Product Vibrational State Distributions Research Articles

Six-dimensional quantum dynamics of an Eley-Rideal reaction between gaseous and adsorbed hydrogen atoms on Cu(111).

In the form of direct abstraction of a surface adsorbate by a gaseous projectile, the Eley-Rideal (ER) reaction at the gas-surface interface manifests interesting dynamics. Unfortunately, high-dimensional quantum dynamical (QD) studies for ER reactions remain very challenging, which demands a large configuration space and the coordinate transformation of wavefunctions. Here, we report the first six-dimensional (6D) fully coupled quantum scattering method for studying the ER reaction between gas phase H(D) atoms and adsorbed D(H) atoms on a rigid Cu(111) surface. Reaction probabilities and product rovibrational state distributions obtained by this 6D model are found to be quite different from those obtained by reduced-dimensional QD models, demonstrating the high-dimensional nature of the ER reaction. Using two distinct potential energy surfaces (PESs), we further discuss the influence of the PES on the calculated product vibrational and rotational state distributions, in comparison with experimental results. The lateral corrugation and the exothermicity of the PES are found to play a critical role in controlling the energy disposal in the ER reaction.

Product State-Resolved Reactive Scattering Studies of the H + Cl2 (v0 = 1-3, j0 = 0) → HCl + Cl Reaction by the Time-Dependent Wave Packet Method.

The typical hydrogen atom plus halogen molecule reaction H + Cl2 → HCl + Cl has implications across many fields. In this paper, product state-resolved quantum dynamics calculations for the vibrationally excited reaction H + Cl2 (v0 = 1-3, j0 = 0) → HCl + Cl were conducted using the time-dependent wave packet method on a newly developed accurate potential energy surface. Numerical results indicate that the initial vibrational excitation of Cl2 does enhance the reactivity for this early barrier reaction, although less than the enhancement of the translational energy. The calculated product vibrational state-resolved integral cross sections and rate constants reveal that the product vibrational state distribution and the initial vibrational state of Cl2 are highly correlated. The thermal rate constant in the temperature range from 100 to 1000 K was given and is found to be in reasonable agreement with the experimental measurements.

Quantum state-to-state nonadiabatic dynamics of the charge transfer reaction H+ + NO(X2Π) → H + NO+(X1Σ+): Influence of ro-vibrational excitation of NO

Quantum state-to-state nonadiabatic dynamics of the charge transfer reaction H+ + NO(X2Π, vi = 1, 3, ji = 0, 1) → H + NO+(X1Σ+) has been studied based on the recently constructed diabatic potential energy matrix. It was found that the vibrational excitation of reactant NO inhibits the reactivity, while the rotational excitation of reactant NO has little effect on the reaction probability. These attributes were also observed in the semi-classical trajectory calculations employed in the adiabatic representation. Such an inhibitory effect of the vibrational excitation of reactant NO was owing to lower accessibility of the conical intersection and avoided crossing regions, which are located in the wells with respect to the Π diabat, as evidenced by the analysis of the population of the time-independent wave functions. Calculated vibrational state distributions of the product show that the decrease of the reaction mainly leads to the less formation of low vibrational states (vf < 6), and the product vibrational state distributions are more evenly populated for vi = 1 and 3, suggesting a non-statistical behavior. However, the overall shapes of the product rotational distributions remain unchanged, indicating that the redistribution of energy into the rotation of product NO is sufficient in the charge transfer process between H+ and NO. While the reaction is dominated by the forward and backward scattering in differential cross sections (DCSs), consistent with the complex-forming mechanism, a clear forward bias in the DCSs appears, indicating that the occurrence of the reaction is not sufficiently long to undergo the whole phase space of the interaction configurations.

Photodissociation dynamics of the ethyl radical via the Ã2A'(3s) state: H-atom product channels and ethylene product vibrational state distribution.

The photodissociation dynamics of jet-cooled ethyl radical (C2H5) via the Ã2A'(3s) states are studied in the wavelength region of 230-260nm using the high-n Rydberg H-atom time-of-flight (TOF) technique. The H + C2H4 product channels are reexamined using the H-atom TOF spectra and photofragment translational spectroscopy. A prompt H + C2H4(X̃1Ag) product channel is characterized by a repulsive translational energy release, anisotropic product angular distribution, and partially resolved vibrational state distribution of the C2H4(X̃1Ag) product. This fast dissociation is initiated from the 3s Rydberg state and proceeds via a H-bridged configuration directly to the H + C2H4(X̃1Ag) products. A statistical-like H + C2H4(X̃1Ag) product channel via unimolecular dissociation of the hot electronic ground-state ethyl (X̃2A') after internal conversion from the 3s Rydberg state is also examined, showing a modest translational energy release and isotropic angular distribution. An adiabatic H + excited triplet C2H4(ã3B1u) product channel (a minor channel) is identified by energy-dependent product angular distribution, showing a small translational energy release, anisotropic angular distribution, and significant internal excitation in the C2H4(ã3B1u) product. The dissociation times of the different product channels are evaluated using energy-dependent product angular distribution and pump-probe delay measurements. The prompt H + C2H4(X̃1Ag) product channel has a dissociation time scale of <10ps, and the upper bound of the dissociation time scale of the statistical-like H + C2H4(X̃1Ag) product channel is <5ns.

Quasi-Classical Trajectory Dynamics Study of the Reaction OH + H2S→H2O + SH and Its Isotopic Variants: Comparison with Experiment

The hydrogen abstraction reaction OH + H2S→H2O + SH plays an important role in acid rain formation, air pollution and climate change. In this work, the product energy disposals of the reaction and its isotopic variants OD + H2S and OD + D2S are calculated on a new ab-initio-based ground electronic state potential energy surface (PES) using the quasi-classical trajectory method. The PES is developed by fitting a total of 72,113 points calculated at the level of UCCSD(T)-F12a/aug-cc-pVTZ and using the fundamental invariant-neural network method, resulting in a total RMSE of 4.14 meV. The product H2O formed in the OH + H2S reaction at 298 K is found to be largely populated in the first overtone states of its symmetric and asymmetric stretching modes, while the vibrational distributions of the products HOD and D2O in the isotopically substituted reactions are visibly different. The computed product vibrational state distributions agree reasonably well with experimental results and are rationalized by the sudden vector projection model.

Reaction Pathway Control via Reactant Vibrational Excitation and Impact on Product Vibrational Distributions: The O + HO2 → OH + O2 Atmospheric Reaction.

Chemical reactions often have multiple pathways, the control of which is of fundamental and practical importance. In this Letter, we examine the dynamics of the O + HO2 → OH + O2 reaction, which plays an important role in atmospheric chemistry, using quasi-classical trajectories on a recently developed full-dimensional potential energy surface (PES). This reaction has two pathways leading to the same products: the H abstraction pathway (Oa + HObOc → OaH + ObOc) and the O abstraction pathway (Oa + HObOc → ObH + OaOc). Under thermal conditions, the reaction is dominated by the latter channel, which is barrierless, leading to vibrational excitation of the O2 product. However, we demonstrate that excitation of the HO2 reactant in its O-H (v1) vibrational mode results in dramatic switching of the reaction pathway to the activated H abstraction channel, which leads to a highly excited OH product vibrational state distribution. The implications of such dynamical effects in the atmospheric chemistry are discussed.

Non-adiabatic couplings induced complex-forming mechanism in H+MgH+ → Mg++H2 reaction

A chemical process may involve multiple adiabatic electronic states, and non-adiabatic couplings play an important role in the reaction mechanism. In this work, the effect of non-adiabatic couplings in the H+MgH+ → Mg+ + H2 reaction are studied using the time-dependent wave packet method and trajectory surface hopping method. The calculated results show that the reaction follows a direct abstraction process when the non-adiabatic couplings are neglected. However, when non-adiabatic couplings are included in the calculations, a long-lived excited state complex (MgH2+)* can be formed during the reaction. These direct and complex-forming reaction pathways are revealed by trajectory surface hopping calculations. The non-adiabatic couplings induced complex-forming mechanism not only increases the reactivity but also has significant effect on the product vibrational state distribution.

Product vibrational state distributions of F+CH3OH reaction on full-dimensional accurate potential energy surface

The hydrogen abstraction reaction of methanol with fluorine atoms can produce HF and CH3O or CH2OH radicals, which are important in the environment, combustion, radiation, and interstellar chemistry. In this work, the dynamics of this typical reaction is investigated by the quasi-classical trajectory method based on a recently developed globally accurate full-dimensional potential energy surface. Particularly, the vibrational state distributions of the polyatomic products CH3O and CH2OH are determined by using the normal mode analysis method. It is found that CH3O and CH2OH are dominantly populated in the ground state when the reactants are at the ground ro-vibrational state. The OH stretching mode, torsional mode, H2CO out-of-plane bending mode and their combination bands in the CH2OH product can be effectively excited once the OH stretching mode of the reactant CH3OH is excited to the first vibrationally excited state. Most of the available energy flows into the HF vibrational energy and the translational energy in both channels, while the radical products, CH3O or CH2OH, receive a small amount of energy, consistent with experiment, which is an indication of its spectator nature.

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'.

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.

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.

Quasi-Classical Trajectory–Gaussian Binning Study of the OH + D2 → HOD(v1′,v2′,v3′) + D Angle–Velocity and Vibrational Distributions at a Collision Energy of 0.28 eV

The angle-velocity and product vibrational state distributions for the OH + D(2) reaction at a collision energy of 0.28 eV have been calculated using the quasi-classical trajectory-gaussian binning (QCT-GB) method and the Wu-Schatz-Lendvay-Fang-Harding (WSLFH) analytical potential energy surface. Comparison with high resolution molecular beam experiments shows that, differing from what happens when using the standard QCT method (i.e., histogram binning), very good results are obtained for both distributions. Hence, the strong differences previously observed between QCT and experimental results mainly come from an inadequate pseudoquantization of HOD rather than from other quantum effects. This is probably the first time that such a high level of agreement between theory and high resolution experimental data has been found in polyatomic reaction dynamics.

Tunnelling under a conical intersection: Application to the product vibrational state distributions in the UV photodissociation of phenols

When phenol is photoexcited to its S(1) (1(1)ππ∗) state at wavelengths in the range 257.403 ≤ λ(phot) ≤ 275.133 nm the O-H bond dissociates to yield an H atom and a phenoxyl co-product, with the available energy shared between translation and well characterised product vibration. It is accepted that dissociation is enabled by transfer to an S(2) (1(1)πσ∗) state, for which the potential energy surface (PES) is repulsive in the O-H stretch coordinate, R(O-H). This S(2) PES is cut by the S(1) PES near R(O-H) = 1.2 Å and by the S(0) ground state PES near R(O-H) = 2.1 Å, to give two conical intersections (CIs). These have each been invoked-both in theoretical studies and in the interpretation of experimental vibrational activity-but with considerable controversy. This paper revisits the dynamic mechanisms that underlie the photodissociation of phenol and substituted phenols in the light of symmetry restrictions arising from torsional tunnelling degeneracy, which has been neglected hitherto. This places tighter symmetry constraints on the dynamics around the two CIs. The non-rigid molecular symmetry group G(4) necessitates vibronic interactions by a(2) modes to enable coupling at the inner, higher energy (S(1)/S(2)) CI, or by b(1) modes at the outer, lower energy (S(2)/S(0)) CI. The experimental data following excitation through many vibronic levels of the S(1) state of phenol and substituted phenols demonstrate the effective role of the ν(16a) (a(2)) ring torsional mode in enabling O-H bond fission. This requires tunnelling under the S(1)/S(2) CI, with a hindering barrier of ∼5000 cm(-1) and with the associated geometric phase effect. Quantum dynamic calculations using new ab initio PESs provide quantitative justification for this conclusion. The fates of other excited S(1) modes are also rationalised, revealing both spectator modes and intramolecular vibrational redistribution between modes. A common feature in many cases is the observation of an extended, odd-number only, progression in product mode ν(16a) (i.e., the parent mode which enables S(1)/S(2) tunnelling), which we explain as a Franck-Condon consequence of a major change in the active vibration frequency. These comprehensive results serve to confirm the hypothesis that O-H fission following excitation to the S(1) state involves tunnelling under the S(1)/S(2) CI-in accord with conclusions reached from a recent correlation of the excited state lifetimes of phenol (and many substituted phenols) with the corresponding vertical energy gaps between their S(1) and S(2) PESs.

Dynamics and mechanism of the non-adiabatic transitions from the ungerade I2(D0+u) state induced by collisions with rare gas atoms

The stepwise three-photon two-color laser excitation scheme is used for selective population of the first-tier ion-pair D0(+)(u) state of molecular iodine. Collection and analysis of the luminescence after the excitation of the v(D) = 6, 8, 13 and 18 vibronic levels of the D state in the pure iodine vapor and the gas-phase mixtures with He, Ar and Xe provide the total and, whenever possible, partial rate constants for the collision-induced non-adiabatic transitions to the other ion-pair states of the first tier. Comparison with the analogous data obtained previously for the non-adiabatic transitions from the E0(+)(g) state reveals the similarity between two cases. For He, the D ↔ E transitions are preferable, whereas for Ar and Xe transitions to the D' and β states dominate at v(D) = 6, 8 and 13, in accord with the statistical considerations. Efficient population of the δ state at v(D) = 18 in Ar and Xe is the most prominent non-statistical feature observed. The vibrational product state distributions for the D → E transitions are also obtained. In contrast to the previously studied E → D transition, they show significant positive vibronic energy transfer. The measurements for He and Ar are accompanied by the quantum scattering calculations that reproduce well the main qualitative features of the experimental results.

Real-time dissociation dynamics of the Ne2Br2 van der Waals complex

We have characterized the vibrational predissociation (VP) of the Ne(2)Br(2) van der Waals complex using time- and frequency-resolved pump-probe spectroscopy. After exciting Br(2) within the complex to a vibrational level 16<or=nu(')<or=23 in the B state, we follow the flow of halogen vibrational energy to the van der Waals modes in real time by recording the time-dependent behavior of Ne(2)Br(2) (nu(')), the NeBr(2) (nu(')-m) intermediates, and the Br(2) (nu(')-n) products. For Ne(2)Br(2) (nu(')=16-18), the only intermediate observed is NeBr(2) (nu(')-1), and the majority of the final product is Br(2) (nu(')-2), indicating the dissociation happens via two sequential direct VP steps. We fit the time-dependent behavior of these species to a sequential mechanism and extracted time constants for each step. For higher nu(') levels, the results show that the dissociation occurs via multiple pathways. Product Br(2) from levels lower than (nu(')-2) becomes much more important, with products as low as (nu(')-5) being observed. For nu(')=21, we observe both NeBr(2) (nu(')-1) and (nu(')-2) intermediates. The intermediates have significantly different kinetics, with the decay rate of the (nu(')-1) transient being nearly twice that of the (nu(')-2) transient. Similarly, both Br(2) (nu(')-2) and (nu(')-3) are formed in almost equal amounts, but the (nu(')-2) product formation rate is faster than the (nu(')-3) rate. The broad vibrational product state distributions and multiple dissociation pathways indicate that intramolecular vibrational energy redistribution becomes increasingly important for nu(')>19. We also report vibrational product state distributions for direct excitation to NeBr(2) 16<or=nu(')<or=23. For NeBr(2), the dominant product channel is Br(2) (nu(')-1) for all initial nu(') studied, consistent with this complex dissociating primarily via direct VP.

Quasi-classical trajectory study of the CD/CH product branching ratios for the C( 1D) + HD reaction

Quasi-classical trajectory (QCT) calculation of the integral cross-sections and the CD/CH product branching ratios as a function of collision energy for the C( 1D) + HD ( v, j) reaction have been performed on an ab initio potential energy surface (Bussery-Honvault et al. (2001) [8]). Our QCT calculations show that the integral cross-sections and the CD/CH product branching ratios strongly depend on the initial rotation quantum number j and the vibrational quantum number v. The integral cross-sections decrease with the increment of the collision energy. The product vibrational and rotational state distributions are also presented. The calculated results are in general good agreement with experimental data and some previous theoretical results.

Reaction of C2HCl2+O2: Combined TR-FTIR Spectroscopy and Electronic Structure

The product channels and mechanisms of the C2HCl2+O2 reaction are investigated by step-scan time-resolved Fourier transform infrared emission spectroscopy and the G3MP2//B3LYP/6311G(d,p) level of electronic structure calculations. Vibrationally excited products of HCl, CO, and CO2 are observed in the IR emission spectra and the product vibrational state distribution are determined which shows that HCl and CO are vibrationally excited with the nascent average vibrational energy estimated to be 59.8 and 51.8 kJ/mol respectively. In combination with the G3MP2//B3LYP/6311G(d,p) calculations, the reaction mechanisms have been characterized and the energetically favorable reaction pathways have been suggested.

Product vibrational distributions in CH 3Br photodissociation

We performed a theoretical study of the photodissociation dynamics of CH 3Br in the A ∼ band using a wavepacket propagation technique on coupled ab initio potential energy surfaces corresponding to the 3Q 1 and 1Q 1 states correlated at large distance with the Br ground spin–orbit state, as well as the 3Q 0 and 4E states correlated to the excited one. The methyl umbrella vibrational product state distributions are found in very good agreement with experimental results. They are hotter for Br than for Br ∗, and this is related to the shapes of the 3Q 0 and 1Q 1 potentials.

Dynamics and mechanism of the E→D, D′, β, γ, and δ nonadiabatic transitions induced in molecular iodine by collisions with CF4 and SF6 molecules

Nonadiabatic transitions among the first-tier ion-pair states of the iodine molecule in collisions with CF(4) and SF(6) partners are investigated by detecting the luminescence following the optical-optical double resonance excitation of the E0(g) (+)-state to the vibrational levels v(E)=8, 13, and 19. Total and partial rate constants, as well as vibrational product state distributions, are determined. It is found that electronic energy transfer in all channels is predominantly assisted by excitation of the dipole-allowed nu(3) and nu(4) modes of the partner. The measurements are accompanied by quantum scattering calculations that implement a close coupling treatment for the electronic and vibrational degrees of freedom and combine diatomics-in-molecule and long-range models for diabatic potential energy surfaces and coupling matrix elements. The analysis of experimental and theoretical data shows that the transitions without excitation of the partner are due to short-range couplings, whereas the vibrational excitation of the partner in the D0(u) (+) channel originates from the long-range coupling of two transition dipole moments: electronic of the iodine molecule and vibrational of the partner. Unexpectedly efficient excitations of the partner in the other ion-pair states, which are not coupled to the initial E0(g) (+)-state by the transition dipole, are interpreted within the postcollision mechanism. Qualitatively, this implies that during a single collision the long-range nonadiabatic transitions to D, nu(3) and D, nu(4) channels are followed by secondary short-range transitions without changing the state of the partner.

Quantum Mechanical Calculation of Energy Dependence of OCl/OH Product Branching Ratio and Product Quantum State Distributions for the O(1D) + HCl Reaction on All Three Contributing Electronic State Potential Energy Surfaces

OCl/OH product branching ratios are calculated as a function of total energy for the O( (1) D) + HCl reaction using quantum wavepacket methods. The calculations take account of reaction on all the three electronic state potential energy surfaces which correlate with both reactants and products. Our results show that reaction on the excited electronic state surfaces has a large effect on the branching ratio at higher energies and that these surfaces must therefore be fully taken into account. The calculations use the potential energy surfaces of Nanbu and co-workers. Product vibrational and rotational quantum state distributions are also calculated as a function of energy for both product channels. Inclusion of the excited electronic state potential energy surfaces improves the agreement of the predicted product vibrational quantum state distributions with experiment for the OH product channel. For OCl agreement between theory and experiment is retained for the vibrational quantum state distributions when the excited electronic state potential energy surfaces are included in the analysis. For the rotational state distributions good agreement between theory and experiment is maintained for energies at which experimental results are available. At higher energies, above 0.7 eV of total energy, the OCl rotational state distributions predicted using all three electronic state potential energy surfaces shift to markedly smaller rotational quantum numbers.