The time-dependent quantum wave packet approach to the electronically nonadiabatic processes in chemical reactions

Large-Scale Non-Adiabatic Dynamics Simulation Based on Machine Learning Hamiltonian and Force Field: The Case of Charge Transport in Monolayer MoS2

We present an efficient and reliable large-scale non-adiabatic dynamics simulation method based on machine learning Hamiltonian and force field. The quasi-diabatic Hamiltonian network (DHNet) is trained in the Wannier basis based on well-designed translation and rotation invariant structural descriptors, which can effectively capture both local and nonlocal environmental information. Using the representative two-dimensional transition metal dichalcogenide MoS2 as an illustration, we show that density functional theory (DFT) calculations of only ten structures are sufficient to generate the training set for DHNet due to the high efficiency of Wannier analysis and orbital classification in sampling the interorbital couplings. DHNet demonstrates good transferability, thus enabling direct construction of the electronic Hamiltonian matrices for large systems. Compared with direct DFT calculations, DHNet significantly reduces the computational cost by about 5 orders of magnitude. By combining DHNet with the DeePMD machine learning force field, we successfully simulate electron transport in monolayer MoS2 with up to 3675 atoms and 13475 electronic levels by using a state-of-the-art surface hopping method. The electron mobility is calculated to be 110 cm2/(V s), which is in good agreement with the extensive experimental results in the range of 3-200 cm2/(V s) during 2013-2023. Due to the high performance, the proposed DHNet and large-scale non-adiabatic dynamics methods have great potential to be applied to study charge carrier dynamics in a wide range of material systems.

Electronically Nonadiabatic Quenching of Excited States of O2 by Collisions with O Atoms

The kinetics of electronically inelastic quenching of O2(a1Δg) and O2(b1Σg+) by collisions with O(3P) have been investigated using mixed quantum-classical trajectories governed by adiabatic potential energy surfaces and state couplings generated from a recently developed diabatic potential energy matrix (DPEM) for the 14 lowest-energy 3A' states of O3. Using the coherent switching with decay of mixing (CSDM) method, dynamics calculations were performed both with 14 coupled electronic states and with 8 coupled electronical states, and similar results were obtained. The calculated thermal quenching rate coefficients are generally small, but they increase with temperature. The positive temperature dependence is attributed to high-energy locally avoided crossings that can only be easily accessed by high collision energies. We find that, depending on the temperature, 86-97% of the b state quenches are into the a state with the remainder into the ground electronic state of O2. The calculated rate coefficients for quenching of O2(b1Σg+) and O2(a1Δg) by O(3P), coupled with the assumption that electronically nonadiabatic probabilities for collisions on the 3A' surfaces are similar to those on 3A″ surfaces, are compared with the available experimental results.

State-to-State Time-Dependent Quantum Dynamics Studies of the Si(3P) + OH(X 2Π) → OSi(X 1Σg+) + H(2S) Reaction Based on a New HOSi(X2A') Potential Energy Surface

Quantum and quasi-classical dynamics calculations were conducted for the reaction of Si with OH on the latest potential energy surface (PES), which is obtained by fitting tens of thousands of ab initio energy points by using the many-body expansion formula. To obtain an accurate PES, all energy points calculated with aug-cc-pVQZ and aug-cc-pV5Z basis sets were extrapolated to the complete basis set limit. The accuracy of our new PES was verified by comparing the topographic characteristics and contour maps of potential energy with other works. In addition, the anharmonic vibrational frequencies of HOSi and HSiO based on the present ab initio and PES by means of quantum dynamics methods were calculated. Dynamics information such as reaction probability, integral cross sections (ICS), product distribution, and rate constants was obtained on the new HOSi(X2A') PES. The dynamic information calculated using the quasi-classical trajectory method and time-dependent wave packet method is generally in good agreement, except for the vibrational state-resolved ICSs of product. The calculated differential cross section and capture time reveal that the reaction is primarily governed by the complex formation mechanism.

Theoretical Investigation on the Reversible Photoswitch Mechanism of Benzylidene-Oxazolone System

The design and application of molecular photoswitches have attracted much attention. Herein, we performed a detailed computational study on the photoswitch benzylidene-oxazolone system based on static electronic structure calculations and on-the-fly excited-state dynamic simulations. For the Z and E isomer, we located six and four minimum energy conical intersections (MECIs) between the first excited state (S1) and the ground state (S0), respectively. Among them, the relaxation pathway driven by ring-puckering motion is the most competitive channel with the photoisomeization process, leading to the low photoisomerization quantum yield. In the dynamic simulations, about 88 % and 66 % trajectories decay from S1 to S0 for Z and E isomer, respectively, within the total simulation time of ~2 ps. The photoisomeization quantum yields obtained in our study (0.20 for Z→E and 0.12 for E→Z) agree well with the experimental measured values (0.25 and 0.11), even though the number of trajectories is limited to 50. Our study sheds light on the complexity of the benzylidene-oxazolone system 's deactivation process and the competitive mechanisms among different reaction channels, which provides theoretical guidance for further design and development of benzylidene-oxazolone based molecular photoswitches.

Theoretical Insights into the Dynamics of Gas-Phase Bimolecular Reactions with Submerged Barriers

Much attention has been paid to the dynamics of both activated gas-phase bimolecular reactions, which feature monotonically increasing integral cross sections and Arrhenius kinetics, and their barrierless capture counterparts, which manifest monotonically decreasing integral cross sections and negative temperature dependence of the rate coefficients. In this Perspective, we focus on the dynamics of gas-phase bimolecular reactions with submerged barriers, which often involve radicals or ions and are prevalent in combustion, atmospheric chemistry, astrochemistry, and plasma chemistry. The temperature dependence of the rate coefficients for such reactions is often non-Arrhenius and complex, and the corresponding dynamics may also be quite different from those with significant barriers or those completely dominated by capture. Recent experimental and theoretical studies of such reactions, particularly at relatively low temperatures or collision energies, have revealed interesting dynamical behaviors, which are discussed here. The new knowledge enriches our understanding of the dynamics of these unusual reactions.

Quantum and semiclassical studies of nonadiabatic electronic transitions between N(4S) and N(2D) by collisions with N2

The dynamics and kinetics of spin-forbidden transitions between N(2D) and N(4S) via collisions with N2 molecules are investigated using a quantum wave packet (WP) method and the semi-classical coherent switches with decay of mixing (CSDM) method. These electronic transition processes are competing with exchange reaction channels on both the doublet and quartet potential energy surfaces. The WP and CSDM quenching rate coefficients are found in reasonable agreement with each other, and both reproduce the previous theoretical results. For the excitation process, the agreement between the two approaches is dependent on the treatment of the zero-point energy (ZPE) in the product, because the high endoergicity of this process leads to severe violation of the vibrational ZPE. The Gaussian-binning (GB) method is found to improve the agreement with the quantum result. The excitation rate coefficients are found to be two orders of magnitude smaller than that of the adiabatic exchange reaction, underscoring the inefficient intersystem crossing due to the weak spin-orbit coupling between the two spin manifolds of the N3 system.

Decoherence and Its Role in Electronically Nonadiabatic Dynamics

Decoherence is the tendency of a time-evolved reduced density matrix for a subsystem to assume a form corresponding to a statistical ensemble of states rather than a coherent combination of pure-state wave functions. When a molecular process involves changes in the electronic state and the coordinates of the nuclei, as in ultraviolet or visible light photochemistry or electronically inelastic collisions, the reduced density matrix of the electronic subsystem suffers decoherence, due to its interaction with the nuclear subsystem. We present the background necessary to conceptualize this decoherence; in particular, we discuss the density matrix description of pure states and mixed states, and we discuss pointer states and decoherence time. We then discuss how decoherence is treated in the coherent switching with decay of mixing algorithm and the trajectory surface hopping method for semiclassical calculations of electronically nonadiabatic processes.

An accurate many-body expansion potential energy surface for AlH2 (22A') and quantum dynamics in Al(3P) + H2 (v0 = 0-3, j0 = 0, 2, 4, 6) collisions

An accurate potential energy surface is constructed for the excited state of AlH₂ by fitting extensive ab initio points calculated at the multi-reference configuration interaction level based on aug-cc-pV(Q+d)Z and aug-cc-pV(5+d)Z basis sets. All the calculated energies are corrected via the many-body expansion method and extrapolated to the complete basis set limit. The various topographic features of the new potential energy surface are investigated to demonstrate the correct behavior of Al(³P) + H₂(X¹Σ_g⁺) and AlH(a³Π) + H(²S) dissociation limits. By employing the time-dependent wave packet approach, the integral scattering cross-sections obtained from the Coriolis coupling calculation and the centrifugal sudden approximation, respectively, are compared in detail and show that the former has a higher effect on the reaction. Moreover, the thermal rate constants for Al(³P) + H₂ (v₀ = 0-3, j₀ = 0, 2, 4, 6) in the temperature range of 0-5000 K are calculated, thereby providing insights into the influence of ro-vibrational quantum numbers on the thermal rate constants.

Multilayer Subsystem Surface Hopping Method for Large-Scale Nonadiabatic Dynamics Simulation with Hundreds of Thousands of States

We present a multilayer subsystem surface hopping (MSSH) method to deal with nonadiabatic dynamics in large-scale systems. A small subsystem instead of the full system is adopted for surface hopping and is updated on-the-fly to achieve a reliable description of important adiabatic states and the wave function evolution. Additional subsystems for molecular dynamics and statistical description are introduced to further improve the simulation reliability. The global flux hopping probabilities with optimal state assignments are utilized to treat the complex surface crossings. As demonstrated in a series of one- and two-dimensional Holstein models with up to hundreds of thousands of states, MSSH shows weak parameter dependence in all investigated systems. Especially, the computational costs are reduced by 2-6 orders of magnitude compared to traditional surface hopping simulations in full systems, and size-independent results are achieved with a large time-step size of 2-5 fs. The new method is compatible with different decoherence correction strategies and achieves a much better balance between efficiency and reliability, thus promising for applications in general charge and exciton dynamics simulations.

Nonadiabatic Dynamics Algorithms with Only Potential Energies and Gradients: Curvature-Driven Coherent Switching with Decay of Mixing and Curvature-Driven Trajectory Surface Hopping

Direct dynamics by mixed quantum-classical nonadiabatic methods is an important tool for understanding processes involving multiple electronic states. Very often, the computational bottleneck of such direct simulation comes from electronic structure theory. For example, at every time step of a trajectory, nonadiabatic dynamics requires potential energy surfaces, their gradients, and the matrix elements coupling the surfaces. The need for the couplings can be alleviated by employing the time derivatives of the wave functions, which can be evaluated from overlaps of electronic wave functions at successive time steps. However, evaluation of overlap integrals is still expensive for large systems. In addition, for electronic structure methods for which the wave functions or the coupling matrix elements are not available, nonadiabatic dynamics algorithms become inapplicable. In this work, building on recent work by Baeck and An, we propose new nonadiabatic dynamics algorithms that only require adiabatic potential energies and their gradients. The new methods are named curvature-driven coherent switching with decay of mixing (κCSDM) and curvature-driven trajectory surface hopping (κTSH). We show how powerful these new methods are in terms of computation time and accuracy as compared to previous mixed quantum-classical nonadiabatic dynamics algorithms. The lowering of the computational cost will allow longer nonadiabatic trajectories and greater ensemble averaging to be affordable, and the ability to calculate the dynamics without electronic structure coupling matrix elements extends the dynamics capability to new classes of electronic structure methods.

All-Atom Nonadiabatic Dynamics Simulation of Hybrid Graphene Nanoribbons Based on Wannier Analysis and Machine Learning

Trajectory surface hopping combined with ab initio electronic structure calculations is a popular and powerful approach for on-the-fly nonadiabatic dynamics simulations. For large systems, however, this remains a significant challenge because of the unaffordable computational cost of large-scale electronic structure calculations. Here, we present an efficient divide-and-conquer approach to construct the system Hamiltonian based on Wannier analysis and machine learning. In detail, the large system under investigation is first decomposed into small building blocks, and then all possible segments formed by building blocks within a cutoff distance are found out. Ab initio molecular dynamics is carried out to generate a sequence of geometries for each equivalent segment with periodicity. The Hamiltonian matrices in the maximum localized Wannier function (MLWF) basis are obtained for all geometries and utilized to train artificial neural networks (ANNs) for the structure-dependent Hamiltonian elements. Taking advantage of the orthogonality and spatial locality of MLWFs, the one-electron Hamiltonian of a large system at arbitrary geometry can be directly constructed by the trained ANNs. As demonstrations, we study charge transport in a zigzag graphene nanoribbon (GNR), a coved GNR, and a series of hybrid GNRs with a state-of-the-art surface hopping method. The interplay between delocalized and localized states is found to determine the electron dynamics in hybrid GNRs. Our approach has successfully studied GNRs with >10 000 atoms, paving the way for efficient and reliable all-atom nonadiabatic dynamics simulation of general systems.

A new global analytical ab initio potential energy surface for the dynamics of the C+(2P) + SH(X2Π) reaction

The global potential energy surface (PES) of HCS⁺(X¹Σ⁺) is constructed using many-body expansion (MBE) methodology. The obtained analytical function is found by fitting the 7907 ab initio energy points computed at the Davidson-corrected multi-reference configuration interaction level with the aug-cc-pV(5+d)Z basis set. The final root mean square error is 0.0419 eV, and the maximum deviation is 0.2039 eV, showing that the analytical formula agrees well with the energy points. The topological features are calculated and discussed based upon the analytical PES of HCS⁺(X¹Σ⁺). The reaction probability, integral cross sections and other details of the C⁺(²P) + SH(X²Π) → H(²S) + CS⁺(X²Σ⁺) reaction are investigated using the quasi-classical trajectory and time-dependent quantum wave packet methods.

Accurate many-body expansion potential energy surface for SiH2 (11 A′) using a switching function formalism

An accurate many-body expansion potential energy surface for the ground state of SiH2 is reported. To warrant the correct behavior at the Si (1D) + H2 (X1Σ+g) dissociation channels...

Quantum Wave Packet Treatment of Cold Nonadiabatic Reactive Scattering at the State-To-State Level

Cold and ultracold collisions are dominated by quantum effects, such as resonances, tunneling, and nonadiabatic transitions between different electronic states. Due to the extremely long de Broglie wavelength in such processes, quantum reactive scattering is most conveniently characterized using the time-independent close-coupling (TICC) methods. However, the TICC approach is difficult for systems with a large number of channels because of its steep numerical scaling laws. Here, a recently proposed quantum wave packet (WP) approach for solving adiabatic reactive scattering problems at low collision energies is extended to include nonadiabatic transitions. To impose the outgoing boundary conditions, the total scattering wavefunction is split into three parts, the interaction, the asymptotic, and the long-range regions. Each region is associated with a different set of basis functions, which could be optimized separately. In this way, an extremely long grid can be used to accommodate the characteristic long de Broglie wavelengths in the scattering coordinate. The better numerical scaling laws of the WP approach have the potential for handling larger nonadiabatic reactive systems at low temperatures in the future.

High-fidelity first principles nonadiabaticity: diabatization, analytic representation of global diabatic potential energy matrices, and quantum dynamics

Nonadiabatic dynamics, which goes beyond the Born-Oppenheimer approximation, has increasingly been shown to play an important role in chemical processes, particularly those involving electronically excited states. Understanding multistate dynamics requires rigorous quantum characterization of both electronic and nuclear motion. However, such first principles treatments of multi-dimensional systems have so far been rather limited due to the lack of accurate coupled potential energy surfaces and difficulties associated with quantum dynamics. In this Perspective, we review recent advances in developing high-fidelity analytical diabatic potential energy matrices for quantum dynamical investigations of polyatomic uni- and bi-molecular nonadiabatic processes, by machine learning of high-level ab initio data. Special attention is paid to methods of diabatization, high fidelity construction of multi-state coupled potential energy surfaces and property surfaces, as well as quantum mechanical characterization of nonadiabatic nuclear dynamics. To illustrate the tremendous progress made by these new developments, several examples are discussed, in which direct comparison with quantum state resolved measurements led to either confirmation of the observation or sometimes reinterpretation of the experimental data. The insights gained in these prototypical systems greatly advance our understanding of nonadiabatic dynamics in chemical systems.

H(D)+LiH+→H2(HD)+Li+ reaction dynamics on its ground electronic state X1A1 and vector correlations

Dynamics of the [Formula: see text] reaction has been investigated by means of quasi-classical trajectory (QCT) calculations on the ground state X1A1 potential energy surface. The H2 (HD) product rotational alignment parameters as well as the angular distributions show that the reaction is dominated by fast abstraction reaction mechanism. The reaction evolving scenario is proposed so that the product rotational angular moment tends to be perpendicular to the reactant velocity vector. The rupture time is inferred near to or less than within one rotational period. We predicted that the increasing collision energy cannot be channeled into the product vibrational excitation effectively. This can help for further experimental tests.

Accurate Potential Energy Surfaces for the Three Lowest Electronic States of N(2D) + H2(X1∑g +) Scattering Reaction

The three lowest full three-dimensional adiabatic and three diabatic global potential energy surfaces are reported for the title system. The accurate ab initio method (MCSCF/MRCI) with larger basis sets (aug-cc-pVQZ) is used to reduce the adiabatic potential energies, and the global adiabatic potential energy surfaces are deduced by a three-dimensional B-spline fitting method. The conical intersections and the mixing angles between the lowest three adiabatic potential energy surfaces are precisely studied. The most possible nonadiabatic reaction pathways are predicted, i.e., N(2D) + H2(X1∑g +) → NH2(22A') → CI (12A'-22A') → NH2(12A') → CI (12A″-12A') → NH2(12A″) → NH(X3∑-) + H(2S). The products of the first excited state (NH(a1Δ) + H(2S)) and the second excited state (NH(b1∑g +) + H(2S)) can be generated in these nonadiabatic reaction pathways too.

Does the wavelength dependent photoisomerization process of the p‑coumaric acid come out from the electronic state dependent pathways?

Similar to the anion photoactive yellow protein (PYP) chromophore, the neutral form of the PYP chromophore was also found to exhibit a the wavelength-dependent photoisomerization quantum yield. The isomerization quantum yield increases with the increasing excitation energy on the S₁ state, while decreases when being excited to the S₂ state. Does this wavelength dependent product yield come out from the specific reaction pathways of the S₁ and S₂ states? This would mean that, the relaxation pathway of the S₂ state is distinct from that of the S₁ state and does not involve twisting motion. Does it break Kasha's rule by exhibiting a direct transition from the S₂ state to the ground state? The underlying mechanism needs further in. In this article, we employed the on-the-fly dynamics simulations and static electronic structure calculations to reveal the deactivation mechanism of the neutral form of the PYP chromophore. Our results indicated that the CC twisting motion dominates the S₁ state decay process. In contrast, for the decay process of the S₂ state, an ultrafast transition from the S₂ to the S₁ state through a planar conical intersection is observed, and the excess energy activates a new reaction channel to the ground state characterized by a puckering distortion of the ring. This pathway competes with the photoisomerization channel. No direct transition from S₂ to S₀ is observed, hence Kasha's rule is valid for this process. Our calcualtions can provide a reasonable explanation of the wavelength-dependent isomerization quantum yield of neutral PYP chromophore, and we hope it can provide theoretical foundations for comparing the effect of protonation state on the dynamcal behaviors of PYP chromophore.

Quantum state-to-state study for (H−(D−),HD) collisions on two potential energy surfaces

Revealing the reaction mechanisms of the H⁻/D⁻ + HD reaction – an exact quantum dynamics study on two potential energy surfaces.

Quasiclassical trajectory calculations of CD3CHO dissociation to CD2H + DCO on a global potential energy surface

We present a quasiclassical trajectory study of the photodissociation of CD3CHO based on a global ab initio-based potential energy surface. Calculations are performed at the total energy corresponding to the photolysis wavelength of 280[Formula: see text]nm. In addition to the major radical and molecular products, CD[Formula: see text] and CD3H [Formula: see text] CO, respectively, this paper focuses on the unusual radical channel CD2H [Formula: see text] DCO, which requires a D/H exchange process before the conventional C–C bond cleavage. Five D/H exchange mechanisms are reported, which are related to the isomerizations from acetaldehyde to vinyl alcohol and back, to oxirane and back, and to the intermediate (CD–CHD–OD) and back. These D/H exchange mechanisms are in good agreement with the experimental findings [Heazlewood BR, Maccarone AT, Andrews DU, Osborn DL, Harding LB, Klippenstein SJ, Jordan MJT, Kable SH, Nat Chem 3:443, 2011].

The photoinduced isomerization mechanism of the 2-(1-(methylimino)methyl)-6-chlorophenol (SMAC): Nonadiabatic surface hopping dynamics simulations

The photophysical properties of the Schiff base family are crucial for their applications such as molecular switches and molecular memories. However, it was found that the photophysical behavior is not uniform for all Schiff base molecules, which shows a significant substituent dependent property. In this article, we studied the photoisomerization mechanism of one Schiff base chlorosubstituted derivative 2-(1-(methylimino)methyl)-6-chlorophenol by employing geometrical optimization, energy profiles scanning, and on-the-fly dynamical simulations. Three types of minimum energy conical intersections were located on the S₁/S₀ crossing seam, with two characterized by twisting motion of the C=N bond and one featured with the excited state intramolecular proton transfer process and then twisting motion around the C=C bond [excited-state intramolecular proton transfer process (ESIPT)-then-twisting]. By a combination of the dynamics simulation results with the energy profiles scanned along with the ESIPT coordinate, it was found that the photophysical property of the targeted molecule is different from that of most Schiff base members, which prefer to decay by a twisting motion around the C=N bridge bond rather than the ESIPT-then-twisting channel. The minor ESIPT channel is probably governed by a tunneling mechanism. The proposed deactivation mechanism can provide a reasonable explanation for the observations in the experiment and would provide fundamental indications for further design of new and efficient photochromic products.