Permutation Invariant Polynomial-neural Network Research Articles

Accurate Global Potential Energy Surfaces for the H + CH3OH Reaction by Neural Network Fitting with Permutation Invariance.

The H + CH3OH reaction, which plays an important role in combustion and the interstellar medium, presents a prototypical system with multi channels and tight transition states. However, no globally reliable potential energy surface (PES) has been available to date. Here we develop global analytical PESs for this system using the permutation-invariant polynomial neural network (PIP-NN) and the high-dimensional neural network (HD-NN) methods based on a large number of data points calculated at the level of the explicitly correlated unrestricted coupled cluster single, double, and perturbative triple level with the augmented correlation corrected valence triple-ζ basis set (UCCSD(T)-F12a/AVTZ). We demonstrate that both machine learning PESs are able to accurately describe all dynamically relevant reaction channels. At a collision energy of 20 kcal/mol, quasi-classical trajectory calculations reveal that the dominant channel is the hydrogen abstraction from the methyl site, yielding H2 + CH2OH. The reaction of this major channel takes place mainly via the direct rebound mechanism. Both the vibrational and rotational states of the H2 product are relatively cold, and large portions of the available energy are converted into the product translational motion.

Dynamics Studies of O2 Collision on Pt(111) Using a Global Potential Energy Surface

The dynamics of O2 collision on Pt(111) has been studied by molecular dynamics simulations using a global potential energy surface (PES), which was developed by fitting ∼4800 plane-wave density functional theory points using the permutation invariant polynomial-neural network method. The simulations were performed for the normal and off-normal incidences at a wide range of incident energies and surface temperatures. A generalized Langevin oscillator model was used to incorporate the molecule–surface coupling that plays an important role in this collision process. The trapping probability, final energy distribution, scattering angle distributions of scattered molecules, and the energy transfer to surface distribution were determined and analyzed. The PES shows an activated path to the chemisorption states, as the trapping probability directly increases with incident energy (larger than 0.1 eV) to reach a maximum and then decreases at high incident energy. The trapping probability obviously reduces by raising surface temperature at low incident energy because the initial kinetic energy of molecule is more likely to be dissipated into surface motions than molecular internal ro-vibrational modes. Additional parallel momentum of off-normal incidence leads to a strong suppression of the trapping probability, caused by the energetic corrugation of the lateral barrier heights. The scattering angular distributions are found to be quasispecular and the final translational energy slightly increases with scattering angle deviating significantly from the hard-cube model, indicating the nonconservation of parallel momentum during the collision on the corrugate PES.

A full-dimensional ab initio intermolecular potential energy surface and ro-vibrational spectra for N2-HF and N2-DF.

A full-dimensional ab initio intermolecular potential energy surface (IPES) is reported in this paper for van der Waals complex N2-HF. The calculations were performed by employing the explicitly correlated coupled cluster [CCSD (T)-F12a] method with the augmented correlation-consistent aug-cc-pVTZ basis set plus bond functions. The basis set superposition error was corrected by the full counterpoise procedure. About 55 000 ab initio points were calculated and then fitted by the permutation invariant polynomial neural network approach with a root-mean-square error of 0.433 cm-1. The potential energy surface features two equivalent linear minima with a well depth of 811.012 cm-1 separated by a barrier of 635.836 cm-1. The ro-vibrational energy levels for N2-HF and N2-DF were calculated based on the vibrationally averaged 4D IPESs with the radial discrete variable representation/angular finite basis representation method and Lanczos propagation algorithm. The calculated frequencies and the relative line intensities in the HF (DF) stretching band agree well with the available observed spectra. The theoretical band origins are all red shifted relative to the isolated HF (DF) molecule and reproduce the experimental values well. The results of ro-vibrational state calculations demonstrate the high accuracy of our new PES.

Dynamics studies of the H + HBr reaction: Based on a new potential energy surface.

The initial state specific quantum wave packet dynamics studies of the H + HBr (v0 = 0, j0 = 0-2) reaction were performed using a new global potential energy surface (PES) of the ground state of the BrH2 system for the collision energy ranging from 0.01 to 2.0 eV. The PES was constructed using the permutation invariant polynomial neural network method based on approximately 63 000 ab initio points, which were calculated by the multireference configuration interaction method with AVTZ and AVQZ basis sets. To improve the accuracy of the PES, Davidson's correction and spin-orbit coupling effects were considered in the ab initio calculation and the basis set was extrapolated to complete basis set limit. The new PES was compared with the previous ones and also the available experimental data, which suggests that the new PES is more accurate. The state-to-state quantum wave packet dynamics was carried out using the reactant-coordinate based approach. The reaction probabilities, integral and differential cross sections, rovibrational state distributions of product and rate constants, etc., were compared with the available theoretical and experimental studies. In general, the present work is in better agreement with the available experimental data. The quantum dynamics studies suggest that the rotational excitation of HBr has little effect on the reaction.

Globally Accurate Full-Dimensional Potential Energy Surface for H2 + HCl Inelastic Scattering.

A globally accurate full-dimensional potential energy surface (PES) for the inelastic scattering between H2 and HCl is developed on the basis of a large number of points calculated at the coupled-cluster singles, doubles, and perturbative triples level of theory. The machine-learned PES is trained with 42 417 ab initio points using the permutation invariant polynomial-neural network method, resulting in a root-mean-square fitting error of 5.6 cm-1. Both full- and reduced-dimensional quantum calculations for rotationally inelastic scattering are performed on this new PES and good agreement is obtained with previous quantum dynamical results on a reduced-dimensional model. Furthermore, strong resonances are identified at collision energies below 100 K, including cold conditions. This new PES provides a reliable platform for future studies of scattering dynamics with vibrationally excited collision partners in a wide range of collision energies extending to cold and ultracold conditions.

Competition between Proton Transfer and Proton Isomerization in the N2 + HOC+ Reaction on an Ab Initio-Based Global Potential Energy Surface.

The dynamics of the N2 + HOC+ multichannel reaction is investigated up to 1.0 eV of collision energy on an accurate global potential energy surface (PES) for the ground electronic state. The PES is constructed using the permutation invariant polynomial-neural network (PIP-NN) method by fitting ∼37 000 points at the CCSD(T)-F12a/cc-pVTZ-F12 level with a root-mean-square error of about 3.0 meV. It was found that the total reaction integral cross section decreases monotonically with the collision energy, consistent with the barrierless complex-forming mechanism. Throughout the energy range, the proton transfer channel, which leads to the N2H+ + CO products, dominates the proton isomerization channel, which forms the N2 + HCO+ products. The differential cross section of the proton transfer channel is backward biased, signaling a relatively direct process, while that of the proton isomerization channel shows strong forward-backward symmetry, which can be attributed to a long-lived intermediate.

A new full-dimensional ab initio intermolecular potential energy surface and vibrational states for (HF)2 and (DF)2.

We present a new full-dimensional ab initio potential energy surface (PES) of a hydrogen fluoride dimer [(HF)2] using the supermolecular approach. The calculations were performed at the coupled-cluster single double triple level, with an augmented correlation-consistent polarized valence quadruple-zeta basis set plus bond functions. The basis set superposition error was corrected by a full counterpoise procedure. With the exchange symmetry of the two HF molecules, the permutation invariant polynomial neural network approach was used to fit the hypersurface with a root-mean-square-error of 0.465 cm-1 for about 110 000 points. The ab initio noise of intermolecular potential in the long range was smoothed by the long-range coefficients method. The equilibrium configuration of the complex was found to be a Cs structure located at two equivalent minima with the well depth of 1573.495 cm-1. The eigenstates were calculated by employing a symmetry-adapted Lanczos propagation algorithm in the mixed radical discrete variable representation/angular finite basis representation. The tunneling splitting for the ground state of (HF)2 is 0.665 cm-1, agreeing well with experimental value of 0.65869 cm-1. Vibrational fundamentals are also very close to the observed values. The results of vibrational states calculations demonstrate the high accuracy of our new PES.

Rate coefficients and branching ratio for multi-channel hydrogen abstractions from CH3OH by F

The hydrogen abstraction reaction F+CH3OH has two possible reaction pathways: HF+CH3O and HF+CH2OH. Despite the absence of intrinsic barriers for both channels, the former has a branching ratio comparable to the latter, which is far from the statistical limit of 0.25 (one out of four available H atoms). Furthermore, the measured branching ratio of the two abstraction channels spans a large range and is not quantitatively reproduced by previous theoretical predictions based on the transition-state theory with the stationary point information calculated at the levels of Møller-Plesset perturbation theory and G2. This work reports a theoretical investigation on the kinetics and the associated branching ratio of the two competing channels of the title reaction using a quasi-classical trajectory approach on an accurate full-dimensional potential energy surface (PES) fitted by the permutation invariant polynomial-neural network approach to ca. 1.21 × 105 points calculated at the explicitly correlated (F12a) version of coupled cluster singles doubles and perturbative triples (CCSD(T)) level with the aug-cc-pVDZ basis set. The calculated room temperature rate coefficient and branching ratio of the HF+CH3O channel are in good agreement with the available experimental data. Furthermore, our theory predicts that rate coefficients have a slightly negative temperature dependence, consistent with barrierless nature of the reaction.

Anomalous kinetics of the reaction between OH and HO2 on an accurate triplet state potential energy surface.

The reaction OH + HO2→ H2O + O2 is of great significance in interstellar media, the atmosphere, and combustion. In addition, it presents a prototypical reaction between two non-atom radical species. However, the temperature dependence of its rate coefficients has been debated for several decades. In this work, the rate coefficients are revisited by the quasi-classical trajectory (QCT) approach. To this end, a globally accurate full-dimensional potential energy surface of the ground triplet state for the title reaction is constructed using the permutation invariant polynomial-neural network (PIP-NN) method based on 108 000 points calculated at the level of CCSD(T)-F12a/AVTZ, in which particular attention is paid to the initial guess in the preceding Hartree-Fock procedure to obtain reliable ab initio energies. The QCT rate coefficients are compared to available experimental and theoretical results. It has been found that not only the trend, but also the magnitude, i.e. the large negative temperature dependence at low temperatures, and slightly positive temperature dependence at high temperatures, are consistent with some experiments.

Dissection of the multichannel reaction of acetylene with atomic oxygen: from the global potential energy surface to rate coefficients and branching dynamics.

The O(3P) + C2H2 reaction is the first step in acetylene oxidation. The accurate kinetic data and the understanding of the reaction dynamics is of great importance. To this end, a full-dimensional global potential energy surface (PES) for the ground triplet state of the O(3P) + C2H2 reaction is constructed based on approximately 85 000 ab initio points calculated at the level of explicitly correlated unrestricted coupled cluster single, double, and perturbative triple excitations with the explicitly correlated polarized valence triple zeta basis set (UCCSD(T)-F12b/VTZ-F12). The PES is fit using the permutation invariant polynomial-neural network (PIP-NN) approach with a total root mean square error of 0.21 kcal mol-1. The key topographic features of the PES, including multiple potential wells and saddle points along different reaction pathways, are well represented by this fit PES. The kinetics and dynamics of the O(3P) + C2H2 reaction are investigated using the quasi-classical trajectory (QCT) method. The calculated rate coefficients are in good agreement with experimental data over a wide temperature range, especially when the temperature is lower than 1500 K. The product branch ratio has also been determined, which indicates the H + HCCO channel as the dominant reaction pathway at 298-3000 K, accounting for 80-90% of the overall rate coefficient, in agreement with experimental observations. The dynamics of the reaction is analyzed in detail.

An accurate full-dimensional permutationally invariant potential energy surface for the interaction between H2O and CO.

The interaction between H2O and CO has been the subject of numerous experimental and theoretical investigations for a long time due to their important roles in various environments, such as the atmosphere, combustion of hydrocarbons, and the interstellar medium. In this work, the first full-dimensional accurate potential energy surface (PES) was developed for the CO + H2O system based on ca. 102 000 points calculated at the level of an explicitly correlated coupled-cluster method with single, double, and perturbative triple excitations with the augmented correlation-consistent polarized triple zeta basis set (CCSD(T)-F12a/AVTZ) using the permutation invariant polynomial-neural network (PIP-NN) method. The geometries, energies, and frequencies of the two complex wells, CO-H2O and OC-H2O, and one transition state connecting them, as well as some interconversions between different conformers, are accurately reproduced by the PES, thanks to the small fitting error of only 1.08 meV. With full-dimensional degrees of freedom considered in the PES, we found that there exist strong dependences of the CO and OH bond lengths on the OC-H2O and CO-H2O interaction energies, which is not possible in reduced dimensional PESs. Finally, classical dynamics was carried out to study the energy transfer between H2O and CO with different initial vibrational energies in H2O and different vibrational states in CO.

Permutation invariant polynomial neural network approach to fitting potential energy surfaces. IV. Coupled diabatic potential energy matrices.

A machine learning method is proposed for representing the elements of diabatic potential energy matrices (PEMs) with high fidelity. This is an extension of the so-called permutation invariant polynomial-neural network (PIP-NN) method for representing adiabatic potential energy surfaces. While for one-dimensional irreducible representations the diagonal elements of a diabatic PEM are invariant under exchange of identical nuclei in a molecular system, the off-diagonal elements require special symmetry consideration, particularly in the presence of a conical intersection. A multiplicative factor is introduced to take into consideration the particular symmetry properties while maintaining the PIP-NN framework. We demonstrate here that the extended PIP-NN approach is accurate in representing diabatic PEMs, as evidenced by small fitting errors and by the reproduction of absorption spectra and product branching ratios in both H2O( ) and NH3( ) non-adiabatic photodissociation.

New global potential energy surface of the MgH2 system and dynamics studies of the reaction H + MgH → Mg + H2

AbstractA new global potential energy surface for the ground state of MgH2 was constructed using the permutation invariant polynomial neural network method. About 70 000 ab initio energy points were calculated via the multi‐reference configuration interaction method method with aug‐cc‐pVTZ and aug‐cc‐pVQZ basis sets, and these points were used to construct the potential energy surface (PES). To avoid basis set superposition error, the basis set was extrapolated to the complete basis set limit using the two point energy extrapolation formula. The root mean square error of the present PES is only 8.85 meV. Initial state (v = 0, j = 0) dynamics studies were performed using the time‐dependent wave packet method with a second‐order split operator for the total angular momentum J up to a value of 50. Furthermore, the reaction probability, integral cross section, and thermal rate constant are reported and compared with available theoretical studies.

Vibrational enhancement in the dynamics of ammonia dissociative chemisorption on Ru(0001).

The vibrationally selective dissociative chemisorption dynamics of ammonia on the Ru(0001) surface is investigated using a quasi-classical trajectory (QCT) method on a new global potential energy surface (PES) with twelve dimensions. The PES is constructed by fitting 92 524 density functional theory points using the permutation invariant polynomial-neural network method, which rigorously enforces the permutation symmetry of the three hydrogen atoms as well as the surface periodicity. The PES enables highly efficient QCT simulations as well as future quantum dynamical studies of the scattering/dissociation dynamics. The QCT calculations yield satisfactory agreement with experiment and suggest strong activation of dissociation by both translational and vibrational excitations.

Kinetics studies of the F + HCl → HF + Cl reaction on an accurate potential energy surface

A full-dimensional electronic ground state potential energy surface for the hydrogen abstraction reaction F + HCl → HF + Cl is developed by using the permutation invariant polynomial neural network approach based on 6509 points computed at the level of CCSD(T)-F12a/AVTZ. Spin-orbit correction is also taken into account at the complete active space self-consistent field level. Theoretical thermal rate coefficients determined by the ring polymer molecular dynamics (RPMD) approach agree well with experiment, validating the accuracy of the PES. Kinetic isotope effect is also investigated.

A global coupled cluster potential energy surface for HCl + OH ↔ Cl + H2O.

A new and more accurate full-dimensional global potential energy surface (PES) for the ground electronic state of the ClH2O system is developed by fitting 15 777 points obtained using an explicitly correlated unrestricted coupled-cluster method with single, double, and perturbative triple excitations (UCCSD(T)-F12b). The fitting is carried out using the permutation invariant polynomial-neural network (PIP-NN) method and has an error of 6.9 meV. The new PES has a slightly lower barrier for the atmospherically important HCl + OH → Cl + H2O reaction than the previous PES based on multi-reference configuration interaction (MRCI) calculations. As a result, it should provide a better characterization of the kinetics. Quantum dynamical calculations of reaction probabilities for both the forward and reverse reactions are performed on this new PES and compared with those on the MRCI PES. They reveal notable differences, resulting apparently from subtle differences in the PESs.

Dissociative chemisorption of methane on Ni(111) using a chemically accurate fifteen dimensional potential energy surface.

A fifteen-dimensional global potential energy surface for the dissociative chemisorption of methane on the rigid Ni(111) surface is developed by a high fidelity fit of ∼200 000 DFT energy points computed using a specific reaction parameter density functional designed to reproduce experimental data. The permutation symmetry and surface periodicity are rigorously enforced using the permutation invariant polynomial-neural network approach. The fitting accuracy of the potential energy surface is thoroughly investigated by examining both static and dynamical attributes of CHD3 dissociation on the frozen surface. This potential energy surface is expected to be chemically accurate as after correction for surface temperature effects it reproduces the measured initial sticking probabilities of CHD3 on Ni(111) for various incidence conditions.

Quasi-classical trajectory studies on the full-dimensional accurate potential energy surface for the OH + H2O = H2O + OH reaction.

For the symmetric reaction OH + H2O → H2O + OH, ∼48 000 data points are sampled and calculated at the level of the explicitly correlated unrestricted coupled cluster method with single, double, and perturbative triple excitations with the augmented correlation-consistent polarized triple zeta basis set (CCSD(T)-F12a/AVTZ). The data set is then employed to fit the full dimensional accurate potential energy surface (PES) by using the permutation invariant polynomial-neural network (PIP-NN) method, resulting in a total root mean square error (RMSE) of 0.12 kcal mol-1. The quasi-classical trajectory (QCT) method is used to study its reaction dynamics. It has been found that the integral cross section (ICS) is increased gradually as a function of the collision energy ranging from 8 to 30 kcal mol-1 with a threshold around 8 kcal mol-1. At a collision energy of 20 kcal mol-1, detailed dynamics show that the OH product is a spectator and the differential cross section (DCS) is dominated by backward scattering with considerable contributions from sideway scattering, consistent with the direct rebound and stripping mechanisms.

Full-dimensional global potential energy surfaces describing abstraction and exchange for the H + H2S reaction.

For the H + H2S system, ∼34 000 data points are sampled over a large configuration space including both abstraction and exchange channels, and calculated at the level of explicitly correlated unrestricted coupled cluster method with singles, doubles, and perturbative triples excitations with the augmented correlation-consistent polarized triple zeta basis set (UCCSD(T)-F12a/aug-cc-pVTZ). The data set was fit using the newly proposed permutation invariant polynomial-neural network (PIP-NN) method with three different vectors as the input: two redundant sets of PIPs, one with the maximum order four (PES-I) and one with the maximum order three (PES-II), and nine non-redundant PIPs (PES-III). All these PESs show small fitting errors and essentially the same performance in representing the title system. Various kinetics and dynamical properties are calculated using the tunneling corrected transition state theory and quasi-classical trajectory, and compared with available experimental results. At a collision energy of 10 kcal/mol, both the H2 and SH products are found to be internally cold, with ∼20% of H2 at its first vibrational excited state, while SH is essentially a spectator. The angular distributions of the products are mainly in backward with considerable contributions from sideway direction. In addition, analytical partial derivatives of any PIP-NN PES with respect to the coordinates of atoms are derived by making use of the monomial symmetrization algorithm [Z. Xie and J. M. Bowman, J. Chem. Theory Comput. 6, 26-34 (2010)]. It can not only accelerate the evaluation of the derivatives, but also improve the energy convergence significantly.

Ring polymer molecular dynamics fast computation of rate coefficients on accurate potential energy surfaces in local configuration space: Application to the abstraction of hydrogen from methane.

To fast and accurately compute rate coefficients of the H/D + CH4 → H2/HD + CH3reactions, we propose a segmented strategy for fitting suitable potential energy surface (PES), on which ring-polymer molecular dynamics (RPMD) simulations are performed. On the basis of recently developed permutation invariant polynomial neural-network approach [J. Li et al., J. Chem. Phys. 142, 204302 (2015)], PESs in local configuration spaces are constructed. In this strategy, global PES is divided into three parts, including asymptotic, intermediate, and interaction parts, along the reaction coordinate. Since less fitting parameters are involved in the local PESs, the computational efficiency for operating the PES routine is largely enhanced by a factor of ∼20, comparing with that for global PES. On interaction part, the RPMD computational time for the transmission coefficient can be further efficiently reduced by cutting off the redundant part of the child trajectories. For H + CH4, good agreements among the present RPMD rates and those from previous simulations as well as experimental results are found. For D + CH4, on the other hand, qualitative agreement between present RPMD and experimental results is predicted.