Quantum mechanics and quasiclassical study of the H/D+FO → OH/OD+F,HF/DF+O reactions: Chemical stereodynamics

The time‐dependent quantum wave packet and the quasi‐classical trajectory (QCT) calculations for the title reactions are carried out using three recent‐developed accurate potential energy surfaces of the 1¹A′, 1³A′, and 1³A″ states. The two commonly used polarization‐dependent differential cross sections, dσ₀₀/dω_t, dσ₂₀/dω_t, with ω_t being the polar coordinates of the product velocity ω′, and the three angular distributions, P(θ_r), P(Φ_r), and P(θ_r,Φ_r), with θ_r, Φ_r being the polar angles of the product angular momentum, are generated in the center‐of‐mass frame using the QCT method to gain insight into the alignment and the orientation of the product molecules. Influences of the potential energy surface, the collision energy, and the isotope mass on the stereodynamics are shown and discussed. Validity of the QCT calculation has been examined and proved in the comparison with the quantum wave packet calculation. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

Stereo‐dynamics of the F + HCl → HF + Cl reaction

We present a quasi‐classical trajectory (QCT) study on product polarization for the reaction F(²P) + HCl(v = 0, j = 0) → HF + Cl(²P) on a recently computed 1² A′ ground‐state surface reported by Deskevich et al. J Chem Phys, 2006, 124, 224303. Four polarization dependent generalized differential cross‐sections (2π/σ)(dσ₀₀/dω_t), (2π/σ)(dσ₂₀/dω_t), (2π/σ)(dσ₂₂₊/dω_t), and (2π/σ)(dσ_21?/dω_t) were calculated in the center‐of‐mass frame at four different collision energies. The obtained P(θ_r), P(?_r), and P(θ_r, ?_r), which denote respectively the distribution of angles between k and j′, the distribution of dihedral angle denoting k‐k′‐j′ correlation and the angular distribution of product rotational vectors in the form of polar plots, indicate that the degree of rotational alignment of the product HF molecule is strong and the degree of the rotational alignment decreases as collision energy increases. The product rotational angular momentum vector j′ is not only aligned, but also oriented along the y‐axis, and the molecular rotation of the product prefers an in‐plane reaction mechanism rather than the out‐of‐plane mechanism. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Fully converged sudden rotation total integral cross sections for 4He + H2 (ν = 0, j = 0) → 4He + H2 (ν′ = 1, j′)

Total integral cross sections for ⁴He + H₂ (ν = 0, j = 0) → ⁴He + H₂ (ν′ = 1, j′ = 0, 2) have been calculated in the total energy range 1.2 to 5.5 eV, according to a quantal sudden approximation for the H₂ rotational degrees of freedom and a close coupling expansion of the vibrational degree of freedom. Convergence of the above cross sections is investigated by employing four vibration basis sets in the close coupling calculations, i.e., ν = 0,1, ν = 0,1, 2, ν = 0, 1, 2, 3 and ν = 0, 1, 2, 3, 4. Between 4.2 and 5.5 eV calculations were done with three vibration basis sets; ν = 0.–4, ν = 0–5, and ν = 0–6. It is found that at least four vibrational basis functions are needed to converge (to within 5–10%) these cross sections in the above energy range. Comparison of breathing sphere calculations and summed sudden rotation results shows good agreement for the (weakly anisotropic) Mies-Krauss potential. However, as expected the former results underestimate the vibrational 0 → 1 total integral cross sections.     

Molecular beam scattering studies of the reaction D + H2 (v = 0) and D + H2 (v = 1) → HD + H

The reaction D + H₂ → HD + H has been investigated in two molecular beam scattering experiments. Angular and time-of-flight distributions have been measured for the initial vibrational ground state (v = 0) at a most probable collision energy of E_cm = 1.5 eV and for the first vibrational excited state (v = 1) at E_cm = 0.28 eV with the same apparatus. Results for the ground-state experiment are compared with quasiclassical trajectory calculations(QCT) on the LSTH-hypersurface transformed into the laboratory system and averaged over the apparatus distributions. The agreement isquite satisfactory. At this high collision energy the HD products are no longer scattered in a backward direction but in a wide angular region concentrated about θ = 90° in the center-of-mass system. The absolute reactive cross section has been determined and the agreement with the theoretical value from QCT calculations is within the experimental error. The high sensitivity of the experiment to different properties of the doubly differential cross section has also been demonstrated. A preliminary evaluation of the experiment with initial vibrational excitation (v = 1) shows that the HD-product molecules are preferably backward scattered and the change of internal energy is small supporting the concept of a reaction which is adiabatic with respect to the internal degrees of freedom.     

A time-dependent wave packet quantum scattering study of the reaction HD+ (v = 0 - 3;j0 = 1) + He --> HeH+(HeD+) + D(H)

Time-dependent wave packet quantum scattering (TWQS) calculations are presented for HD(+) (v = 0 - 3;j(0)=1) + He collisions in the center-of-mass collision energy (E(T)) range of 0.0-2.0 eV. The present TWQS approach accounts for Coriolis coupling and uses the ab initio potential energy surface of Palmieri et al. [Mol. Phys. 98, 1839 (2000)]. For a fixed total angular momentum J, the energy dependence of reaction probabilities exhibits quantum resonance structure. The resonances are more pronounced for low J values and for the HeH(+) + D channel than for the HeD(+) + H channel and are particularly prominent near threshold. The quantum effects are no longer discernable in the integral cross sections, which compare closely to quasiclassical trajectory calculations conducted on the same potential energy surface. The integral cross sections also compare well to recent state-selected experimental values over the same reactant and translational energy range. Classical impulsive dynamics and steric arguments can account for the significant isotope effect in favor of the deuteron transfer channel observed for HD(+)(v<3) and low translational energies. At higher reactant energies, angular momentum constraints favor the proton-transfer channel, and isotopic differences in the integral cross sections are no longer significant. The integral cross sections as well as the J dependence of partial cross sections exhibit a significant alignment effect in favor of collisions with the HD(+) rotational angular momentum vector perpendicular to the Jacobi R coordinate. This effect is most pronounced for the proton-transfer channel at low vibrational and translational energies.     

A coupled-states approximation study of Li+-H2 collisions

The recently developed coupled-states approximation for describing atom-molecule collisions is applied in a slightly modified form to the Li⁺-H₂ system. Due to the large anisotropy in the potential, a preferred orientation for rotational excitation exists which suggests the use of l = J-j rather than l = J as the angular momentum quantum number in approximating the eigenvalue of 1² by l(l + 1). Here, J and j are respectively the total and rotator angular momentum quantum numbers. The coupled-states integral and differential cross sections are compared with results of close-coupling calculations at 0.6, 0.9, and 1.2 eV.     

Exploring the reaction dynamics of O(3P)+ (X2 )→OH+(X3Σ−)+ H(2S) reaction with time‐dependent wave packet method

The O(³P)+ reaction has been investigated by employing time‐dependent quantum wave packet with split operator method on potential energy surface of the doublet ground‐state H₂O⁺(1²A″). The reaction probabilities and integral cross sections are calculated using centrifugal sudden approximation, which basically agree with the quasi‐classical results of Paniagua et al. [Phys. Chem. Chem. Phys. 2014, 16, 23594]. Moreover, the effect of vibrational and rotational excitation of reactant is investigated. The results show that the vibrational and rotational excitation effects on the integral cross section are not obvious. The little differences between Coriolis coupling results and centrifugal sudden approximation ones show that the cheaper centrifugal sudden calculations here reported are effective for this reaction.     

Time‐dependent quantum study of H(2S) + FO(2Π) → OH(2Π) + F(2P) reaction on the 13A′ and 13A″ states

The dynamics of the H(²S) + FO(²Π) → OH(²Π) + F(²P) reaction on the adiabatic potential energy surface of the 1³A′ and 1³A″ states is investigated. The initial state selected reaction probabilities for total angular momentum J = 0 have been calculated by using the quantum mechanical real wave packet method. The integral cross sections and initial state selected reaction rate constants have been obtained from the corresponding J = 0 reaction probabilities by means of the simple J‐Shifting technique. The initial state‐selected reaction probabilities and reaction cross section do not manifest any sharp oscillations and the initial state selected reaction rate constants are sensitive to the temperature. © 2010 Wiley Periodicals, Inc. J Comput Chem 2010     

Distorted-wave calculations for the three dimensional chemical reaction H + H2(v ⩽ 2, j = 0) → H2(v′ ⩽ 2, j′, mj) + H

Calculations of the vibrational—rotational product state population distributions and differential cross sections for the chemical reaction H + H₂(v ? 2, j = 0) → H₂(v′ ? 2, j′, m_j) + H have been carried out on the Porter—Karplus potential energy surface. The vibrationally-adiabatic-distorted-wave (VADW) method has been used. The relative rotational product distributions, differential cross sections and the helicity m_j, dependences of these quantities for the v = 0 reaction agree well with accurate close-coupling results. The absolute integral cross sections are considerably smaller than the accurate quantum values, however. The calculations for the v = 1 reaction agree with the findings of previous sudden quantum, limited close-coupling and quasiclassical theoretical studies and experiments that product H₂(v′ = 1) is more likely to be produced than H₂(v′ = 0). For the reaction with v = 2, it is found that at high translational energies product H₂(v′ = 2) is favoured over H₂(v′ = 1) or H₂(v′ = 0). The VADW differential cross sections for the v = 1 and v = 2 reactions have a similar shape to those of the v = 0 reaction, with backward peaking when summed over all m_j states. The relative rotational distributions for the v = 2, j = 0 → v′ = 2, j and v = 1, j = 0 → v′ = 1, j reactions are also similar to those obtained for the v = 0, j = 0 → v′ = 0, j reaction, with low rotational excitation.     

Quasi-classical trajectory approach to the stereo-dynamics of the reaction F+HO→HF+O

Quasi-classical trajectory (QCT) calculations are employed for the reaction F + HO(0,0)→HF + O based on the adiabatic potential energy surface (PES) of the ground 3A″triplet state. The average rotational alignment factor P2(j′·k) as a function of collision energy and the four polarization dependent generalized differential cross sections have been calculated in the center-of-mass (CM) frame, separately. The distribution P(θr) of the angle between k and j′, the distribution P(θr) of dihedral angle denoting k-k′-j′ correlation, and the angular distribution P(θr, Φr) of product rotational vectors in the form of polar plots are calculated as well. The effect of Heavy-Light-Heavy (HLH) mass combination and atom F's relatively strong absorbability to charges on the alignment and the orientation of product molecule HF rotational angular momentum vectors j′ is revealed.     

Quantum and classical studies of the O(3P) + H2(v = 0-3,j = 0) --> OH + H reaction using benchmark potential surfaces

We present results of time-dependent quantum mechanics (TDQM) and quasiclassical trajectory (QCT) studies of the excitation function for O(3P) + H2(v = 0-3,j = 0) --> OH + H from threshold to 30 kcal/mol collision energy using benchmark potential energy surfaces [Rogers et al., J. Phys. Chem. A 104, 2308 (2000)]. For H2(v = 0) there is excellent agreement between quantum and classical results. The TDQM results show that the reactive threshold drops from 10 kcal/mol for v = 0 to 6 for v = 1, 5 for v = 2 and 4 for v = 3, suggesting a much slower increase in rate constant with vibrational excitation above v = 1 than below. For H2(v > 0), the classical results are larger than the quantum results by a factor approximately 2 near threshold, but the agreement monotonically improves until they are within approximately 10% near 30 kcal/mol collision energy. We believe these differences arise from stronger vibrational adiabaticity in the quantum dynamics, an effect examined before for this system at lower energies. We have also computed QCT OH(v',j') state-resolved cross sections and angular distributions. The QCT state-resolved OH(v') cross sections peak at the same vibrational quantum number as the H2 reagent. The OH rotational distributions are also quite hot and tend to cluster around high rotational quantum numbers. However, the dynamics seem to dictate a cutoff in the energy going into OH rotation indicating an angular momentum constraint. The state-resolved OH distributions were fit to probability functions based on conventional information theory extended to include an energy gap law for product vibrations.     

Close-coupling elastic and inelastic integral and differential cross sections for Li+ + H2 collisions

The quantum mechanical close-coupling formalism is applied to the study of elastic and rotationally inelastic Li⁺ + H₂ collisions making use of the Kutzelnigg-Staemmler-Hoheisel potential energy surface. Integral and differential cross sections for j = 0 → 0 and j = 0 → 2 are obtained in the collision energy range 0.2 to 0.9 eV and for j = 1 → 1 and j = 1 → 3 at 0.6 eV. A rainbow structure is observed in both the elastic and inelastic angular distributions and a quenching of the fast oscillations is found in the cross sections for j = 1 initially compared to the case j = 0 initially. At 0.6 eV. the calculated quantum mechanical angular distributions are compared to those from a classical trajectory calculation using the same surface and to the experimental ones. The dynamics of rotational excitation in the Li⁺ + H₂ system is contrasted to rotational excitation in systems for which the atom-diatom interaction is predominantly repulsive.     

A time-dependent wave-packet quantum scattering study of the reaction H2+(v = 0-2,4,6;j = 1) + He--> HeH+ + H

The quantum scattering dynamics calculation was carried out for the titled reaction in the collision energy range of 0.0-2.4 eV with reactant H(2) (+) in the rotational state j = 1 and vibrational states v = 0-2, 4, and 6. The present time-dependent wave-packet calculation takes into account the Coriolis coupling (CC) and uses the accurate ab initio potential-energy surface of Palmieri et al. [Mol. Phys. 98, 1835 (2000)]. The importance of including the CC quantum scattering calculation has been revealed by the comparison between the CC calculation and the previous coupled state (CS) calculation. The CC total cross sections for the v = 2, 4, and 6 states show collision energy-dependent behaviors different from those based on the CS calculation. Furthermore, the collision energy dependence of the total cross sections obtained in the present CC calculation only exhibits minor oscillations, indicating that the chance is slim for reactive resonances in total cross sections to survive through the partial-wave averaging. The magnitude and profile of the CC total cross sections for v = 0-2 in the collision energy range of 0.0-2.5 eV are found to be consistent with experimental cross sections obtained recently by Tang et al. [J. Chem. Phys. 122, 164301 (2005)] after taking into account the experimental uncertainties.     

A pulsed-field ionization photoelectron secondary ion coincidence study of the H2+ (X,upsilon+=0-15,N+=1)+He proton transfer reaction

The endothermic proton transfer reaction, H2+(upsilon+)+He-->HeH+ + H(DeltaE=0.806 eV), is investigated over a broad range of reactant vibrational levels using high-resolution vacuum ultraviolet to prepare reactant ions either through excitation of autoionization resonances, or using the pulsed-field ionization-photoelectron-secondary ion coincidence (PFI-PESICO) approach. In the former case, the translational energy dependence of the integral reaction cross sections are measured for upsilon+=0-3 with high signal-to-noise using the guided-ion beam technique. PFI-PESICO cross sections are reported for upsilon+=1-15 and upsilon+=0-12 at center-of-mass collision energies of 0.6 and 3.1 eV, respectively. All ion reactant states selected by the PFI-PESICO scheme are in the N+=1 rotational level. The experimental cross sections are complemented with quasiclassical trajectory (QCT) calculations performed on the ab initio potential energy surface provided by Palmieri et al. [Mol. Phys. 98, 1839 (2000)]. The QCT cross sections are significantly lower than the experimental results near threshold, consistent with important contributions due to resonances observed in quantum scattering studies. At total energies above 2 eV, the QCT calculations are in excellent agreement with the present results. PFI-PESICO time-of-flight (TOF) measurements are also reported for upsilon+=3 and 4 at a collision energy of 0.6 eV. The velocity inverted TOF spectra are consistent with the prevalence of a spectator-stripping mechanism.     

Exact quantum dynamics study of the O(+)+H2(v=0,j=0)-->OH(+)+H ion-molecule reaction and comparison with quasiclassical trajectory calculations

The close-coupling hyperspherical (CCH) exact quantum method was used to study the title barrierless reaction up to a collision energy (E(T)) of 0.75 eV, and the results compared with quasiclassical trajectory (QCT) calculations to determine the importance of quantum effects. The CCH integral cross section decreased with E(T) and, although the QCT results were in general quite similar to the CCH ones, they presented a significant deviation from the CCH data within the 0.2-0.6 eV collision energy range, where the QCT method did not correctly describe the reaction probability. A very good accord between both methods was obtained for the OH(+) vibrational distribution, where no inversion of population was found. For the OH(+) rotational distributions, the agreement between the CCH and QCT results was not as good as in the vibrational case, but it was satisfactory in many conditions. The kk(') angular distribution showed a preferential forward character, and the CCH method produced higher forward peaks than the QCT one. All the results were interpreted considering the potential energy surface and plots of a representative sampling of reactive trajectories.     

Coriolis coupling effects in the calculation of state-to-state integral and differential cross sections for the H+D2 reaction

The quantum wavepacket parallel computational code DIFFREALWAVE is used to calculate state-to-state integral and differential cross sections for the title reaction on the BKMP2 surface in the total energy range of 0.4-1.2 eV with D2 initially in its ground vibrational-rotational state. The role of Coriolis couplings in the state-to-state quantum calculations is examined in detail. Comparison of the results from calculations including the full Coriolis coupling and those using the centrifugal sudden approximation demonstrates that both the energy dependence and the angular dependence of the calculated cross sections are extremely sensitive to the Coriolis coupling, thus emphasizing the importance of including it correctly in an accurate state-to-state calculation.     

The quantum dynamics of the reactions N+H2(HD,D2) and their vibrational excitation effect

The N(⁴S)+H₂ reaction and its isotopic variants have been investigated by means of time‐dependent quantum wave packet with split operator method on the ground state potential energy surface (Zhai and Han, J. Chem. Phys. 2011, 135, 104314). The reaction probabilities, integral cross sections, branching ratio of the integral cross sections, and effect of vibrational excitation of H₂, HD, and D₂ diatomic molecules are presented and discussed. The results reveal that the intramolecular isotopic effect is greater than the intermolecular one, and that the vibrational excitation of the diatomic molecules can promote the progress of this reaction. In addition, a limited number of rigorous Coriolis coupling calculations of the integral cross sections of the N(⁴S)+H₂ reaction have been carried out. Also shown is that since the Coriolis coupling plays a small part in this accurate quantum calculation, the cheaper centrifugal sudden calculations here reported are effective for this reactive system. © 2014 Wiley Periodicals, Inc.     

Quantum-mechanical differential reaction cross sections for the F + H2(ν = 0) - FH(ν′= 2.3) + H reaction

Velocity scatterring angle intensity maps for the F + H₂(ν = 0): j = 0) $\text{\$}\text{?}$FH(ν′ = 2, 3: j′) + 11 reaction are predicted from quantum-mechanical J conserving, calculations. The extent of the shift in the angular distribution from backscattering at 1.8 kcal/mole to sideways scattering (intensity peak at 100°) at 3.0 kcal/mole is in quantitative agreement with recent crossed molecular beans experiments.     

State-selected molecular-beam reaction dynamics of K with HF (υ = 1, j = 5, 6 and 7)

The crossed-molecular-beam method has been used to measure relative integral cross sections σ_r (υ = 1, j; E) of the endothermic (0.75 eV) reaction K + HF (υ = 1, j) → KF + H as a function of both the rotational quantum number j (j = 5, 6 and 7) and the translational energy E (0.55 ? E ? 1.32 eV) of the reagents. The vibrational-rotational (υ, j) states of HF were populated by infrared pumping with the radiation of a properly tuned pulsed chemical HF laser. In addition, relative cross sections with υ = 0 but averaged with respect to the initial rotational-state distribution of the HF molecules were also determined. The results exhibit three remarkable features: (a) σ_r (υ = 1, j; E) rises with increasing j, (b) the steepness of the ascent roughly decreases with increasing E, (c) at E = 0.98 eV reagent vibrational energy is about a factor of 200 more efficient in promoting the reaction than reagent translational energy. An intuitive dynamical model suggests that observations (a) and (b) are to be expected for a reaction governed by a potential-energy surface with a late barrier. This is consistent with the well-known interpretation of large vibrational effects as indicated by result (c).     

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