A Simple Solution to Trivial Crossings: A Stochastic State Tracking Approach

Machine learning accelerated nonadiabatic dynamics simulations of materials with excitonic effects

This study presents an efficient methodology for simulating nonadiabatic dynamics of complex materials with excitonic effects by integrating machine learning (ML) models with simplified Tamm-Dancoff approximation (sTDA) calculations. By leveraging ML models, we accurately predict ground-state wavefunctions using unconverged Kohn-Sham (KS) Hamiltonians. These ML-predicted KS Hamiltonians are then employed for sTDA-based excited-state calculations (sTDA/ML). The results demonstrate that excited-state energies, time-derivative nonadiabatic couplings, and absorption spectra from sTDA/ML calculations are accurate enough compared with those from conventional density functional theory based sTDA (sTDA/DFT) calculations. Furthermore, sTDA/ML-based nonadiabatic molecular dynamics simulations on two different materials systems, namely chloro-substituted silicon quantum dot and monolayer black phosphorus, achieve more than 100 times speedup than the conventional linear response time-dependent DFT simulations. This work highlights the potential of ML-accelerated nonadiabatic dynamics simulations for studying the complicated photoinduced dynamics of large materials systems, offering significant computational savings without compromising accuracy.

State Tracking in Nonadiabatic Molecular Dynamics Using Only Forces and Energies

A new algorithm for the identification of unavoided (trivial) crossings in nonadiabatic molecular dynamics calculations is reported. The approach does not require knowledge of wave functions or wave function time overlaps and uses only information on state energies and gradients. In addition, a simple phase consistency correction algorithm for time-derivative nonadiabatic couplings is proposed for situations in which wave function time overlaps are not available. The performance of the two algorithms is demonstrated using several state crossing models. The approaches work best for systems with localized nonadiabatic coupling regions but may have difficulties for those with extended regions of nonadiabatic coupling. It is found that state tracking alone is not sufficient for producing correct population dynamics and that nonadiabatic coupling phase correction is required.

Extending multi-layer energy-based fragment method for excited-state calculations of large covalently bonded fragment systems

Recently, we developed a low-scaling Multi-Layer Energy-Based Fragment (MLEBF) method for accurate excited-state calculations and nonadiabatic dynamics simulations of nonbonded fragment systems. In this work, we extend the MLEBF method to treat covalently bonded fragment ones. The main idea is cutting a target system into many fragments according to chemical properties. Fragments with dangling bonds are first saturated by chemical groups; then, saturated fragments, together with the original fragments without dangling bonds, are grouped into different layers. The accurate total energy expression is formulated with the many-body energy expansion theory, in combination with the inclusion-exclusion principle that is used to delete the contribution of chemical groups introduced to saturate dangling bonds. Specifically, in a two-layer MLEBF model, the photochemically active and inert layers are calculated with high-level and efficient electronic structure methods, respectively. Intralayer and interlayer energies can be truncated at the two- or three-body interaction level. Subsequently, through several systems, including neutral and charged covalently bonded fragment systems, we demonstrate that MLEBF can provide accurate ground- and excited-state energies and gradients. Finally, we realize the structure, conical intersection, and path optimizations by combining our MLEBF program with commercial and free packages, e.g., ASE and SciPy. These developments make MLEBF a practical and reliable tool for studying complex photochemical and photophysical processes of large nonbonded and bonded fragment systems.

Excited electron and spin dynamics in topological insulator: A perspective from ab initio non-adiabatic molecular dynamics

We perform an ab initio non-adiabatic molecular dynamics simulation to investigate the non-equilibrium spin and electron dynamics in a prototypical topological insulator (TI) Bi2Se3. Different from the ground state, we reveal that backscattering can happen in an oscillating manner between time-reversal pair topological surface states (TSSs) in the non-equilibrium dynamics. Analysis shows the phonon excitation induces orbital composition change by electron-phonon interaction, which further stimulates spin canting through spin-orbit coupling. The spin canting of time-reversal pair TSSs leads to the non-zero non-adiabatic coupling between them and then issues in backscattering. Both the spin canting and backscattering result in ultrafast spin relaxation with a timescale around 100 fs. This study provides critical insights into the non-equilibrium electron and spin dynamics in TI at the ab initio level and paves a way for the design of ultrafast spintronic materials.

Nonadiabatic Molecular Dynamics with Extended Density Functional Tight-Binding: Application to Nanocrystals and Periodic Solids

In this work, we report a new methodology for nonadiabatic molecular dynamics calculations within the extended tight-binding (xTB) framework. We demonstrate the applicability of the developed approach to finite and periodic systems with thousands of atoms by modeling "hot" electron relaxation dynamics in silicon nanocrystals and electron-hole recombination in both a graphitic carbon nitride monolayer and a titanium-based metal-organic framework (MOF). This work reports the nonadiabatic dynamic simulations in the largest Si nanocrystals studied so far by the xTB framework, with diameters up to 3.5 nm. For silicon nanocrystals, we find a non-monotonic dependence of "hot" electron relaxation rates on the nanocrystal size, in agreement with available experimental reports. We rationalize this relationship by a combination of decreasing nonadiabatic couplings related to system size and the increase of available coherent transfer pathways in systems with higher densities of states. We emphasize the importance of proper treatment of coherences for obtaining such non-monotonic dependences. We characterize the electron-hole recombination dynamics in the graphitic carbon nitride monolayer and the Ti-containing MOF. We demonstrate the importance of spin-adaptation and proper sampling of surface hopping trajectories in modeling such processes. We also assess several trajectory surface hopping schemes and highlight their distinct qualitative behavior in modeling the excited-state dynamics in superexchange-like models depending on how they handle coherences between nearly parallel states.

Transition orbital projection approach for excited state tracking

Quantitively comparing the features between different electronic excited states (ESs) is a crucial task in both potential energy surface (PES) studies and excited-state fragmentation approaches. However, it is still a challenging problem in regard to the comparison of complex and highly degenerate systems. Herein, we present a transition orbital projection (TOP) method to calculate the similarity of different ESs based on the configuration vectors of two types of transition densities. It fully considers four significant problems, including phase, hole-particle bijectivity, orbital permutation, and sign of configuration coefficients. TOP state-tracking-based excited-state optimization shows high robustness in several high-symmetric systems, which are difficult to describe with traditional state-tracking approaches. The TOP state-tracking method is expected to be widely applied to the PES of photochemical reactions, ES molecular dynamics to track the diabatic states, and fragmentation approaches for local excitation of large systems.

Extending the Time Scales of Nonadiabatic Molecular Dynamics via Machine Learning in the Time Domain

A novel methodology for direct modeling of long-time scale nonadiabatic dynamics in extended nanoscale and solid-state systems is developed. The presented approach enables forecasting the vibronic Hamiltonians as a direct function of time via machine-learning models trained directly in the time domain. The use of periodic and aperiodic functions that transform time into effective input modes of the artificial neural network is demonstrated to be essential for such an approach to work for both abstract and atomistic models. The best strategies and possible limitations pertaining to the new methodology are explored and discussed. An exemplary direct simulation of unprecedentedly long 20 picosecond trajectories is conducted for a divacancy-containing monolayer black phosphorus system, and the importance of conducting such extended simulations is demonstrated. New insights into the excited states photophysics in this system are presented, including the role of decoherence and model definition.

Excited state dynamics in monolayer black phosphorus revisited: Accounting for many-body effects

The dynamics of electron-hole recombination in pristine and defect-containing monolayer black phosphorus (ML-BP) has been studied computationally by several groups relying on the one-particle description of electronic excited states. Our recent developments enabled a more sophisticated and accurate treatment of excited states dynamics in systems with pronounced excitonic effects, including 2D materials such as ML-BP. In this work, I present a comprehensive characterization of optoelectronic properties and nonadiabatic dynamics of the ground state recovery in pristine and divacancy-containing ML-BP, relying on the linear-response time-dependent density functional theory description of excited states combined with several trajectory surface hopping methodologies and decoherence correction schemes. This work presents a revision and new implementation of the decoherence-induced surface hopping methodology. Several popular algorithms for nonadiabatic dynamics algorithms are assessed. The kinetics of nonradiative relaxation of lower-lying excited states in ML-BP systems is revised considering the new methodological developments. A general mechanism that explains the sensitivity of the nonradiative dynamics to the presence of divacancy defect in ML-BP is proposed. According to this mechanism, the excited states' relaxation may be inhibited by the presence of energetically close higher-energy states if electronic decoherence is present in the system.