Revisiting the Gaussian process regression for fitting high-dimensional potential energy surface and its application to the OH + HO2→O2+ H2O reaction

Construction of a Mode-Combination Hamiltonian under the Grid-Based Representation for the Quantum Dynamics of OH + HO2 → O2 + H2O

In this work, a systematic construction framework on a mode-combination Hamiltonian operator of a typical polyatomic reaction, OH + HO2 → O2 + H2O, is developed. First, a set of Jacobi coordinates are employed to construct the kinetic energy operator (KEO) through the polyspherical approach ( Phys. Rep. 2009, 484, 169). Second, due to the multiconfigurational electronic structure of this system, a non-adiabatic potential energy surface (PES) is constructed where the first singlet and triplet states are involved with spin-orbital coupling. To improve the training database, the training set of random energy data was optimized through a popular iterative optimization approach with extensive trajectories. Here, we propose an automatic trajectory method, instead of the classical trajectory on a crude PES, where the gradients are directly computed by the present ab initio calculations. Third, on the basis of the training set, the potential function is directly constructed in the canonical polyadic decomposition (CPD) form ( J. Chem. Theory Comput. 2021, 17, 2702-2713) which is helpful in propagating the nuclear wave function under the grid-based representation. To do this, the Gaussian process regression (GPR) approach for building the CPD form, called the CPD-GPR method ( J. Phys. Chem. Lett. 2022, 13, 11128-11135) is adopted where we further revise CPD-GPR by introducing the mode-combination (mc) scheme leading to the present CPD-mc-GPR approach. Constructing the full-dimension non-adiabatic Hamiltonian operator with mode combination, as test calculations, the nuclear wave function is propagated to preliminarily compute the reactive probability of OH + HO2 → O2 + H2O where the reactants are prepared in vibrational ground states and in the first triplet electronic state.

Chemistry-Informed Generative Model for Classical Dynamics Simulations

In this work, a chemistry-informed generative model was proposed, leading to the chemistry-informed generative adversarial network (CI-GAN) approach. To easily build the input database for complex molecular systems, an image-input algorithm is also implemented, leading to the capability to directly recognize the molecular image. Extensive test calculations and analysis on typical examples, H + H2, OH + HO2, and H2O/TiO2(110), find that the present CI-GAN approach generates distributions of geometry and energy. Calculations on the above examples show that the present CI-GAN approach is able to generate 50%-80% meaningful results among all of the generated data with chemistry constraints. Thus, it has the potential capability to predict classical dynamics simulations as well as ab initio calculations avoiding expensive calculations. These results and the power of CI-GANs in generating ab initio energies and MD trajectories are deeply discussed.

Machine Learning Representations of the Three Lowest Adiabatic Electronic Potential Energy Surfaces for the ArH2+ Reactive System

In this work, we present Gaussian process regression machine learning representations of the three lowest coupled 2A' adiabatic electronic potential energy surfaces of the ArH2+ reactive system in full dimensionality. Additionally, the nonadiabatic coupling matrix elements were calculated. These adiabatic potentials and their nonadiabatic couplings are necessary ingredients in the theoretical investigation of the nonadiabatic reaction dynamics of the Ar + H2+ → ArH+ + H and Ar+ + H2 → ArH+ + H reactions, as well as the competing charge transfer process, Ar + H2+↔ Ar+ + H2. Accurate ab initio electronic structure calculations (ic-MRCI+Q/aug-cc-pVQZ), whereby the effect of spin-orbit coupling in Ar+ has been accounted for through the state interaction method, serve as input for the machine learning training process. The potential energy surfaces are fitted with high accuracies, with root-mean-square errors on the order of 10-7 eV for the three surfaces, which meet the requirements for chemical dynamics at low temperature. It was found that quite a large number of training points (of the order of 5000 ab initio points) are needed in order to achieve these accuracies due to the complex topography of these electronic surfaces.

New Measurements and Calculations on the Kinetics of an Old Reaction: OH + HO2 → H2O + O2

Literature rate coefficients for the prototypical radical-radical reaction at 298 K vary by close to an order of magnitude; such variations challenge our understanding of fundamental reaction kinetics. We have studied the title reaction at room temperature via the use of laser flash photolysis to generate OH and HO₂ radicals, monitoring OH by laser-induced fluorescence using two different approaches, looking at the direct reaction and also the perturbation of the slow OH + H₂O₂ reaction with radical concentration, and over a wide range of pressures. Both approaches give a consistent measurement of k_1,298K ∼1 × 10^-11 cm³ molecule^-1 s^-1, at the lowest limit of previous determinations. We observe, experimentally, for the first time, a significant enhancement in the rate coefficient in the presence of water, k_1,H2O, 298K = (2.17 ± 0.09) × 10^-28 cm⁶ molecule^-2 s^-1, where the error is statistical at the 1σ level. This result is consistent with previous theoretical calculations, and the effect goes some way to explaining some, but not all, of the variation in previous determinations of k_1,298K. Supporting master equation calculations, using calculated potential energy surfaces at the RCCSD(T)-F12b/CBS//RCCSD/aug-cc-pVTZ and UCCSD(T)/CBS//UCCSD/aug-cc-pVTZ levels, are in agreement with our experimental observations. However, realistic variations in barrier heights and transition state frequencies give a wide range of calculated rate coefficients showing that the current precision and accuracy of calculations are insufficient to resolve the experimental discrepancies. The lower value of k_1,298K is consistent with experimental observations of the rate coefficient of the related reaction, Cl + HO₂ → HCl + O₂. The implications of these results in atmospheric models are discussed.

Globally Accurate Gaussian Process Potential Energy Surface and Quantum Dynamics Studies on the Li(2S) + Na2 → LiNa + Na Reaction at Low Collision Energies

The LiNa2 reactive system has recently received great attention in the experimental study of ultracold chemical reactions, but the corresponding theoretical calculations have not been carried out. Here, we report the first globally accurate ground-state LiNa2 potential energy surface (PES) using a Gaussian process model based on only 1776 actively selected high-level ab initio training points. The constructed PES had high precision and strong generalization capability. On the new PES, the quantum dynamics calculations on the Li(2S) + Na2(v = 0, j = 0) → LiNa + Na reaction were carried out in the 0.001–0.01 eV collision energy range using an improved time-dependent wave packet method. The calculated results indicate that this reaction is dominated by a complex-forming mechanism at low collision energies. The presented dynamics data provide guidance for experimental research, and the newly constructed PES could be further used for ultracold reaction dynamics calculations on this reactive system.

Direct Canonical-Polyadic-Decomposition of the Potential Energy Surface from Discrete Data by Decoupled Gaussian Process Regression

A Gaussian process regression (GPR) approach for directly constructing the canonical polyadic decomposition (CPD) of a multidimensional potential energy surface (PES) by discrete training energies is proposed and denoted by CPD-GPR. The present CPD-GPR method requires the kernel function in a product of a series of one-dimensional functions. To test CPD-GPR, the reactive probabilities of H + H₂ as a function of kinetics energy are performed. Comparing the dynamics results computed by the CPD-GPR PES with those by the original PES, a good agreement between these results can be clearly found. Discussions on the previous algorithms for building the decomposed form are also given. We further show that the CPD-GPR method might be the general algorithm for building the decomposed form. However, further development is needed to reduce the CPD rank. Therefore, the present CPD-GPR method might be helpful to inspire ideas for developing new tools in building decomposed potential functions.

Quantum Gaussian process model of potential energy surface for a polyatomic molecule

With gates of a quantum computer designed to encode multi-dimensional vectors, projections of quantum computer states onto specific qubit states can produce kernels of reproducing kernel Hilbert spaces. We show that quantum kernels obtained with a fixed ansatz implementable on current quantum computers can be used for accurate regression models of global potential energy surfaces (PESs) for polyatomic molecules. To obtain accurate regression models, we apply Bayesian optimization to maximize marginal likelihood by varying the parameters of the quantum gates. This yields Gaussian process models with quantum kernels. We illustrate the effect of qubit entanglement in the quantum kernels and explore the generalization performance of quantum Gaussian processes by extrapolating global six-dimensional PESs in the energy domain.

Representing Globally Accurate Reactive Potential Energy Surfaces with Complex Topography by Combining Gaussian Process Regression and Neural Network

There has been increasing attention in using machine learning technologies, such as neural network (NN) and Gaussian process regression (GPR), to model multidimensional potential energy surfaces (PESs). NN PES features...

Machine learning meets chemical physics

Over recent years, the use of statistical learning techniques applied to chemical problems has gained substantial momentum. This is particularly apparent in the realm of physical chemistry, where the balance between empiricism and physics-based theory has traditionally been rather in favor of the latter. In this guest Editorial for the special topic issue on "Machine Learning Meets Chemical Physics," a brief rationale is provided, followed by an overview of the topics covered. We conclude by making some general remarks.

Kinetic study of the OH + HO2 → H2O + O2 reaction using ring polymer molecular dynamics and quantum dynamics

The reaction OH + HO2 → H2O + O2 is a prototype of radical-radical reactions. It plays an important role in interstellar/atmospheric chemistry and combustion, and considerable attention has thus been dedicated to its kinetics. In our previous work, we reported an accurate full-dimensional potential energy surface for the title reaction on the ground triplet electronic state. The quasi-classical trajectory (QCT) approach was employed to investigate its kinetics. Although the QCT rate coefficients were in good agreement with some experimental and theoretical results, QCT cannot account for the quantum mechanical effects, such as zero-point vibrational energy, recrossing, and tunneling, which may significantly affect the rate coefficients, particularly at low temperatures. In this work, the reduced-dimensional quantum dynamics and ring polymer molecular dynamics calculations were carried out to examine these effects and their impact on rate coefficients over the temperature range of 300-1300 K.