Electronically Nonadiabatic Effects on the Quantum Dynamics of the Ha + BeHb+ → Be+ + HaHb; Hb + BeHa+ Reactions

Nonadiabatic effects are ubiquitous and play an important role in many chemical processes. Here, the adiabatic and nonadiabatic quantum scattering calculations of the H + BeH⁺ reaction are performed using the time-dependent wave packet method based on an accurate diabatic potential energy matrix that includes the lowest two electronic states and their couplings. The resulting integral cross sections reveal that the nonadiabatic effect significantly inhibits the reactivity of the BeH⁺-depletion channel but enhances that of the H-exchange channel. The vibrational excitation is suppressed, but the translational excitation is promoted for the H₂ product in the BeH⁺-depletion channel when the nonadiabatic coupling is included. However, the nonadiabatic coupling has a mild effect on the H-exchange product-state distribution. When the nonadiabatic effect is considered, the differential cross sections of the H₂ product become less polarized because of the formation of an excited-state complex, whereas the corresponding results of the H-exchange channel only present an increase in the magnitude at the backward region.

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.

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...

A new permutation-symmetry-adapted machine learning diabatization procedure and its application in MgH2 system

This work introduces a new permutation-symmetry-adapted machine learning diabatization procedure, termed the diabatization by equivariant neural network (DENN). In this approach, the permutation symmetric and anti-symmetric elements in diabatic potential energy metrics (DPEMs) were simultaneously simulated by the equivariant neural network. The diabatization by deep neural network scheme was adopted for machine learning diabatization, and non-zero diabatic coupling was included to increase accuracy in the near degenerate region. Based on DENN, the global DPEMs for 1¹A' and 2¹A' states of MgH₂ have been constructed. To the best of our knowledge, these are the first global DPEMs for the MgH₂ system. The root-mean-square-errors (RMSEs) for diagonal elements (H₁₁ and H₂₂) and the off-diagonal element (H₁₂) around the conical intersection region were 5.824, 5.307, and 5.796 meV, respectively. The RMSEs of global adiabatic energies for two adiabatic states were 4.613 and 12.755 meV, respectively. The spectroscopic calculations of the 1¹A' state in the linear HMgH region are in good agreement with the experiment and previous theoretical results. The differences between calculated frequencies and corresponding experiment values are 1.38 and 1.08 cm^-1 for anti-symmetric stretching fundamental vibrational frequency and first overtone. The global DPEMs obtained in this work should be useful for further quantum mechanics dynamic simulations on the MgH₂ system.

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.

An orbital picture extracted from correlated electronic wavefunctions and application to forbidden reactions: 70 years of the frontier orbital theory

The one-electron picture in molecular electronic state theory, particularly the molecular orbital (MO) theory with the Hartree-Fock approximation, has set a foundation to develop chemical science. Frontier orbital theory, or the theory of HOMO (highest occupied MO)-LUMO (lowest unoccupied MO) interaction, and the conservation rule of orbital symmetry are among the brightest achievements in a molecular orbital picture. After 70 years from the birth of frontier orbital theory, however, electronic wavefunctions treated in current quantum chemistry are often highly correlated and consist of extensive scales of electronic configurations to be more accurate and to cope with far more complicated reactions than concerted reactions. Under such circumstances, the MO approximation itself readily loses its validity, let alone the utter dominance of the HOMO-LUMO interaction. Recently, we have proposed an invariant method to extract general orbitals from such correlated electronic wavefunctions, which we refer to as Energy Natural Orbitals (ENOs) [K. Takatsuka and Y. Arasaki, J. Chem. Phys. 154, 094103 (2021)]. The energies of ENOs are summed exactly to the total electronic energy. The topological (symmetry) properties of a total wavefunction are represented by the relative phases of ENOs along with the continuity and crossing (avoided and conical intersection) among them. Only a small number of ENOs often dominate and characterize chemical reactions. With these properties of ENO, we explore a couple of simple and typical symmetry forbidden reactions, illustrating the effects of electron correlation and degeneracy in relevant ENOs. We propose the notion of "internal conical intersection" among ENOs, which leads to Jahn-Teller effect, pseudo-Jahn-Teller effect, and so on. We dare to explain the primary origin of elementary conical intersections and multidimensional avoided crossing in chemical reactions with the use of the notion of orbital crossing between those of HOMO-HOMO and LUMO-LUMO interactions and so on.

Molecular excited states through a machine learning lens

Theoretical simulations of electronic excitations and associated processes in molecules are indispensable for fundamental research and technological innovations. However, such simulations are notoriously challenging to perform with quantum mechanical methods. Advances in machine learning open many new avenues for assisting molecular excited-state simulations. In this Review, we track such progress, assess the current state of the art and highlight the critical issues to solve in the future. We overview a broad range of machine learning applications in excited-state research, which include the prediction of molecular properties, improvements of quantum mechanical methods for the calculations of excited-state properties and the search for new materials. Machine learning approaches can help us understand hidden factors that influence photo-processes, leading to a better control of such processes and new rules for the design of materials for optoelectronic applications.

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.

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

The FI-NN approach is capable of representing highly accurate diabatic PESs with particular and complicated symmetry problems.

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.

Exclusive Neural Network Representation of the Quasi-Diabatic Hamiltonians Including Conical Intersections

We propose a numerically simple and straightforward, yet accurate and efficient neural networks-based fitting strategy to construct coupled potential energy surfaces (PESs) in a quasi-diabatic representation. The fundamental invariants are incorporated to account for the complete nuclear permutation inversion symmetry. Instead of derivative couplings or interstate couplings, a so-called modified derivative coupling term is fitted by neural networks, resulting in accurate description of near degeneracy points, such as the conical intersections. The adiabatic energies, energy gradients, and derivative couplings are well reproduced, and the vanishing of derivative couplings as well as the isotropic topography of adiabatic and diabatic energies in asymptotic regions are automatically satisfied. All of these features of the coupled global PESs are requisite for accurate dynamics simulations. Our approach is expected to be very useful in developing highly accurate coupled PESs in a quasi-diabatic representation in an efficient machine learning-based way.

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.

Quantum dynamics studies of isotope effects in the Mg+(3p) + HD → MgH+/MgD+ + D/H insertion reaction

The time-dependent wave packet quantum dynamics studies for the Mg+(3p) + HD → MgH+/MgD+ + D/H diabatic reaction are carried out for the first time on recently developed diabatic YHWCH potential energy surfaces [Phys. Chem. Chem. Phys., 2018, 20, 6638-6647]. The results of reaction probabilities and total integral cross sections show a dramatic preference to the formation of MgD+ over MgH+ owing to the insertion reaction mechanism in the title reaction. The MgD+/MgH+ branching ratio witnesses a monotonic decrease from 10.58 to 3.88 at collision energy range of 0.01 to 0.20  eV, and at the collision energy of 0.114  eV, it is close to the experimental value of 5. The rovibrational state-resolved ICSs of the two channels show the products MgD+ have higher vibrational excitation and hotter rotational state distributions. The opacity function P(J) suggests that the MgH+ + D channel and MgD+ + H channel are dominated by high-b and low-b collisions, respectively. Both forward and backward scattering peaks are found in the differential cross section curves, whereas the angle distributions of products are not strictly forward-backward symmetric because of the short lifetime of the complex in the reaction.

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.

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.

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.