A new potential energy surface for the ground electronic state of the LiH2 system, and dynamics studies on the H((2)S) + LiH(X(1)Σ(+)) → Li((2)S) + H2(X(1)Σg(+)) reaction

New Diabatic Potential Energy Surfaces for the Li + H2 Reaction and Time-Dependent Quantum Wave Packet Studies

New global diabatic potential energy surfaces (DPESs) for the ground (12A') and first excited (22A') states for the Li + H2 system were developed, with more than 30,000 energy points at the IC-MRCI+Q level of theory, utilizing the aug-cc-pV5Z basis set for the H atoms and the cc-pCV5Z basis set for the Li atom, fitted by a single neural network (NN) with symmetry. Product state-resolved quantum dynamics calculations of the nonadiabatic reaction Li (2P) + H2 (X 1 ∑g+, v0 = 0, j0 = 0) → LiH (X 1∑+) + H(2S) were carried out using these new DPESs and also the previous HYLC-DPESs. The numerical results suggested that our newly constructed DPESs provided an accurate description of the LiH2 system.

An effective approximation of Coriolis coupling in reactive scattering: application to the time-dependent wave packet calculations

Coriolis coupling plays a crucial role in reactive scattering, but dynamics calculations including the complete Coriolis coupling significantly increase the difficulty of numerical evolution due to the corresponding expensive matrix processing. The coupled state approximation that completely ignores the off-diagonal Coriolis coupling saves computational cost significantly but its error is usually unacceptable. In this paper, an improved coupled state approximation inspired by recently published results [D. Yang, X. Hu, D. H. Zhang and D. Xie, J. Chem. Phys., 2018, 148, 084101.] of the inelastic scattering problem is extended to deal with the reactive scattering. The calculations using the time-dependent wave packet method reveal that the new method can accurately reproduce the rigorous results of the H + HD (j0 < 3) → D + H2 reaction and immensely improve the computational efficiency. Additionally, we extend the new method to the non-adiabatic Li(2p) + H2 (v0 = 0, j0 = 0, 1) → H + LiH reaction, showcasing its advantages of low computational cost and high accuracy.

Globally Accurate Gaussian Process Potential Energy Surface and Quantum Dynamics Studies on the Li(2S) + Na2 → LiNa + Na Reaction at Low Collision Energies

The LiNa2 reactive system has recently received great attention in the experimental study of ultracold chemical reactions, but the corresponding theoretical calculations have not been carried out. Here, we report the first globally accurate ground-state LiNa2 potential energy surface (PES) using a Gaussian process model based on only 1776 actively selected high-level ab initio training points. The constructed PES had high precision and strong generalization capability. On the new PES, the quantum dynamics calculations on the Li(2S) + Na2(v = 0, j = 0) → LiNa + Na reaction were carried out in the 0.001–0.01 eV collision energy range using an improved time-dependent wave packet method. The calculated results indicate that this reaction is dominated by a complex-forming mechanism at low collision energies. The presented dynamics data provide guidance for experimental research, and the newly constructed PES could be further used for ultracold reaction dynamics calculations on this reactive system.

Accurate Adiabatic and Diabatic Potential Energy Surfaces for the Reaction of He + H2

The accurate adiabatic and diabatic potential energy surfaces, which are for the two lowest states of He + H₂, are presented in this study. The Molpro 2012 software package is used, and the large basis sets (aug-cc-pV5Z) are selected. The high-level MCSCF/MRCI method is employed to calculate the adiabatic potential energy points of the title reaction system. The triatomic reaction system is described by Jacobi coordinates, and the adiabatic potential energy surfaces are fitted accurately using the B-spline method. The equilibrium structures and electronic energies for the H₂ are provided, and the corresponding different levels of vibrational energies of the ground state are deduced. To better express the diabatic process of the whole reaction, avoid crossing points being calculated and conical intersection also being optimized. Meanwhile, the diabatic potential energy surfaces of the reaction process are constructed. This study will be helpful for the analysis of histopathology and for the study in biological and medical mechanisms.

Stereodynamics-Controlled Product Branching in the Nonadiabatic H + NaD → Na(3s, 3p) + HD Reaction at Low Temperatures

Nonadiabatic processes play an important role at energies near or higher than conical intersection of adiabatic potential energy surfaces in chemical reactions. In this work, dynamics of the nonadiabatic H + NaD reaction at low temperatures are studied by using the quantum wave packet method based on an improved L-shaped grid. The nonadiabatic H + NaD reaction has two exothermic reaction channels: Na(3s) + HD and Na(3p) + HD; the latter can only occur via nonadiabatic transition. The dynamics results show that the product branching of the H + NaD reaction at collision energies ranging from 20 to 80 cm^-1 is controlled by stereodynamics. The Na(3s) and Na(3p) reaction channels occur through collinear collision and side-on collision, respectively. When the collision energy is lower than 20 cm^-1, the resonance-mediated reaction mechanism is dominant in both the Na(3s) and Na(3p) reaction channels.

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

Reactive collisions of Ca+ ion with H2 molecule play a crucial role in ultracold chemistry, quantum information and other cutting-edge fields, and have been widely concerned experimentally, but the corresponding...

Representing Globally Accurate Reactive Potential Energy Surfaces with Complex Topography by Combining Gaussian Process Regression and Neural Network

There has been increasing attention in using machine learning technologies, such as neural network (NN) and Gaussian process regression (GPR), to model multidimensional potential energy surfaces (PESs). NN PES features...

Theoretical Study of the Energy Disposal Mechanism and the State-Resolved Quantum Dynamics of the H + LiH+ → H2 + Li+ Reaction

Despite several studies in the literature, the detailed quantum state-to-state level mechanism of the astrophysically important exoergic barrierless H + LiH⁺ → H₂ + Li⁺ reaction is yet to be understood. In this work, we have investigated the energy disposal mechanism of the reaction in terms of integral reaction cross section, product internal state distributions, differential cross section, and rate constant. Fully converged and Coriolis coupled quantum mechanical calculations based on a time-dependent wave packet method have been performed at the state-to-state level on the ab initio electronic ground state potential energy surface (PES) constructed by Martinazzo et al. (J. Chem. Phys. 2003, 119, 11241-11248). The agreement between the present quantum mechanical and previous quasi-classical results is found even at very low relative translational energies of reagents. A non-statistical inverse Boltzmann vibrational distribution for the product is found. This is attributed to the "attractive" nature of the underlying PES, which facilitates the excess energy release mostly as product vibration (60-80%). The energy disposal in products is found to be unaffected by the rovibrational excitation of the reagent diatom due to the weak coupling between the vibrational modes of the reagent and the product. The mild effect of collision energy on the product energy disposal is ascribed to the effective coupling between the translational modes of the reagent and the product. It is found that the collisions lead to the formation of the product H₂ in its rovibrationally excited levels.

Non-adiabatic dynamics studies of the H(2S) + LiH(X1Σ+) reaction by time-dependent wave packet method

Non-adiabatic dynamics studies of the H + LiH (v₀ = 0, j₀ = 0) reaction are carried out based on the diabatic potential energy surfaces (PESs) reported by He and co-workers (Sci. Rep., 2016, 6, 25083) in the collision energy range from 0.001 to 1.0 eV. The H(²S) + LiH(X¹Σ⁺) → Li(2²S)/Li(2²P) + H₂(X¹Σ_g⁺) depletion reactions and the H'(²S) + LiH(X¹Σ⁺) → H(²S) + LiH'(X¹Σ⁺) exchange reaction are studied at the state-to-state level of theory. The dynamics properties, such as reaction probability, integral cross section, differential cross section, the ro-vibrational state distributions of the product and specific-state rate constant are calculated. In addition, the dynamics values of the H(²S) + LiH(X¹Σ⁺) → Li(2²S) + H₂(X¹Σ_g⁺) depletion reaction are compared with available theoretical results, which are based on the adiabatic PESs. Large discrepancies are found between the adiabatic and diabatic values, especially at low J values, which indicate that the non-adiabatic effect is very great and cannot be simply ignored. Furthermore, the deviations between adiabatic and diabatic values gradually decrease as the collision energy increases.

Instanton rate constant calculations using interpolated potential energy surfaces in nonredundant, rotationally and translationally invariant coordinates

A trivial flaw in the utilization of artificial neural networks in interpolating chemical potential energy surfaces (PES) whose descriptors are Cartesian coordinates is their dependence on simple translations and rotations of the molecule under consideration. A different set of descriptors can be chosen to circumvent this problem, internuclear distances, inverse internuclear distances or z-matrix coordinates are three such descriptors. The objective is to use an interpolated PES in instanton rate constant calculations, hence information on the energy, gradient, and Hessian is required at coordinates in the vicinity of the tunneling path. Instanton theory relies on smoothly fitted Hessians, therefore we use energy, gradients, and Hessians in the training procedure. A major challenge is presented in the proper back-transformation of the output gradients and Hessians from internal coordinates to Cartesian coordinates. We perform comparisons between our method, a previous approach and on-the-fly rate constant calcuations on the hydrogen abstraction from methanol and on the hydrogen addition to isocyanic acid. © 2018Wiley Periodicals, Inc.

Neural network potential energy surface and dynamical isotope effects for the N+(3P) + H2 → NH+ + H reaction

Dynamical isotope effects are calculated for the N⁺(³P) + H₂ → NH⁺ + H reaction on a new neural network potential energy surface.

New diabatic potential energy surfaces of the NaH2 system and dynamics studies for the Na(3p) + H2 → NaH + H reaction

The Na(3p) + H2(X1Σg+) → NaH(X1Σ+) + H(2S) reaction plays an important role in the field of diabatic reaction dynamics. A set of new diabatic potential energy surfaces (PESs) of the NaH2 system are structured, which include the diabatic coupling between the lowest two adiabatic states. The electronic structure calculations are performed on the multi-reference configuration interaction level with the cc-pwCVQZ and aug-cc-PVQZ basis sets for Na and H atoms. 32402 geometries are chosen to construct the diabatic data by a unitary transformation based on the molecular property method. The diabatic matrix elements of [Formula: see text], [Formula: see text] and [Formula: see text] ([Formula: see text]) are fitted by the artificial neural network model. The spectroscopic constants of diatoms obtained from the present PESs are consistent with the experimental data. The topographical and intersection characteristics of the [Formula: see text] and [Formula: see text] surfaces are discussed. Based on the new PESs, the time-dependent quantum wave packet calculations are carried out to study the reaction mechanism of the title reaction in detail.

Significant effects of vibrational excitation of reactant in K + H2 → H + KH reaction based on a new neural network potential energy surface

The study of K + H2 collision has a long experimental history, but there have been few theoretical studies due to lack of a global potential energy surface (PES). In this study, a new global PES for the ground state of KH2 system was constructed based on numerous ab initio points, using the permutation invariant polynomial neural network method. The root mean square error (RMSE) of PES is very small (5.64 meV). On the new PES, time-dependent quantum wave packet (TDWP) and quasiclassical trajectory (QCT) calculations were carried out to study the dynamics of the K(2S) + H2(X1Σ+g) → H(2S) + KH(X1Σ+) reaction. Dynamics results show that (i) the K + H2(v = 0) → H + KH reaction scarcely occurred, (ii) the K + H2(v = 1) → H + KH reaction took place in small quantities, and (iii) the K + H2(v = 2) → H + KH reaction occurred in large quantities. This indicates that vibrational energy of the reactant is significantly more effective at promoting the reaction than the translational energy. This characteristic stems from a major physical model in reactive collisions: the vibrationally excited H2 molecule and K atom collide first in a T-geometric configuration and the vibrational motion of the H2 molecule helps separate the two H atoms a large distance after the collision. At a large H-H distance, a broad well exists on the PES, so the heavy K atom could pull back the light H atom to initiate the reaction. Similar to the reactive channel, vibrational excitation of the reactant also has a significant effect on the collision-induced dissociation channel.

Global diabatic potential energy surfaces for the BeH2 + system and dynamics studies on the Be+(2P) + H2(X1Σg +) → BeH+(X1Σ+) + H(2S) reaction

The Be+(2P) + H2(X1Σg +) → BeH+(X1Σ+) + H(2S) reaction has great significance for studying diabatic processes and ultracold chemistry. The first global diabatic potential energy surfaces (PESs) which are correlated with the lowest two adiabatic states 12A' and 22A' of the BeH2 + system are constructed by using the neural network method. Ab initio energy points are calculated using the multi-reference configuration interaction method with the Davidson correction and AVQZ basis set. The diabatic energies are obtained from the transformation of ab initio data based on the dipole moment operators. The topographical characteristics of the diabatic PESs are described in detail, and the positions of crossing between the V d 11 and V d 22 are pinpointed. On new diabatic PESs, the time-dependent quantum wave packet method is carried out to study the mechanism of the title reaction. The results of dynamics calculations indicate the reaction has no threshold and the product BeH+ is excited to high vibrational states easily. In addition, the product BeH+ tends to backward scattering at most collision energies.

Accurate potential energy surfaces for the first two lowest electronic states of the Li (2p) + H2 reaction

The accuracy of three-dimensional adiabatic and diabatic potential energy surfaces is calculated using ab initio methods and is numerically fitted for the two lowest electronic states 1 and 2²A′ of the LiH₂ system, which are very important for the Li (2p) + H₂ reaction. The finite difference method is performed to generate the mixing angles, which are used to educe the diabatic potential from the adiabatic potential. The accurate conical intersection (CI) is studied in this work with three different basis sets. The energy of the conical intersection is slightly lower (nearly 0.12 eV) than that of the perpendicular intermediate on the first excited state. By analyzing the potential energy surfaces in this work we can suggest that the most possible reaction pathway for the title reaction is Li (2p) + H₂ → LiH₂ (2²A′) (C_2v) → CI → LiH₂ (1²A′) (C_2v) → LiH⋯H → LiH (X¹∑_g⁺) + H. The conical intersection and (2²A′) intermediate may play a vital role in the title reaction.

Accurate diabatic potential energy surfaces for the Li (2p) + H₂ → LiH (X) + H reaction are produced.

A new potential energy surface of the OH2+ system and state-to-state quantum dynamics studies of the O+ + H2 reaction

A new global potential energy surface of the O⁺ + H₂ system was constructed with neural network method, using about 63000 ab initio points, which were calculated by employing the multi-reference configuration interaction method with aug-cc-pVTZ and aug-cc-pVQZ basis sets.

Diabatic potential energy surfaces of MgH2+ and dynamic studies for the Mg+(3p) + H2 → MgH+ + H reaction

The global diabatic potential energy surfaces for the Mg⁺(3p) + H₂ → MgH⁺ + H reaction are structured for the first time.

Development of a new UHV/XHV pressure standard (Cold Atom Vacuum Standard)

The National Institute of Standards and Technology has recently begun a program to develop a primary pressure standard that is based on ultra-cold atoms, covering a pressure range of 1 × 10^-6 Pa to 1 × 10^-10 Pa and possibly lower. These pressures correspond to the entire ultra-high vacuum (UHV) range and extend into the extreme-high vacuum (XHV). This cold-atom vacuum standard (CAVS) is both a primary standard and absolute sensor of vacuum. The CAVS is based on the loss of cold, sensor atoms (such as the alkali-metal lithium) from a magnetic trap due to collisions with the background gas (primarily H₂) in the vacuum. The pressure is determined from a thermally-averaged collision cross section, which is a fundamental atomic property, and the measured loss rate. The CAVS is primary because it will use collision cross sections determined from ab initio calculations for the Li + H₂ system. Primary traceability is transferred to other systems of interest using sensitivity coefficients.

A neural network potential energy surface for the NaH2 system and dynamics studies on the H(2S) + NaH(X1Σ+) → Na(2S) + H2(X1Σg+) reaction

In order to study the dynamics of the reaction H(²S) + NaH(X¹Σ⁺) → Na(²S) + H₂(X¹Σ_g⁺), a new potential energy surface (PES) for the ground state of the NaH₂ system is constructed based on 35 730 ab initio energy points. Using basis sets of quadruple zeta quality, multireference configuration interaction calculations with Davidson correction were carried out to obtain the ab initio energy points. The neural network method is used to fit the PES, and the root mean square error is very small (0.00639 eV). The bond lengths, dissociation energies, zero-point energies and spectroscopic constants of H₂(X¹Σ_g⁺) and NaH(X¹Σ⁺) obtained on the new NaH₂ PES are in good agreement with the experiment data. On the new PES, the reactant coordinate-based time-dependent wave packet method is applied to study the reaction dynamics of H(²S) + NaH(X¹Σ⁺) → Na(²S) + H₂(X¹Σ_g⁺), and the reaction probabilities, integral cross-sections (ICSs) and differential cross-sections (DCSs) are obtained. There is no threshold in the reaction due to the absence of an energy barrier on the minimum energy path. When the collision energy increases, the ICSs decrease from a high value at low collision energy. The DCS results show that the angular distribution of the product molecules tends to the forward direction. Compared with the LiH₂ system, the NaH₂ system has a larger mass and the PES has a larger well at the H-NaH configuration, which leads to a higher ICS value in the H(²S) + NaH(X¹Σ⁺) → Na(²S) + H₂(X¹Σ_g⁺) reaction. Because the H(²S) + NaH(X¹Σ⁺) → Na(²S) + H₂(X¹Σ_g⁺) reaction releases more energy, the product molecules can be excited to a higher vibrational state.

Influence of rovibrational excitation on the non-diabatic state-to-state dynamics for the Li(2p) + H2 → LiH + H reaction

The non-adiabatic state-to-state dynamics of the Li(2p) + H2 → LiH + H reaction has been studied using the time-dependent wave packet method, based on a set of diabatic potential energy surfaces recently developed by our group. Integral cross sections (ICSs) can be increase more than an order of magnitude by the vibrational excitation of H2, whereas the ICSs are barely affected by the rotational excitation of H2. Moreover, ICSs of the title reaction with vibrationally excited H2 decrease rapidly with increasing collision energy, which is a typical feature of non-threshold reaction. This phenomenon implies that the title reaction can transformed from an endothermic to an exothermic reaction by vibrational excitation of H2. With the increase of the collision energy, the sideways and backward scattered tendencies of LiH for the Li(2p) + H2(v = 0, j = 0, 1) → LiH + H reactions are enhanced slightly, while the backward scattering tendency of LiH for the Li(2p) + H2(v = 1, j = 0) → LiH + H reaction becomes remarkably weakened. For the reaction with vibrationally excited H2 molecule, both direct and indirect reaction mechanism exist simultaneously.

A new potential energy surface for the ground state of the LiH2+system and dynamic studies on LiH+(X2Σ+) + H(2S) → Li+(1S) + H2(X1Σ+g)

An accurate potential energy surface for the ground state of the LiH₂⁺system is constructed with the neural network method.

A new potential energy surface of LiHCl system and dynamic studies for the Li(2S) + HCl(X1Σ+) → LiCl(X1Σ+) + H(2S) reaction

A new global potential energy surface (PES) is constructed for the ground state of LiHCl system based on high-quality ab initio energy points calculated using multi-reference configuration interaction calculations with the Davidson correction. The AVQZ and WCVQZ basis sets are employed for H and Li atoms, respectively. To compensate the relativistic effects of heavy element, the AWCVQZ-DK basis set is employed for Cl atom. The neural network method is used for fitting the PES, and the root mean square error is small (1.36 × 10^-2 eV). The spectroscopic constants of the diatoms obtained from the new PES agree well with experimental data. The geometric characteristics of the transition state and the complex are examined and compared with the previous theoretical values. To study the reaction dynamics of the Li(²S) + HCl(X¹Σ⁺) → LiCl(X¹Σ⁺) + H(²S) reaction, quantum reactive scattering dynamics calculations using collection reactant-coordinate-based wave packet method are conducted based on the new PES. The results of the reaction probabilities indicate that a small barrier exists along the reaction path as observed from the PES. The integral cross section curves reveal that the product molecule LiCl is easily excited. In addition, the reaction is dominated by forward scattering, and similar pattern is observed from Becker's experiment.

Global diabatic potential energy surfaces and quantum dynamical studies for the Li(2p) + H2(X(1)Σ(+)g) → LiH(X(1)Σ(+)) + H reaction

The global diabatic potential energy surfaces which are correlated with the ground state 1A' and the excited state 2A' of the Li(2p) + H2 reaction are presented in this study. The multi-reference configuration interaction method and large basis sets (aug-cc-pVQZ for H atom and cc-pwCVQZ for Li atom) were employed in the ab initio single-point energy calculations. The diabatic potential energies were generated by the diabatization scheme based on transition dipole moment operators. The neural network method was utilized to fit the matrix elements of the diabatic energy surfaces, and the root mean square errors were extremely small (3.69 meV for , 5.34 meV for and 5.06 meV for ). The topographical features of the diabatic potential energy surfaces were characterized and the surfaces were found to be sufficiently smooth for the dynamical calculation. The crossing seam of the conical intersections between the and surfaces were pinpointed. Based on this new analytical diabatic potential energy surfaces, time-dependent wave packet calculation were conducted to investigate the mechanism of the title reaction. At low collision energies, the product LiH molecule tends to forward scattering, while at high collision energies, the forward and backward scatterings exist simultaneously.

Theoretical study of product polarization of O(1D) + HCl(v = 0; j = 0) → ClO + H and its isotope exchange reaction

O(1D) + HCl(v = 0; j = 0) → ClO + H and its isotope exchange reaction O(1D) + DCl(v = 0; j = 0) → ClO + D are studied in the collision energy range 14.0–20.0 kcal/mol based on the potential energy surface 1[Formula: see text] state. Reaction probabilities, integral cross sections, the two angular distribution functions (concerning the initial/final velocity vector, and the product rotational momentum vector), and the product rotational alignment parameters are calculated as a function of the collision energy for the two reactions. The four generalized polarization dependent differential cross sections are presented to manifest the polarization characters. Also, the effect of the collision energy and the kinetic isotope effect are studied.

A new potential energy surface for the H2S system and dynamics study on the S((1)D) + H2(X(1)Σg(+)) reaction

We constructed a new global potential energy surface (PES) for the electronic ground state ((1)A') of H2S based on 21,300 accurate ab initio energy points over a large configuration space. The ab initio energies are obtained from multireference configuration interaction calculations with a Davidson correction using basis sets of quadruple zeta quality. The neural network method is applied to fit the PES, and the root mean square error of fitting is small (1.68 meV). Time-dependent wave packet studies for the S((1)D) + H2(X(1)Σg(+)) → H((2)S) + SH(X(2)Π) reaction on the new PES are conducted to study the reaction dynamics. The calculated integral cross sections decrease with increasing collision energy and remain fairly constant within the high collision energy range. Both forward and backward scatterings can be observed as expected for a barrierless reaction with a deep well on the PES. The calculated integral cross sections and differential cross sections are in good agreement with the experimental results.