Permutation Invariant Polynomial-neural Network Research Articles

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.

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.

An accurate full-dimensional interaction potential energy surface of CO2+N2 incorporating ∆-machine learning approach via permutation invariant polynomial-neural network

The interaction between CO2 and N2, both as essential components of the Earth’s atmosphere, plays a crucial role in investigating the greenhouse effect. In this work, we sampled 40,930 data points within the full-dimensional configuration space of CO2 and N2 and performed calculations at the level of explicitly correlated coupled cluster single, double, and perturbative triple level with the augmented correlation corrected valence triple-ζ basis set (CCSD(T)-F12a/AVTZ). To ensure computational accuracy while reducing computational costs, we employed the recently proposed Δ-machine learning (Δ-ML) method based on Permutation Invariant Polynomial-Neural Network (PIP-NN) for basis set superposition error (BSSE) correction. By leveraging the limited extrapolation capability of NN, efficient sampling was performed within the existing dataset, enabling the construction of the potential energy surface (PES) incorporating BSSE correction with only a small number of data points for BSSE calculations. A total of approximately 1100 data points were selected from the initial dataset to construct a BSSE correction PES. Utilizing this correction PES, BSSE predictions were carried out for all remaining data points, resulting in the successful development of a high-precision full-dimensional PES with BSSE correction for the CO2 + N2 system. The PIP-NN based Δ-ML method significantly reduced the required BSSE calculations by approximately 97.2%, resulting in a final PES with a fitting error of merely 0.026 kcal/mol.

Reaction dynamics for the Cl(2P) + XCl → XCl + Cl(2P) (X = H, D, Mu) reaction on a high-fidelity ground state potential energy surface.

In this work, the dynamics of a prototypical heavy-light-heavy abstract reaction, Cl(2P) + HCl → HCl + Cl(2P), is investigated both by constructing a new potential energy surface (PES) and by rate coefficient calculations. Both the permutation invariant polynomial neural network method and the embedded atom neural network (EANN) method, based on abinitio MRCI-F12+Q/AVTZ level points, are used for obtaining globally accurate full-dimensional ground state PES, with the corresponding total root mean square error being only 0.043 and 0.056 kcal/mol, respectively. In addition, this is also the first application of the EANN in a gas-phase bimolecular reaction. The saddle point of this reaction system is confirmed to be nonlinear. In comparison with both the energetics and rate coefficients obtained on both PESs, we find that the EANN is reliable in dynamic calculations. A full-dimensional approximate quantum mechanical method, ring-polymer molecular dynamics with a Cayley propagator, is employed to obtain the thermal rate coefficients and kinetic isotopic effects of the title reaction Cl(2P) + XCl→ XCl + Cl(2P) (H, D, Mu) on both new PESs, and the kinetic isotope effect (KIE) is also obtained. The rate coefficients reproduce the experimental results at high temperatures perfectly but with moderate accuracy at lower temperatures, but the KIE is with high accuracy. The similar kinetic behavior is supported by quantum dynamics using wave packet calculations as well.

Constructing Diabatic Potential Energy Matrices with Neural Networks Based on Adiabatic Energies and Physical Considerations: Toward Quantum Dynamic Accuracy.

A permutation invariant polynomial-neural network (PIP-NN) approach for constructing the global diabatic potential energy matrices (PEMs) of the coupled states of molecules is proposed. Specifically, the diabatization scheme is based merely on the adiabatic energy data of the system, which is ideally a most convenient way due to not requiring additional ab initio calculations for the data of the derivative coupling or any other physical properties of the molecule. Considering the permutation and coupling characteristics of the system, particularly in the presence of conical intersections, some vital treatments for the off-diagonal terms in diabatic PEM are essentially needed. Taking the photodissociation of H2O()/NH3() and nonadiabatic reaction Na(3p) + H2 → NaH(Σ+) + H for example, this PIP-NN method is shown to build up the global diabatic PEMs effectively and accurately. The root-mean-square errors of the adiabatic potential energies in the fitting for three different systems are all small (<10 meV). Further quantum dynamic calculations show that the absorption spectra and product branching ratios in both H2O() and NH3() nonadiabatic photodissociation are well reproduced on the new diabatic PEMs, and the nonadiabatic reaction probability of Na(3p) + H2 → NaH(Σ+) + H obtained on the new diabatic PEMs of the 12A1 and 12B2 states is in reasonably good agreement with previous theoretical result as well, validating this new PIP-NN method.

Global and Full-Dimensional Potential Energy Surfaces of the N2 + O2 Reaction for Hyperthermal Collisions.

The energy transfer, dissociations, and chemical reactions between O2 and N2 play an important role in the re-entry process of aircraft and many atmospheric, combustion, and plasma processes. Recently, Varga et al. (J. Chem. Phys., 2016, 144, 024310) developed a full-dimensional high-precision potential energy surface (PES) of the ground triplet electronic state for the O2 and N2 system based on ca. 55,000 data points, whose energies were calculated by multi-state complete-active-space second-order perturbation theory/minimally augmented correlation-consistent polarized valence triple-zeta electronic structure calculations plus dynamically scaled external correlation. The fitting function adopted the many-body expansion form with the four-body interactions fitted by the permutationally invariant polynomial in terms of bond-order functions of the six interatomic distances (MB-PIP). In this work, we refit the PES of the N2O2 system by two methods based on the same data set that was used by Varga et al. The first uses the permutation invariant polynomial-neural network (PIP-NN) method to fit the entire energy of the 55,000 data points. In the second approach, the PIP-NN method is used to fit only the four-body interaction component, a similar treatment in the MB-PIP method, and the resulting PES is named MB-PIP-NN. Then, the performances of these new PESs and the MB-PIP PES are comprehensively and systematically compared, such as comparisons of various scans, properties of stationary points, and dynamics simulations. Possible improvements for the PES of N2O2 are suggested. A more reliable PES of the system can be constructed in terms of data sampling range, electronic structure calculation level, and fitting method for high-temperature calculation and simulation in the future.

Global Full-Dimensional Potential Energy Surface for the Reaction 23Na87Rb + 23Na87Rb → 23Na2 + 87Rb2 and the Formation Rate and Lifetime of the 23Na287Rb2 Collision Complex.

A full-dimensional global potential energy surface (PES) for the reaction 23Na87Rb + 23Na87Rb → 23Na2 + 87Rb2 was constructed based on high-level ab initio calculations. The short-range part was expressed as a permutation invariant polynomial-neural network (PIP-NN) fit of 22 003 ab initio points calculated using a coupled cluster method with the one-electron basis 5s5p5d2f plus effective core potentials and core polarizability potentials, while the long-range part was represented in an asymptotically correct form based on multipole expansion. The formation rate of the 23Na287Rb2 complex calculated using a quantum statistical method is in good agreement with experiment, while the estimated 19.20 μs lifetime of the complex from Rice-Ramsperger-Kassel-Marcus (RRKM) theory is significantly shorter than the measured millisecond decay rate, signaling either the inadequacy of RRKM theory or a yet unresolved loss mechanism.

A Full-Dimensional ab initio Intermolecular Potential Energy Surface and Dipole Moment Surfaces for H2O-Ar

Background: The H2O–Ar system has attracted significant interest in recent years because it is an important model to study inelastic scattering between atoms and triatomic molecules. A high-accuracy intermolecular potential energy surface (IPES) is the foundation for theoretical study on molecular collision dynamics for H2O–Ar. In addition, dipole moment surfaces (DMSs) are one of the prerequisites for spectral simulation. Objective: This study aimed to obtain a full-dimensional intermolecular potential energy surface and dipole moment surfaces for the van der Waals complex H2O–Ar. Methods: In this study, ab initio energy points were computed at the frozen-core (FC) explicitly correlated coupled-cluster [FC-CCSD(T)-F12a] level, with the augmented correlation-consistent polarized valence quadruple-zeta basis set plus bond functions. The permutation invariant polynomial neural network (PIP-NN) approach is adopted to fit the IPES, while the DMSs are constructed at the MP2/AVTZ level and fitted by the NN approach. Results: With a root-mean-square-error (RMSE) of 0.284 cm-1, the IPES can accurately describe the motion of the H2O–Ar complex between R = 4 and 20 a0 in the energy range up to 10000 cm-1. The fitting errors of all the data points are 6.192 and 6.509 mDebye for the X and Z components, respectively. The global minimum of -140.633 cm-1 has the plane geometry, while the dipole moment of H2O–Ar is 1.853 Debye at the equilibrium structure. Conclusion: In summary, we report a full-dimensional intermolecular potential energy surface for H2O–Ar. The IPES precisely reproduces CCSD(T)-F12a electronic energies with a large basis set. The corresponding dipole moment surfaces have also been reported. In comparison with previous work, the employment of the high-level ab initio method will make our IPES more reliable. Several typical 2D contour plots of the IPES and DMSs are also shown. The argon atom has a weak effect on the dipole moment of the H2O–Ar complex. The FORTRAN codes to generate 6D potentials and dipole moments reported here are available on request from the authors.

Permutation invariant polynomial neural network based diabatic ansatz for the (E + A) × (e + a) Jahn-Teller and Pseudo-Jahn-Teller systems.

In this work, the permutation invariant polynomial neural network (PIP-NN) approach is employed to construct a quasi-diabatic Hamiltonian for system with non-Abelian symmetries. It provides a flexible and compact NN-based diabatic ansatz from the related approach of Williams, Eisfeld, and co-workers. The example of H3 + is studied, which is an (E + A) × (e + a) Jahn-Teller and Pseudo-Jahn-Teller system. The PIP-NN diabatic ansatz is based on the symmetric polynomial expansion of Viel and Eisfeld, the coefficients of which are expressed with neural network functions that take permutation-invariant polynomials as input. This PIP-NN-based diabatic ansatz not only preserves the correct symmetry but also provides functional flexibility to accurately reproduce ab initio electronic structure data, thus resulting in excellent fits. The adiabatic energies, energy gradients, and derivative couplings are well reproduced. A good description of the local topology of the conical intersection seam is also achieved. Therefore, this diabatic ansatz completes the PIP-NN based representation of DPEM with correct symmetries and will enable us to diabatize even more complicated systems with complex symmetries.

Permutation-Invariant-Polynomial Neural-Network-Based Δ-Machine Learning Approach: A Case for the HO2 Self-Reaction and Its Dynamics Study.

Δ-machine learning, or the hierarchical construction scheme, is a highly cost-effective method, as only a small number of high-level ab initio energies are required to improve a potential energy surface (PES) fit to a large number of low-level points. However, there is no efficient and systematic way to select as few points as possible from the low-level data set. We here propose a permutation-invariant-polynomial neural-network (PIP-NN)-based Δ-machine learning approach to construct full-dimensional accurate PESs of complicated reactions efficiently. Particularly, the high flexibility of the NN is exploited to efficiently sample points from the low-level data set. This approach is applied to the challenging case of a HO2 self-reaction with a large configuration space. Only 14% of the DFT data set is used to successfully bring a newly fitted DFT PES to the UCCSD(T)-F12a/AVTZ quality. Then, the quasiclassical trajectory (QCT) calculations are performed to study its dynamics, particularly the mode specificity.

The global potential energy surface of the RbH2 system and dynamics studies of the H + RbH → Rb + H2 reaction

A new global potential energy surface of the ground state of the RbH2system is constructed by using the permutation invariant polynomial neural network method.In the ab initiocalculations, the aug-cc-pVQZ basis set for H, Def2-QZVPP basis set for Rb, and multi-reference configuration interaction method with Davidson correction are used. The topographical features of the new PES are discussed in detail, and no wells and barriers in the minimum energy path are found. Thereafter, specific initial-state dynamics calculations of the H + RbH (v = 0 ∼ 2,j = 0) → Rb + H2reaction are carried out based on the new PES by means of the time-dependent quantum wave packet method with a second-order split operator. The dynamics results indicate that the vibrational excitation of RbH molecules reduces and increases the reaction probability when the collision energy is below 0.4 eV and above 0.4 eV, respectively.

Dynamics of C&lt;sup&gt;+&lt;/sup&gt; + H&lt;sub&gt;2&lt;/sub&gt; reaction based on a new potential energy surface

The multi-reference interaction method is explicitly dependent on the electron-electron distance, and ACVQZ basis set is used in the &lt;i&gt;ab initio&lt;/i&gt; calculation. The potential energy surface (PES) is fitted by using the permutation invariant polynomial neural network method based on 18222 &lt;i&gt;ab initio&lt;/i&gt; points. In addition, the topographical features of the PES are compared with available theoretical and experimental data. The results indicate that the present PES is more accurate and can be applied to any type of dynamic study. In order to validate the PES, the dynamic study of the C&lt;sup&gt;+&lt;/sup&gt; + H&lt;sub&gt;2&lt;/sub&gt; → H + CH&lt;sup&gt;+&lt;/sup&gt; reaction is carried out by using the quasi-classical trajectory method in a collision energy range of 0.4–1.0 eV. The integral cross sections and differential cross sections are calculated and compared with previous theoretical studies. For the integral cross section, the present results are, in general, in good agreement with previous theoretical studies, both of which increase with collision energy increasing. The forward and backward symmetric differential cross sections indicate that the “complex-forming” mechanism plays a dominant role in the reaction.

A neural network potential energy surface and quantum dynamics studies for the Ca+(2S) + H2 → CaH+ + H reaction.

Reactive collisions of Ca+ ions with H2 molecules play a crucial role in ultracold chemistry, quantum information and other cutting-edge fields, and have been widely studied experimentally, but the corresponding theoretical studies have not been reported due to the lack of an applicable potential energy surface (PES). Herein, a globally accurate PES of the ground-state CaH2+ is constructed using the permutation invariant polynomial neural network method based on 27 780 ab initio points calculated at the multi-reference configuration interaction level. On the new PES, the quantum time-dependent wave packet calculations are performed to study the dynamics mechanisms of the Ca+(2S) + H2(ν0 = 0, j0 = 0) → CaH+ + H reaction. The calculated results suggest that the reaction follows a direct abstraction process when the collision energy is below 5.0 eV. The dynamics results would have a great reference significance for the experimental research of this reactive system at a finer level, and further dynamics studies, such as the effects of isotope substitution and rovibrational excitations of the reactant molecule, could be carried out on this newly constructed PES.

An accurate full-dimensional H4O potential energy surface and dynamics of an exchange reaction.

H2O and H2 are ubiquitous in the universe and their collisions play a crucial role in astrophysical processes. The reaction between the two also provides a prototype for understanding dynamics through four-center transition states. In this work, we adopted a strategy of combing two ab initio methods, CCSD(T)-F12a/AVTZ and MRCI-F12 + Qrot/AVTZ, to provide a balanced description for all regions of the configuration space, including one hydrogen exchange channel and two dissociation channels, namely H2 + H2O, H + H + H2O, and H + OH + H2. About 40 500 points were sampled to cover all dynamically relevant space, and the permutation invariant polynomial-neural network (PIP-NN) method was employed to develop a high-precision full-dimensional potential energy surface (PES), with a total fitting error of 0.055 kcal mol-1. Using a quasi-classical trajectory (QCT) method, the reaction dynamics and mode specificity of the hydrogen exchange channel were studied on the PES. It has been found that the stretching mode of H2, the bending, the symmetric stretching, the asymmetric stretching mode of H2O, and the translational mode can all promote reactivity. The strongest promotion effect comes from the H-H stretching mode. The Sudden Vector Projection (SVP) model was applied to predict mode specificity effects and rationalize the product energy partitioning. In both cases, the QCT and SVP results are generally consistent with each other. Furthermore, the hydrogen exchange channel was found to be dominated by sideways scattering.

DCl-H2O, HCl-D2O, and DCl-D2O Dimers: Inter- and Intramolecular Vibrational States and Frequency Shifts from Fully Coupled Quantum Calculations on a Full-Dimensional Neural Network Potential Energy Surface.

We report full-dimensional and fully coupled quantum calculations of the inter- and intramolecular vibrational states of three isotopologues of the hydrogen chloride-water dimer: DCl-H2O (DH), HCl-D2O (HD), and DCl-D2O (DD). The present study extends our recent theoretical investigation of the nine-dimensional (9D) vibrational level structure of the HCl-H2O (HH) dimer [Liu, Y.; Li, J.; Felker, P. M.; Bačić, Z. Phys. Chem. Chem. Phys. 2021, 23, 7101-7114]. It employs the same accurate 9D permutation invariant polynomial-neural network potential energy surface and the highly efficient bound-state methodology. The objective of this work is to elucidate the isotopologue variations of a range of bound-state properties of the hydrogen chloride-water dimer and compare them to those of the HH dimer. In order to achieve this, for the isotopologues considered, the rigorous 9D quantum calculations performed encompass all intramolecular vibrational fundamentals, and their frequency shifts relative to the isolated monomer values, together with the low-lying intermolecular vibrational states in each of the intramolecular vibrational manifolds of interest. Moreover, for the ground state of each isotopologue, several informative vibrationally averaged intermolecular geometric properties of the dimer are computed, as well as the three rotational constants. The energies of the intermolecular inversion and rock modes, which mainly involve the motions of the water moiety, differ greatly for H2O and D2O, but are much less sensitive to whether the hydrogen chloride isotopologue is HCl or DCl. On the other hand, the excitation of the HCl/DCl stretch changes significantly the energies of the water inversion and rock modes. The DCl stretch frequency shift computed in 9D for the DD dimer, -114.91 cm-1, agrees extremely well with the corresponding experimental value of -115.20 cm-1 measured by Saykally and co-workers.

A new global potential energy surface of X2A′ state of Li2H system and quantum dynamics calculation of the H + Li2 → Li + LiH reaction

A new potential energy surface (PES) of the ground state (X 2 A′) of Li 2 H was built using 18,403 ab initio points. The MRCI-F12 method with AVQZ basis set were used in the ab initio calculation. Furthermore, the widely used permutation invariant polynomial neural network method was adopted in the fitting process. The features of new PES were compared with previous theoretical and experimental studies. The results indicated that the spectroscopic parameters of PES are in good agreement with experimental data. In addition, the dynamics calculations of the H + Li 2 → Li + LiH reaction were carried out using time-dependent wave packet method based on the new PES. The dynamics properties such as reaction probability, integral cross section and thermal rate constant were reported and compared with previous theoretical studies.

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.

Intra- and intermolecular rovibrational states of HCl-H2O and DCl-H2O dimers from full-dimensional and fully coupled quantum calculations

We report full-dimensional and fully coupled quantum bound-state calculations of the J=1 intra- and intermolecular rovibrational states of two isotopologues of the hydrogen chloride-water dimer, HCl-H2O (HH) and DCl-H2O (DH). The present study complements our recent theoretical investigations of the J=0 nine-dimensional (9D) vibrational level structure of these and two other H/D isotopologues of this noncovalently bound molecular complex, and employs the same accurate 9D permutation invariant polynomial-neural network potential energy surface. The calculations yield all intramolecular vibrational fundamentals of the HH and DH dimers and the low-energy intermolecular rovibrational states in these intramolecular vibrational manifolds. The results are compared with those of the 9D J=0 calculations of the same dimers. The energy differences between the K=1 and K=0 eigenstates exhibit pronounced variations with the intermolecular rovibrational states, for which a qualitative explanation is provided.

An accurate full-dimensional potential energy surface for the reaction OH + SO → H + SO2.

In this work, we report a full-dimensional accurate potential energy surface (PES-2020) for the reaction OH + SO → H + SO2, a prototype with deep complexes HOSO and HSO2. About 44 700 points are calculated at the level of UCCSD(T)-F12a/aug-cc-pVTZ and fitted by the permutation invariant polynomial-neural network (PIP-NN) approach. Particular attention is paid to the treatment of the electronic structure calculation so that the UCCSD(T)-F12a/aug-cc-pVTZ method can efficiently provide a reliable description for the ground electronic state of the title reaction. Comprehensive analyses and comparison show that the only available DMBE-PES is significantly different from the new PES-2020. Dynamics simulations on this new PES-2020 show that the reactivity decreases with the increase in collision energy. The isotropic product angular distributions remain within the studied collision energy range, 1-20 kcal mol-1, complying with the deep intermediates involved during the reaction process. The product energy partitioning is also analyzed. This accurate full-dimensional PES-2020 paves the way to fully understand the dynamics of the title reaction.

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.