy derivative allows one to avoid common problems pertinent to the finite-difference approach. The procedure is implemented on a reactive scattering code which employs the hyperquantization algorithm and the Johnson-Manolopoulos [J. Comput. Phys. 13, 455 (1973); J. Chem. Phys 85, 6425 (1986)] propagation to obtain the complete S matrix and scattering observables. As an application of the developed formalism, we focus on the total angular momentum dependence of narrow under-barrier resonances supported by van der Waals wells of the title reaction. Using our method, we fully characterize these metastable states obtaining their positions and lifetimes from Lorentzian fits to the largest eigenvalue of the lifetime matrix. Remarkable splittings of the resonances observed at J>0 are rationalized in terms of a hyperspherical model. In order to provide an insight on the decay mechanism, the Q-matrix eigenvectors are analyzed and the dominant channels populated during the decomposition of metastable states are determined. Possible relevance of the present results to reactive scattering experiments is discussed.

A resonance-mediated non-adiabatic reaction: F*(2P1/2) + HD --> HF(v' = 3) + D

The reaction of F(2P3/2,1/2) + HD --> HF(v' = 3) + D was investigated in a rotating-source, crossed-beam machine. The high translational energy resolution afforded by the Doppler-selected time-of-flight technique enabled us to distinguish the differential attributes of the HF(v' = 3) + D products of the ground state (2P3/2) reaction from those due to the spin-orbit excited (2P1/2) one. It was found that the F*(2P1/2) reactivity is significantly smaller than that for F(2P3/2), and the two state-to-state angular distributions exhibit remarkable similarities, though some differences were noted. Comparing the results with those concluded previously, we assert that both the adiabatic (F(2P3/2) + HD) and, in particular, the non-adiabatic (F*(2P1/2) + HD) reactions are predominantly mediated by a resonance mechanism for the formation of the HF(v' = 3) + D channel.

A time-dependent wave packet study of the vibronic and spin-orbit interactions in the dynamics of Cl(2P)+H2→HCl(X̃ 1Σg+)+H(2S) reaction

We investigate the vibronic and spin-orbit (SO) coupling effects in the state-selected dynamics of the title reaction with the aid of a time-dependent wave packet approach. The ab initio potential energy surfaces of Capecchi and Werner [Science 296, 715 (2002)] have been employed for this purpose. Collinear approach of the Cl((2)P) atom to the H(2) molecule splits the degeneracy of the (2)P state and gives rise to (2)Sigma and (2)Pi electronic states. These two surfaces form a conical intersection at this geometry. These states transform as 1 (2)A('), 1 (2)A("), and 2 (2)A('), respectively, at the nonlinear configurations of the nuclei. In addition, the SO interaction due to Cl atom further splits these states into (2)Sigma(1/2), (2)Pi(3/2), and (2)Pi(1/2) components at the linear geometry. The ground-state reagent Cl((2)P(3/2))+H(2) correlates with (2)Sigma(1/2) and (2)Pi(3/2), where as the SO excited reagent Cl(*)((2)P(1/2))+H(2) correlates with (2)Pi(1/2) at the linear geometry. In order to elucidate the impact of the vibronic and SO coupling effects on the initial state-selected reactivity of these electronic states we carry out quantum scattering calculations based on a flux operator formalism and a time-dependent wave packet approach. In this work, total reaction probabilities and the time dependence of electronic population of the system by initiating the reaction on each of the above electronic states are presented. The role of conical intersection alone on the reaction dynamics is investigated with a coupled two-state model and for the total angular momentum J=0 (neglecting the electronic orbital angular momentum) both in a diabatic as well as in the adiabatic electronic representation. The SO interaction is then included and the dynamics is studied with a coupled three-state model comprising six diabatic surfaces for the total angular momentum J=0.5 neglecting the Coriolis Coupling terms of the Hamiltonian. Companion calculations are carried out for the uncoupled adiabatic and diabatic surfaces in order to explicitly reveal the impact of two different surface coupling mechanisms in the dynamics of this prototypical reaction.

Dynamically weighted multiconfiguration self-consistent field: Multistate calculations for F+H2O→HF+OH reaction paths

A novel method of dynamically adjusted weighting factors in state-averaged multiconfiguration self-consistent-field calculations (SA-MCSCF) is described that is applicable to systems of arbitrary dimensionality. The proposed dynamically weighted approach automatically weights the relevant electronic states in each region of the potential energy surface, smoothly adjusting between these regions with an energy dependent functional. This method is tested on the F(2P)+H2O-->HF+OH(2Pi) reaction, which otherwise proves challenging to describe with traditional SA-MCSCF methods due to (i) different asymptotic degeneracies of reactant (threefold) and product (twofold) channels, and (ii) presence of low-lying charge transfer configurations near the transition state region. The smoothly varying wave functions obtained by dynamically weighted multiconfigurational self-consistent field represent excellent reference states for high-level multireference configuration interaction calculations and offer an ideal starting point for construction of multiple state potential energy surfaces.

Coherent control of resonance-mediated reactions: F+HD

Cross sections resulting from scattering that proceeds via an intermediate resonance are shown to be exceptionally controllable using a coherent superposition of only two initial states. Full quantum computations on F+HD(v=0;j=0,1)-->H+DF, D+HF, which exhibits a resonance in one of the reactive channels, support the formal arguments, showing that control is indeed vast. In this case the ratio of reactive integral cross sections can be altered by a factor of 62 (compared to a noncoherent factor of only 3.3), while the ratio of reactive differential cross sections can be altered by a factor of over 6000 (compared to a noncoherent factor of less than 7). These results constitute the first prediction of extensive quantum control in a collisional process.

The investigation of spin–orbit effect for the F(2P)+HD reaction

In this paper, we employ the time-dependent quantum wave packet method to study the reaction of F((2)P(3/2), (2)P(1/2)) with HD on the Alexander-Stark-Werner potential energy surface. The reaction probabilities and total integral cross sections of the spin-orbit ground and excited states for the two possible products of the system are calculated. Because the reaction channel of the excited spin-orbit state is closed at the resonance energy, the resonance feature does not appear in the reaction probabilities and cross section for the F((2)P(1/2))+HD(v=j=0)-->HF+D reaction, in contrast with that found for the ground spin--orbit state. We also compare the average cross sections of the two possible products with the experimental measurement. The resonance peak in the present average cross section for the HF+D product is slightly larger than the experimental result, but much smaller than that of the single-state calculations on the potential energy surface of Stark and Werner. It seems that the spin--orbit coupling would play a relatively important role in this reaction. Moreover, the isotope effects of the ground and excited spin--orbit states and the reactivity of the two product channels from the excited spin--orbit state are presented.

Quantum scattering calculations on chemical reactions

This review discusses recent quantum scattering calculations on bimolecular chemical reactions in the gas phase. This theory provides detailed and accurate predictions on the dynamics and kinetics of reactions containing three atoms. In addition, the method can now be applied to reactions involving polyatomic molecules. Results obtained with both time-independent and time-dependent quantum dynamical methods are described. The review emphasises the recent development in time-dependent wave packet theories and the applications of reduced dimensionality approaches for treating polyatomic reactions. Calculations on over 40 different reactions are described.