Product Vibrational Distributions Research Articles

Probing the rate-determining region of the potential energy surface for a prototypical ion-molecule reaction.

We report a joint experimental-theoretical study of the F- + HCl → HF + Cl- reaction kinetics. The experimental measurement of the rate coefficient at several temperatures was made using the selected ion flow tube method. Theoretical rate coefficients are calculated using the quasi-classical trajectory method on a newly developed global potential energy surface, obtained by fitting a large number of high-level ab initio points with augmentation of long-range electrostatic terms. In addition to good agreement between experiment and theory, analyses suggest that the ion-molecule reaction rate is significantly affected by shorter-range interactions, in addition to the traditionally recognized ion-dipole and ion-induced dipole terms. Furthermore, the statistical nature of the reaction is assessed by comparing the measured and calculated HF product vibrational state distributions to that predicted by the phase space theory.This article is part of the theme issue 'Modern theoretical chemistry'.

A velocity-map imaging study of methyl non-resonant multiphoton ionization from the photodissociation of CH3I in the A-band.

Chemical reaction dynamics and, particularly, photodissociation in the gas phase are generally studied using pump-probe schemes where a first laser pulse induces the process under study and a second one detects the produced fragments. Providing an efficient detection of ro-vibrationally state-selected photofragments, the resonance enhanced multiphoton ionization (REMPI) technique is, without question, the most popular approach used for the probe step, while non-resonant multiphoton ionization (NRMPI) detection of the products is scarce. The main goal of this work is to test the sensitivity of the NRMPI technique to fragment vibrational distributions arising from molecular photodissociation processes. We revisit the well-known process of methyl iodide photodissociation in the A-band at around 280 nm, using the velocity-map imaging technique in conjunction with NRMPI of the methyl fragment. The detection wavelength, carefully selected to avoid any REMPI transition, was scanned between 325 and 335 nm seeking correlations between the different observables-the product vibrational, translational and angular distributions-and the excitation wavelength of the probe laser pulse. The experimental results have been discussed on the base of quantum dynamics calculations of photofragment vibrational populations carried out on available ab initio potential-energy surfaces using a four-dimensional model.This article is part of the themed issue 'Theoretical and computational studies of non-equilibrium and non-statistical dynamics in the gas phase, in the condensed phase and at interfaces'.

Quasi-classical trajectory study of the reaction dynamics of calcium ground state and metastable atoms with CH2Cl2

The dynamics properties of the Ca(1S0,3P) + CH2Cl2 reaction system have been calculated by means of the quasi-classical trajectory method based on the extended London–Eyring–Polanyi–Sato potential energy surface. By the calculations, the vibrational distribution, reaction cross section, rotational alignment, and reaction rate constant are obtained. The peak location of vibrational quantum numbers is at ν = 0 when the collision energy is 2.302 kcal/mol, whether the calcium atom is at the ground state or metastable state. The product vibrational distribution agrees well with the experiment value in Han, K. L.; He, G. Z.; Lou, N. Q. Chem. Phys. Lett. 1991, 178, 528. The cross section thoroughly decreases with the increase of the collision energy. The rotational alignment of the product greatly deviates from –0.5. The reaction rate constant increases with rising temperature.

Product Translational and Vibrational Distributions for the OH/OD + CH4/CD4 Reactions from Quasiclassical Trajectory Calculations. Comparison with Experiment.

For the OH + CH4/CD4 hydrogen abstraction reactions, the methyl radical (CH3 and CD3) product translational distributions and the water (H2O and HOD) product vibrational distributions experimentally reported by Liu's group are reproduced by quasi-classical trajectory (QCT) calculations on an analytical full-dimensional potential energy surface when a quantum spirit is included in the analysis. Our simulations correctly predict: (i) the vibrational excitation of the water product, (ii) the inversion of the water vibrational population, and (iii) the propensity of transfer from reactant kinetic energy to product translational energy. These reactions therefore present a marked isotopic effect. In addition, the water product vibrational distributions for the OH/OD + CH4 reactions agree reasonably well with Butkovskaya and Setser's experiments for a similar alkane reaction. The theory/experiment agreement is better for the HOD than for the H2O product due to the mode coupling in the H2O molecule, which is absent in the HOD stretching modes, which show a more "local" character. In summary, for polyatomic systems with many degrees of freedom (15 in the present reaction), QCT calculations analyzed with a quantum spirit represent a useful alternative to quantum scattering methods.

F+DClCl+DF REAKSİYONU İÇİN DALGA PAKETİ METODU KULLANILARAK BAĞ DURUMLARININ VE BİREYSEL KUANTUM SEVİYELERİ ARASINDAKİ SAÇILMALARIN HESAPLANMASI

Accurate state-to-state quantum wave packet calculations of integral cross sections for the title reaction are presented. Calculations are carried out on the best available ground 12A' global adiabatic potential energy surface of Deskevich et. al.[1]. Converged state-to-state wave packet reaction cross sections with the DCl (v=0, j=0-1; v=1, j=0) reagent have been calculated for the collision energy range from threshold up to 0.5 eV. Accurate product vibrational and rotational distributions of cross sections have been calculated at selected collision energies. State-to-state and total initial-state resolved rate constants of the title reaction have been calculated in a temperature range of 100-300 K. The present accurate calculations at v=0, j=0, J=0 show noticeable differences with previous calculations for the F+HCl reaction. Assuming the reaction coordinate in the F-Cl distance and to estimate the zero point energy in the orthogonal coordinate we have calculated the bound states along the reaction path for frozen F-Cl distance to interpret the results.

Ultracold chemistry with alkali-metal–rare-earth molecules

A first principles study of the dynamics of $^6$Li($^{2}$S) + $^6$Li$^{174}$Yb($^2\Sigma^+$)$ \to ^6$Li$_2(^1\Sigma^+$) + $^{174}$Yb($^1$S) reaction is presented at cold and ultracold temperatures. The computations involve determination and analytic fitting of a three-dimensional potential energy surface for the Li$_2$Yb system and quantum dynamics calculations of varying complexities, ranging from exact quantum dynamics within the close-coupling scheme, to statistical quantum treatment, and universal models. It is demonstrated that the two simplified methods yield zero-temperature limiting reaction rate coefficients in reasonable agreement with the full close-coupling calculations. The effect of the three-body term in the interaction potential is explored by comparing quantum dynamics results from a pairwise potential that neglects the three-body term to that derived from the full interaction potential. Inclusion of the three-body term in the close-coupling calculations was found to reduce the limiting rate coefficients by a factor of two. The reaction exoergicity populates vibrational levels as high as $v=19$ of the $^6$Li$_2$ molecule in the limit of zero collision energy. Product vibrational distributions from the close-coupling calculations reveal sensitivity to inclusion of three-body forces in the interaction potential. Overall, the results indicate that a simplified model based on the long-range potential is able to yield reliable values of the total reaction rate coefficient in the ultracold limit but a more rigorous approach based on statistical quantum or quantum close-coupling methods is desirable when product rovibrational distribution is required.

A chirped-pulse Fourier-transform microwave/pulsed uniform flow spectrometer. I. The low-temperature flow system.

We report the development of a new instrument that combines chirped-pulse microwave spectroscopy with a pulsed uniform supersonic flow. This combination promises a nearly universal detection method that can deliver isomer and conformer specific, quantitative detection and spectroscopic characterization of unstable reaction products and intermediates, product vibrational distributions, and molecular excited states. This first paper in a series of two presents a new pulsed-flow design, at the heart of which is a fast, high-throughput pulsed valve driven by a piezoelectric stack actuator. Uniform flows at temperatures as low as 20 K were readily achieved with only modest pumping requirements, as demonstrated by impact pressure measurements and pure rotational spectroscopy. The proposed technique will be suitable for application in diverse fields including fundamental studies in spectroscopy, kinetics, and reaction dynamics.

Signatures of a conical intersection in photofragment distributions and absorption spectra: photodissociation in the Hartley band of ozone.

Photodissociation of ozone in the near UV is studied quantum mechanically in two excited electronic states coupled at a conical intersection located outside the Franck-Condon zone. The calculations, performed using recent ab initio PESs, provide an accurate description of the photodissociation dynamics across the Hartley/Huggins absorption bands. The observed photofragment distributions are reproduced in the two electronic dissociation channels. The room temperature absorption spectrum, constructed as a Boltzmann average of many absorption spectra of rotationally excited parent ozone, agrees with experiment in terms of widths and intensities of diffuse structures. The exit channel conical intersection contributes to the coherent broadening of the absorption spectrum and directly affects the product vibrational and translational distributions. The photon energy dependences of these distributions are strikingly different for fragments created along the adiabatic and the diabatic paths through the intersection. They can be used to reverse engineer the most probable geometry of the non-adiabatic transition. The angular distributions, quantified in terms of the anisotropy parameter β, are substantially different in the two channels due to a strong anticorrelation between β and the rotational angular momentum of the fragment O2.

The non-statistical dynamics of the ¹⁸O + ³²O₂ isotope exchange reaction at two energies.

The dynamics of the (18)O((3)P) + (32)O2 isotope exchange reaction were studied using crossed atomic and molecular beams at collision energies (E(coll)) of 5.7 and 7.3 kcal/mol, and experimental results were compared with quantum statistical (QS) and quasi-classical trajectory (QCT) calculations on the O3(X(1)A') potential energy surface (PES) of Babikov et al. [D. Babikov, B. K. Kendrick, R. B. Walker, R. T. Pack, P. Fleurat-Lesard, and R. Schinke, J. Chem. Phys. 118, 6298 (2003)]. In both QS and QCT calculations, agreement with experiment was markedly improved by performing calculations with the experimental distribution of collision energies instead of fixed at the average collision energy. At both collision energies, the scattering displayed a forward bias, with a smaller bias at the lower E(coll). Comparisons with the QS calculations suggest that (34)O2 is produced with a non-statistical rovibrational distribution that is hotter than predicted, and the discrepancy is larger at the lower E(coll). If this underprediction of rovibrational excitation by the QS method is not due to PES errors and/or to non-adiabatic effects not included in the calculations, then this collision energy dependence is opposite to what might be expected based on collision complex lifetime arguments and opposite to that measured for the forward bias. While the QCT calculations captured the experimental product vibrational energy distribution better than the QS method, the QCT results underpredicted rotationally excited products, overpredicted forward-bias and predicted a trend in the strength of forward-bias with collision energy opposite to that measured, indicating that it does not completely capture the dynamic behavior measured in the experiment. Thus, these results further underscore the need for improvement in theoretical treatments of dynamics on the O3(X(1)A') PES and perhaps of the PES itself in order to better understand and predict non-statistical effects in this reaction and in the formation of ozone (in which the intermediate O3* complex is collisionally stabilized by a third body). The scattering data presented here at two different collision energies provide important benchmarks to guide these improvements.

A detailed reactive cross section study of X + Li2 → Li + LiX, with X = H, D, T, and Mu.

In this work we apply quasiclassical trajectory theory to the X + Li2 → Li + LiX reactions, with X standing for H, D, T, and Mu, in order to determine dynamical properties such as state-to-state reactive cross-section, rotational, vibrational, and translational product distributions. By using the literature benchmark potential energy surface, we were able to predict the aforementioned dynamical property in remarkable qualitative agreement with data in the literature for the H + Li2 → Li + LiH channel. Particularly, our results points toward the well known cross section independence with ro-vibrational excitations for high excitation regimes. Since the methodology is known to be well suited for the other species, as we considered the same PES, our results are expected to be similarly accurate for D, T, and Mu. The present work consists on a significant progress in this area of research, since previous theoretical calculations-based on known potential energy surface-deviated from the experimental results.

Reaction Dynamics of Methane with F, O, Cl, and Br on ab Initio Potential Energy Surfaces

The bimolecular hydrogen abstraction reactions of methane with atoms have become benchmark systems to test and extend our knowledge of polyatomic chemical reactivity. We review the state-of-the-art methodologies for reaction dynamics computations of X + methane [X = F, O((3)P), Cl, Br] reactions, which consist of two key steps: (1) potential energy surface (PES) developments and (2) reaction dynamics computations on the PES using either classical or quantum methods. We briefly describe the permutationally invariant polynomial approach for step 1 and the quasiclassical trajectory method, focusing on the mode-specific polyatomic product analysis and the Gaussian binning (1GB) techniques, and reduced-dimensional quantum models for step 2. High-quality full-dimensional ab initio PESs and dynamical studies of the X + CH4 and CHD3 reactions are reviewed. The computed integral cross-sections, angular, vibrational, and rotational product distributions are compared with available experiments. Both experimental and theoretical findings shed light on the rules of mode-selective polyatomic reactivity.

Photodissociation of CO2between 13.540 eV and 13.678 eV

Photodissociation of CO2 is investigated between 13.540 eV and 13.678 eV using the time-sliced velocity-mapped ion imaging (TSVMI) apparatus that is combined with one-color and two-color pump-probe VUV + VUV and VUV + UV detection schemes by probing oxygen fragments at different levels. Several CO2 dissociation channels are directly observed from the ion images, namely CO(X (1)Σ(+)) + O((1)D), CO(X (1)Σ(+)) + O((1)S), CO(a (3)Π) + O((3)P), CO(a (3)Π) + O((1)D), CO(a' (3)Σ(+)) + O((3)P), CO(d (3)Δ) + O((3)P) and CO(e (3)Σ(-)) + O((3)P), whereas no CO(X (1)Σ(+)) + O((3)P) production has been found. The product kinetic energy distributions of these channels are reported for the first time. Possible dissociation mechanisms have been discussed based upon the product vibrational and rotational distributions.

Ultracold collisions of O(1D) and H2: The effects of H2 vibrational excitation on the production of vibrationally and rotationally excited OH

A quantum dynamics study of the O((1)D) + H2(v = 0 - 2, j = 0) system has been carried out using the potential energy surfaces of Dobbyn and Knowles [Mol. Phys. 91, 1107 (1997)]. A time-independent quantum mechanical method based on hyperspherical coordinates is adopted for the dynamics calculations. Energy dependent cross section, probability, and rate coefficients are computed for the elastic, inelastic, and reactive channels over collision energies ranging from the ultracold to thermal regimes and for total angular momentum quantum number J = 0. The effect of initial vibrational excitation of the H2 molecule on vibrational and rotational populations of the OH product is investigated as a function of the collision energy. Comparison of results for vibrational levels v = 0 - 2 of H2 demonstrates that the vibrational excitation of H2 and its non-reactive relaxation pathway play a minor role in the overall collisional outcome of O((1)D) and H2. It is also found that while the state-resolved product vibrational distributions are sensitive to the initial collision energy and H2 vibrational level, the product rotational distribution depicts an inverted population that is largely insensitive to initial conditions. Rate coefficients evaluated using a J-shifting approximation show reasonable agreement with available theoretical and experimental results suggesting that the J-shifting approximation may be used to evaluate the rate coefficients for O((1)D) + H2 reaction.

Classical dynamics of state-resolved hyperthermal O(3P) + H2O(1A1) collisions

Classical dynamics calculations are performed for O((3)P) + H2O((1)A1) collisions from 2 to 10 km s(-1) (4.1-101.3 kcal mol(-1)), focusing on product internal energies. Several methods are used to produce ro-vibrationally state-resolved product cross sections and to enforce zero-point maintenance from analysis of the classical trajectories. Two potential energy surfaces are used: (1) a recently developed set of global reactive surfaces for the three lowest triplet states which model OH formation, H elimination to make H + OOH, O-atom exchange, and collisional excitation and (2) a non-reactive surface used in past classical and quantum collision studies. Comparisons to these previous studies suggest that for H2O vibrational excitation, classical dynamics which include gaussian binning procedures and/or selected zero-point maintenance algorithms can produce results which approximate quantum scattering cross sections fairly well. Without these procedures, the classical cross sections can be many orders of magnitude greater than the quantum cross sections for exciting the bending vibration of H2O, especially near threshold. The classical cross section over-estimate is due to energy borrowing from stretching modes which dip below zero-point values. For results on the reactive surfaces, the present calculations show that at higher velocities there is an unusually large amount of product internal excitation. For OOH, where 40% of available collision energy goes into internal motion, the excited product vibrational and rotational energy distributions are relatively flat and values of the OOH rotational angular momentum exceed J = 100. Other product channel distributions show an exponential fall-off with energy consistent with an energy gap law. The present detailed distributions and cross sections can serve as a guide for future hyperthermal measurements of this system.

Quasiclassical calculation of the chemical reaction Ba+C3H7Br→BaBr+C3H7

The quasi-classical trajectory (QCT) method based on the extended London—Eyring—Polanyi—Sato potential energy surface is used to investigate the product vibrational distribution, angular distribution and angle-resolved kinetic distribution of the reaction Ba+C3H7Br→BaBr+C3H7 at 2.58 kcal/mol. The calculated results show that the product BaBr vibrational distribution is quite hot, the vibrational population peaks are located at v = 12, and the angular product distribution tends to backward scattering. The calculated angle-resolved kinetic distribution shows that the kinetic distribution is obviously related to angle. The QCT results are always qualitatively acceptable and sometimes even quantitatively.

A classical versus quantum mechanics study of the $$\hbox{OH}\,+\,\hbox{CO} \rightarrow\,\hbox{H}\,+\,\hbox{CO}_2$$ (J = 0) reaction

Quasiclassical trajectory calculations have been performed for the OH + CO reaction at zero total angular momentum and collision energies up to 0.4 eV. Calculations have been carried out on the same potential energy surface which was used for full-dimensional state-to-state quantum dynamical calculation. The resulting quasiclassical total reaction probability as well as the product rotational and vibrational distributions have been analyzed and compared with the outcomes of a pseudo-quantization treatment of the product vibrational energy. Energy-conserving classical trajectories reproduce fairly well all the quantum features but the oscillatory patterns, whereas this does not apply to the energy non-conserving ones. Total reaction probabilities obtained from quasiclassical calculations at several fixed total angular momentum are also compared with centrifugal sudden quantum results. These results have also allowed to investigate the effect of the total angular momentum on the translational energy and angular distributions of the products.

STATE-TO-STATE REACTION DYNAMICS OF THE D(H) + FO → OD(OH) + F REACTIONS ON THE LOWEST TWO TRIPLET STATES

Quasiclassical trajectory (QCT) calculations have been performed to investigate the reaction dynamics of the title reactions at a state-to-state level. The recently developed adiabatic potential energy surfaces (PESs) of the two triplet electronic states of 13A″ and 13A′ (Gómez-Carrasco S. et al., J Chem Phys121:4605, 2004; J Chem Phys123:114310, 2005) are employed in the present QCT calculations. Product vibrational and rotational state distributions have been calculated at three collision energies of 0.5, 0.7 and 0.9 eV. The product vibrational state distributions are found to be Gaussian distributions. Both the vibrational and rotational state distributions depend clearly on the isotope substitution, electronic PESs and collision energies. The observed phenomena are probably attributed to the competition of direct and indirect reactions.

Vibrational energy redistribution in catechol during ultraviolet photolysis

This article reports the striking interplay between the molecular structure and the photodissociation dynamics of catechol (a key dihydroxybenzene), identified using a combination of electronic spectroscopy, hydrogen (Rydberg) atom photofragment translational spectroscopy, density functional theory and second order approximate coupled cluster methods. We describe how the non-planar (C(1) symmetry) ← planar (C(s) symmetry) geometry change during S(1) (1(1)ππ*) ←S(0) excitation in catechol, as well as the presence of internal hydrogen bonding, can perturb the photodissociation dynamics relative to that of phenol (a monohydroxybenzene), particularly with respect to O-H bond fission via the lowest dissociative (1)πσ* state. For λ(phot) > 270 nm, O-H bond fission (of the non hydrogen bonded hydroxyl moiety) is deduced to proceed via H atom tunnelling from the photo-prepared 1(1)ππ* state into the lowest (1)πσ* state of the molecule. The vibrational energy distribution in the resulting catechoxyl product changes notably as λ(phot) is tuned on resonance with either the v' = 0, m(2)' = 1(+) or m(2)' = 2(+) torsional levels of the photo-prepared 1(1)ππ* state: the product state distribution is highly sensitive to the degree of OH torsional excitation (m(2)) prepared during photo-excitation. It is deduced that such torsional excitation can be redistributed very efficiently into ring puckering (and likely also in-plane ring stretch) vibrations as the molecule tunnels to its repulsive 1(1)πσ* state and dissociates. These observations can be rationalised by consideration of the photo-prepared nuclear wavefunctions. Analysis of the product vibrational energy distribution also reveals that the O-H bond strength of the non hydrogen bonded O-H moiety in catechol, D(0)(H-catechoxyl) ≤ 27 480 ± 50 cm(-1), ∼2500 cm(-1) lower than that of the sole O-H bond in bare phenol. As a consequence, the vertical excitation energy of the 1(1)πσ* state in catechol is reduced relative to that in phenol, yielding a particularly broad distribution of product vibrations for λ(phot) < 270 nm. This study highlights the interplay between molecular geometry and redistribution of vibrational energy during ultraviolet photolysis of phenols.

State-to-state quantum dynamics of the N(4S) + OH(X 2Π) → H(2S) + NO(X 2Π) reaction

Quantum state-to-state dynamics for the N((4)S) + OH(X( 2)Π) → H((2)S) + NO(X( 2)Π) reaction is reported on an accurate ab initio potential energy surface of the lowest triplet electronic state (a(3)A(")) of HNO∕HON. It was found that the reaction is dominated by long-lived resonances supported by the HNO and HON wells. Significant non-reactive scattering was observed, indicating substantial deviations from the statistical limit. Due to the large exothermicity of the reaction, the NO product has hot internal state distributions: its rotational state distribution is inverted and peaks near the highest accessible rotational level; and its vibrational state distribution extends to υ = 10 and decays monotonically with the vibrational quantum number. In particular, the predicted product vibrational distribution is in reasonably good agreement with experiment. The calculated differential cross section is dominated by scattering in both the forward and backward directions, consistent with the formation of reaction intermediates.

Classical versus quantum vibrational state distributions for the benchmark polyatomic reaction OH + D2: Checking the validity of the QCT method

We report quasi-classical trajectory (QCT) and exact quantum scattering (EQS) calculations on the title process performed on the Ochoa–Clary potential energy surface. Total angular momentum was kept at zero for simplicity’s sake. The product vibrational state distributions obtained from the two approaches are found to be in good agreement. In particular, the third most populated state is significantly less probable than observed experimentally for both methods. The present study tends to rule out the possible failure of the classical description as the source of the discrepancy with experimental measurements.