Supercollisions of NaCl + NaCl on an Accurate Full-Dimensional Potential Energy Surface.

An accurate, global, full-dimensional potential energy surface (PES) of NaCl + NaCl has been constructed by the fundamental invariant-neural network (FI-NN) fitting based on roughly 13,000 ab initio energies at the level of CCSD(T)-F12a/aug-cc-pVTZ, with the small fitting error of 0.16 meV. Extensive quasiclassical trajectory (QCT) calculations were performed on this PES to investigate the energy transfer process of the NaCl + NaCl collision at four different collision energies. Various quantities were obtained, including the cross-sections, energy transfer probability, average energy transfer, and collision lifetime. The probabilities of energy transfer (P(ΔE)) for prompt trajectories, nonreactive trajectories, and reactive trajectories deviate from a simple exponential decay pattern. Instead, a noteworthy probability is observed in the high-energy transfer region, indicative of supercollisions. The formation of the (NaCl)2 complex, coupled with a comparatively extended collision lifetime, promotes vibrational excitation in NaCl molecules. The reactive trajectories exhibit enhanced energy transfer, attributed to the longer lifetime of the NaCl dimer. This study not only provides an accurate and extensive understanding of the NaCl + NaCl collision dynamics but also reveals intriguing phenomena, such as supercollisions and enhanced energy transfer in reactive trajectories, shedding light on the complex intricacies of molecular interactions.

Bond-selective effect for the dissociative chemisorption of HOD on the Ni(100) surface revealed at the full-dimensional quantum dynamical level.

We present a comprehensive investigation into the dissociative chemisorption of HOD on a rigid Ni(100) surface using an approximate full-dimensional (9D) quantum dynamics approach, which was based on the time-dependent wave-packet calculations on a full-dimensional potential energy surface obtained through neural network fitting to density functional theory energy points. The approximate-9D probabilities were computed by averaging the seven-dimensional (7D) site-specific dissociation probabilities across six impact sites with appropriate relative weights. Our results uncover a distinctive bond-selective effect, demonstrating that the vibrational excitation of a specific bond substantially enhances the cleavage of that excited bond. The product branching ratios are substantially influenced by which bond undergoes excitation, exhibiting a clear preference for the product formed through the cleavage of the excited bond over the alternative product.

Six-dimensional quantum dynamics study for the dissociative chemisorption of H2 on pure and alloyed AgAu surfaces.

The 6D time-dependent wave packet calculations were performed to explore H2 dissociation on Ag, Au, and two AgAu alloy surfaces, using four newly fitted potential energy surfaces based on the neural network fitting to density functional theory energy points. The ligand effect resulting from the Ag-Au interaction causes a reduction in the barrier height for H2+Ag/Au(111) compared to H2+Ag(111). However, the scenario is reversed for H2+Au/Ag(111) and H2+Au(111). The 6D dissociation probabilities of H2 on Ag/Au(111) surfaces are significantly higher than those on the pure Ag(111) surface, but the corresponding results for H2 on Au/Ag(111) surfaces are substantially lower than those on the pure Au(111) surface. The reactivity of H2 on Au(111) is larger than that on Ag(111), despite Ag(111) having a slightly lower static barrier height. This can be attributed to the exceptionally small dissociation probabilities at the hcp and fcc regions, which are at least 100 times smaller compared to those at the bridge or top site for H2+Ag(111). Due to the late barrier being more pronounced, the vibrational excitation of H2 on Ag(111) is more effective in promoting the reaction than on Au(111). Moreover, a high degree of alignment dependence is detected for the four reactions, where the H2 dissociation has the highest probability at the helicopter alignment, as opposed to the cartwheel alignment.

A highly accurate full-dimensional ab initio potential surface for the rearrangement of methylhydroxycarbene (H3C-C-OH).

We report here a full-dimensional machine learning global potential surface (PES) for the rearrangement of methylhydroxycarbene (H3C-C-OH, 1t). The PES is trained with the fundamental invariant neural network (FI-NN) method on 91 564 ab initio energies calculated at the UCCSD(T)-F12a/cc-pVTZ level of theory, covering three possible product channels. FI-NN PES has the correct symmetry properties with respect to permutation of four identical hydrogen atoms and is suitable for dynamics studies of the 1t rearrangement. The averaged root mean square error (RMSE) is 11.4 meV. Six important reaction pathways, as well as the energies and vibrational frequencies at the stationary geometries on these pathways are accurately preproduced by our FI-NN PES. To demonstrate the capacity of the PES, we calculated the rate coefficient of hydrogen migration in -CH3 (path A) and hydrogen migration of -OH (path B) with instanton theory on this PES. Our calculations predicted the half-life of 1t to be 95 min, which is excellent in agreement with experimental observations.

Roaming Dynamics in Hydroxymethyl Hydroperoxide Decomposition Revealed by the Full-Dimensional Potential Energy Surface of the CH2OO + H2O Reaction.

The CH2OO + H2O reaction is an important atmospheric process that leads to the formation of formic acid (HCOOH) and water via the intermediate hydroxymethyl hydroperoxide (HOCH2OOH, HMHP). We investigated the intricacies of this process by employing quasiclassical trajectory calculations on an accurate, full-dimensional ab initio potential energy surface (PES). In addition to the direct mechanism via the transition state (TS), an interesting roaming mechanism was found to play the predominant role in producing H2O and HCOOH. This roaming pathway is featured as the near direct dissociation of HMHP into OH and hydroxymethoxy radical, followed by the retraction of OH and abstraction of the H atom, culminating in the formation of H2O. Due to the longer interaction time of the roaming mechanism, less product translational energy was released, but more internal energies of HCOOH were obtained, as compared with the direct TS mechanism. The enhanced yield of H2O and formic acid achieved through roaming dynamics underscores the significance of dynamics simulations based on an accurate full-dimensional PES. This work provides new insights into the dynamics of the CH2OO + H2O reaction and its implications for atmospheric chemistry.

Mode specificity of water dissociating on Ni(100): An approximate full-dimensional quantum dynamics study.

The mode-specific dynamics for the dissociative chemisorption of H2O on rigid Ni(100) is investigated by approximate nine-dimensional (9D) quantum dynamics calculations. The vibrational state-specific 9D dissociation probabilities are obtained by site-averaging the site-specific seven-dimensional results based on an accurate full-dimensional potential energy surface newly developed by neural network fitting to density functional theory energy points with the revised version of the Perdew, Burke, and Ernzerhof functional. The mode specificity of H2O/Ni(100) is very different from that of H2O/Ni(111) or H2O/Cu(111) whose reactivity enhancement by vibrational excitations is quite efficient. For H2O/Ni(100), it is found that the excitation in the symmetric stretching mode is more efficacious than increasing the translational energy in promoting the reaction, while the excitations in the asymmetric stretching mode and bending mode are less efficacious than the translational energy at low collision energies. These interesting observations can be attributed to the near central-barrier reaction for H2O/Ni(100), as well as large discrepancies between the site-specific mode specificities at different impact sites. The mode-specific dynamics obtained in this study is different from that obtained with the reaction path Hamiltonian approach, indicating the importance of full-dimensional quantum dynamics for gas-surface reactions.

Full-dimensional quantum mechanical study of three-body recombination for cold 4He-4He-20Ne system.

The increase of the number of the two-body recombination channels strongly challenges the numerical calculation of the accurate rates for the three-body recombination (TBR) process and its reverse process, collision-induced dissociation (CID), at ultracold temperatures. By taking the 4He-4He-20Ne collision system as an example, we have obtained the rates for its TBR and CID processes involving all four recombination channels, including the two-body states 4He2 (l = 0) and 4He20Ne (l = 0, 1, 2) with l the rotational quantum number. By using the adiabatic hyperspherical method, we have considered not only total angular momentum J = 0 but also J > 0 in the ultracold collision energies (E = 0.01 - 100 mK × kB). It is found that 4He2 (l = 0) is the major product after the TBR process in the ultracold limit (E ≤ 0.1 mK × kB). The TBR rate into 4He2 (l = 0) is nearly one order of magnitude larger than the sum of the other three products, 4He20Ne (l = 0, 1, 2). Moreover, the CID rates for the three 4He20Ne (l = 0, 1, 2) + 4He initial states are close to each other and are smaller than that for the 4He2 (l = 0) + 20Ne initial state. Additionally, we have, for the first time, performed the channel-resolved scattering calculation that can explain the above-mentioned findings quantitatively.

Quantum dynamics reveal different ligand effects by vibrational excitation in the dissociative chemisorption of HCl on the Au/Ag(111) surface.

The reactivity and selectivity of bimetallic surfaces are of fundamental importance in industrial applications. Here, we report the first six-dimensional (6D) quantum dynamics study for the role of surface strain and ligand effects on the reactivity of HCl on a strained pseudomorphic monolayer of Au deposited onto a Ag(111) substrate, with the aid of accurate machine learning-based potential energy surfaces. The substitute of Au into Ag changes the location of the transition state; however, the static barrier height remains roughly the same as pure Au(111). The 6D quantum dynamics calculations reveal that the surface strain due to lattice expansion slightly enhances the reactivity. The ligand effect due to electronic structure interactions between Au and Ag substantially suppresses the reactivity of HCl in the ground vibrational state but promotes the reactivity via vibrational excitation at high kinetic energies. This finding can be attributed to more close interaction with Ag atoms at the transition state close to the fcc site, as well as the tight transition-state region, making the vibrational excitation highly efficient in enhancing the reactivity. Our study quantitatively unravels the dynamical origin of reactivity control by two metals, which will ultimately provide valuable insight into the selectivity of the catalyst.

A fundamental invariant-neural network representation of quasi-diabatic Hamiltonians for the two lowest states of H3.

The fundamental invariant neural network (FI-NN) approach is developed to represent coupled potential energy surfaces in quasidiabatic representations with two-dimensional irreducible representations of the complete nuclear permutation and inversion (CNPI) group. The particular symmetry properties of the diabatic potential energy matrix of H3 for the 1A' and 2A' electronic states were resolved arising from the E symmetry in the D3h point group. This FI-NN framework with symmetry adaption is used to construct a new quasidiabatic representation of H3, which reproduces accurately the ab initio energies and derivative information with perfect symmetry behaviors and extremely small fitting errors. The quantum dynamics results on the new FI-NN diabatic PESs give rise to accurate oscillation patterns in the product state-resolved differential cross sections. These results strongly support the accuracy and efficiency of the FI-NN approach to construct reliable diabatic representations with complicated symmetry problems.

Supercollisions of fast H-atom with ethylene on an accurate full-dimensional potential energy surface.

The collisions transferring large portions of energy are often called supercollisions. In the H + C2H2 reactive system, the rovibrationally cold C2H2 molecule can be activated with substantial internal excitations by its collision with a translationally hot H atom. It is interesting to investigate the mechanisms of collisional energy transfer in other important reactions of H with hydrocarbons. Here, an accurate, global, full-dimensional potential energy surface (PES) of H + C2H4 was constructed by the fundamental invariant neural network fitting based on roughly 100 000 UCCSD(T)-F12a/aug-cc-pVTZ data points. Extensive quasi-classical trajectory calculations were carried out on the full-dimensional PES to investigate the energy transfer process in collisions of the translationally hot H atoms with C2H4 in a wide range of collision energies. The computed function of the energy-transfer probability is not a simple exponential decay function but exhibits large magnitudes in the region of a large amount of energy transfer, indicating the signature of supercollisions. The supercollisions among non-complex-forming nonreactive (prompt) trajectories are frustrated complex-forming processes in which the incoming H atom penetrates into C2H4 with a small C-H distance but promptly and directly leaves C2H4. The complex-forming supercollisions, in which either the attacking H atom leaves (complex-forming nonreactive collisions) or one of the original H atoms of C2H4 leaves (complex-forming reactive trajectories), dominate large energy transfer from the translational energy to internal excitation of molecule. The current work sheds valuable light on the energy transfer of this important reaction in the combustion and may motivate related experimental investigations.

Dynamics and kinetics of the OH + HO2 → H2O + O2 (1Δg) reaction on a global full-dimensional singlet-state potential energy surface.

The OH + HO2 → H2O + O2 reaction is a prototype of radical-radical reactions, which plays an eminent role in combustion and atmosphere chemistry. Extensive studies have been focused on the ground triplet electronic state, but investigation on the singlet excited state is rare. Here, we report a full-dimensional singlet-state potential energy surface (PES) for this reaction, which was constructed using the fundamental invariant neural network (FI-NN) fitting to roughly 130 000 energy points calculated by the CASPT2/AVTZ method. Extensive quasiclassical trajectory (QCT) calculations were performed on the FI-NN PES in a wide range of collision energies and temperatures. The pathway via a shallow minimum with a direct abstraction mechanism is identified as a dominant reaction path due to a low barrier, with most available energy released into the rovibrational motion of the products, and angular distributions showing predominantly backward and sideways scattering amplitudes. The QCT thermal rate coefficients on the singlet-state PES show small, but non-negligible contributions to the overall rate of the OH + HO2 reaction.

A global ab initio potential energy surface and dynamics of the proton-transfer reaction: OH- + D2 → HOD + D.

We report an accurate full-dimensional potential energy surface (PES) of the anion-molecule system OH3-. The PES was constructed by fitting 55 406 ab inito energies from the CCSD(T)/aug-cc-pVTZ level of theory with the fundamental invariant neural network (FI-NN) approach, resulting in an extremely small fitting error of 0.52 meV. Extensive quasiclassical trajectory (QCT) simulations were carried out on the PES to investigate the proton transfer dynamics (OH- + D2 → D- + HOD). The product D- translational energy distribution and angular distribution were calculated and compared with previous experimental measurements, in which reasonably good agreement has been achieved. The angular distribution at a high collision energy exhibits an exclusively forward scattering peak, indicating the direct stripping mechanism at high energies. With the decrease of the collision energy, the reaction shows a predominantly forward scattering feature, with very small sideways and backward scattering amplitudes, revealing combined mechanisms from direct abstraction with a short reaction time and a complex-forming process with a long reaction time.

Photodissociation Dynamics of OCS near 150 nm: The S(1SJ=0) and S(3PJ=2,1,0) Product Channels.

Vacuum ultraviolet photodissociation dynamics of carbonyl sulfide (OCS) was investigated by using the time-sliced velocity map ion imaging technique. Images of the S(1SJ=0) and S(3PJ=2,1,0) photofragments formed in the OCS photodissociation were acquired at six photolysis wavelengths from 147.24 to 156.48 nm. Vibrational states of the CO coproducts were partially resolved and identified in the images. Two main dissociation product channels, namely, the spin-allowed S(1SJ=0) + CO(X1Σg+) and spin-forbidden S(3PJ=2,1,0) + CO(X1Σg+), were observed. At each photolysis wavelength, the total kinetic energy releases, the relative population of different CO vibrational states, and the anisotropic parameters were derived. Variations of the relative population were noticed between different spin-orbit states of the S(3PJ) channel. It was found that the S(1SJ=0) + CO(X1Σg+) channel is dominated by the 1Σ+ ← 1Σ+ parallel transition of OCS. Interestingly, two types of anisotropic parameters are found at different photolysis wavelengths for the spin-forbidden S(3PJ=2,1,0) + CO(X1Σg+) product channel. The anisotropic parameters at 147.24 and 150.70 nm are significantly smaller than at the other four photolysis wavelengths. This phenomenon indicates two different nonadiabatic pathways are responsible for the spin-forbidden channels, which is consistent with the barrier structure in the exit channel of one of the triplet states.

Fitting potential energy surfaces with fundamental invariant neural network. II. Generating fundamental invariants for molecular systems with up to ten atoms.

Symmetry adaptation is crucial in representing a permutationally invariant potential energy surface (PES). Due to the rapid increase in computational time with respect to the molecular size, as well as the reliance on the algebra software, the previous neural network (NN) fitting with inputs of fundamental invariants (FIs) has practical limits. Here, we report an improved and efficient generation scheme of FIs based on the computational invariant theory and parallel program, which can be readily used as the input vector of NNs in fitting high-dimensional PESs with permutation symmetry. The newly developed method significantly reduces the evaluation time of FIs, thereby extending the FI-NN method for constructing highly accurate PESs to larger systems beyond five atoms. Because of the minimum size of invariants used in the inputs of the NN, the NN structure can be very flexible for FI-NN, which leads to small fitting errors. The resulting FI-NN PES is much faster on evaluating than the corresponding permutationally invariant polynomial-NN PES.

Two-state diabatic potential energy surfaces of ClH2 based on nonadiabatic couplings with neural networks.

A general neural network (NN)-fitting procedure based on nonadiabatic couplings is proposed to generate coupled two-state diabatic potential energy surfaces (PESs) with conical intersections. The elements of the diabatic potential energy matrix (DPEM) can be obtained directly from a combination of the NN outputs in principle. Instead, to achieve higher accuracy, the adiabatic-to-diabatic transformation (ADT) angle (mixing angle) for each geometry is first solved from the NN outputs, followed by individual NN fittings of the three terms of the DPEM, which are calculated from the ab initio adiabatic energies and solved mixing angles. The procedure is applied to construct a new set of two-state diabatic potential energy surfaces of ClH2. The ab initio data including adiabatic energies and derivative couplings are well reproduced. Furthermore, the current diabatization procedure can describe well the vicinity of conical intersections in high potential energy regions, which are located in the T-shaped (C2v) structure of Cl-H2. The diabatic quantum dynamical results on diabatic PESs show large differences as compared with the adiabatic results in high collision energy regions, suggesting the significance of nonadiabatic processes in conical intersection regions at high energies.

Theoretical Investigations of Rate Coefficients of H + H2O2 → OH + H2O on a Full-Dimensional Potential Energy Surface.

The thermal rate coefficients of H + H2O2 → OH + H2O were obtained theoretically based on a recent fundamental invariant-neural network potential energy surface. The ring polymer molecular dynamics (RPMD) calculations were performed to get the rate coefficients with quantum effects, which are in good accord with some experimental values. The rate coefficients derived from extensive quasi-classical trajectory and canonical variational transition-state calculations also predict well the experimental results at high temperatures. The RPMD rate coefficients for H + H2O2 → OH + H2O are larger than H + H2O2 → H2 + HO2, but at very low temperatures below the room temperature, the H2 + HO2 channel becomes dominant due to significant quantum tunneling effects in the H atom transfer process. Considering that the old experimental values vary widely from different groups, we expect that our theoretical investigations can motivate new experimental work, which facilitates a more reliable comparison between theory and experiment.

Six-dimensional potential energy surfaces for the dissociative chemisorption of HCl on rigid Ag(100) and Ag(110) surfaces.

The dependence of reactivity on different facets of a surface is an interesting subject in dynamics at gas-surface interfaces. Here, we constructed new six-dimensional (6D) potential energy surfaces (PESs) for the dissociative chemisorption of HCl on rigid Ag(100) and Ag(110) surfaces, using the neural network method based on extensive density functional theory (DFT) calculations with the Perdew-Burke-Ernzerhof (PBE) functional, and compared the two PESs with the previously fitted PES of HCl/Ag(111). Time-dependent wave packet calculations show that the new PESs are very well converged with respect to the fitting procedure as well as to the number of DFT data points. The 6D dissociation probabilities for HCl initially in the ground rovibrational state decrease gradually for HCl/Ag(110), HCl/Ag(100), and HCl/Ag(111), consistent with the increasing barrier heights for the three reactions. The validity of the site-averaging approximation for HCl/Ag(110) does not hold well as compared with HCl/Ag(100) and HCl/Ag(111), in particular, at low kinetic energies, due to the strong steering effect this reaction exhibits if it is modeled with the semilocal PBE functional, which results in a low reaction barrier and a deep physisorption well.

Direct diabatization and analytic representation of coupled potential energy surfaces and couplings for the reactive quenching of the excited 2Σ+ state of OH by molecular hydrogen.

We have employed extended multiconfiguration quasidegenerate perturbation theory, fourfold-way diabatic molecular orbitals, and configurational uniformity to develop a global three-state diabatic representation of the potential energy surfaces and their couplings for the electronically nonadiabatic reaction OH* + H2 → H2O + H, where * denotes electronic excitation to the A 2Σ+ state. To achieve sign consistency of the computed diabatic couplings, we developed a graphics processing unit-accelerated algorithm called the cluster-growing algorithm. Having obtained consistent signs of the diabatic couplings, we fit the diabatic matrix elements (which consist of the diabatic potentials and the diabatic couplings) to analytic representations. Adiabatic potential energy surfaces are generated by diagonalizing the 3 × 3 diabatic potential energy matrix. The comparisons between the fitted and computed diabatic matrix elements and between the originally computed adiabatic potential energy surfaces and those generated from the fits indicate that the current fit is accurate enough for dynamical studies, and it may be used for quantal or semiclassical dynamics calculations.

An accurate full-dimensional potential energy surface and quasiclassical trajectory dynamics of the H + H2O2 two-channel reaction.

We report a new full-dimensional potential energy surface (PES) of the H + H2O2 reaction, covering both H2 + HO2 and OH + H2O product channels. The PES was constructed using the recently proposed fundamental invariant neural network (FI-NN) approach based on roughly 110 000 ab initio energy points by high level UCCSD(T)-F12/aug-cc-pVTZ calculations. The small fitting error (5.7 meV) and various tests imply a faithful representation of the discrete ab initio data over a large configuration space. Extensive quasiclassical trajectory (QCT) calculations were carried out on the new PES at a collision energy (Ec) of 15.0 kcal mol-1. The reaction yields dominantly OH + H2O, because of the lower reaction barrier and much larger reaction exothermicity (∼71 kcal mol-1) for this channel. Due to the exit barrier of both reaction channels, the most available energy is partitioned into the translational motion of the products. Considerable vibrational excitations of the H2O product are seen, particularly for the symmetric stretching and bending modes. The angular distributions show predominantly backward scattering, which is consistent with the direct rebound mechanism.

Six-dimensional quantum dynamics for the dissociative chemisorption of HCl on rigid Ag(111) on three potential energy surfaces with different density functionals.

We carried out six-dimensional quantum dynamics calculations for the dissociative chemisorption of HCl on a rigid Ag(111) surface, employing three potential energy surfaces (PESs) which were recently constructed using the neural network approach based on extensive density functional theory calculations with Perdew-Burke-Ernzerhof, Perdew-Wang91, and revised Perdew-Burke-Ernzerhof functionals, respectively. The vibrational excitation of HCl enhances the reactivity substantially, and the dissociation is most favored for HCl molecules colliding with rotation in a plane parallel to the Ag(111) surface (helicopter alignment). The influence of rotational excitation on the dissociation probability is much more complicated, with different trends at high and at low kinetic energies. The usage of three different PESs does not change the effects of vibrational excitation, rotational excitation, and rotational-alignment qualitatively, but it does change the magnitude of dissociation probabilities quantitatively due to the different barrier heights.