A realistic double many-body expansion (DMBE) potential energy surface for ground-state O3from a multiproperty fit toab initiocalculations, and to experimental spectroscopic, inelastic scattering, and kinetic isotope thermal rate data

Gaussian Process Regression for State-to-State Integral Cross Sections: The Case of the O + O2 Collision Dissociation Reactions

Research on hypersonic vehicles has become increasingly important worldwide in recent years. However, accurately simulating the dynamics of the nonequilibrium high-temperature reactions that are in the hypersonic flow around the vehicles presents a significant challenge as a large number of states and transitions are accessible even for the smallest atom-diatom reaction systems. It is quite difficult, sometimes even impossible, to exhaustively investigate all relevant combinations or determine high-dimensional analytical representations for the state-to-state reaction probabilities. In this study, we used Gaussian process regression (GPR) to fit a model based on only 807 QCT data for training. The confidence interval of the GPR prediction and the Kullback-Leibler (KL) divergence were used to help minimize the sampling amount of data for fitting the converged GPR model. The model aims to predict the state-to-state integral cross section (ICS) of the O + O2 → 3O dissociation reaction under random initial conditions (Et, v, j). In total, it took almost a month to obtain this converged GPR model, but it took only a few seconds to predict the ICS value for any initial condition. For 330 initial conditions not included in the training set, the mean-square error (MSE) between the QCT-calculated ICSs and the GPR-predicted ones is only 0.08 Å2 and the R2 is 0.9986, indicating that the GPR model can replace the direct expensive QCT calculation with high accuracy. Finally, we calculated the equilibrium dissociation rate coefficients based on the StS ICS values predicted by the GPR model, and the results were in good agreement with available experimental and theoretical results. Thus, this study provides an effective and accurate approach to the extensive direct state-to-state reaction dynamic calculations.

Reformulation of All ONIOM-Type Molecular Fragmentation Approaches and Many-Body Theories Using Graph-Theory-Based Projection Operators: Applications to Dynamics, Molecular Potential Surfaces, Machine Learning, and Quantum Computing

We present a graph-theory-based reformulation of all ONIOM-based molecular fragmentation methods. We discuss applications to (a) accurate post-Hartree-Fock AIMD that can be conducted at DFT cost for medium-sized systems, (b) hybrid DFT condensed-phase studies at the cost of pure density functionals, (c) reduced cost on-the-fly large basis gas-phase AIMD and condensed-phase studies, (d) post-Hartree-Fock-level potential surfaces at DFT cost to obtain quantum nuclear effects, and (e) novel transfer machine learning protocols derived from these measures. Additionally, in previous work, the unifying strategy discussed here has been used to construct new quantum computing algorithms. Thus, we conclude that this reformulation is robust and accurate.

Graph-|Q⟩⟨C|: A Quantum Algorithm with Reduced Quantum Circuit Depth for Electronic Structure

The accurate determination of chemical properties is known to have a critical impact on multiple fundamental chemical problems but is deeply hindered by the steep algebraic scaling of electron correlation calculations and the exponential scaling of quantum nuclear dynamics. With the advent of new quantum computing hardware and associated developments in creating new paradigms for quantum software, this avenue has been recognized as perhaps one way to address exponentially complex challenges in quantum chemistry and molecular dynamics. In this paper, we discuss a new approach to drastically reduce the quantum circuit depth (by several orders of magnitude) and help improve the accuracy in the quantum computation of electron correlation energies for large molecular systems. The method is derived from a graph-theoretic approach to molecular fragmentation and enables us to create a family of projection operators that decompose quantum circuits into separate unitary processes. Some of these processes can be treated on quantum hardware and others on classical hardware in a completely asynchronous and parallel fashion. Numerical benchmarks are provided through the computation of unitary coupled-cluster singles and doubles (UCCSD) energies for medium-sized protonated and neutral water clusters using the new quantum algorithms presented here.

Graph-Theoretic Molecular Fragmentation for Potential Surfaces Leads Naturally to a Tensor Network Form and Allows Accurate and Efficient Quantum Nuclear Dynamics

Molecular fragmentation methods have revolutionized quantum chemistry. Here, we use a graph-theoretically generated molecular fragmentation method, to obtain accurate and efficient representations for multidimensional potential energy surfaces and the quantum time-evolution operator, which plays a critical role in quantum chemical dynamics. In doing so, we find that the graph-theoretic fragmentation approach naturally reduces the potential portion of the time-evolution operator into a tensor network that contains a stream of coupled lower-dimensional propagation steps to potentially achieve quantum dynamics with reduced complexity. Furthermore, the fragmentation approach used here has previously been shown to allow accurate and efficient computation of post-Hartree-Fock electronic potential energy surfaces, which in many cases has been shown to be at density functional theory cost. Thus, by combining the advantages of molecular fragmentation with the tensor network formalism, the approach yields an on-the-fly quantum dynamics scheme where both the electronic potential calculation and nuclear propagation portion are enormously simplified through a single stroke. The method is demonstrated by computing approximations to the propagator and to potential surfaces for a set of coupled nuclear dimensions within a protonated water wire problem exhibiting the Grotthuss mechanism of proton transport. In all cases, our approach has been shown to reduce the complexity of representing the quantum propagator, and by extension action of the propagator on an initial wavepacket, by several orders, with minimal loss in accuracy.

Graph Theoretic Molecular Fragmentation for Multidimensional Potential Energy Surfaces Yield an Adaptive and General Transfer Machine Learning Protocol

Over a series of publications we have introduced a graph-theoretic description for molecular fragmentation. Here, a system is divided into a set of nodes, or vertices, that are then connected through edges, faces, and higher-order simplexes to represent a collection of spatially overlapping and locally interacting subsystems. Each such subsystem is treated at two levels of electronic structure theory, and the result is used to construct many-body expansions that are then embedded within an ONIOM-scheme. These expansions converge rapidly with many-body order (or graphical rank) of subsystems and have been previously used for ab initio molecular dynamics (AIMD) calculations and for computing multidimensional potential energy surfaces. Specifically, in all these cases we have shown that CCSD and MP2 level AIMD trajectories and potential surfaces may be obtained at density functional theory cost. The approach has been demonstrated for gas-phase studies, for condensed phase electronic structure, and also for basis set extrapolation-based AIMD. Recently, this approach has also been used to derive new quantum-computing algorithms that enormously reduce the quantum circuit depth in a circuit-based computation of correlated electronic structure. In this publication, we introduce (a) a family of neural networks that act in parallel to represent, efficiently, the post-Hartree-Fock electronic structure energy contributions for all simplexes (fragments), and (b) a new k-means-based tessellation strategy to glean training data for high-dimensional molecular spaces and minimize the extent of training needed to construct this family of neural networks. The approach is particularly useful when coupled cluster accuracy is desired and when fragment sizes grow in order to capture nonlocal interactions accurately. The unique multidimensional k-means tessellation/clustering algorithm used to determine our training data for all fragments is shown to be extremely efficient and reduces the needed training to only 10% of data for all fragments to obtain accurate neural networks for each fragment. These fully connected dense neural networks are then used to extrapolate the potential energy surface for all molecular fragments, and these are then combined as per our graph-theoretic procedure to transfer the learning process to a full system energy for the entire AIMD trajectory at less than one-tenth the cost as compared to a regular fragmentation-based AIMD calculation.

Graph-Theory-Based Molecular Fragmentation for Efficient and Accurate Potential Surface Calculations in Multiple Dimensions

We present a multitopology molecular fragmentation approach, based on graph theory, to calculate multidimensional potential energy surfaces in agreement with post-Hartree-Fock levels of theory but at the density functional theory cost. A molecular assembly is coarse-grained into a set of graph-theoretic nodes that are then connected with edges to represent a collection of locally interacting subsystems up to an arbitrary order. Each of the subsystems is treated at two levels of electronic structure theory, the result being used to construct many-body expansions that are embedded within an ONIOM scheme. These expansions converge rapidly with the many-body order (or graphical rank) of subsystems and capture many-body interactions accurately and efficiently. However, multiple graphs, and hence multiple fragmentation topologies, may be defined in molecular configuration space that may arise during conformational sampling or from reactive, bond breaking and bond formation, events. Obtaining the resultant potential surfaces is an exponential scaling proposition, given the number of electronic structure computations needed. We utilize a family of graph-theoretic representations within a variational scheme to obtain multidimensional potential surfaces at a reduced cost. The fast convergence of the graph-theoretic expansion with increasing order of many-body interactions alleviates the exponential scaling cost for computing potential surfaces, with the need to only use molecular fragments that contain a fewer number of quantum nuclear degrees of freedom compared to the full system. This is because the dimensionality of the conformational space sampled by the fragment subsystems is much smaller than the full molecular configurational space. Additionally, we also introduce a multidimensional clustering algorithm, based on physically defined criteria, to reduce the number of energy calculations by orders of magnitude. The molecular systems benchmarked include coupled proton motion in protonated water wires. The potential energy surfaces and multidimensional nuclear eigenstates obtained are shown to be in very good agreement with those from explicit post-Hartree-Fock calculations that become prohibitive as the number of quantum nuclear dimensions grows. The developments here provide a rigorous and efficient alternative to this important chemical physics problem.

Weighted-Graph-Theoretic Methods for Many-Body Corrections within ONIOM: Smooth AIMD and the Role of High-Order Many-Body Terms

We present a weighted-graph-theoretic approach to adaptively compute contributions from many-body approximations for smooth and accurate post-Hartree-Fock (pHF) ab initio molecular dynamics (AIMD) of highly fluxional chemical systems. This approach is ONIOM-like, where the full system is treated at a computationally feasible quality of treatment (density functional theory (DFT) for the size of systems considered in this publication), which is then improved through a perturbative correction that captures local many-body interactions up to a certain order within a higher level of theory (post-Hartree-Fock in this publication) described through graph-theoretic techniques. Due to the fluxional and dynamical nature of the systems studied here, these graphical representations evolve during dynamics. As a result, energetic "hops" appear as the graphical representation deforms with the evolution of the chemical and physical properties of the system. In this paper, we introduce dynamically weighted, linear combinations of graphs, where the transition between graphical representations is smoothly achieved by considering a range of neighboring graphical representations at a given instant during dynamics. We compare these trajectories with those obtained from a set of trajectories where the range of local many-body interactions considered is increased, sometimes to the maximum available limit, which yields conservative trajectories as the order of interactions is increased. The weighted-graph approach presents improved dynamics trajectories while only using lower-order many-body interaction terms. The methods are compared by computing dynamical properties through time-correlation functions and structural distribution functions. In all cases, the weighted-graph approach provides accurate results at a lower cost.

Rovibrationally state-specific collision model for the O2(Σg-3) + O(P3) system in DSMC

A rovibrationally state-specific collision model for the O₂(Σg-3)+O(P3) system is presented for direct simulation Monte Carlo, including rotation-vibration-translation energy transfer, exchange, dissociation, and recombination processes. The two-step binary collision approach is employed to model recombination reactions. Two available cross section databases by Andrienko/Boyd and Esposito/Capitelli are employed for the rovibrationally resolved model (rv-STS) and vibrationally resolved model (v-STS), respectively. The difference between rv-STS and v-STS comes from two contributions: the multisurface factor of dissociation (f_MS) and the rotational averaging process. The dissociation cross section with the constant f_MS is typically larger than with the variable f_MS, especially for the low vibrational energy states. On the other hand, the cross sections resulting from the rotationally averaged database are found to underpredict the dissociation rate coefficient at low temperatures. In the rovibrational heating case, the rv-STS predicts faster relaxation than the v-STS, which also shows a lower quasi-steady-state temperature than v-STS. In the rovibrational cooling case, the rv-STS shows a faster relaxation than v-STS, which also presents a thermal non-equilibrium between rovibrational and translational mode during the cooling process.

Data-Inspired and Physics-Driven Model Reduction for Dissociation: Application to the O2 + O System

This work presents an in-depth discussion on the nonequilibrium dissociation of O₂ molecules colliding with O atoms, combining quasi-classical trajectory calculations, master equation, and dimensionality reduction. A rovibrationally resolved database for all of the elementary collisional processes is constructed by including all nine adiabatic electronic states of O₃ in the QCT calculations. A detailed analysis of the ab initio data set reveals that for a rovibrational level, the probability of dissociating is mostly dictated by its deficit in internal energy compared to the centrifugal barrier. Because of the assumption of rotational equilibrium, the conventional vibrational-specific calculations fail to characterize such a dependence. Based on this observation, a new physics-based grouping strategy for application to coarse-grained models is proposed. By relying on a hybrid technique made of rovibrationally resolved excitation coupled to coarse-grained dissociation, the new approach is compared to the vibrational-specific model and the direct solution of the rovibrational state-to-state master equation. Simulations are performed in a zero-dimensional isothermal and isochoric chemical reactor for a wide range of temperatures (1500-20,000 K). The study shows that the main contribution to the model inadequacy of vibrational-specific approaches originates from the incapability of characterizing dissociation, rather than the energy transfers. Even when constructed with only twenty groups, the new reduced-order model outperforms the vibrational-specific one in predicting all of the QoIs related to dissociation kinetics. At the highest temperature, the accuracy in the mole fraction is improved by 2000%.

The importance of O3 excited potential energy surfaces in O2-O high-temperature kinetics

The mechanism of vibrational relaxation and dissociation in the O₂-O system at elevated temperatures is investigated by means of molecular dynamics. The most recent O₃ potential energy surfaces (PESs), obtained from the first principles quantum mechanical calculations [Varga et al., J. Chem. Phys. 147, 154312 (2017)], are used to derive a complete set of state-specific rate coefficients of vibrational energy transfer and dissociation. Unlike most of the previous efforts that utilize only the lowest and supposedly most reactive 1¹A' O₃ PES [A. Varandas and A. Pais, Mol. Phys. 65, 843 (1988)], this paper demonstrates the necessity to account for a complete ensemble of all excited O₃ PESs that correlate with O₂(X) and O(³P) when high-temperature kinetics is of interest. At the same time, it is found that the Varandas 1¹A' O₃ PES adequately describes vibrational energy transfer and dissociating dynamics when compared to the most recent 1¹A' O₃ PES by Varga et al. [J. Chem Phys. 147, 154312 (2017)]. The differences between this new dataset and previous rate coefficients are quantified by the master equation model.

Calculation of Vibrational Relaxation Times Using a Kinetic Theory Approach

In the present work, a method for computation of vibrational relaxation times based on a kinetic theory definition is utilized to calculate vibrational relaxation times of molecules present in air (N₂, O₂, and NO) in collisions with air species particles. An overview of available experiment VT relaxation time measurements, as well as quasi-classical trajectory (QCT) calculation results, and various empirical models, is given. Different inelastic cross-section models are used for the computation of the relaxation times, and their parameters are adjusted to fit the available experimental data and QCT results. It is shown that the proposed method of calculation can give a quantitative and qualitative agreement with the available data in a wide range of temperatures; the obtained interaction parameters may be used not only for vibrational relaxation time calculation within a multitemperature framework but also for development of state-specific models for use in CFD and DSMC codes.

Dissociation cross sections for N2 + N → 3N and O2 + O → 3O using the QCT method

Cross sections for the homo-nuclear atom-diatom collision induced dissociations (CIDs): N₂ + N and O₂ + O are calculated using Quasi-Classical Trajectory (QCT) method on ab initio Potential Energy Surfaces (PESs). A number of studies for these reactions carried out in the past focused on the CID cross section values generated using London-Eyring-Polanyi-Sato PES and seldom listed the CID cross section data. A highly accurate CASSCF-CASPT2 N₃ and a new O₃ global PES are used for the present QCT analysis and the CID cross section data up to 30 eV relative energy are also published. In addition, an interpolating scheme based on spectroscopic data is introduced that fits the CID cross section for the entire ro-vibrational spectrum using QCT data generated at chosen ro-vibrational levels. The rate coefficients calculated using the generated CID cross section compare satisfactorily with the existing experimental and theoretical results. The CID cross section data generated will find an application in the development of a more precise chemical reaction model for Direct Simulation Monte Carlo code simulating hypersonic re-entry flows.

Rovibrational energy transfer and dissociation in O2-O collisions

A set of state-specific transition rates for each rovibrational level is generated for the O2(X(3)Σ(g)(-))-O(3)P system using the quasi-classical trajectory method at temperatures observed in hypersonic flows. A system of master equations describes the relaxation of the rovibrational ensemble to thermal equilibrium under ideal heat bath conditions at a constant translational temperature. Vibrational and rotational relaxation times, obtained from the average internal energies, exhibit a pattern inherent in a chemically reactive collisional pair. An intrinsic feature of the O3 molecular system with a large attractive potential is a weak temperature dependence of the rovibrational transition rates. For this reason, the quasi-steady vibrational and rotational temperatures experience a maximum at increasing translational temperature. The energy rate coefficients, that characterize the average loss of internal energy due to dissociation, quickly diminish at high temperatures, compared to other molecular systems.

Quantum-mechanical calculations on pressure and temperature dependence of three-body recombination reactions: application to ozone formation rates

A quantum-mechanical model is designed for the calculation of termolecular association reaction rate coefficients in the low-pressure fall-off regime. The dynamics is set up within the energy transfer mechanism and the kinetic scheme is the steady-state approximation. We applied this model to the formation of ozone O + O2 + M --> O3 + M for M = Ar, making use of semiquantitative potential energy surfaces. The stabilization process is treated by means of the vibrational close-coupling infinite order sudden scattering theory. Major approximations include the neglect of the O3 vibrational bending mode and rovibrational couplings. We calculated individual isotope-specific rate constants and rate constant ratios over the temperature range 10-1000 K and the pressure fall-off region 10(-7)-10(2) bar. The present results show a qualitative and semiquantitative agreement with available experiments, particularly in the temperature region of atmospheric interest.

DYNAMICAL STUDIES OF THE OZONE ISOTOPE EFFECT: A Status Report

▪ Abstract  Dynamical studies of the recombination of O and O2 to form ozone are reviewed. The focus is the intriguing isotope dependence of the recombination rate coefficient as observed by Mauersberger and coworkers in the last decade. The key quantity for understanding of this dependence appears to be the difference of zero-point energies of the two fragmentation channels to which excited ozone can dissociate, i.e., X + YZ ← XYZ* → XY + Z, where X, Y, and Z stand for the three isotopes of oxygen. Besides the isotope dependence, the variation of the recombination rate coefficient with pressure and temperature is also addressed. Despite the numerous approaches of recent years, the recombination of ozone is far from being satisfactorily explained; there are still several essential questions to be solved by detailed theoretical analysis. We mainly discuss—and critically assess—the results of our own investigations of the ozone kinetics. The work of other research groups is also evaluated.

Quantum Statistical Study of O + O2 Isotopic Exchange Reactions: Cross Sections and Rate Constants

Using a wave packet based statistical model, we compute cross sections and thermal rate constants for various isotopic variants of the O + O2 exchange reaction on a recently modified ab initio potential energy surface. The calculation predicts a highly excited rotational distribution and relatively cold vibrational distribution for the diatomic product. A small but important threshold effect was identified for the (16)O + 18O2 reaction, which is suggested to contribute to the experimentally observed negative temperature dependence of the rate ratio, k(18O + 16O2)/k(16O + 18O2). Despite reasonable agreement with quasiclassical trajectory results, however, the calculated thermal rate constants are smaller than experimental measurements by a factor from 2 to 5. The experimentally observed negative temperature dependence of the rate constants is not reproduced. Possible reasons for the theory-experiment discrepancies are discussed.

New Double Many-Body Expansion Potential Energy Surface for Ground-State HCN from a Multiproperty Fit to Accurate ab Initio Energies and Rovibrational Calculations

An accurate single-sheeted double many-body expansion potential energy surface has been obtained for the ground electronic state of the hydrogen cyanide molecule via a multiproperty fit to ab initio energies and rovibrational data. This includes 106 rovibrational levels and 2313 discrete points, which are fit with a rmsd of 4 cm(-1) and 2.42 kcal mol(-1), respectively, and seven zero first-derivatives that are reproduced at three stationary points. Since the potential also describes accurately the appropriate asymptotic limits at the various dissociation channels, it is commended both for the simulation of rovibrational spectra and reaction dynamics.