On the Effect of Initial Rotation on Reactivity. A Multi-Configuration Time-Dependent Hartree (MCTDH) Wave Packet Propagation Study on the H + D2 and D + H2 Reactive Scattering Systems

An effective approximation of Coriolis coupling in reactive scattering: application to the time-dependent wave packet calculations

Coriolis coupling plays a crucial role in reactive scattering, but dynamics calculations including the complete Coriolis coupling significantly increase the difficulty of numerical evolution due to the corresponding expensive matrix processing. The coupled state approximation that completely ignores the off-diagonal Coriolis coupling saves computational cost significantly but its error is usually unacceptable. In this paper, an improved coupled state approximation inspired by recently published results [D. Yang, X. Hu, D. H. Zhang and D. Xie, J. Chem. Phys., 2018, 148, 084101.] of the inelastic scattering problem is extended to deal with the reactive scattering. The calculations using the time-dependent wave packet method reveal that the new method can accurately reproduce the rigorous results of the H + HD (j0 < 3) → D + H2 reaction and immensely improve the computational efficiency. Additionally, we extend the new method to the non-adiabatic Li(2p) + H2 (v0 = 0, j0 = 0, 1) → H + LiH reaction, showcasing its advantages of low computational cost and high accuracy.

Temperature Dependence of the Electronic Absorption Spectrum of NO2

The nitrogen dioxide (NO₂) radical is composed of the two most abundant elements in the atmosphere, where it can be formed in a variety of ways including combustion, detonation of energetic materials, and lightning. Relevant also to smog and ozone cycles, together these processes span a wide range of temperatures. Remarkably, high-resolution NO₂ electronic absorption spectra have only been reported in a narrow range below about 300 K. Previously, we reported [ J. Phys. Chem. A 2021, 125, 5519-5533] the construction of quasi-diabatic potential energy surfaces (PESs) for the lowest four electronic states (X̃, Ã, B̃, and C̃) of NO₂. In addition to three-dimensional PESs based on explicitly correlated MRCI(Q)-F12/VTZ-F12 ab initio data, the geometry dependence of each component of the dipoles and transition dipoles was also mapped into fitted surfaces. The multiconfigurational time-dependent Hartree (MCTDH) method was then used to compute the 0 K electronic absorption spectrum (from the ground rovibrational initial state) employing those energy and transition dipole surfaces. Here, in an extension of that work, we report an investigation into the effects of elevated temperature on the spectrum, considering the effects of the population of rotationally and vibrationally excited initial states. The calculations are complemented by new experimental measurements. Spectral contributions from hundreds of rotational states up to N = 20 and from 200 individually-characterized vibrational states were computed. A spectral simulation tool was developed that enables modeling the spectrum at various temperatures─by weighting individual spectral contributions via the partition function, or for pure excited initial states, which can be probed via transient absorption spectroscopy. We validate these results against experimental absorption spectroscopy data at high temperatures, as well as via a new measurement from the (1,0,1) initial vibrational state.

Rotational Mode-Specificity in the Cl + C2H6 → HCl + C2H5 Reaction

We perform rotational mode-specific quasi-classical trajectory simulations using a high-quality ab initio analytical potential energy surface for the Cl(²P_3/2) + C₂H₆ → HCl + C₂H₅ reaction. As ethane, being a prolate-type symmetric top, can be characterized by the J and K rotational quantum numbers, the excitation of two rotational modes, the tumbling (J, K = 0) and spinning (J, K = J) rotations of the reactant is carried out with J = 10, 20, 30, and 40 at a wide range of collision energies. The impacts of rotational excitation on the reactivity, the mechanism, and the post-reaction distribution of energy are investigated: (1) exciting both rotational modes enhances the reactivity with the spinning rotation being more effective due to its coupling to the C-H stretching vibrational normal modes (C-H bond elongating effect) and larger rotational energies, (2) rotational excitation increases the dominance of direct rebound over the stripping mechanism, while collision energy favors the latter, (3) investing energy in tumbling rotation excites the translational motion of the products, while the excess spinning rotational energy readily flows into the internal degrees of freedom of the ethyl radical or, less significantly, into the HCl vibration, probably due to the pronounced rovibrational coupling in this case. We also study the relative efficiency of vibrational and rotational excitation on the reactivity of the barrierless and thus translationally hindered title reaction.

Comparison of the multi-layer multi-configuration time-dependent Hartree (ML-MCTDH) method and the density matrix renormalization group (DMRG) for ground state properties of linear rotor chains

We demonstrate the applicability of the Multi-Layer Multi-Configuration Time-Dependent Hartree (ML-MCTDH) method to the problem of computing ground states of one-dimensional chains of linear rotors with dipolar interactions. Specifically, we successfully obtain energies, entanglement entropies, and orientational correlations that are in agreement with the Density Matrix Renormalization Group (DMRG), which has been previously used for this system. We find that the entropies calculated by ML-MCTDH for larger system sizes contain nonmonotonicity, as expected in the vicinity of a second-order quantum phase transition between ordered and disordered rotor states. We observe that this effect remains when all couplings besides nearest-neighbor are omitted from the Hamiltonian, which suggests that it is not sensitive to the rate of decay of the interactions. In contrast to DMRG, which is tailored to the one-dimensional case, ML-MCTDH (as implemented in the Heidelberg MCTDH package) requires more computational time and memory, although the requirements are still within reach of commodity hardware. The numerical convergence and computational demand of two practical implementations of ML-MCTDH and DMRG are presented in detail for various combinations of system parameters.

High-Dimensional Quantum Dynamics Study on Excitation-Specific Surface Scattering Including Lattice Effects of a Five-Atom Surface Cell

In this work, high-dimensional (21D) quantum dynamics calculations on the mode-specific surface scattering of a carbon monoxide molecule on a copper(100) surface with lattice effects of a five-atom surface cell are performed through the multilayer multiconfiguration time-dependent Hartree (ML-MCTDH) method. We employ a surface model in which five surface atoms near the impact site are treated as fully flexible quantum particles, while all other more distant atoms are kept at fixed locations. To efficiently perform the 21D ML-MCTDH wave packet propagation, the potential energy surface is transferred to a canonical polyadic decomposition form with the aid of a Monte Carlo-based method. Excitation-specific sticking probabilities of CO on Cu(100) are computed, and lattice effects caused by the flexible surface atoms are demonstrated by comparison with sticking probabilities computed for a rigid surface. The dependence of the sticking probability of the initial state of the system is studied, and it is found that the sticking probability is reduced when the surface atom on the impact site is initially vibrationally excited.

Direct product-type grid representations for angular coordinates in extended space and their application in the MCTDH approach

Multi-configurational time-dependent Hartree (MCTDH) calculations using time-dependent grid representations can be used to accurately simulate high-dimensional quantum dynamics on general ab initio potential energy surfaces. Employing the correlation discrete variable representation, sets of direct product type grids are employed in the calculation of the required potential energy matrix elements. This direct product structure can be a problem if the coordinate system includes polar and azimuthal angles that result in singularities in the kinetic energy operator. In the present work, a new direct product-type discrete variable representation (DVR) for arbitrary sets of polar and azimuthal angles is introduced. It employs an extended coordinate space where the range of the polar angles is taken to be [-π, π]. The resulting extended space DVR resolves problems caused by the singularities in the kinetic energy operator without generating a very large spectral width. MCTDH calculations studying the F·CH₄ complex are used to investigate important properties of the new scheme. The scheme is found to allow for more efficient integration of the equations of motion compared to the previously employed cot-DVR approach [G. Schiffel and U. Manthe, Chem. Phys. 374, 118 (2010)] and decreases the required central processing unit times by about an order of magnitude.

Theoretical investigation of the H + HD → D + H2 chemical reaction for astrophysical applications: A state-to-state quasi-classical study

We report a large set of state-to-state rate constants for the H + HD reactive collision, using Quasi-Classical Trajectory (QCT) simulations on the accurate H₃ global potential energy surface of Mielke et al. [J. Chem. Phys. 116, 4142 (2002)]. High relative collision energies (up to ≈56 000 K) and high rovibrational levels of HD (up to ≈50 000 K), relevant to various non thermal equilibrium astrophysical media, are considered. We have validated the accuracy of our QCT calculations with a new efficient adaptation of the Multi Configuration Time Dependent Hartree (MCTDH) method to compute the reaction probability of a specific reactive channel. Our study has revealed that the high temperature regime favors the production of H₂ in its highly rovibrationnally excited states, which can de-excite radiatively (cooling the gas) or collisionally (heating the gas). Those new state-to-state QCT reaction rate constants represent a significant improvement in our understanding of the possible mechanisms leading to the destruction of HD by its collision with a H atom.

Dynamics and resonances of the H(2S) + CH+(X1Σ+) reaction in the electronic ground state: a detailed quantum wavepacket study

Initial state-selected and energy resolved channel-specific reaction probabilities, integral cross sections and thermal rate constants of the H(²S) + CH⁺(X¹Σ⁺) reaction are calculated within the coupled states approximation by a time-dependent wave packet propagation method. The new ab initio global potential energy surface (PES) of the electronic ground state (1 ²A') of the system, recently reported by Li et al. [J. Chem. Phys., 2015, 142, 124302], is employed for this purpose. All partial wave contributions up to the total angular momentum J = 60 are considered to obtain the converged integral reaction cross section up to a collision energy of 1.0 eV. Thermal rate constants are calculated by averaging the reaction cross sections over the Boltzmann distribution of energies and compared with the available theoretical and experimental results for the temperature range 10-1000 K. Investigation of the channel-specific reaction attributes shows that the H abstraction (CH⁺ destruction) channel is highly favored over the H exchange channel. The effect of rotational and vibrational excitations of the CH⁺ reagent on the dynamics is also studied. The resonances formed during the course of the reaction are also identified by calculating the transition state spectrum and characterized in terms of the eigenfunctions and lifetimes. More than 260 vibrational levels are obtained and their eigenfunctions are calculated, which are represented in terms of the nodal assignments and the eigenenergies. They reveal both the local and hyperspherical behavior for the bound and quasibound states of the CH₂⁺ complex in the ground 1 ²A' surface. The lifetime analysis of the quasibound states indicates that the CH₂⁺ resonances survive for as long as ∼400 fs at high energies (E ∼ 2.0 eV) and are expected to decay faster with further increasing energy. Finally, the type of mechanism for the formation of the product (C⁺ + H₂) is elucidated.

Quantum and quasi-classical collisional dynamics of O2-Ar at high temperatures

A hypersonic vehicle traveling at a high speed disrupts the distribution of internal states in the ambient flow and introduces a nonequilibrium distribution in the post-shock conditions. We investigate the vibrational relaxation in diatom-atom collisions in the range of temperatures between 1000 and 10 000 K by comparing results of extensive fully quantum-mechanical and quasi-classical simulations with available experimental data. The present paper simulates the interaction of molecular oxygen with argon as the first step in developing the aerothermodynamics models based on first principles. We devise a routine to standardize such calculations also for other scattering systems. Our results demonstrate very good agreement of vibrational relaxation time, derived from quantum-mechanical calculations with the experimental measurements conducted in shock tube facilities. At the same time, the quasi-classical simulations fail to accurately predict rates of vibrationally inelastic transitions at temperatures lower than 3000 K. This observation and the computational cost of adopted methods suggest that the next generation of high fidelity thermochemical models should be a combination of quantum and quasi-classical approaches.

Influence of the Reactants Rotational Excitation on the H + D2(v = 0, j) Reactivity

We have analyzed the influence of the rotational excitation on the H + D2(v = 0, j) reaction through quantum mechanical (QM) and quasiclassical trajectories (QCT) calculations at a wide range of total energies. The agreement between both types of calculations is excellent. We have found that the rotational excitation largely increases the reactivity at large values of the total energy. Such an increase cannot be attributed to a stereodynamical effect but to the existence of recrossing trajectories that become reactive as the target molecule gets rotationally excited. At low total energies, however, recrossing is not significant and the reactivity evolution is dominated by changes in the collision energy; the reactivity decreases with the collision energy as it shrinks the acceptance cone. When state-to-state results are considered, rotational excitation leads to cold product's rovibrational distributions, so that most of the energy is released as recoil energy.

Effect of Coriolis coupling in chemical reaction dynamics

It is essential to evaluate the role of Coriolis coupling effect in molecular reaction dynamics. Here we consider Coriolis coupling effect in quantum reactive scattering calculations in the context of both adiabaticity and nonadiabaticity, with particular emphasis on examining the role of Coriolis coupling effect in reaction dynamics of triatomic molecular systems. We present the results of our own calculations by the time-dependent quantum wave packet approach for H + D2 and F(2P3/2,2P1/2) + H2 as well as for the ion-molecule collisions of He + H2 +, D(-) + H2, H(-) + D2, and D+ + H2, after reviewing in detail other related research efforts on this issue.

Rovibrational energy transfer in ortho-H2+para-H2 collisions

We present the results of a full-dimensional quantum mechanical study of the rovibrational energy transfer in the collision between ortho-H2 and para-H2 in the energy range of 0.1-1.0 eV. The multiconfiguration time-dependent Hartree algorithm has been used to propagate the wave packets on the global potential energy surface by Boothroyd et al. [J. Chem. Phys. 116, 666 (2002)] and on a modification of this surface where the short range anisotropy is reduced. State-to-state attributes such as probabilities or integral cross sections are obtained using the formalism of Tannor and Weeks [J. Chem. Phys. 98, 3884 (1993)] by Fourier transforming the correlation functions. The effect of initial rotation of the diatoms on the inelastic and de-excitation processes is investigated.

Theoretical investigation of highly excited vibrational states in DFCO: Calculation of the out-of-plane bending states and simulation of the intramolecular vibrational energy redistribution

A previously developed modified Davidson scheme [C. Iung and F. Ribeiro, J. Chem. Phys. 121, 174105 (2005)] is applied to compute and analyze highly excited (nu2,nu6) eigenstates in DFCO. The present paper is also devoted to the simulations of the intramolecular vibrational energy redistribution (IVR) initiated by an excitation of the out-of-plane bending vibration (nnu6, n=2,4,6, . . . ,18, and 20). The multiconfiguration time-dependent Hartree method is exploited to propagate the corresponding six-dimensional wave packets. A comprehensive comparison with experimental data as well as with previous simulations of IVR in HFCO [G. Pasin et al. J. Chem. Phys. 124, 194304 (2006)] is presented.

Influence of rotation and isotope effects on the dynamics of the N(D2)+H2 reactive system and of its deuterated variants

Integral cross sections and thermal rate constants have been calculated for the N((2)D)+H(2) reaction and its isotopic variants N((2)D)+D(2) and the two-channel N((2)D)+HD by means of quasiclassical trajectory and statistical quantum-mechanical model methods on the latest ab initio potential-energy surface [T.-S. Ho et al., J. Chem. Phys. 119, 3063 (2003)]. The effect of rotational excitation of the diatom on the dynamics of these reactions has been investigated and interesting discrepancies between the classical and statistical model calculations have been found. Whereas a net effect of reagent rotation on reactivity is always observed in the classical calculations, only a very slight effect is observed in the case of the asymmetric N((2)D)+HD reaction for the statistical quantum-mechanical method. The thermal rate constants calculated on this Potential-Energy Surface using quasiclassical trajectory and statistical model methods are in good agreement with the experimental determinations, although the latter are somewhat larger. A reevaluation of the collinear barrier of the potential surface used in the present study seems timely. Further theoretical and experimental studies are needed for a full understanding of the dynamics of the title reaction.

Rotational excitation cross sections of para-H2+para-H2 collisions. A full-dimensional wave-packet propagation study using an exact form of the kinetic energy

A full-dimensional quantum dynamical study of the rotational excitation in para-para H2 + H2 collisions using the potential-energy surface of Boothroyd et al. [J. Chem. Phys. 116, 666 (2002)] is reported. The multiconfiguration time-dependent Hartree algorithm is utilized to propagate wave packets and the cross sections for collision energies up to 1.2 eV are determined by a flux analysis through the interaction of the wave packet with a complex absorbing potential. Calculations for a collection of total angular momenta up to J = 70 are performed; the missing channels are obtained with a J-interpolation algorithm.

Quasiclassical determination of reaction probabilities as a function of the total angular momentum

This article presents a quasiclassical trajectory (QCT) method to determine the reaction probability as a function of the total angular momentum J for any given value of the initial rotational angular momentum j. The proposed method is based on a discrete sampling of the total and orbital angular momenta for each trajectory and on the development of equations that have a clear counterpart in the quantum-mechanical (QM) case. The reliability of the method is illustrated by comparing QCT and time-dependent wave-packet QM results for the H+D(2)(upsilon=0,j=4,10) reaction. The small discrepancies between both sets of calculations, when they exist, indicate some genuine quantum effects. In addition, a procedure to extract the reaction probabilities as a function of J when trajectories are calculated in the usual way using a continuous distribution of impact parameters is also described.

Multiconfigurational time-dependent Hartree calculations for dissociative adsorption of H2 on Cu(100)

The efficiency of the multiconfigurational time-dependent Hartree (MCTDH) method for calculating the initial-state selected dissociation probability of H(2)(v=0,j=0) on Cu(100) is investigated. The MCTDH method is shown to be significantly more efficient than standard wave packet methods. A large number of single-particle functions is required to converge the initial-state selected reaction probability for dissociative adsorption. Employing multidimensional coordinates in the MCTDH ansatz (mode combination) is found to be crucial for the efficiency of these MCTDH calculations. Perspectives towards the application of the MCTDH approach to study dissociative adsorption of polyatomic molecules on surfaces are discussed.