Global Potential Energy Surface Research Articles

Theoretical study of the Cl(2P) + SiH4 reaction: global potential energy surface and product pair-correlated distributions. Comparison with experiment.

For the theoretical study of the title reaction, an analytical full-dimensional potential energy surface named PES-2021 was developed for the first time, by fitting high-level explicitly-correlated ab initio data. This reaction presented high exothermicity, (298 K) = -11.6 kcal mol-1, reproducing the experimental evidence; it is a barrierless reaction and no intermediate complexes were found. PES-2021 is a continuous and smooth potential energy surface, it includes intuitive concepts in its development and fitting, such as stretching and bending nuclear motions, and it presents analytical first energy derivatives. Based on PES-2021, kinetics and dynamics studies were carried out using quasi-classical trajectory calculations. In the kinetics study, over the temperature range 300-450 K, we observed that rate constants were practically independent of temperature, with an almost zero activation energy, as compared to 0.0 and -0.48 kcal mol-1 experimentally reported. In this kinetics study the role of the spin-orbit effect on reactivity was analysed. In the dynamics study, different product pair-correlated dynamics properties were compared with the only experimental evidence: product energy partition, product vibrational distribution, product angular distribution and product speed distribution. We observed two mechanisms of reaction, a stripping mechanism associated with large impact parameters and forward scattering, and an indirect mechanism associated with sideways-backward scattering related with "nearly-trapped" trajectories due to the product rotation. In general, theoretical results reasonably simulate the experimental measurements when they consider some rotational and vibrational constraints as well as binning techniques to mimic a quantum-mechanical behaviour. Although the agreement is not quantitative, the present results shed light on the mechanism of this difficult polyatomic reactive system.

A new global potential energy surface of the SH2+(X4A'') system and quantum calculations for the S+ + H2(v = 0-3, j = 0) reaction.

A new global potential energy surface (PES) for the ground state of the SH2+(X4A'') system is constructed using a permutation invariant polynomial neural network method. In ab initio calculations, the MRCI-F12 method with the AVTZ basis set is used. Furthermore, the dynamics calculations of the S+ + H2(v = 0-3, j = 0) → SH+ + H reaction are carried out based on the new PES. The reaction probabilities and integral cross sections are compared with available theoretical calculations. Present values are in general good agreement with the previous theoretical studies. However, some discrepancies can still be found due to different PESs used in the calculation. Furthermore, the vibrational energy of the reactant molecule can significantly enhance the reactivity compared to the translational energy. The differential cross sections indicated that the reaction mechanism is changed from the "head-on" rebound mechanism to the tripping mechanism with the increasing number of initial vibrational excitation state.

A neural network potential energy surface for the F + H2O ↔ HF + OH reaction and quantum dynamics study of the isotopic effect.

A global potential energy surface for the F + H2O ↔ HF + OH reaction has been constructed using the neural network method based on ∼24 000 ab initio energies calculated at the all-electron CCSD(T)-F12a/cc-pCVTZ-F12 level of theory. The correction term accounting for the influence of spin-orbit couplings has also been included with a hierarchical scheme. The isotopic effect on the total reaction probabilities of the reaction was investigated using the time-dependent wave packet method.

The C(3P) + O2(3Σg-) → CO2 ↔ CO(1Σ+) + O(1D)/O(3P) reaction: thermal and vibrational relaxation rates from 15 K to 20 000 K.

Thermal rates for the C(3P) + O2(3Σg−) ↔ CO(1Σ+)+ O(1D)/O(3P) reaction are investigated over a wide temperature range based on quasi classical trajectory (QCT) simulations on 3-dimensional, reactive potential energy surfaces (PESs) for the 1A′, (2)1A′, 1A′′, 3A′ and 3A′′ states. These five states are the energetically low-lying states of CO2 and their PESs are computed at the MRCISD+Q/aug-cc-pVTZ level of theory using a state-average CASSCF reference wave function. Analysis of the different electronic states for the CO2 → CO + O dissociation channel rationalizes the topography of this region of the PESs. The forward rates from QCT simulations match measurements between 15 K and 295 K whereas the equilibrium constant determined from the forward and reverse rates is consistent with that derived from statistical mechanics at high temperature. Vibrational relaxation, O + CO(ν = 1,2) → O + CO(ν = 0), is found to involve both, non-reactive and reactive processes. The contact time required for vibrational relaxation to take place is τ ≥ 150 fs for non-reacting and τ ≥ 330 fs for reacting (oxygen atom exchange) trajectories and the two processes are shown to probe different parts of the global potential energy surface. In agreement with experiments, low collision energy reactions for the C(3P) + O2(3Σg−, ν = 0) → CO(1Σ+) + O(1D) lead to CO(1Σ+, ν′ = 17) with an onset at Ec ∼ 0.15 eV, dominated by the 1A′ surface with contributions from the 3A′ surface. Finally, the barrier for the COA(1Σ+) + OB(3P) → COB(1Σ+) + OA(3P) atom exchange reaction on the 3A′ PES yields a barrier of ∼7 kcal mol−1 (0.300 eV), consistent with an experimentally reported value of 6.9 kcal mol−1 (0.299 eV).

Recent implementations in LASP 3.0: Global neural network potential with multiple elements and better long-range description

LASP (large-scale atomistic simulation with neural network potential) software developed by our group since 2018 is a powerful platform (www.lasphub.com) for performing atomic simulation of complex materials. The software integrates the neural network (NN) potential technique with the global potential energy surface exploration method, and thus can be utilized widely for structure prediction and reaction mechanism exploration. Here we introduce our recent update on the LASP program version 3.0, focusing on the new functionalities including the advanced neural network training based on the multi-network framework, the newly-introduced S7 and S8 power type structure descriptor (PTSD). These new functionalities are designed to further improve the accuracy of potentials and accelerate the neural network training for multiple-element systems. Taking Cu-C-H-O neural network potential and a heterogeneous catalytic model as the example, we show that these new functionalities can accelerate the training of multi-element neural network potential by using the existing single-network potential as the input. The obtained double-network potential CuCHO is robust in simulation and the introduction of S7 and S8 PTSDs can reduce the root-mean-square errors of energy by a factor of two.

Theoretical H + O3 rate coefficients from ring polymer molecular dynamics on an accurate global potential energy surface: assessing experimental uncertainties

Thermal rate coefficients and kinetic isotope effects have been calculated for an important atmospheric reaction H/D + O3 → OH/OD + O2 based on an accurate permutation invariant polynomial-neural network potential energy surface, using ring polymer molecular dynamics (RPMD), quasi-classical trajectory (QCT) and variational transition-state theory (VTST) with multidimensional tunneling. The RPMD approach yielded results that are generally in better agreement with experimental rate coefficients than the VTST and QCT ones, especially at low temperatures, attributable to its capacity to capture quantum effects such as tunneling and zero-point energy. The theoretical results support one group of existing experiments over the other. In addition, rate coefficients for the D + O3 → OD + O2 reaction are also reported using the same methods, which will allow a stringent assessment of future experimental measurements, thus helping to reduce the uncertainty in the recommended rate coefficients of this reaction.

Potential energy surface and bound states of the H2O-HF complex.

We present the first global five-dimensional potential energy surface for the H2O-HF dimer, a prototypical hydrogen bonded complex. Large scale ab initio calculations were carried out using the explicitly correlated coupled cluster approach with single- and double-excitations together with non-iterative perturbative treatment of triple excitations with the augmented correlation-consistent triple zeta basis sets, in which the water and hydrogen fluoride monomers were frozen at their vibrationally averaged geometries. The ab initio data points were fitted to obtain a global potential energy surface for the complex. The equilibrium geometry of the complex corresponds to the formation of a hydrogen bond with water acting as a proton acceptor and a binding energy of De = 3059 cm-1 (8.75 kcal/mol). The energies and wavefunctions of the lowest bound states of the complex were computed using a variational approach, and the dissociation energies of both ortho-H2O-HF (D0 = 2089.4 cm-1 or 5.97 kcal/mol) and para-H2O-HF (D0 = 2079.6 cm-1 or 5.95 kcal/mol) were obtained. The rotational constant of the complex was found to be in good agreement with the available experimental data.

Kinetics theoretical study of the O(3P) + C2H6 reaction on an ab initio-based global potential energy surface

Based on a recently developed analytical full-dimensional potential energy surface describing the gas-phase O(3P) + C2H6 reaction (Espinosa-Garcia et al. in Phys Chem Chem Phys 22:22,591, 2020), thermal rate constants and kinetic isotope effects (KIEs) were studied in the temperature range 200–3000 K using three different kinetics tools: variational transition-state theory with multidimensional tunnelling corrections (VTST/MT), ring polymer molecular dynamics (RPMD), and quasi-classical trajectory (QCT) calculations. Except the last method, which failed in the description at low temperatures, as was expected due to its classical nature, the other two methods present rate constants with differences between them of 3% at low temperatures and 25% at high temperatures, simulate the experimental measurements in the intermediate temperature range, 500–1000 K, and are intermediate between two reviews of experimental measurements at low and high temperatures, where the experimental evidence shows differences of a factor of about 5. This result shows that both methods capture quantum effects, such as zero-point energy, tunnelling, and recrossing effects. The kinetics of the title reaction presents a non-Arrhenius behavior, where the activation energy increases with temperature. Two KIEs were analyzed. For the H/D isotopes, the KIE decreases with temperature, from 46.55 to 1.18 in the temperature range 200–3000 K, while the 12C/13C KIE presents values close to unity. Unfortunately, no experimental information is available for comparison.

Beyond Born-Oppenheimer constructed diabatic potential energy surfaces for F + H2 reaction.

First principles based beyond Born-Oppenheimer theory has been implemented on the F + H2 system for constructing multistate global diabatic Potential Energy Surfaces (PESs) through the incorporation of Nonadiabatic Coupling Terms (NACTs) explicitly. The spin-orbit (SO) coupling effect on the collision process of the F + H2 reaction has been included as a perturbation to the non-relativistic electronic Hamiltonian. Adiabatic PESs and NACTs for the lowest three electronic states (12A', 22A', and 12A″) are determined in hyperspherical coordinates as functions of hyperangles for a grid of fixed values of the hyperradius. Jahn-Teller (JT) type conical intersections between the two A' states translate along C2v and linear geometries in F + H2. In addition, A' and A″ states undergo Renner-Teller (RT) interaction at collinear configurations of this system. Both JT and RT couplings are validated by integrating NACTs along properly chosen contours. Subsequently, we have solved adiabatic-to-diabatic transformation (ADT) equations to evaluate the ADT angles for constructing the diabatic potential matrix of F + H2, including the SO coupling terms. The newly calculated diabatic PESs are found to be smooth, single-valued, continuous, and symmetric and can be invoked for performing accurate scattering calculations on the F + H2 system.

Interaction of cyanogen (NCCN) with proton: A new ab initio potential energy surface

NCCNH+ is detected in interstellar medium recently. To characterize and study the collision dynamics, a new global potential energy surface for the NCCNH+ system has been generated using CCSD(T)/aug-cc-pVQZ method. NCCN–H+ has a large potential well of 7 eV indicating high stability of complex. The surface has been expanded in terms of Legendre polynomials. NCCN and NCCNH+ have been accurately characterized. The surface will be helpful for detailed understanding of quantum dynamics parameters such as ro-vibrational cross-sections and rate coefficients. The data obtained in this work will have perceptible impact to understand the cyanogen and protonated cyanogen chemistry in space.

Large-Scale Atomic Simulation via Machine Learning Potentials Constructed by Global Potential Energy Surface Exploration.

Atomic simulations based on quantum mechanics (QM) calculations have entered into the tool box of chemists over the past few decades, facilitating an understanding of a wide range of chemistry problems, from structure characterization to reactivity determination. Due to the poor scaling and high computational cost intrinsic to QM calculations, one has to either sacrifice accuracy or time when performing large-scale atomic simulations. The battle to find a better compromise between accuracy and speed has been central to the development of new theoretical methods.The recent advances of machine-learning (ML)-based large-scale atomic simulations has shown great promise to the benefit of many branches of chemistry. Instead of solving the Schrödinger equation directly, ML-based simulations rely on a large data set of accurate potential energy surfaces (PESs) and complex numerical models to predict the total energy. These simulations feature both a high speed and a high accuracy for computing large systems. Due to the lack of a physical foundation in numerical models, ML models are often frustrated in their predictivity and robustness, which are key to applications. Focusing on these concerns, here we overview the recent advances in ML methodologies for atomic simulations on three key aspects. Namely, the generation of a representative data set, the extensity of ML models, and the continuity of data representation. While global optimization methods are the natural choice for building a representative data set, the stochastic surface walking method is shown to provide the desired PES sampling for both minima and transition regions on the PES. The current ML models generally utilize local geometrical descriptors as an input and consider the total energy as the sum of atomic energies. There are many flavors of data descriptors and ML models, but the applications for material and reaction predictions are still limited, not least because of the difficulty to train the associated vast global data sets. We show that our recently designed power-type structure descriptors together with a feed-forward neural network (NN) model are compatible with highly complex global PES data, which has led to a large family of global NN (G-NN) potentials.Two recent applications of G-NN potentials in material and reaction simulations are selected to illustrate how ML-based atomic simulations can help the discovery of new materials and reactions.

Ab Initio-Based Global Potential Energy Surface and Reaction Dynamics for H2S + C

Dynamics of the reaction of hydrogen sulfide, H2S(X1A1), with ground state atomic carbon, C(3Pj), was investigated over the interpolated ab initio based potential energy surface using the quasi-classical trajectory (QCT) simulation. The reaction probability and total reactive cross section were calculated at wide range of collision energies from 2.6 kJ mol-1 to 78.8 kJ mol-1. The total rate constant of the reaction was calculated using collision theory. The energy distribution for the formation of main products (HCS/HSC + H) were also investigated. At 44.6 kJ mol-1 collision energy approximately 39.5% and 12% of total available energy release to translational and rotational energy levels of the HCS + H products, respectively, while for HSC + H these values were found to be about 61.6% and 25.7% of total available energy. The rest of total energy deposited in the vibrational modes of the products.

A general code for fitting global potential energy surfaces via CHIPR method: Direct-Fit Diatomic and tetratomic molecules

A general program to fit global adiabatic potential energy surfaces of up to tetratomic molecules to ab initio points and available spectroscopic data for simple diatomics is reported. It is based on the Combined-Hyperbolic-Inverse-Power-Representation (CHIPR) method. The final form describes all dissociating fragments and long-range/valence interactions, while obeying the system permutational symmetry. The code yields as output a Fortran 90 subroutine that readily evaluates the potential and gradient at any arbitrary geometry. Program summaryProgram title: CHIPR-4.0CPC Library link to program files:http://dx.doi.org/10.17632/8wdv87gt5x.2Licensing provisions: GPLv3Programming language: Fortran 90Journal reference of previous version: C. M. R. Rocha, A. J. C. Varandas, Comput. Phys. Commun. 247 (2020) 106913Does the new version supersede the previous version?: YesReasons for the new version: CHIPR-4.0 is a major extension of the previous CHIPR-3.0 code [1] which, besides diatomics and triatomics, also includes the possibility of fitting global adiabatic potential energy surfaces (PESs) of A4-, AB3-, A2B2-, ABC2- and ABCD-type tetratomic molecules [3]. Additionally, a new feature is that it allows the user to fine-tune ab initio diatomic curves using available spectroscopic data.Summary of revisions:• Implementation of CHIPR’s polynomial form and permutation operators for tetratomic molecules• Implementation of a direct-fit module to fine-tune ab initio potential energy curves using spectroscopic data• Automatic global minimum search on the diatomic, triatomic or tetratomic final PESs• Automatic harmonic vibrational analysis at the optimum molecular geometriesNature of problem: This version of the CHIPR code, CHIPR-4.0, provides a set of subroutines to fit global adiabatic potential energy surfaces of up to tetratomic molecules using ab initio and (for diatomics) optional fine-tuning experimental data.Solution method: CHIPR-4.0 uses the Combined-Hyperbolic-Inverse-Power-Representation (CHIPR) [2] method to interpolate and extrapolate ab initio data points.Additional comments including restrictions and unusual features: For triatomic and tetratomic fits, the user must supply subroutines containing the analytic forms defining the sum of two- and two-plus-three-bodies, respectively. These are utilized internally to calculate (from ab initio data) the corresponding three- and four-body energies to be fitted. The current version of this code is strictly based on single-sheeted analytical PESs. High-accuracy in diatomic refinements is currently limited to the 1Σ single-curve case.

Theoretical investigation of the H + HD → D + H2 chemical reaction for astrophysical applications: A state-to-state quasi-classical study.

We report a large set of state-to-state rate constants for the H + HD reactive collision, using Quasi-Classical Trajectory (QCT) simulations on the accurate H3 global potential energy surface of Mielke et al. [J. Chem. Phys. 116, 4142 (2002)]. High relative collision energies (up to ≈56 000 K) and high rovibrational levels of HD (up to ≈50 000 K), relevant to various non thermal equilibrium astrophysical media, are considered. We have validated the accuracy of our QCT calculations with a new efficient adaptation of the Multi Configuration Time Dependent Hartree (MCTDH) method to compute the reaction probability of a specific reactive channel. Our study has revealed that the high temperature regime favors the production of H2 in its highly rovibrationnally excited states, which can de-excite radiatively (cooling the gas) or collisionally (heating the gas). Those new state-to-state QCT reaction rate constants represent a significant improvement in our understanding of the possible mechanisms leading to the destruction of HD by its collision with a H atom.

Exclusive Neural Network Representation of the Quasi-Diabatic Hamiltonians Including Conical Intersections.

We propose a numerically simple and straightforward, yet accurate and efficient neural networks-based fitting strategy to construct coupled potential energy surfaces (PESs) in a quasi-diabatic representation. The fundamental invariants are incorporated to account for the complete nuclear permutation inversion symmetry. Instead of derivative couplings or interstate couplings, a so-called modified derivative coupling term is fitted by neural networks, resulting in accurate description of near degeneracy points, such as the conical intersections. The adiabatic energies, energy gradients, and derivative couplings are well reproduced, and the vanishing of derivative couplings as well as the isotropic topography of adiabatic and diabatic energies in asymptotic regions are automatically satisfied. All of these features of the coupled global PESs are requisite for accurate dynamics simulations. Our approach is expected to be very useful in developing highly accurate coupled PESs in a quasi-diabatic representation in an efficient machine learning-based way.

Final-State-Resolved Dynamics of the H3+ + CO → H2 +HCO+/HOC+ Reaction: A Quasi-Classical Trajectory Study.

The ion-molecule reaction H3+ + CO → H2 + HCO+/HOC+, which initiates the formation of crucial organic molecules, plays a key role in interstellar and circumstellar environments. In this work, the quasi-classical trajectory method is employed to study the reaction dynamics on a recently developed full-dimensional global potential energy surface (PES). The calculated product internal energy distributions and relative internal excited fractions agree reasonably well with the experimental measurements. For the two reaction channels, most of the available energy flows into the vibrational modes of HCO+ or HOC+ at low collision energies, followed by the translational mode and the rotational modes of HCO+ or HOC+. As the collision energy increases, the proportion of the product translational energy increases while the proportion of the product vibrational energy decreases. Furthermore, the CH and CO stretching modes and their combination bands are effectively excited for the product HCO+ while the bending mode is remarkably excited for the product HOC+.

Theoretical Investigations of Rate Coefficients for H + O3 and HO2 + O Reactions on a Full-Dimensional Potential Energy Surface.

In this work, a machine learning method is used to construct a high-fidelity multichannel global reactive potential energy surface (PES) for the HO3 system from 21452 high-level ab initio calculations at the explicitly correlated multireference configuration interaction (MRCI-F12) level of theory. The permutation invariance of the PES with respect to the three identical oxygen atoms is enforced using permutation invariant polynomials (PIPs) in the input layer of a neural network (NN). This PIP-NN representation is highly faithful to the ab initio points, with a root-mean-square error of 0.20 kcal/mol. Using this PES, the kinetics of H + O3 → OH + O2 (R1) and HO2 + O → OH + O2 (R2) reactions were investigated using a quasi-classical trajectory method over a wide temperature range (200-2000 K). It was found that the calculated thermal rate coefficients of R1 and R2, exhibiting positive and negative temperature dependences, respectively, are in reasonably good agreement with most experimental measured values. These temperature dependences can be attributed to the presence and absence of an entrance channel potential barrier.

A global potential energy surface for the ground electronic state of SSiH

An analytical global potential energy surface for the ground electronic state of SSiH is here reported. The function is based upon ab initio energies calculated at Davidson-corrected multi-reference configuration interaction level with the aug-cc-pV(T + d)Z and aug-cc-pV (Q + d)Z basis sets and subsequently extrapolated to the complete basis set (CBS) limit. The analytical representation follows the Aguado and Paniagua many-body expansion methodology. A total of 2487 ab initio points were used in the fitting. The topological features of the so constructed potential are here discussed. A quasi-classical trajectory study for the SH + Si → SSi + H is carried out using the new function. Excitation function, rate constants and details of the reactive collisions are also discussed.

Theoretical study of the T+D2 and D+T2 collisions in low-temperature hydrogen plasmas

The study of low-temperature hydrogen plasmas is relevant for many technological plasma applications. The theoretical investigation of elementary processes, especially those involving H, D, and T species, is crucial for the modeling of nonequilibrium plasma systems such as those found in fusion plasmas. We report fully quantum time-independent calculations of rate coefficients for the vibrationally inelastic and reactive collisions of T with ${\mathrm{D}}_{2}(v=0)$ and of D with ${\mathrm{T}}_{2}(v=0)$. Our calculations are based on the ${\mathrm{H}}_{3}$ global potential-energy surface of Mielke et al. [S. L. Mielke et al., J. Chem. Phys. 116, 4142 (2002)]. We obtain state-to-state rate coefficients for the formation of DT through $\mathrm{T}+{\mathrm{D}}_{2}$ and $\mathrm{D}+{\mathrm{T}}_{2}$ reactions and for the vibrational excitation of ${\mathrm{D}}_{2}$ by T and of ${\mathrm{T}}_{2}$ by D for temperatures up to 2500 K. The results are compared to existing ones for other hydrogen isotopes and significant differences are found between the different sets of results, confirming that specific data have to be obtained for all the collisional systems of interest of hydrogen plasmas. We expect that this data will allow a more accurate modeling of hydrogen plasmas of interest for technological applications.

Accurate potential energy surfaces for the excited state of CF2 molecule

Multi-configurational self-consistent field and Multireference configuration interaction (MCSCF/MRCI) level have been carried out for the lowest two electronic potential energy surfaces (PESs) for excited state of CF2ã(3B1) in Jacobi coordinate. For getting the accurate global PESs, the authors used B-spline fitted method with 34816 potential energy points for each state. Four kinds of PESs in different angles and the significant avoided crossing point were discussed. We found that there are three important isomers and two transion states in the most possible isomerization process, which started from linear geometry to C2v symmetry structure. The needed additional reaction barrier energy is 0.813 eV for this process. In addition the electronic structures were discussed and the result was good agreement with experiment and former’s theoretical calculation works.