Global Potential Energy Surface Research Articles

Study on Quantum Dynamics of the Na + Na2 Exchanged Reaction and Lifetime Prediction of Na3 Complex Based on the Neural Network Potential Energy Surface.

A high-precision global potential energy surface (PES) is constructed for the Na3 system based on high-level ab initio calculations and the fundamental invariant neural network (FI-NN) method. The root-mean-square error (RMSE) of the PES is 2.88 cm-1. The state-resolved quantum dynamics of the ground-state Na + Na2 (v = 0, j = 0) → Na2 (v', j') + Na reaction is studied using the time-dependent wave packet (TDWP) method on the new PES. Analysis of the relevant integral cross sections revealed a complicated energy-transfer mechanism during collisions. Similarly, the characteristics of the differential cross sections indicate that the complex-forming mechanism plays a dominant role in the reaction, providing conditions for a comprehensive exploration of the lifetimes of the complexes. Based on the Rice-Ramsperger-Kassel-Marcus (RRKM) theory, the calculated lifetime of the Na3 complex is approximately 3.9 ns.

Calculations of Dissociation Dynamics of CH3OH on a Global Potential Energy Surface Reveal the Mechanism for the Formation of HCOH; Roaming Plays a Role.

The experimental observation of hydroxymethylene, HCOH, following excitation of methanol at 193 nm, was reported recently (Hockey, E. K.; McLane, N.; Martí, C.; Duckett, L.; Osborn, D. L.; Dodson, L. G. Direct Observation of Gas-Phase Hydroxymethylene: Photoionization and Kinetics Resulting from Methanol Photodissociation. J. Am. Chem. Soc. 2024, 146, 14416-14421, 10.1021/jacs.4c03090). This stimulated us to investigate a dynamic mechanism for its formation using a global potential energy surface for the ground electronic state (S0) of methanol. We show via quasi-classical trajectory calculations that hydroxymethylene is indeed formed under the reasonable assumption that the initially excited state undergoes rapid internal conversion to S0. From the trajectories, fractional yields of the six major product channels are determined as a function of excitation energy, and the rate of production of each is determined from the fractions and rate of methanol disappearance. Roaming is observed in trajectories leading to the OH and CH3 products as well as in those leading to CH2OH + H and non-reactive trajectories. A "frustrated" roaming accounts for roughly 20% of the HCOH production.

Full-dimensional coupled-channel statistical approach to atom-triatom systems and applications to H/D + O3 reaction.

The statistical quantum model (SQM), which assumes that the reactivity is controlled by entrance/exit channel quantum capture probabilities, is well suited for chemical reactions with a long-lived intermediate complex. In this work, a time-independent coupled-channel implementation of the SQM approach is developed for atom-triatom systems in full dimensionality. As SQM treats the capture dynamics quantum mechanically, it is capable of handling quantum effects such as tunneling. A detailed study of the H/D + O3 capture dynamics was performed by applying the newly developed SQM method on an accurate global potential energy surface. Agreement with previous ring polymer molecular dynamics (RPMD) results on the same potential energy surface is excellent except for very low temperatures. The SQM results are also in reasonably good agreement with available experimental rate coefficients. The strong H/D kinetic isotope effect underscores the dominant role of quantum tunneling under an entrance channel barrier at low temperatures.

Benchmarking of quantum fidelity kernels for Gaussian process regression

Abstract Quantum computing algorithms have been shown to produce performant quantum kernels for machine-learning classification problems. Here, we examine the performance of quantum kernels for regression problems of practical interest. For an unbiased benchmarking of quantum kernels, it is necessary to construct the most optimal functional form of the classical kernels and the most optimal quantum kernels for each given data set. We develop an algorithm that uses an analog of the Bayesian information criterion to optimize the sequence of quantum gates used to estimate quantum kernels for Gaussian process models. The algorithm increases the complexity of the quantum circuits incrementally, while improving the performance of the resulting kernels, and is shown to yield much higher model accuracy with fewer quantum gates than a fixed quantum circuit ansatz. We demonstrate that quantum kernels thus obtained can be used to build accurate models of global potential energy surfaces (PES) for polyatomic molecules. The average interpolation error of the six-dimensional PES obtained with a random distribution of 2000 energy points is 16 cm−1 for H3O+, 15 cm−1 for H2CO and 88 cm−1 for HNO2. We show that a compositional optimization of classical kernels for Gaussian process regression converges to the same errors. This indicates that quantum kernels can achieve the same, though not better, expressivity as classical kernels for regression problems.

Non-adiabatic dynamics studies of the C+(2P1/2, 3/2) + H2 reaction: Based on global diabatic potential energy surfaces of CH2.

Global diabatic potential energy surfaces (PESs) of CH2+ are constructed using the neural network method with a specific function based on 18 213 abinitio points. The multi-reference configuration interaction method with the aug-cc-pVQZ basis set is adopted to perform the abinitio calculations. The topographical properties of the diabatic PESs are examined in detail. In general, the diabatic PESs provide an accurate quasi-diabatic representation. To validate the diabatic PESs, the dynamics studies of the C+(2P1/2, 3/2) + H2 (v0 = 0, j0 = 0) → H + CH+(X1Σ+) reaction are performed using the time-dependent wave packet method. The reaction probabilities, integral cross sections, differential cross sections, and rate constants are calculated and compared with the experimental and theoretical results. Non-adiabatic dynamics results are in good agreement with experimental data. In addition, the non-adiabatic effect in the C+(2P1/2, 3/2) + H2 reaction is significant due to the non-adiabatic results being obviously larger than adiabatic values. The reasonable non-adiabatic dynamics results indicate that present diabatic PESs can be recommended for any type of dynamics study.

Intersystem Crossing Control of the Nb+ + CO2 → NbO+ + CO Reaction.

The transfer of an oxygen atom from carbon dioxide (CO2) to a transition metal cation in the gas phase offers atomic level insights into single-atom catalysis for CO2 activation. Given that these reactions often involve open-shell transition metals, they may proceed through intersystem crossing between different spin manifolds. However, a definitive understanding of such spin-forbidden reaction requires dynamical calculations on multiple global potential energy surfaces (PESs) coupled by spin-orbit couplings. In this work, we report global PESs and spin-orbit couplings for three low-lying spin (quintet, triplet, and singlet) states for the reaction between the niobium cation (Nb+) and CO2, which are used to investigate the nonadiabatic reaction dynamics and kinetics. Comparison with experimental data of kinetics and collision dynamics shows satisfactory agreement. This reaction is found to be very similar to that between Ta+ + CO2. Specifically, our theoretical findings suggest that the rate-limiting step in this reaction is intersystem crossing, rather than potential barriers.

High-Energy Reaction Dynamics of N3.

The atom-exchange and atomization dissociation dynamics for the N(4S) + N2(1Σg+) reaction are studied using a reproducing kernel Hilbert space (RKHS)-based, global potential energy surface (PES) at the MRCI-F12/aug-cc-pVTZ-F12 level of theory (MRCI, multireference configuration interaction). For the atom exchange reaction (NANB + NC → NANC + NB), computed thermal rates and their temperature dependence from quasi-classical trajectory (QCT) simulations agree to within error bars with the available experiments. Companion QCT simulations using a recently published CASPT2-based PES confirm these findings. For the atomization reaction, leading to three N(4S) atoms, the computed rates from the RKHS-PES overestimate the experimentally reported rates by 1 order of magnitude, whereas those from the permutationally invariant polynomial (PIP)-PES agree favorably, and the T dependence of both computations is consistent with the experiment. These differences can be traced back to the different methods and basis sets used. The lifetime of the metastable N3 molecule is estimated to be ∼200 fs depending on the initial state of the reactants. Finally, neural-network-based exhaustive state-to-distribution models are presented using both PESs for the atom exchange reaction. These models will be instrumental for a broader exploration of the reaction dynamics of air.

A Globally Accurate Neural Network Potential Energy Surface and Quantum Dynamics Studies on Be+(2S) + H2/D2 → BeH+/BeD+ + H/D Reactions.

Chemical reactions between Be+ ions and H2 molecules have significance in the fields of ultracold chemistry and astrophysics, but the corresponding dynamics studies on the ground-state reaction have not been reported because of the lack of a global potential energy surface (PES). Herein, a globally accurate ground-state BeH2+ PES is constructed using the neural network model based on 18,657 ab initio points calculated by the multi-reference configuration interaction method with the aug-cc-PVQZ basis set. On the newly constructed PES, the state-to-state quantum dynamics calculations of the Be+(2S) + H2(v0 = 0; j0 = 0) and Be+(2S) + D2(v0 = 0; j0 = 0) reactions are performed using the time-dependent wave packet method. The calculated results suggest that the two reactions are dominated by the complex-forming mechanism and the direct abstraction process at relatively low and high collision energies, respectively, and the isotope substitution has little effect on the reaction dynamics characteristics. The new PES can be used to further study the reaction dynamics of the BeH2+ system, such as the effects of rovibrational excitations and alignment of reactant molecules, and the present dynamics data could provide an important reference for further experimental studies at a finer level.

Revealing new pathways for the reaction of Criegee intermediate CH2OO with SO2

Criegee intermediates play an important role in the tropospheric oxidation models through their reactions with atmospheric trace chemicals. We develop a global full-dimensional potential energy surface for the CH2OO + SO2 system and reveal how the reaction happens step by step by quasi-classical trajectory simulations. A new pathway forming the main products (CH2O + SO3) and a new product channel (CO2 + H2 + SO2) are predicted in our simulations. The new pathway appears at collision energies greater than 10 kcal/mol whose behavior demonstrates a typical barrier-controlled reaction. This threshold is also consistent with the ab initio transition state barrier height. For the minor products, a loose complex OCH2O ∙ ∙ ∙ SO2 is formed first, and then in most cases it soon turns into HCOOH + SO2, in a few cases it decomposes into CO2 + H2 + SO2 which is a new product channel, and rarely it remains as ∙OCH2O ∙ + SO2.

A Neural Network Potential Energy Surface and Quantum Dynamics Study of Ca(1S) + H2(v 0 = 0, j 0 = 0) → CaH + H Reaction.

The reactive collision between Ca and H2 molecules has attracted great interest experimentally due to the key role of the product CaH molecule in the field of astrophysics and cold molecules. However, quantum dynamics calculations for this system have not been reported due to the lack of a global potential energy surface (PES). Herein, a globally accurate PES of the ground-state CaH2 is developed by combining 11365 high-level ab initio points and permutation invariant polynomial neural network method. Based on the newly constructed PES, the state-to-state quantum dynamics calculations for the Ca(1S) + H2 (v 0 = 0, j 0 = 0) → CaH + H reaction are carried out using the time-dependent wave packet method. The dynamic results reveal that the reaction follows the complex-forming mechanism near the reactive threshold, whereas both the indirect insertion mechanism and direct abstraction mechanism have effects at higher collision energies. The newly constructed PES can be used to further study the influence of isotope substitution, rovibrational excitation, and spatial orientation of reactant molecules on reaction dynamics.

New Potential Energy Surface for the H + Cl2 Reaction and Quantum Dynamics Studies.

The reaction of H + Cl2 → HCl + Cl plays a crucial role in various fields. However, no previous study has investigated this reaction using accurate quantum mechanical methods. In this paper, we construct a global potential energy surface (PES) using the neural network method with more than 20,000 ab initio energies obtained by the MRCI-F12+Q method with the aug-cc-pV5Z basis and extrapolated to the complete basis set limit. The spin-orbit coupling of the Cl atom has been considered in the PES. With this new PES, product state-resolved quantum dynamics calculations for the H + Cl2 (v0 = 0, j0 = 0-2) → HCl + Cl reaction was carried out. Numerical results show that the initial rotational excitation of the Cl2 has negligible effects on the reactivity. Product state-resolved integral cross sections (ICS) and rate constants reveal that the HCl is most favorably produced in its v' = 2 vibrational state. The calculated product vibrational state-resolved and total reaction rate constants suggest that the new global PES is accurate enough, as compared with the available experimental measurements.

New Diabatic Potential Energy Surfaces for the Li + H2 Reaction and Time-Dependent Quantum Wave Packet Studies.

New global diabatic potential energy surfaces (DPESs) for the ground (12A') and first excited (22A') states for the Li + H2 system were developed, with more than 30,000 energy points at the IC-MRCI+Q level of theory, utilizing the aug-cc-pV5Z basis set for the H atoms and the cc-pCV5Z basis set for the Li atom, fitted by a single neural network (NN) with symmetry. Product state-resolved quantum dynamics calculations of the nonadiabatic reaction Li (2P) + H2 (X 1 ∑g+, v0 = 0, j0 = 0) → LiH (X 1∑+) + H(2S) were carried out using these new DPESs and also the previous HYLC-DPESs. The numerical results suggested that our newly constructed DPESs provided an accurate description of the LiH2 system.

Multistate Dynamics and Kinetics of CO2 Activation by Ta+ in the Gas Phase: Insights into Single-Atom Catalysis.

The activation of carbon dioxide (CO2) by a transition-metal cation in the gas phase is a unique model system for understanding single-atom catalysis. The mechanism of such reactions is often attributed to a "two-state reactivity" model in which the high-energy barrier of a spin state correlating with ground-state reactants is avoided by intersystem crossing (ISC) to a different spin state with a lower barrier. However, such a "spin-forbidden" mechanism, along with the corresponding dynamics, has seldom been rigorously examined theoretically, due to the lack of global potential energy surfaces (PESs). In this work, we report full-dimensional PESs of the lowest-lying quintet, triplet, and singlet states of the TaCO2+ system, machine-learned from first-principles data. These PESs and the corresponding spin-orbit couplings enable us to provide an extensive theoretical characterization of the dynamics and kinetics of the reaction between the tantalum cation (Ta+) and CO2, which have recently been investigated experimentally at high collision energies using crossed beams and velocity map imaging, as well as at thermal energies using a selected-ion flow tube apparatus. The multistate quasi-classical trajectory simulations with surface hopping reproduce most of the measured product translational and angular distributions, shedding valuable light on the nonadiabatic reaction dynamics. The calculated rate coefficients from 200 to 600 K are also in good agreement with the latest experimental measurements. More importantly, these calculations revealed that the reaction is controlled by intersystem crossing, rather than potential barriers.

Global Potential Energy Surfaces by Compressed-State Multistate Pair-Density Functional Theory for Hyperthermal Collisions in the O2+O2 System.

Interactions between oxygen molecules play an important role in atmospheric chemistry and hypersonic flow chemistry in atmospheric entries. Recently, high-quality ab initio potential energy surface (PES) of the quintet O4 was reported by Paukku et al. [J. Chem. Phys. 147, 034301 (2017)]. 10543 configurations were sampled and calculated at the level of MS-CASPT2/maug-cc-pVTZ with scaled external correlation. The PES was fitted to a many-body (MB) form with the many-body part described by the permutationally invariant polynomial approach (MB-PIP). In this work, the PIP-Neural Network (PIP-NN) and MB-PIP-NN methods were used to refit the PES based on the same data by Paukku et al. Three PESs were compared. It was found that the performances differ significantly in the O+O3 region as well as in the long-range region. Therefore, additional 1300 points were sampled, and the efficient compressed-state multistate pair-density functional theory (CMS-PDFT) was used to calculate the electronic structure of these 1300 points and 10543 points by Paukku et al. Then, a completely new quintet PES was fitted using the MB-PIP-NN method. Based on this PES, the quasi-classical trajectory (QCT) approach was used to reveal all possible reaction channels for hyperthermal O2-O2 collisions.

A new global potential energy surface of CaH2 system constructed with neural network method and dynamics studies of the Ca(4s21S) + H2 reaction

A new global potential energy surface (PES) for the ground state of CaH2 system was constructed by using neural network method. This paper provides a comprehensive discussion on the topographical characteristics of the PES and the spectral properties of stationary points. Furthermore, a time-dependent wave packet method was used to perform the dynamics studies on the Ca(4 s2 1S) + H2 reaction based on the newly constructed PES. Some meaningful dynamics results are reported, including reaction probabilities, integral cross sections and differential cross sections. In addition, the reaction mechanism of the Ca(4 s2 1S) + H2 reaction was discussed in detail.

New Full-Dimensional Reactive Potential Energy Surface for the H4 System.

As the most abundant molecule in the universe, collisions involving H2 have important implications in astrochemistry. Collisions between hydrogen molecules also represent a prototype for assessing various dynamic methods for understanding fundamental few-body processes. In this work, we develop a new and highly accurate full-dimensional potential energy surface (PES) covering all reactive channels of the H2 + H2 system, which extends our previously reported H2 + H2 nonreactive PES [J. Chem. Theory Comput., 2021, 17, 6747] by adding 39,538 additional ab initio points calculated at the MRCI/AV5Z level in the reactive channels. The global PES is represented with high fidelity (RMSE = 0.6 meV for a total of 79,000 points) by a permutation invariant polynomial neural network (PIP-NN) and is suitable for studying collision-induced dissociation, single-exchange, as well as four-center exchange reactions. Preliminary quasi-classical trajectory studies on the new PIP-NN PES reveal strong vibrational enhancement of all reaction channels.

Parametrically Managed Activation Functions for Improved Global Potential Energy Surfaces for Six Coupled 5A' States and Fourteen Coupled 3A' States of O + O2.

We report new potential energy surfaces for six coupled 5A' states and 14 coupled 3A' states of O3. The new surfaces are created by parametrically managed diabatization by deep neural network (PM-DDNN). The PM-DDNN method uses calculated adiabatic potential energy surfaces to discover and fit an underlying adiabatic-equivalent set of diabatic surfaces and their couplings and obtains the fit to the adiabatic surfaces by diagonalization of the diabatic potential energy matrix (DPEM). The procedure yields the adiabatic surfaces and their gradients, as well as the DPEM and its gradient. If desired one can also compute the nonadiabatic coupling due to the transformation. The present work improves on previous work by using a new coordinate to guide the decay of the neural network contribution to the many-body fit to the whole DPEM. The main objective was to obtain smoother potentials than the previous ones with better suitability for dynamics calculations, and this was achieved. Furthermore, we obtained suitably small deviations from the input reference data. For the six coupled 5A' surfaces, the 60,366 data below 10 eV are fit with a mean unsigned error (MUE) of 49 meV, and for the 14 coupled 3A' surfaces, the 76,733 data below 10 eV are fit with an MUE of 28 meV. The data below 5 eV fit even more accurately with MUEs of 37 meV (5A') and 20 meV (3A').

Global potential energy surface survey of pentanitrogen cation

We reported hitherto the most extensive isomeric, interconversion and decomposition landscape of the pentanitrogen cation (N5 +) at the CCSD(T)_CBS//MP2/cc-pVTZ, CBS-QB3 and CCSD(T)_CBS//CCSD/cc-pVTZ levels. A maximum number of eleven isomers and fourteen transition states were located, among which three and eight were reported for the first time. Moreover, the counterion stabilisation effect by the model BF4 − anion as well as the solvation effect in anhydrous HF solvent at different temperatures were investigated. Notably, although 01 is rather well known, a new type of N2-extrusion process for the 01 salt (with BF4 − counterion) was identified.

Dynamics studies for the multi-well and multi-channel reaction of OH with C2H2 on a full-dimensional global potential energy surface.

The C2H2 + OH reaction is an important acetylene oxidation pathway in the combustion process, as well as a typical multi-well and multi-channel reaction. Here, we report an accurate full-dimensional machine learning-based potential energy surface (PES) for the C2H2 + OH reaction at the UCCSD(T)-F12b/cc-pVTZ-F12 level, based on about 475 000 ab initio points. Extensive quasi-classical trajectory (QCT) calculations were performed on the newly developed PES to obtain detailed dynamic data and analyze reaction mechanisms. Below 1000 K, the C2H2 + OH reaction produces H + OCCH2 and CO + CH3. With increasing temperature, the product channels H2O + C2H and H + HCCOH are accessible and the former dominates above 1900 K. It is found that the formation of H2O + C2H is dominated by a direct reaction process, while other channels belong to the indirect mechanism involving long-lived intermediates along the reaction pathways. At low temperatures, the C2H2 + OH reaction behaves like an unimolecular reaction due to the unique PES topographic features, of which the dynamic features are similar to the decomposition of energy-rich complexes formed by C2H2 + OH collision. The classification of trajectories that undergo different reaction pathways to generate each product and their product energy distributions were also reported in this work. This dynamic information may provide a deep understanding of the C2H2 + OH reaction.

Artificial intelligence driven molecule adsorption prediction (AIMAP) applied to chirality recognition of amino acid adsorption on metals.

Predicting the adsorption structure of molecules has long been a challenging topic given the coupled complexity of surface binding sites and molecule flexibility. Here, we develop AIMAP, an Artificial Intelligence Driven Molecule Adsorption Prediction tool, to achieve the general-purpose end-to-end prediction of molecule adsorption structures. AIMAP features efficient exploration of the global potential energy surface of the adsorption system based on global neural network (G-NN) potential, by rapidly screening qualified adsorption patterns and fine searching using stochastic surface walking (SSW) global optimization. We demonstrate the AIMAP efficiency in constructing the Cu-HCNO6 adsorption database, encompassing 1 182 351 distinct adsorption configurations of 9592 molecules on three copper surfaces. AIMAP is then utilized to identify the best adsorption structure for 18 amino acids (AAs) on achiral Cu surfaces and the chiral Cu(3,1,17) S surface. We find that AAs chemisorb on copper surfaces in their highest deprotonated state, through both the carboxylate-amino skeleton and side groups. The chiral recognition is identified for the d-preference of Asp, Glu, and Tyr, and l-preference for His. The physical origin for the enantiospecific adsorption is thus rationalized, pointing to the critical role of the competitive adsorption between functional side groups and the carboxylate-amino skeleton at surface low-coordination sites.