Global Potential Energy Surface Research Articles

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.

Dual Pt atoms stabilized by an optimized coordination environment for propane dehydrogenation

Tailoring atomically dispersed catalysts by various methods has been the subject of intense current research in heterogeneous catalysis. In this work, the structural stability and propane dehydrogenation performance of Pt-TiO2 catalysts with single, dual, and triple Pt atoms doped on the reduced TiO2 surface have been examined. Experimental results indicate the atomically dispersed Pt is thermally very stable and shows exceptionally high activity (TOFpropane = 4.93 s−1) and selectivity (∼98.5 %) for the dehydrogenation reaction. The recently developed machine-learning-based SSW-NN method is then employed to explore the global potential energy surface of the atomically dispersed Pt atom-doped TiO2, which suggests that the single and dual Pt atoms can be tightly held by the vacancies created on the reduced transition-metal oxide, as confirmed by DFT + U calculated energetics. After that, advanced characterization techniques are used in conjunction with microkinetic analysis to establish the quantitative structure–activity relationships. It is found that the dual-Pt-atom structure with two Pt atoms embedded in adjacent Ti and O vacancies is the only active ensemble that dramatically promotes the CH bond activation and hydrogen recombination, as compared to single Pt atoms accommodated by either Ti or O vacancies. These results provide new and direct evidence in support of the idea that specific function can be imparted to specific active sites by tuning their coordination environments, which makes it possible to tailor the catalytic properties of metal oxides to a particular reaction such as propane dehydrogenation.

High-level analytical potential-energy-surface-based dynamics of the OH- + CH3CH2Cl SN2 and E2 reactions in full (24) dimensions.

We develop a coupled-cluster full-dimensional global potential energy surface (PES) for the OH- + CH3CH2Cl reactive system, using the Robosurfer program package, which automatically samples configurations along PES-based trajectories as well as performs ab initio computations with Molpro and fitting with the monomial symmetrization approach. The analytical PES accurately describes both the bimolecular nucleophilic substitution (SN2) and elimination (E2) channels leading to the Cl- + CH3CH2OH and Cl- + H2O + C2H4 products, respectively, and allows efficient quasi-classical trajectory (QCT) simulations. QCT computations on the new PES provide accurate statistically-converged integral and differential cross sections for the OH- + CH3CH2Cl reaction, revealing the competing dynamics and mechanisms of the SN2 and E2 (anti, syn, β-α transfer) channels as well as various additional pathways leading to induced inversion of the CH3CH2Cl reactant, H-exchange between the reactants, H2O⋯Cl- complex formation, and H2O + CH3CHCl- products via proton abstraction.

Fast and accurate excited states predictions: machine learning and diabatization.

The efficiency of machine learning algorithms for electronically excited states is far behind ground-state applications. One of the underlying problems is the insufficient smoothness of the fitted potential energy surfaces and other properties in the vicinity of state crossings and conical intersections, which is a prerequisite for an efficient regression. Smooth surfaces can be obtained by switching to the diabatic basis. However, diabatization itself is still an outstanding problem. We overcome these limitations by solving both problems at once. We use a machine learning approach combining clustering and regression techniques to correct for the deficiencies of property-based diabatization which, in return, provides us with smooth surfaces that can be easily fitted. Our approach extends the applicability of property-based diabatization to multidimensional systems. We utilize the proposed diabatization scheme to achieve higher prediction accuracy for adiabatic states and we show its performance by reconstructing global potential energy surfaces of excited states of nitrosyl fluoride and formaldehyde. While the proposed methodology is independent of the specific property-based diabatization and regression algorithm, we show its performance for kernel ridge regression and a very simple diabatization based on transition multipoles. Compared to most other algorithms based on machine learning, our approach needs only a small amount of training data.

A global 2A″ state potential energy surface for the Al (2P) + O2 (Σg−3) → AlO (2Σ+) + O (3P) reaction based on the doubly hybrid functional XYG3

In this paper, a global and full-dimensional potential energy surface at the 2A″ ground state for the Al + O2 → AlO + O reaction was constructed, for the first time, based on extensive electronic structure calculations using the doubly hybrid functional XYG3 and potential energy surface fittings by neural networks. Details of the reaction paths have been analyzed. It was found that both two intermediates, the cyclic-AlO2 and the linear-OAlO, were able to dissociate to the AlO + O products, and the isomerization process between these two intermediates was controlled by conical intersections between two 2A″ states. Ro-vibrational state resolved integral cross sections have also been calculated at collision energies from 1.0 to 10.0 kcal/mol. The results support the harpooning mechanism in this metal-oxidant-involved reaction.

A new global potential energy surface for the BH2 molecule and dynamics studies of the B(2p2P) + H2 reaction

A new global potential energy surface (PES) for the ground state of the BH2 system was constructed using permutation invariant polynomial neural network. In ab initio calculation, the AVQZ basis set and multi-reference configuration interaction method was used. The topographic features of the new PES were discussed in detail. To further clarify the accuracy of PES, the dynamics studies of the B(2p2P) + H2 reaction were carried out using time-dependent wave packet method. The dynamics properties such as reaction probabilities, integral cross sections, differential cross sections (DCSs) and rate constants were reported. The DCSs indicated that the “complex-forming” reaction mechanism plays a dominant role at low collision energies and the forward abstraction mechanism dominates the reaction at high collision energies.

Global Neural Network Potential with Explicit Many-Body Functions for Improved Descriptions of Complex Potential Energy Surface.

The high dimensional machine learning potential (MLP) that has developed rapidly in the past decade represents a giant step forward in large-scale atomic simulation for complex systems. The long-range interaction and the poor description of chemical reactions are typical problems of high dimensional MLP, which are mainly caused by the poor structure discrimination of the atom-centered ML model. Herein, we propose a low-cost neural-network-based MLP architecture for fitting global potential energy surface data, namely, G-MBNN, that can offer improved energy and force resolution on a complex potential energy surface. In G-MBNN, a set of many-body energy terms based on the local atomic environment are explicitly included in computing the total energy─the total energy of the system is written as the sum of atomic energy and many-body energy contributions. These extra many-body energy terms are computationally low-cost and, importantly, can provide easy access to delicate energy terms in complex systems such as very short repulsion, long-range attractions, and sensitive angular-dependent covalent interactions. We implement G-MBNN in the LASP code and demonstrate the improved accuracy of the new framework in representative systems, including ternary-element energy materials LiCoOx, TiO2 with defects, and a series of organic reactions.

Polyatomic radiative association by quasiclassical trajectory calculations: Formation of HCN and HNC molecules in H + CN collisions.

We have developed the polyatomic extension of the established [M. Gustafsson, J. Chem. Phys. 138, 074308 (2013)] classical theory of radiative association in the absence of electronic transitions. The cross section and the emission spectrum of the process is calculated by a quasiclassical trajectory method combined with the classical Larmor formula which can provide the radiated power in collisions. We have also proposed a Monte Carlo scheme for efficient computation of ro-vibrationally quantum state resolved cross sections for radiative association. Besides the method development, the global potential energy and dipole surfaces for H + CN collisions have been calculated and fitted to test our polyatomic semiclassical method.

Molecular dynamics-driven global potential energy surfaces: Application to the AlF dimer.

In this work, we present a full-dimensional potential energy surface for AlF-AlF. We apply a general machine learning approach for full-dimensional potential energy surfaces, employing an active learning scheme trained on abinitio points, whose size grows based on the accuracy required. The training points are selected based on molecular dynamics simulations, choosing the most suitable configurations for different collision energy and mapping the most relevant part of the potential energy landscape of the system. The present approach does not require long-range information and is entirely general. As a result, it is possible to provide the full-dimensional AlF-AlF potential energy surface, requiring ≲0.01% of the configurations to be calculated abinitio. Furthermore, we analyze the general properties of the AlF-AlF system, finding critical differences with other reported results on CaF or bi-alkali dimers.

Reaction dynamics of P(4S) + O2(X3Σ−g) → O(3P) + PO(X2Π) on a global CHIPR potential energy surface of PO2(X2A1): implications for atmospheric modelling

Abstract. The reaction dynamics of P(4S) + O2(X3Σg-) → O(3P) + PO(X2Π) are thought to be important in atmospheric and interstellar chemistry. Based on the state-of-the-art ab initio energy points, we analytically constructed a global potential energy surface (PES) for the ground-state PO2(X2A1) using the combined-hyperbolic-inverse-power-representation (CHIPR) method. A total of 6471 energy points were computed by the multireference configuration interaction method with the Davidson correction and aug-cc-pV5Z basis set. The analytical CHIPR PES reproduces ab initio energies accurately with a root-mean-square deviation of 91.5 cm−1 (or 0.262 kcal mol−1). The strongly bound valence region of the PES has complicated topographical features with multiple potential wells and barriers. The attributes of the important intermediates are carefully validated with our geometry optimization results, as well as previous experimental and computational results. Finally, the reaction probability, integral cross sections, and rate constants for P(4S) + O2(X3Σg-) → O(3P) + PO(X2Π) are calculated using the quasi-classical trajectory and time-dependent wave packet methods. The trends of probability and integral cross section versus the collision energy can be divided into three stages, which are governed by the entrance barriers or exothermicity of the reaction. The rate constant demonstrates strong Arrhenius linear behaviour at relatively low temperatures but deviates from this pattern at high temperatures. The calculated cross sections and rate constants are helpful for modelling the phosphorus chemistry in atmospheric and interstellar media.

PotLib 2023: New version of a potential energy surface library for chemical systems

POTLIB is a library of global and semiglobal potential energy surface subprograms. The library currently features 410 entries, including both single-state entries and multi-state entries. When one calls the routine of a single-state entry, it returns the ground-electronic-state adiabatic potential energy surface at the input geometry. In addition, some entries also return the gradient of the surface. When one calls a multi-state entry, it returns a diabatic potential energy matrix (DPEM). If the entry also has the gradient of the DPEM, one can compute adiabatic surfaces, their gradients, and the nonadiabatic coupling vectors (NACs) from the DPEM and its gradient by diagonalization. Some but not all the routines conform to one of a set of standard interfaces. The goal is to facilitate chemical dynamics research by collecting and disseminating a comprehensive collection of state-of-the-art potential energy routines (developed by a wide, international group of researchers) with systematic and well-defined interfaces for use with chemical dynamics programs. Systems in the library include CHArO2, CHN2O+, CH2O, CH2O2, CH3N2, CH3O, CH4, CH4Br, CH4Cl, CH4F, CH4O, CH4OCl, CH4OF, CH4OH, CH5, CH5+, CH5N, CH5O2, CH8O2, C2H2N2O, C2H2O, C2H4N, C2H4O4, C2H6Cl, C2H6F, C2H6H, C2H6O, C2H6OH, C2H7, C2O2, C3H4O2, C3H7NO, C6H6O, C6H6S, C7H8S, HBrCl, HCl2, HF2, HI2, HLiF, HNaF, HO2, HO3, HOBr, HSiO, H2Br, H2ClO, H2F, H2F2, H2FO, H2Na, H2O, H2O2, H2OBr, H3, H3Cl, H3ClN, H3ClO, H3N, H3O, H3O2, H3+, H3S, H4ClSi, H4N, H4NO, H4O2, H5GeO, H5Si, H7+, AlmHn, Aln, ArNO, K2Rb2, NO2, N2O, N2O2, N3, N4, O3, and O4. New version program summaryProgram title: PotLib 2023CPC Library link to program files:https://doi.org/10.17632/chxxhnnt4p.1Licensing provisions: Apache 2.0Programming language: FortranDoes the new version supersede the previous version?: YesJournal references of previous versions: Comput. Phys. Comm. 144 (2002) 169–187 [1]; Erratum: Comput. Phys. Comm. 156 (2004) 319–32.Nature of problem: Within the Born–Oppenheimer approximation, the electronically adiabatic interactions of atoms and molecules can be represented by a potential energy surface (PES) that depends on the geometry of the reacting species [2-4]. An electronically nonadiabatic system can be approximately described by a diabatic potential energy matrix (DPEM) that also depends on molecular geometry [5,6]. The library contains Fortran subroutines of PESs and DPEMs for reactive and non-reactive systems.Solution method: The user can incorporate a PES, DPEM, or PES set from a DPEM into a chemical dynamics computer code to supply the needed potential or potentials and optionally the gradients (forces) and surface couplings.Summary of revisions: The new version includes many more potentials than the original version of the library.

Semiclassical Multistate Dynamics for Six Coupled 5A' States of O + O2.

Dynamics simulations of high-energy O2-O collisions play an important role in simulating thermal energy content and heat flux in flows around hypersonic vehicles. To carry out such dynamics simulations efficiently requires accurate global potential energy surfaces and (in most algorithms) state couplings for many energetically accessible electronic states. The ability to treat collisions involving many coupled electronic states has been a challenge for decades. Very recently, a new diabatization method, the parametrically managed diabatization by deep neural network (PM-DDNN), has been developed. The PM-DDNN method uses a deep neural network architecture with an activation function parametrically dependent on input data to discover and fit the diabatic potential energy matrix (DPEM) as a function of geometry, and the adiabatic potential energy surfaces are obtained by diagonalization of a small matrix with analytic matrix elements. Here, we applied the PM-DDNN method to the six lowest-energy potential energy surfaces in the 5A' manifold of O3 to perform simultaneous diabatization and fitting; the data are obtained by extended multistate complete-active-space second-order perturbation theory. We then used the adiabatic surfaces for dynamics calculations with three methods: coherent switching with decay of mixing (CSDM), curvature-driven CSDM (κCSDM), and electronically curvature-driven CSDM (eκCSDM). The κCSDM calculations require only adiabatic potential energies and gradients. The three dynamical methods are in good agreement. We then calculated electronically nonadiabatic, electronically inelastic, and dissociative cross sections for seven initial collision energies, five initial vibrational levels, and four initial rotational levels. Trends in the electronically inelastic cross sections as functions of the initial collision energy and vibrational level were rationalized in terms of the coordinate ranges where the gaps between the second and third potential energy surfaces are small.