Performance of trajectory surface hopping method in the treatment of ultrafast intersystem crossing dynamics

Unsupervised Machine Learning in the Analysis of Nonadiabatic Molecular Dynamics Simulation

The all-atomic full-dimensional-level simulations of nonadiabatic molecular dynamics (NAMD) in large realistic systems has received high research interest in recent years. However, such NAMD simulations normally generate an enormous amount of time-dependent high-dimensional data, leading to a significant challenge in result analyses. Based on unsupervised machine learning (ML) methods, considerable efforts were devoted to developing novel and easy-to-use analysis tools for the identification of photoinduced reaction channels and the comprehensive understanding of complicated molecular motions in NAMD simulations. Here, we tried to survey recent advances in this field, particularly to focus on how to use unsupervised ML methods to analyze the trajectory-based NAMD simulation results. Our purpose is to offer a comprehensive discussion on several essential components of this analysis protocol, including the selection of ML methods, the construction of molecular descriptors, the establishment of analytical frameworks, their advantages and limitations, and persistent challenges.

A Phase-Space Electronic Hamiltonian For Vibrational Circular Dichroism

We show empirically that a phase-space non-Born-Oppenheimer electronic Hamiltonian approach to quantum chemistry (where the electronic Hamiltonian is parametrized by both nuclear position and momentum, ĤPS(R,P)) is both a practical and accurate means to recover vibrational circular dichroism spectra. We further hypothesize that such a phase-space approach may lead to very new dynamical physics beyond spectroscopic circular dichroism, with potential implications for understanding chiral induced spin selectivity (CISS), noting that classical phase-space approaches conserve the total nuclear plus electronic momentum, whereas classical Born-Oppenheimer approaches do not (they conserve only the nuclear momentum).

MLatom Software Ecosystem for Surface Hopping Dynamics in Python with Quantum Mechanical and Machine Learning Methods

We present an open-source MLatom@XACS software ecosystem for on-the-fly surface hopping nonadiabatic dynamics based on the Landau-Zener-Belyaev-Lebedev algorithm. The dynamics can be performed via Python API with a wide range of quantum mechanical (QM) and machine learning (ML) methods, including ab initio QM (CASSCF and ADC(2)), semiempirical QM methods (e.g., AM1, PM3, OMx, and ODMx), and many types of ML potentials (e.g., KREG, ANI, and MACE). Combinations of QM and ML methods can also be used. While the user can build their own combinations, we provide AIQM1, which is based on Δ-learning and can be used out-of-the-box. We showcase how AIQM1 reproduces the isomerization quantum yield of trans-azobenzene at a low cost. We provide example scripts that, in dozens of lines, enable the user to obtain the final population plots by simply providing the initial geometry of a molecule. Thus, those scripts perform geometry optimization, normal mode calculations, initial condition sampling, parallel trajectories propagation, population analysis, and final result plotting. Given the capabilities of MLatom to be used for training different ML models, this ecosystem can be seamlessly integrated into the protocols building ML models for nonadiabatic dynamics. In the future, a deeper and more efficient integration of MLatom with Newton-X will enable a vast range of functionalities for surface hopping dynamics, such as fewest-switches surface hopping, to facilitate similar workflows via the Python API.

Ab initio molecular dynamics study of intersystem crossing dynamics for MH2 (M = Si, Ge, Sn, Pb) on spin-pure and spin-mixed potential energy surfaces

Recently, surface-hopping ab initio molecular dynamics (SH-AIMD) simulations have come to be used to discuss the mechanisms and dynamics of excited-state chemical reactions, including internal conversion and intersystem crossing. In dynamics simulations involving intersystem crossing, there are two potential energy surfaces (PESs) governing the motion of nuclei: PES in a spin-pure state and PES in a spin-mixed state. The former gives wrong results for molecular systems with large spin-orbit coupling (SOC), while the latter requires a potential gradient that includes a change in SOC at each point, making the computational cost very high. In this study, we systematically investigate the extent to which the magnitude of SOC affects the results of the spin-pure state-based dynamics simulations for the hydride MH2 (M = Si, Ge, Sn, Pb) by performing SH-AIMD simulations based on spin-pure and spin-mixed states. It is clearly shown that spin-mixed state PESs are indispensable for the dynamics simulation of intersystem crossing in systems containing elements Sn and Pb from the fifth period onward. Furthermore, in addition to the widely used Tully's fewest switches (TFS) algorithm, the Zhu-Nakamura (ZN) global switching algorithm, which is computationally less expensive, is applied to SH for comparison. The results from TFS- and ZN-SH-AIMD methods are in qualitative agreement, suggesting that the less expensive ZN-SH-AIMD can be successfully utilized to investigate the dynamics of photochemical reactions based on quantum chemical calculations.

Nonadiabatic Forward Flux Sampling for Excited-State Rare Events

We present a rare event sampling scheme applicable to coupled electronic excited states. In particular, we extend the forward flux sampling (FFS) method for rare event sampling to a nonadiabatic version (NAFFS) that uses the trajectory surface hopping (TSH) method for nonadiabatic dynamics. NAFFS is applied to two dynamically relevant excited-state models that feature an avoided crossing and a conical intersection with tunable parameters. We investigate how nonadiabatic couplings, temperature, and reaction barriers affect transition rate constants in regimes that cannot be otherwise obtained with plain, traditional TSH. The comparison with reference brute-force TSH simulations for limiting cases of rareness shows that NAFFS can be several orders of magnitude cheaper than conventional TSH and thus represents a conceptually novel tool to extend excited-state dynamics to time scales that are able to capture rare nonadiabatic events.

Overcoming positivity violations for density matrices in surface hopping

Fewest-switches surface hopping (FSSH) has emerged as one of the leading methods for modeling the quantum dynamics of molecular systems. While its original formulation was limited to adiabatic populations, the growing interest in the application of FSSH to coherent phenomena prompts the question of how one should construct a complete density matrix based on FSSH trajectories. A straightforward solution is to define adiabatic coherences based on wavefunction coefficients. In this paper, we demonstrate that inconsistencies introduced in the density matrix through such treatment may lead to a violation of positivity. We furthermore show that a recently proposed coherent generalization of FSSH results in density matrices that satisfy positivity while yielding improved accuracy throughout much (but not all) of parameter space.

Enhanced Electron Transfer and Spin Flip through Spin-Orbital Couplings in Organic/Inorganic Heterojunctions: A Nonadiabatic Surface Hopping Simulation

The circumstances of transferred electrons across organic/inorganic interfaces have attracted intensive interest because of the distinctive electronic structure properties of those two components. Leveraging ab initio nonadiabatic molecular dynamics methods in conjunction with spin dynamics induced by spin-orbital couplings (SOCs), this study reports two competitive channels during photoinduced dynamical processes in the prototypical ZnPc/monolayer MoS₂ heterojunction. Interestingly, the electron-transfer and relaxation processes occur simultaneously because of the enhancement of electron-phonon couplings and expansion of dynamical pathways by SOCs, suggesting that the electron-transfer rate and relaxation processes can be tuned by SOCs, hence yielding the performance promotion of photovoltaic and photocatalytic devices. Additionally, approximately half of the transferred electrons flip their spin within 1.6 ps because of strong SOCs in MoS₂, achieving great agreement with experimental measurements. This investigation provides instructive perspectives for designing novel devices and applications based on organic/inorganic heterojunctions, demonstrating the importance of spin dynamics simulations in exploring sophisticated photoinduced processes in materials.

An efficient implementation of spin-orbit coupling within the framework of semiempirical orthogonalization-corrected methods for ultrafast intersystem crossing dynamics

We implement spin-orbit coupling (SOC) within the framework of semiempirical orthogonalization-corrected methods (OMx). The excited-state wavefunction is generated from configuration interaction with single excitations (CIS). The SOC Hamiltonian in terms of the one-electron Breit-Pauli operator with effective nuclear charges is adopted in this work. Benchmark calculations show that SOCs evaluated using the OMx/CIS method agree very well with those obtained from time-dependent density functional theory. As a particularly attractive application, we incorporate SOCs between singlet and triplet states into Tully's fewest switches surface hopping algorithm to enable excited-state nonadiabatic dynamics simulations, treating internal conversion and intersystem crossing on an equal footing. This semiempirical dynamics simulation approach is applied to investigate ultrafast intersystem crossing processes in core-substituted naphthalenediimides.

Branching Corrected Mean Field Method for Nonadiabatic Dynamics

When nonadiabatic dynamics are described on the basis of trajectories, severe trajectory branching occurs when the nuclear wave packets on some potential energy surfaces are reflected while those on the remaining surfaces are not. As a result, the traditional Ehrenfest mean field (EMF) approximation breaks down. In this study, two versions of the branching corrected mean field (BCMF) method are proposed. Namely, when trajectory branching is identified, BCMF stochastically selects either the reflected or the nonreflected group to build the new mean field trajectory or splits the mean field trajectory into two new trajectories with the corresponding weights. As benchmarked in six standard model systems and an extensive model base with two hundred diverse scattering models, BCMF significantly improves the accuracy while retaining the high efficiency of the traditional EMF. In fact, BCMF closely reproduces the exact quantum dynamics in all investigated systems, thus highlighting the essential role of branching correction in nonadiabatic dynamics simulations of general systems.

Modeling nonadiabatic dynamics in condensed matter materials: some recent advances and applications

This review focuses on recent developments in the field of nonadiabatic molecular dynamics (NA-MD), with particular attention given to condensed-matter systems. NA-MD simulations for small molecular systems can be performed using high-level electronic structure (ES) calculations, methods accounting for the quantization of nuclear motion, and using fewer approximations in the dynamical methodology itself. Modeling condensed-matter systems imposes many limitations on various aspects of NA-MD computations, requiring approximations at various levels of theory-from the ES, to the ways in which the coupling of electrons and nuclei are accounted for. Nonetheless, the approximate treatment of NA-MD in condensed-phase materials has gained a spin lately in many applied studies. A number of advancements of the methodology and computational tools have been undertaken, including general-purpose methods, as well as those tailored to nanoscale and condensed matter systems. This review summarizes such methodological and software developments, puts them into the broader context of existing approaches, and highlights some of the challenges that remain to be solved.