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

Nonadiabatic dynamics studies of the H(2S) + RbH(X1Σ+) reaction: based on new diabatic potential energy surfaces

The global diabatic potential energy surfaces (PESs) that correspond to the ground (1²A') and first excited states (2²A') of the RbH₂ system PES are constructed based on 17 786 ab initio points. The neural network method is used to fit the PESs and the topographic features of the new diabatic PESs are discussed in detail. Based on the newly constructed diabatic PESs, the dynamics calculations of the H(²S) + RbH(X¹Σ⁺) → Rb(5²S) + H₂(X¹Σ_g ⁺)/Rb(5²P) + H₂(X¹Σ_g ⁺) reactions are performed using the time-dependent wave packet method. The dynamics properties of these two channels such as the reaction probabilities, integral cross sections, and differential cross sections (DCSs) are calculated at state-to-state level of theory. The nonadiabatic effects are discussed in detail, and the results indicate that the adiabatic results are overestimated from the dynamics values. The DCSs of these two channels are forward biased, which indicates that the abstraction mechanism plays a dominant role in the reaction.

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.

Machine Learning for Electronically Excited States of Molecules

Electronically excited states of molecules are at the heart of photochemistry, photophysics, as well as photobiology and also play a role in material science. Their theoretical description requires highly accurate quantum chemical calculations, which are computationally expensive. In this review, we focus on not only how machine learning is employed to speed up such excited-state simulations but also how this branch of artificial intelligence can be used to advance this exciting research field in all its aspects. Discussed applications of machine learning for excited states include excited-state dynamics simulations, static calculations of absorption spectra, as well as many others. In order to put these studies into context, we discuss the promises and pitfalls of the involved machine learning techniques. Since the latter are mostly based on quantum chemistry calculations, we also provide a short introduction into excited-state electronic structure methods and approaches for nonadiabatic dynamics simulations and describe tricks and problems when using them in machine learning for excited states of molecules.

Machine Learning for Electronically Excited States of Molecules

Electronically excited states of molecules are at the heart of photochemistry, photophysics, as well as photobiology and also play a role in material science. Their theoretical description requires highly accurate quantum chemical calculations, which are computationally expensive. In this review, we focus on not only how machine learning is employed to speed up such excited-state simulations but also how this branch of artificial intelligence can be used to advance this exciting research field in all its aspects. Discussed applications of machine learning for excited states include excited-state dynamics simulations, static calculations of absorption spectra, as well as many others. In order to put these studies into context, we discuss the promises and pitfalls of the involved machine learning techniques. Since the latter are mostly based on quantum chemistry calculations, we also provide a short introduction into excited-state electronic structure methods and approaches for nonadiabatic dynamics simulations and describe tricks and problems when using them in machine learning for excited states of molecules.

Quantum Dynamics Studies of the Significant Intramolecular Isotope Effects on the Nonadiabatic Be+(2P) + HD → BeH+/BeD+ + D/H Reaction

Quantum time-dependent wave packet dynamics studies on the nonadiabatic Be⁺(²P) + HD → BeH⁺/BeD⁺ + D/H reaction are performed for the first time employing recently constructed diabatic potential energy surfaces. Strong intramolecular isotope effects and unusual results are presented, which are attributed to the dynamic effects of shallow wells induced by avoided crossing on the diagonal V₂₂^d surface. The BeH⁺ + D and BeD⁺ + H channels are dominated by high-J and low-J partial waves, respectively. The BeD⁺/BeH⁺ branching ratio is larger than 10 at low energy and gradually decreases with increasing collision energy. The BeH⁺ product is primarily distributed at low vibrational states, whereas there exists an obvious population inversion of vibrational states on the BeD⁺ product. The results of differential cross sections suggest that the formation of the BeH⁺ + D channel favors a direct reaction process, while the BeD⁺ + H channel is mainly generated by the complex-forming mechanism.

Time-dependent quantum mechanical wave packet dynamics

Starting from a model study of the collinear (H, H₂) exchange reaction in 1959, the time-dependent quantum mechanical wave packet (TDQMWP) method has come a long way in dealing with systems as large as Cl + CH₄. The fast Fourier transform method for evaluating the second order spatial derivative of the wave function and split-operator method or Chebyshev polynomial expansion for determining the time evolution of the wave function for the system have made the approach highly accurate from a practical point of view. The TDQMWP methodology has been able to predict state-to-state differential and integral reaction cross sections accurately, in agreement with available experimental results for three dimensional (H, H₂) collisions, and identify reactive scattering resonances too. It has become a practical computational tool in predicting the observables for many A + BC exchange reactions in three dimensions and a number of larger systems. It is equally amenable to determining the bound and quasi-bound states for a variety of molecular systems. Just as it is able to deal with dissociative processes (without involving basis set expansion), it is able to deal with multi-mode nonadiabatic dynamics in multiple electronic states with equal ease. We present an overview of the method and its strength and limitations, citing examples largely from our own research groups.

Global accurate diabatic potential surfaces for the reaction H + Li2

The adiabatic potential energies for the lowest three states of a Li2H system are calculated with a high level ab initio method (MCSCF/MRCI) with a large basis set (aV5Z). The accurate three dimensional B-spline fitting method is used to map the global adiabatic potential energy surfaces, using the existing adiabatic potential energies, for the lowest two adiabatic states of the title reaction system. The different vibrational states and corresponding energies are studied for the diatomic molecule of reactant and products. In order to clearly understand the nonadiabatic process, the avoided crossing area and conical intersection are carefully studied. For further study of the nonadiabatic dynamic reaction, the diabatic potential energy surfaces are deduced in the present work.

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.

Non-adiabatic dynamics studies of the K(4p2P) + H2(X1Σ) reaction based on new diabatic potential energy surfaces

Global diabatic potential energy surfaces (PESs) of the KH2 system corresponding to the ground (12A') and first excited (22A') states were constructed for the first time. In ab initio calculations, the MRCI-F12 method with AVTZ and def2-QZVP basis sets was adopted and 17 865 ab initio energy points were calculated. The mixing angle, which is used to obtain the diabatic energies, was calculated by the molecular properties of the transition dipole moment. The diabatic PESs were fitted individually by the permutation invariant polynomial neural network method and the topographical features of the diabatic PESs are discussed in detail. The non-adiabatic dynamics studies of the K(4p2P) + H2(v0 = 0, 1, j0 = 0) reaction were carried out using the APH method based on the new diabatic PESs. The collision reaction processes K(4p2P) + H2(v0 = 0, 1, j0 = 0) → H + KH and the quenching processes K(4p2P) + H2(v0 = 0, 1, j0 = 0) → K(4s2S) + H2 were studied at the state-to-state level of theory. For the reaction process, the dynamics results indicated that the vibrational excitation of H2 was significantly more effective at promoting the reaction than the translational energy. In addition, the differential cross-sections were forward-biased scattering, which indicated that the direct abstraction mechanism plays a dominant role in the reaction. For the quenching process, the vibrational excitation of H2 molecules could improve the quenching efficiency obviously.

Dynamics study on the non-adiabatic Na(3p) + HD → NaH/NaD + D/H reaction: insertion-abstraction mechanism

Time-dependent wave packet calculations are carried out for two reaction channels of the non-adiabatic Na(3p) + HD → NaH/NaD + D/H reaction. The potential well on the excited state potential energy surface makes the reaction preferable to proceed through the insertion reaction path. The dominance of the NaD + H reaction channel and product rotational state distributions are found to be in agreement with the characteristics of typical adiabatic insertion reactions. However, significant forward scattering peaks in the differential cross sections (DCS) are found to be inconsistent with the forward-backward symmetric scattering characteristic of typical adiabatic insertion reactions, which indicate that the Na(3p) + HD reaction is dominated by a direct reaction mechanism. The comparison between adiabatic and non-adiabatic calculated DCSs reveals that the non-adiabatic couplings in the reaction could reduce the lifetime of the intermediate complex. Finally, the insertion-abstraction mechanism is put forward for the non-adiabatic Na(3p) + HD reaction.

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.

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.

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 global potential energy surface and dynamics study of the Au+ + H2 → H + Au+H reaction

A global potential energy surface (PES) of the ground state of the Au⁺H₂ system was constructed using a neural network method with permutation invariant polynomials.

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.