Scattering Theory and Dynamics: Time-Dependent and Time-Independent Methods

Modeling of collision-induced excitation and quenching of atomic nitrogen

Excited atomic nitrogen atoms play an important role in plasma formation in hypersonic shock-waves, as happens during spacecraft reentry and other high velocity vehicle applications. In this study, we have thoroughly studied collision induced excitation associated with two colliding nitrogen atoms in the N(4S), N(2D), and N(2P) states at collision energies up to 6 eV, using time-independent scattering calculations to determine cross sections and temperature-dependent rate coefficients. The calculations are based on potential curves and couplings determined in earlier multireference configuration interaction calculations with large basis sets, and the results are in good agreement with experiments where comparisons are possible. To properly consider the spin-orbit coupling matrix, we have developed a scaling method for treating transitions between different fine-structure components that only require calculations with two coupled states, and with this, we define accurate degeneracy factors for determining cross sections and rate coefficients that include all states. The results indicate that both spin-orbit and derivative coupling effects can play important roles in collisional excitation and quenching, and that although derivative coupling is always much stronger than spin-orbit, there are many transitions where only spin-orbit can contribute. As part of this, we identify two distinct pathways associated with N(2P) relaxation and one Auger-like mechanism leading to two N(2D) that could be important at high temperatures.

Simulation of Chemical Reactions on a Quantum Computer

Studying chemical reactions, particularly in the gas phase, relies heavily on computing scattering matrix elements. These elements are essential for characterizing molecular reactions and accurately determining reaction probabilities. However, the intricate nature of quantum interactions poses challenges, necessitating the use of advanced mathematical models and computational approaches to tackle the inherent complexities. In this study, we develop and apply a quantum computing algorithm for the calculation of scattering matrix elements. In our approach, we employ the time-dependent method based on the Møller operator formulation where the S-matrix element between the respective reactant and product channels is determined through the time correlation function of the reactant and product Møller wavepackets. We successfully apply our quantum algorithm to calculate scattering matrix elements for 1D semi-infinite square well potential and on the colinear hydrogen exchange reaction. As we navigate the complexities of quantum interactions, this quantum algorithm is general and emerges as a promising avenue, shedding light on new possibilities for simulating chemical reactions on quantum computers.

Progress towards machine learning reaction rate constants

Quantum and classical reaction rate constant calculations come at the cost of exploring potential energy surfaces. Due to the "curse of dimensionality", their evaluation quickly becomes unfeasible as the system size grows. Machine learning algorithms can accelerate the calculation of reaction rate constants by predicting them using low cost input features. In this perspective, we briefly introduce supervised machine learning algorithms in the context of reaction rate constant prediction. We discuss existing and recently created kinetic datasets and input feature representations as well as the use and design of machine learning algorithms to predict reaction rate constants or quantities required for their computation. Amongst these, we first describe the use of machine learning to predict activation, reaction, solvation and dissociation energies. We then look at the use of machine learning to predict reactive force field parameters, reaction rate constants as well as to help accelerate the search for minimum energy paths. Lastly, we provide an outlook on areas which have yet to be explored so as to improve and evaluate the use of machine learning algorithms for chemical reaction rate constants.

Quantum Dynamics and Kinetics of the F + H2 and F + D2 Reactions at Low and Ultra-Low Temperatures

Integral cross sections and rate constants for the prototypical chemical reactions of the fluorine atom with molecular hydrogen and deuterium have been calculated over a wide interval of collision energy and temperature ranging from the sub-thermal (50 K) down to the ultra-cold regimes (0.5 mK). Rigorous close coupling time-independent quantum reactive scattering calculations have been carried out on two potential energy surfaces, differing only at long-range in the reactants' channel. The results show that tunnel, resonance and virtual state effects enhance under-barrier reactivity giving rise to pronounced deviations from the Arrhenius law as temperature is lowered. Within the ultra-cold domain (below 1 mK), the reactivity is governed by virtual state effects and by tunneling through the reaction barrier; in the cold regime (1 mK–1 K), the shape resonances in the entrance channel of the potential energy surface make the quantum tunneling contribution larger so enhancing cross sections and rate constants by about one order of magnitude; at higher temperatures (above 10 K), the tunneling pathway enhanced by the constructive interference between two Feshbach resonances trapped in the reaction exit channel competes with the thermally activated mechanism, as the energy gets closer to the reaction barrier height. The results show that at low temperatures cross sections and rate constants are extremely sensitive to small changes in the long-range intermolecular interaction in the entrance channel of the potential energy surface, as well as to isotopic substitution.

Quantum state-to-state study for (H−(D−),HD) collisions on two potential energy surfaces

Revealing the reaction mechanisms of the H⁻/D⁻ + HD reaction – an exact quantum dynamics study on two potential energy surfaces.

Steepest-entropy-ascent nonequilibrium quantum thermodynamic framework to model chemical reaction rates at an atomistic level

The steepest entropy ascent (SEA) dynamical principle provides a general framework for modeling the dynamics of nonequilibrium (NE) phenomena at any level of description, including the atomistic one. It has recently been shown to provide a precise implementation and meaning to the maximum entropy production principle and to encompass many well-established theories of nonequilibrium thermodynamics into a single unifying geometrical framework. Its original formulation in the framework of quantum thermodynamics (QT) assumes the simplest and most natural Fisher-Rao metric to geometrize from a dynamical standpoint the manifold of density operators, which represent the thermodynamic NE states of the system. This simplest SEAQT formulation is used here to develop a general mathematical framework for modeling the NE time evolution of the quantum state of a chemically reactive mixture at an atomistic level. The method is illustrated for a simple two-reaction kinetic scheme of the overall reaction F+H_{2}⇔HF+F in an isolated tank of fixed volume. However, the general formalism is developed for a reactive system subject to multiple reaction mechanisms. To explicitly implement the SEAQT nonlinear law of evolution for the density operator, both the energy and the particle number eigenvalue problems are set up and solved analytically under the dilute gas approximation. The system-level energy and particle number eigenvalues and eigenstates are used in the SEAQT equation of motion to determine the time evolution of the density operator, thus effectively describing the overall kinetics of the reacting system as it relaxes toward stable chemical equilibrium. The predicted time evolution in the near-equilibrium limit is compared to the reaction rates given by a standard detailed kinetic model so as to extract the single time constant needed by the present SEA model.

Decoherence Allows Model Reduction in Nonadiabatic Dynamics Simulations

A nonadiabatic (NA) molecular dynamics (MD) simulation requires calculation of NA coupling matrix elements, the number of which scales as a square of the number of basis states. The basis size can be huge in studies of nanoscale materials, and calculation of the NA couplings can present a significant bottleneck. A quantum-classical approximation, NAMD overestimates coherence in the quantum, electronic subsystem, requiring decoherence correction. Generally, decoherence times decrease with increasing energy separation between pairs of states forming coherent superpositions. Since rapid decoherence stops quantum dynamics, one expects that decoherence-corrected NAMD can eliminate the need for calculation of NA couplings between energetically distant states, notably reducing the computational cost. Considering several types of dynamics in a semiconductor quantum dot, we demonstrate that indeed, decoherence allows one to reduce the number of needed NA coupling matrix elements. If the energy levels are spaced closer than 0.1 eV, one obtains good results while including only three nearest-neighbor couplings, and in some cases even with just the first nearest-neighbor coupling scheme. If the energy levels are spaced by about 0.4 eV, the nearest-neighbor model fails, while three or more nearest-neighbor schemes also provide good results. In comparison, the results of NAMD simulation without decoherence vary continuously with changes in the number of NA couplings. Thus, decoherence effects induced by coupling to a quantum-mechanical environment not only provide the physical mechanism for NAMD trajectory branding and improve the accuracy of NAMD simulations, but also afford significant computational savings.

Theoretical methods for ultrafast spectroscopy

Time-resolved spectroscopy in the femtosecond and attosecond time domain is a tool to unravel the dynamics of nuclear and electronic motion in molecular systems. Theoretical insight into the underlying physical processes is ideally gained by solving the time-dependent Schrödinger equation. In this work, methods currently used to solve this equation are reviewed in a compact presentation. These methods involve numerical representations of wavefunctions and operators, the calculation of time evolution operators, the setting up of the Hamiltonian operators and the types of coordinates to be used hereto. The advantages and disadvantages of some methods are discussed.

QUANTITATIVE QUANTUM DYNAMICS CALCULATION OF H2 + CH3 → H + CH4 REACTION

We report in this paper quantum dynamics calculation of state-selected reaction probabilities for a benchmark chemical reaction H 2 + CH 3 → H + CH 4 on an ab initio potential energy surface. The quantum dynamics calculation is based on the recently developed semirigid vibrating rotor target (SVRT) model and involves six degrees of freedom. The present result is the first such high-level quantum dynamics calculation of microscopic reaction probability for a chemical reaction between two molecules with at least one of the reagents being larger than a diatomic molecule.

Accurate ab initio potential energy curve of F2. I. Nonrelativistic full valence configuration interaction energies using the correlation energy extrapolation by intrinsic scaling method

The recently introduced method of correlation energy extrapolation by intrinsic scaling (CEEIS) is used to calculate the nonrelativistic electron correlations in the valence shell of the F(2) molecule at 13 internuclear distances along the ground state potential energy curve from 1.14 A to 8 A, the equilibrium distance being 1.412 A. Using Dunning's correlation-consistent double-, triple-, and quadruple-zeta basis sets, the full configuration interaction energies are determined, with an accuracy of about 0.3 mhartree, by successively generating up to octuple excitations with respect to multiconfigurational reference functions that strongly change along the reaction path. The energies of the reference functions and those of the correlation energies with respect to these reference functions are then extrapolated to their complete basis set limits. The applicability of the CEEIS method to strongly multiconfigurational reference functions is documented in detail.

Three Dimensional Quantum Dynamics of (H-, H2) and Its Isotopic Variants

We present the results of a time-dependent quantum mechanical investigation using centrifugal sudden approximation in the form of reaction probability as a function of collision energy (E(trans)) in the range 0.3-3.0 eV for a range of total angular momentum (J) values and the excitation function sigma(E(trans)) for the exchange reaction H(-) + H(2) (v = 0, j = 0) --> H(2) + H(-) and its isotopic variants in three dimensions on an accurate ab initio potential energy surface published recently (J. Chem. Phys. 2004, 121, 9343). The excitation function results are shown to be in excellent agreement with those obtained from crossed beam measurements by Zimmer and Linder for H(-) + D(2) collisions for energies below the threshold for electron detachment channel and somewhat larger than the most recent results of Haufler et al. for (H(-), D(2)) and (D(-), H(2)) collisions.

Spatial distributions of angular momenta in quantum and quasiclassical stereodynamics

We have recently reported a derivation of the relationship between the quantum and classical descriptions of angular momentum polarization [M. P. de Miranda and F. Javier Aoiz, Phys. Rev. Lett. 93, 083201 (2004)]. This paper presents a detailed account of the derivation outlined in that paper, and discusses the implications of the new results. These include (i) a new expression of the role of the uncertainty principle in the broadening of angular momentum distributions, (ii) the attribution of azimuthal fluctuations of angular momentum distributions to spatial quantum beats, (iii) the definition of a new Fourier transform of the density matrix, distinct from those suggested in the past, that provides an alternative view of how the quantum description of angular momentum polarization approaches the classical one in the correspondence principle limit, (iv) a prescription for the determination of a quasiclassical angular momentum distribution function that does not suffer from problems encountered with its purely classical counterpart, and (v) a description of how angular momentum distributions commonly visualized with recourse to the classical vector model can be depicted with exact and well-defined quantum mechanics.

Dynamics of (H−,H2) collisions: A time-dependent quantum mechanical investigation on a newab initiopotential energy surface

A global analytical potential energy surface for the ground state of H(3)(-) has been constructed by fitting an analytic function to the ab initio potential energy values computed using coupled cluster singles and doubles with perturbative triples [CCSD(T)] method and Dunning's augmented correlation consistent polarized valence triple zeta basis set. Using this potential energy surface, time-dependent quantum mechanical wave packet calculations were carried out to calculate the reaction probabilities (P(R)) for the exchange reaction H(-)+H(2)(v, j)-->H(2)+H(-), for different initial vibrational (v) and rotational (j) states of H(2), for total angular momentum equal to zero. With increase in v, the number of oscillations in the P(R)(E) plot increases and the oscillations become more pronounced. While P(R) increases with increase in rotational excitation from j=0 to 1, it decreases with further increase in j to 2 over a wide range of energies. In addition, rotational excitation quenches the oscillations in P(R)(E) plots.

Mode-specific energy disposal in the four-atom reaction OH + D2 --> HOD + D

Experiments, employing crossed molecular beams, with vibrational state resolution have been performed on the simplest four-atom reaction, OH + D2 --> HOD + D. In good agreement with the most recent quantum scattering predictions, mode-specific reaction dynamics is observed, with vibration in the newly formed oxygen-deuterium bond preferentially excited to v = 2. This demonstrates that quantum theoretical calculations, which in the past decade have achieved remarkable accuracy for three-atom reactions involving three dimensions, have progressed to the point where it is now possible to accurately predict energy disposal in four-atom reactions involving six dimensions.

First-principles theory for the H + H2O, D2O reactions

A full quantum dynamical study of the reactions of a hydrogen atom with water, on an accurate ab initio potential energy surface, is reported. The theoretical results are compared with available experimental data for the exchange and abstraction reactions in H + D2O and H + H2O. Clear agreement between theory and experiment is revealed for available thermal rate coefficients and the effects of vibrational excitation of the reactants. The excellent agreement between experiment and theory on integral cross sections for the exchange reaction is unprecedented beyond atom-diatom reactions. However, the experimental cross sections for abstraction are larger than the theoretical values by more than a factor of 10. Further experiments are required to resolve this.

Quantum theory of chemical reaction dynamics

It is now possible to use rigorous quantum scattering theory to perform accurate calculations on the detailed state-to-state dynamics of chemical reactions in the gas phase. Calculations on simple reactions, such as H + D2 --> HD + D and F + H2 --> HF + H, compete with experiment in their accuracy. Recent advances in theory promise to extend such accurate predictions to more complicated reactions, such as OH + H2 --> H2O + H, and even to reactions of molecules on solid surfaces. New experimental techniques for probing reaction transition states, such as negative-ion photodetachment spectroscopy and pump-probe femtosecond spectroscopy, are stimulating the development of new theories.