Wave packet calculations on ion-molecule reactions

Accurate Calculation of Rate Constant and Isotope Effect for the F + H2 Reaction by the Coupled 3D Time-Dependent Wave Packet Method on the Newly Constructed Ab Initio Ground Potential Energy Surface

We employ coupled three-dimensional (3D) time dependent wave packet formalism in hyperspherical coordinates for reactive scattering problem on the newly constructed ab initio calculated ground adiabatic potential energy surface for the F + H₂/D₂ reaction. The convergence profiles for various reactive channels are depicted at low collision energy regimes with respect to the total angular momentum (J) quantum numbers. For two different reactant diatomic molecules (H₂ and D₂) initially at their respective ground roto-vibrational state (v = 0, j = 0), calculated state-to-state as well as total integral cross sections as a function of collision energy, temperature dependent rate constants, and the kinetic isotope effect for various reactivity profiles of F + H₂ and F + D₂ reactions are presented along with previous theoretical and experimental results.

Dynamical calculations of O(3P) + OH(2Π) reaction on the CHIPR potential energy surface using the fully coupled time-dependent wave-packet approach in hyperspherical coordinates

We have carried out quantum dynamics calculations for the O + OH → H + O₂ reaction on the CHIPR [A. J. C. Varandas, J. Chem. Phys., 2013, 138, 134117] potential energy surface (PES) for ground state HO₂ using the fully coupled 3D time-dependent wavepacket formalism [S. Adhikari and A. J. C. Varandas, Comput. Phys. Commun., 2013, 184, 270] in hyperspherical coordinates. Reaction probabilities for J > 0 are calculated for different initial rotational states of the OH radical (v = 0; j = 0, 1). State-to-state as well as total integral cross sections and rate-coefficients are evaluated and compared with previous theoretical calculations and available experimental studies. Using the rate constant for the forward (hereinafter considered to be H + O₂ → O + OH) and backward (O + OH → H + O₂) reactions of this reactive system, the equilibrium constant of the reversible process [H + O₂ ⇌ O + OH] is calculated as a function of temperature and compared with previous experimental measurements.

Near-resonant effects in the quantum dynamics of the H + H2 + → H2 + H+ charge transfer reaction and isotopic variants

The non-adiabatic quantum dynamics of the H + H₂ ⁺ → H₂ + H⁺ charge transfer reactions, and some isotopic variants, is studied with an accurate wave packet method. A recently developed 3 × 3 diabatic potential model is used, which is based on very accurate ab initio calculations and includes the long-range interactions for ground and excited states. It is found that for initial H₂ ⁺(v = 0), the quasi-degenerate H₂(v' = 4) non-reactive charge transfer product is enhanced, producing an increase in the reaction probability and cross section. It becomes the dominant channel from collision energies above 0.2 eV, producing a ratio between v' = 4 and the rest of v's, which that increase up to 1 eV. The H + H₂ ⁺ → H₂ ⁺ + H exchange reaction channel is nearly negligible, while the reactive and non-reactive charge transfer reaction channels are of the same order, except that corresponding to H₂(v' = 4), and the two charge transfer processes compete below 0.2 eV. This enhancement is expected to play an important vibrational and isotopic effect that needs to be evaluated. For the three proton case, the problem of the permutation symmetry is discussed when using reactant Jacobi coordinates.

Charge Transfer Processes for H + H2+ Reaction Employing Coupled 3D Wavepacket Approach on Beyond Born-Oppenheimer Based Ab Initio Constructed Diabatic Potential Energy Surfaces

The dynamics of the H + H₂⁺ reaction has been analyzed from the electronically first excited state of diabatic potential energy surfaces constructed by employing the Beyond Born-Oppenheimer theory [J. Chem. Phys. 2014, 141, 204306]. We have employed the coupled 3D time-dependent wavepacket formalism in hyperspherical coordinates for multisurface reactive scattering problems. To be specific, the charge transfer processes have been investigated extensively by calculating state-to-state as well as total reaction probabilities and integral cross sections, when the reaction process is initiated from the first excited electronic state (2¹A'). We have depicted the convergence profiles of reaction probabilities for the competing charge transfer processes, namely, reactive charge transfer (RCT) and nonreactive charge transfer (NRCT) processes for different total energies with respect to total angular momentum, J. Total and state-to-state integral cross sections are calculated as a function of total energy for the initial rovibrational state, namely, v = 0, j = 0 level of H₂⁺ (²Σ_g⁺) molecule and are compared with previous theoretical calculations. Finally, we have calculated temperature-dependent rate constants using our presently evaluated cross sections and compared their average with the experimentally measured one.

Time-dependent quantum mechanical wave packet dynamics

Starting from a model study of the collinear (H, H₂) exchange reaction in 1959, the time-dependent quantum mechanical wave packet (TDQMWP) method has come a long way in dealing with systems as large as Cl + CH₄. The fast Fourier transform method for evaluating the second order spatial derivative of the wave function and split-operator method or Chebyshev polynomial expansion for determining the time evolution of the wave function for the system have made the approach highly accurate from a practical point of view. The TDQMWP methodology has been able to predict state-to-state differential and integral reaction cross sections accurately, in agreement with available experimental results for three dimensional (H, H₂) collisions, and identify reactive scattering resonances too. It has become a practical computational tool in predicting the observables for many A + BC exchange reactions in three dimensions and a number of larger systems. It is equally amenable to determining the bound and quasi-bound states for a variety of molecular systems. Just as it is able to deal with dissociative processes (without involving basis set expansion), it is able to deal with multi-mode nonadiabatic dynamics in multiple electronic states with equal ease. We present an overview of the method and its strength and limitations, citing examples largely from our own research groups.

Fully coupled (J > 0) time-dependent wave-packet calculations using hyperspherical coordinates for the H + O2 reaction on the CHIPR potential energy surface

ICS calculation by time dependent wavepacket approach for H + O₂ reaction using non-zero J values.

The low temperature D+ + H2→ HD + H+ reaction rate coefficient: a ring polymer molecular dynamics and quasi-classical trajectory study

The reaction between D⁺ and H₂ plays an important role in astrochemistry at low temperatures and also serves as a prototype for a simple ion-molecule reaction. Its ground X[combining tilde]¹A' state has a very small thermodynamic barrier (up to 1.8 × 10^-2 eV) and the reaction proceeds through the formation of an intermediate complex lying within the potential well with a depth of at least 0.2 eV, thus representing a challenge for dynamical studies. In the present work, we analyze the title reaction within the temperature range of 20-100 K by means of ring polymer molecular dynamics (RPMD) and quasi-classical trajectory (QCT) methods over the full-dimensional global potential energy surface developed by Aguado et al. [A. Aguado, O. Roncero, C. Tablero, C. Sanz and M. Paniagua, J. Chem. Phys., 2000, 112, 1240]. The computed thermal RPMD and QCT rate coefficients are found to be almost independent of temperature and fall within the range of 1.34-2.01 × 10^-9 cm³ s^-1. They are also in very good agreement with previous time-independent quantum mechanical and statistical quantum method calculations. Furthermore, we observe that the choice of asymptotic separation distance between the reactants can markedly alter the rate coefficient in the low temperature regime (20-50 K). Therefore it is of utmost importance to correctly assign the value of this parameter for dynamical studies, particularly at very low temperatures of astrochemical importance. We finally conclude that the experimental rate measurements for the title reaction are highly desirable in future.

3D time-dependent wave-packet approach in hyperspherical coordinates for the H + O2 reaction on the CHIPR and DMBE IV potential energy surfaces

3D wavepacket quantum dynamics methodology ICS calculation of H + O₂ reaction on the CHIPR and DMBE IV PESs by J-shifting scheme.

Non-Born–Oppenheimer stereodynamics study for the D+ + H2 (v, j = 0) reaction using coherent switching with decay of mixing method

A non-Born–Oppenheimer (BO) investigation using coherent switching with decay of mixing method is carried out for both reactive non-charge transfer and charge transfer channels of reaction D+ + H2 (v, j = 0). For the non-charge transfer channel, it is found that the non-BO effect has a small influence on the differential cross section, but it has a large impact on the rotational polarization of the HD product, which is reflected by the joint distribution P(θr, ϕr). And it is also found that the polarization of the charge transfer products shows a quite different form. The rotational polarizations are also investigated at various collision energies and initial vibrational states for both reactive channels.

State-to-state quantum mechanical calculations of rate coefficients for the D+ + H2 → HD + H+ reaction at low temperature

The dynamics of the D(+) + H2 → HD + H(+) reaction on a recent ab initio potential energy surface (Velilla, L.; Lepetit, B.; Aguado, A.; Beswick, J. A.; Paniagua, M. J. Chem. Phys. 2008, 129, 084307) has been investigated by means of a time-independent quantum mechanical approach. Cross-sections and rate coefficients are calculated, respectively, for collision energies below 0.1 eV and temperatures up to 100 K for astrophysical application. An excellent accord is found for collision energy above 5 meV, while a disagreement between theory and experiment is observed below this energy. We show that the rate coefficients reveal a slightly temperature-dependent behavior in the upper part of the temperature range considered here. This is in agreement with the experimental data above 80 K, which give a temperature independent value. However, a significant decrease is found at temperatures below 20 K. This decrease can be related to quantum effects and the decay back to the reactant channel, which are not considered by simple statistical approaches, such as the Langevin model. Our results have been fitted to appropriate analytical expressions in order to be used in astrochemical and cosmological models.

Non-Born-Oppenheimer dynamics calculations using the coherent switching with decay of mixing method

A theoretical investigation of the nonadiabatic processes that are involved in the full three-dimensional D+H(2), H+D(2), D(+)+H(2), and H(+)+D(2) reaction systems has been performed using the method of coherence switching with decay of mixing (CSDM) developed by Truhlar and coworkers. The electronic density matrix for each trajectory is fully coherent in the CSDM method, and a switching algorithm different to the original "decay of mixing" method is used to determine the pure state toward which the decoherent force drives the system. By solving the equations for the evolution of the electronic state populations along the semiclassical trajectory, the ensemble can present effective physical insight into nonadiabatic dynamics. The calculations for the D+H(2) and H+D(2) systems is based on the double many body expansion potential energy surface. The potential energy surface constructed by Kamisaka et al. is employed in the calculation of D(+)+H(2) and H(+)+D(2) reactions. The cross sections and the reaction probabilities for the total angular momentum J = 0 are calculated for all of these systems. The calculated results from the CSDM method are in good agreement with exact quantum mechanical calculations and experimental measurements.

Quantum approaches for the insertion dynamics of the H+ + D2 and D+ + H2 reactive collisions

The H(+)+D(2) and D(+)+H(2) reactive collisions are studied using a recently proposed adiabatic potential energy surface of spectroscopic accuracy. The dynamics is studied using an exact wave packet method on the adiabatic surface at energies below the curve crossing occurring at approximately 1.5 eV above the threshold. It is found that the reaction is very well described by a statistical quantum method for a zero total angular momentum (J) as compared with the exact ones, while for higher J some discrepancies are found. For J >0 different centrifugal sudden approximations are proposed and compared with the exact and statistical quantum treatments. The usual centrifugal sudden approach fails by considering too high reaction barriers and too low reaction probabilities. A new statistically modified centrifugal sudden approach is considered which corrects these two failures to a rather good extent. It is also found that an adiabatic approximation for the helicities provides results in very good agreement with the statistical method, placing the reaction barrier properly. However, both statistical and adiabatic centrifugal treatments overestimate the reaction probabilities. The reaction cross sections thus obtained with the new approaches are in rather good agreement with the exact results. In spite of these deficiencies, the quantum statistical method is well adapted for describing the insertion dynamics, and it is then used to evaluate the differential cross sections.

A detailed quantum mechanical and quasiclassical trajectory study on the dynamics of the H++H2→H2+H+ exchange reaction

The H+ + H2 exchange reaction has been studied theoretically by means of a different variety of methods as an exact time independent quantum mechanical, approximate quantum wave packet, statistical quantum, and quasiclassical trajectory approaches. Total and state-to-state reaction probabilities in terms of the collision energy for different values of the total angular momentum obtained with these methods are compared. The dynamics of the reaction is extensively studied at the collision energy of E(coll)=0.44 eV. Integral and differential cross sections and opacity functions at this collision energy have been calculated. In particular, the fairly good description of the exact quantum results provided by the statistical quantum method suggests that the dynamics of the process is governed by an insertion mechanism with the formation of a long-lived collision complex.

Quantum Wave Packet Study of the H+ + D2 Reaction on Diabatic Potential Energy Surfaces

The exact three-dimensional nonadiabatic quantum dynamics calculations were carried out for the title reaction by a time-dependent wave packet approach based on a newly constructed diabatic potential energy surface (Kamisaka et al. J. Chem. Phys. 2002, 116, 654). Three processes including those of reactive charge transfer, nonreactive charge transfer, and reactive noncharge transfer were investigated to determine the initial state-resolved probabilities and reactive cross sections. The results show that a large number of resonances can be observed in the calculated probabilities due to the deep well on adiabatic ground surface and the dominant process is the reactive noncharge-transfer process. Some interesting dynamical features such as v-dependent and j-dependent behaviors of the probabilities are also revealed. In addition, a good agreement has been achieved in the comparison between the calculated quantum cross sections from the ground rovibrational initial state and the experimental measurement data.

Nonadiabatic Time-Dependent Wave Packet Study of the D+ + H2 Reaction System

A theoretical investigation on the nonadiabatic processes of the D(+) + H(2) reaction system has been carried out by means of exact three-dimensional nonadiabatic time-dependent wave packet calculations with an extended split operator scheme (XSOS). The diabatic potential energy surface newly constructed by Kamisaka et al. (J. Chem. Phys. 2002, 116, 654) was employed in the calculations. This study provided quantum cross sections for three competing channels of the reactive charge transfer, the nonreactive charge transfer, and the reactive noncharge transfer, which contrasted markedly to many previous quantum theoretical reports on the (DH(2))(+) system restricted to the total angular momentum J = 0. These quantum theoretical cross sections derived from the ground rovibrational state of H(2) show wiggling structures and an increasing trend for both the reactive charge transfer and the nonreactive charge transfer but a decreasing trend for the reactive noncharge transfer throughout the investigated collision energy range 1.7-2.5 eV. The results also show that the channel of the reactive noncharge transfer with the largest cross section is the dominant one. A further investigation of the v-dependent behavior of the probabilities for the three channels revealed an interesting dominant trend for the reactive charge transfer and the nonreactive charge transfer at vibrational excitation v = 4 of H(2). In addition, the comparison between the centrifugal sudden (CS) and exact calculations showed the importance of the Coriolis coupling for the reactive system. The computed quantum cross sections are also compared with the experimental measurement results.