Libra: An open-Source “methodology discovery” library for quantum and classical dynamics simulations

Accelerated Electron-Hole Separation at the Organic-Inorganic Anthracene/Janus MoSSe Interface

Organic light-absorbing materials with two-dimensional semiconductor layers as contact electrodes are promising for efficient and flexible low-cost solar cells. Considering anthracene as an absorber and a MoSSe Janus monolayer, we use non-adiabatic molecular dynamics to show that electron transfer from anthracene to MoSSe is faster on the Se side than the S side. The transfer from anthracene to MoS2 and MoSe2 monolayers takes intermediate times. As a rule, we find that a shorter adsorption distance produces a stronger donor-acceptor coupling. The smaller distance on the Se side is rationalized by the attractive force between the intrinsic dipole moment of the Janus structure and that of the molecule induced due to adsorption. Quantum coherence also affects the transfer time. The study provides detailed insights into adsorption of molecules on Janus structures and the resulting electronic and electron vibrational interactions. The results suggest that the dipole interaction plays an important role in the thermodynamic stability, alignment of electronic levels, and electron vibrational dynamics.

Nonadiabatic Dynamics with Exact Factorization: Implementation and Assessment

In this work, we report our implementation of several independent-trajectory mixed-quantum-classical (ITMQC) nonadiabatic dynamics methods based on exact factorization (XF) in the Libra package for nonadiabatic and excited-state dynamics. Namely, the exact factorization surface hopping (SHXF), mixed quantum-classical dynamics (MQCXF), and mean-field (MFXF) are introduced. Performance of these methods is compared to that of several traditional surface hopping schemes, such as the fewest-switches surface hopping (FSSH), branching-corrected surface hopping (BCSH), and the simplified decay of mixing (SDM), as well as conventional Ehrenfest (mean-field, MF) method. Based on a comprehensive set of 1D model Hamiltonians, we find the ranking SHXF ≈ MQCXF > BCSH > SDM > FSSH ≫ MF, with the BCSH sometimes outperforming the XF methods in terms of describing coherences. Although the MFXF method can yield reasonable populations and coherences for some cases, it does not conserve the total energy and is therefore not recommended. We also find that the branching correction for auxiliary trajectories is important for the XF methods to yield accurate populations and coherences. However, the branching correction can worsen the quality of the energy conservation in the MQCXF. Finally, we find that using the time-dependent Gaussian width approximation used in the XF methods for computing decoherence correction can improve the quality of energy conservation in the MQCXF dynamics. The parameter-free scheme of Subotnik for computing the Gaussian widths is found to deliver the best performance in situations where such widths are not known a priori.

Nonadiabatic molecular dynamics with subsystem density functional theory: application to crystalline pentacene

In this work, we report the development and assessment of the nonadiabatic molecular dynamics approach with the electronic structure calculations based on the linearly scaling subsystem density functional method. The approach is implemented in an open-source embedded Quantum Espresso/Libra software specially designed for nonadiabatic dynamics simulations in extended systems. As proof of the applicability of this method to large condensed-matter systems, we examine the dynamics of nonradiative relaxation of excess excitation energy in pentacene crystals with the simulation supercells containing more than 600 atoms. We find that increased structural disorder observed in larger supercell models induces larger nonadiabatic couplings of electronic states and accelerates the relaxation dynamics of excited states. We conduct a comparative analysis of several quantum-classical trajectory surface hopping schemes, including two new methods proposed in this work (revised decoherence-induced surface hopping and instantaneous decoherence at frustrated hops). Most of the tested schemes suggest fast energy relaxation occurring with the timescales in the 0.7-2.0 ps range, but they significantly overestimate the ground state recovery rates. Only the modified simplified decay of mixing approach yields a notably slower relaxation timescales of 8-14 ps, with a significantly inhibited ground state recovery.

Machine-Learned Kohn-Sham Hamiltonian Mapping for Nonadiabatic Molecular Dynamics

In this work, we report a simple, efficient, and scalable machine-learning (ML) approach for mapping non-self-consistent Kohn-Sham Hamiltonians constructed with one kind of density functional to the nearly self-consistent Hamiltonians constructed with another kind of density functional. This approach is designed as a fast surrogate Hamiltonian calculator for use in long nonadiabatic dynamics simulations of large atomistic systems. In this approach, the input and output features are Hamiltonian matrices computed from different levels of theory. We demonstrate that the developed ML-based Hamiltonian mapping method (1) speeds up the calculations by several orders of magnitude, (2) is conceptually simpler than alternative ML approaches, (3) is applicable to different systems and sizes and can be used for mapping Hamiltonians constructed with arbitrary density functionals, (4) requires a modest training data, learns fast, and generates molecular orbitals and their energies with the accuracy nearly matching that of conventional calculations, and (5) when applied to nonadiabatic dynamics simulation of excitation energy relaxation in large systems yields the corresponding time scales within the margin of error of the conventional calculations. Using this approach, we explore the excitation energy relaxation in C60 fullerene and Si75H64 quantum dot structures and derive qualitative and quantitative insights into dynamics in these systems.

Prediction challenge: First principles simulation of the ultrafast electron diffraction spectrum of cyclobutanone

Computer simulation has long been an essential partner of ultrafast experiments, allowing the assignment of microscopic mechanistic detail to low-dimensional spectroscopic data. However, the ability of theory to make a priori predictions of ultrafast experimental results is relatively untested. Herein, as a part of a community challenge, we attempt to predict the signal of an upcoming ultrafast photochemical experiment using state-of-the-art theory in the context of preexisting experimental data. Specifically, we employ ab initio Ehrenfest with collapse to a block mixed quantum-classical simulations to describe the real-time evolution of the electrons and nuclei of cyclobutanone following excitation to the 3s Rydberg state. The gas-phase ultrafast electron diffraction (GUED) signal is simulated for direct comparison to an upcoming experiment at the Stanford Linear Accelerator Laboratory. Following initial ring-opening, dissociation via two distinct channels is observed: the C3 dissociation channel, producing cyclopropane and CO, and the C2 channel, producing CH2CO and C2H4. Direct calculations of the GUED signal indicate how the ring-opened intermediate, the C2 products, and the C3 products can be discriminated in the GUED signal. We also report an a priori analysis of anticipated errors in our predictions: without knowledge of the experimental result, which features of the spectrum do we feel confident we have predicted correctly, and which might we have wrong?

Energy-Conserving and Thermally Corrected Neglect of Back-Reaction Approximation Method for Nonadiabatic Molecular Dynamics

In this work, the energy-conserving and thermally corrected neglect of the back-reaction approximation approach for nonadiabatic molecular dynamics in extended atomistic systems is developed. The new approach introduces three key corrections to the original method: (1) it enforces the total energy conservation, (2) it introduces an explicit coupling of the system to its environment, and (3) it introduces a renormalization of nonadiabatic couplings to account for a difference between the instantaneous nuclear kinetic energy and the kinetic energy of guiding trajectories. In the new approach, an auxiliary kinetic energy variable is introduced as an independent dynamical variable. The new approach produces nonzero equilibrium populations, whereas the original neglect of the back-reaction approximation method does not. It yields population relaxation time scales that are favorably comparable to the reference values, and it introduces an explicit and controllable way of dissipating energy into a bath without an assumption of the bath being at equilibrium.

Charge Carrier Dynamics at the Interface of 2D Metal-Organic Frameworks and Hybrid Perovskites for Solar Energy Harvesting

Interfacing perovskites with two-dimensional materials such as metal-organic frameworks (MOFs) for improved stability and electron or hole extraction has emerged as a promising path forward for the generation of highly efficient and stable solar cells. In this work, we examine the structural properties and excitation dynamics of two MOF-perovskite systems: UMCM309-a@MAPbI3 and ZrL3@MAPbI3. We find that precise band alignment and electronegativity of the MOF-linkers are necessary to facilitate the capture of excited charge carriers. Furthermore, we demonstrate that intraband relaxation of hot electrons to the MOF subsystem results in optically disallowed transitions across the band gap, suppressing radiative recombination. Furthermore, we elucidate the key mechanisms associated with improved structural stability afforded to the perovskites by the two-dimensional MOFs, highlighting the necessity of broad surface coverage and strong MOF-perovskite interaction.

Convergence of Time-Derivative Nonadiabatic Couplings in Plane-Wave DFT Calculations

Accurate prediction of charge carrier relaxation rates is essential to design molecules and materials with the desired photochemical properties for applications like photocatalysis and solar energy conversion. Nonadiabatic molecular dynamics allows one to simulate the relaxation process of excited charge carriers. Plane-wave density functional theory (DFT) calculations make the time-derivative nonadiabatic couplings (TNACs) simple to compute because the basis is independent of the atomic positions. However, the effect of the kinetic energy cutoff for the plane-wave basis on the accuracy of the dynamics has not been studied. Here, we examine the effect of the kinetic energy cutoff on the TNACs and decay time scales for the prototypical model system of tetracene. These calculations show that the choice of kinetic energy cutoff can change the relaxation time by up to 30%. The relaxation times of states that have small TNACs to other states or are far from degenerate are more sensitive to the kinetic energy cutoff than those of states with large TNACs or near degeneracies. A kinetic energy cutoff of 60 Ry is sufficient for all states to reach semiquantitative agreement (absolute error <10%) with the decay times of our 110 Ry reference data, and a cutoff of 80 Ry is required for all states to reach quantitative agreement (absolute error <2%).

Substrate Ferroelectric Proximity Effects Have a Strong Influence on Charge Carrier Lifetime in Black Phosphorus

By stacking monolayer black phosphorus (MBP) with nonpolarized and ferroelectric polarized bilayer hexagonal boron nitride (h-BN), we demonstrate that ferroelectric proximity effects have a strong influence on the charge carrier lifetime of MBP using nonadiabatic (NA) molecular dynamics simulations. Through enhancing the motion of phosphorus atoms, ferroelectric polarization enhances the overlap of electron-hole wave functions that improves NA coupling and decreases the bandgap, resulting in a rapid electron-hole recombination completing within a quarter of nanoseconds, which is two times shorter than that in nonpolarized stackings. In addition to the dominant in-plane Ag2 mode in free-standing MBP, the out-of-plane high-frequency Ag1 and low-frequency interlayer breathing modes presented in the heterojunctions drive the recombination. Notably, the resonance between the breathing mode within bilayer h-BN and the B1u mode of MBP provides an additional nonradiative channel in ferroelectric stackings, further accelerating charge recombination. These findings are crucial for charge dynamics manipulation in two-dimensional materials via substrate ferroelectric proximity effects.

Efficient Modeling of Quantum Dynamics of Charge Carriers in Materials Using Short Nonequilibrium Molecular Dynamics

Nonadiabatic molecular dynamics provides essential insights into excited-state processes, but it is computationally intense and simplifications are needed. The classical path approximation provides critical savings. Still, long heating and equilibration steps are required. We demonstrate that practical results can be obtained with short, partially equilibrated ab initio trajectories. Once the system's structure is adequate and essential fluctuations are sampled, the nonadiabatic Hamiltonian can be constructed. Local structures require only 1-2 ps trajectories, as demonstrated with point defects in metal halide perovskites. Short trajectories represent anharmonic motions common in defective structures, an essential improvement over the harmonic approximation around the optimized geometry. Glassy systems, such as grain boundaries, require different simulation protocols, e.g., involving machine learning force fields. 10-fold shorter trajectories generate 10-20% time scale errors, which are acceptable, given experimental uncertainties and other approximations. The practical NAMD protocol enables fast screening of excited-state dynamics for rapid exploration of new materials.

WaveTrain: A Python package for numerical quantum mechanics of chain-like systems based on tensor trains

WaveTrain is an open-source software for numerical simulations of chain-like quantum systems with nearest-neighbor (NN) interactions only. The Python package is centered around tensor train (TT, or matrix product) format representations of Hamiltonian operators and (stationary or time-evolving) state vectors. It builds on the Python tensor train toolbox Scikit_tt, which provides efficient construction methods and storage schemes for the TT format. Its solvers for eigenvalue problems and linear differential equations are used in WaveTrain for the time-independent and time-dependent Schrödinger equations, respectively. Employing efficient decompositions to construct low-rank representations, the tensor-train ranks of state vectors are often found to depend only marginally on the chain length N. This results in the computational effort growing only slightly more than linearly with N, thus mitigating the curse of dimensionality. As a complement to the classes for full quantum mechanics, WaveTrain also contains classes for fully classical and mixed quantum-classical (Ehrenfest or mean field) dynamics of bipartite systems. The graphical capabilities allow visualization of quantum dynamics "on the fly," with a choice of several different representations based on reduced density matrices. Even though developed for treating quasi-one-dimensional excitonic energy transport in molecular solids or conjugated organic polymers, including coupling to phonons, WaveTrain can be used for any kind of chain-like quantum systems, with or without periodic boundary conditions and with NN interactions only. The present work describes version 1.0 of our WaveTrain software, based on version 1.2 of scikit_tt, both of which are freely available from the GitHub platform where they will also be further developed. Moreover, WaveTrain is mirrored at SourceForge, within the framework of the WavePacket project for numerical quantum dynamics. Worked-out demonstration examples with complete input and output, including animated graphics, are available.

Pedagogical Overview of the Fewest Switches Surface Hopping Method

The fewest switches surface hopping method continues to grow in popularity to capture electronic nonadiabaticity and quantum nuclear effects due to its simplicity and accuracy. Knowing the basics of the method is essential for the correct implementation and interpretation of results. This review covers the fundamentals of the fewest switches surface hopping method with a detailed discussion of the nuances such as decoherence schemes and frustrated hops and the correct approach to calculating populations. The consequences of incorrect implementation are further discussed toward calculating kinetic and thermodynamic properties. Some tips for practitioners and a step-by-step algorithm for developers are provided. Finally, some of the finer technicalities of the fewest switches surface hopping method that are buried deep in the literature are pointed out to help graduate students better appreciate this method.

Tuning the Nonradiative Electron-Hole Recombination with Defects in Monolayer Black Phosphorus

We use nonadiabatic (NA) molecular dynamics to demonstrate that the nonradiative electron-hole recombination is delayed and accelerated by the Stone-Wales (SWs) and phosphorus divacancy (DV-(5|7)) defects in monolayer black phosphorus (BP). Both types of defects increase the bandgap by 0.1 eV without creating midgap states. Driven by P-P stretching vibrations, the recombination proceeds within 1 ns in the SW and within 100 ps in the DV-(5|7), respectively, which occurs within 332 ps in BP. The SW defect slows down recombination because the notably reduced NA coupling combined with a large bandgap competes to the long-lived coherence. In contrast, the DV defect accelerates recombination since long-lived coherence is superior to the slightly decreased NA coupling correlated with a tiny increased bandgap. The diverse time scales rationalize the broad range of charge carrier lifetimes reported experimentally. The study provides a strategy to engineer excited-state dynamics for improving the BP-based optoelectronics.

How Good Is the Vibronic Hamiltonian Repetition Approach for Long-Time Nonadiabatic Molecular Dynamics?

Multiple applied studies of slow nonadiabatic processes in nanoscale and condensed matter systems have adopted the "repetition" approximation in which long trajectories for such simulations are obtained by concatenating shorter trajectories, directly available from ab initio calculations, many times. Here, we comprehensively assess this approximation using model Hamiltonians with parameters covering a wide range of regimes. We find that state transition time scales may strongly depend on the length of the repeated data, although the convergence is not monotonic and may be slow. The repetition approach may under- or overestimate the time scales by a factor of ≤7-8, does not directly depend on the dispersion of energy gap and nonadiabatic coupling (NAC) frequencies, but may depend on the magnitude of the NACs. We suggest that the repetition-based nonadiabatic dynamics may be inaccurate in simulations with very small NACs, where intrinsic transition times are on the order of ≥100 ps.

Newton-X Platform: New Software Developments for Surface Hopping and Nuclear Ensembles

Newton-X is an open-source computational platform to perform nonadiabatic molecular dynamics based on surface hopping and spectrum simulations using the nuclear ensemble approach. Both are among the most common methodologies in computational chemistry for photophysical and photochemical investigations. This paper describes the main features of these methods and how they are implemented in Newton-X. It emphasizes the newest developments, including zero-point-energy leakage correction, dynamics on complex-valued potential energy surfaces, dynamics induced by incoherent light, dynamics based on machine-learning potentials, exciton dynamics of multiple chromophores, and supervised and unsupervised machine learning techniques. Newton-X is interfaced with several third-party quantum-chemistry programs, spanning a broad spectrum of electronic structure methods.

Photoinduced Small Hole Polarons Formation and Recombination in All-Inorganic Perovskite from Quantum Dynamics Simulation

We conducted ab initio molecular dynamics (AIMD) and nonadiabatic MD to simulate polaron formation and recombination in all-inorganic Cs₃Bi₂Br₉ perovskite. The meticulously designed AIMD simulations show that two types of small hole polaron, including localized and semidelocalized small hole polaron on either an intralayer or an interlayer Br dimer, are adiabatically formed within 1.71 ps. The localized small hole polaron reduces nonadiabatic coupling and decoherence time and, thus, delays charge recombination to 213 ns. In contrast, the dominant semidelocalized polaron increases nonadiabatic coupling by enhancing electron-hole overlap and restores the energy gap and decoherence time to the pristine system, accelerating recombination to 4.7 ns compared to a 10 ns charge carrier lifetime in the pristine system. All the obtained time scales agree well with experiments. The study offers a fundamental understanding of the excited-state dynamics of small hole polaron in Cs₃Bi₂Br₉ and helps to design high-performance perovskite optoelectronics and photovoltaics.

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.

Depleted Oxygen Defect State Enhancing Tungsten Trioxide Photocatalysis: A Quantum Dynamics Perspective

Oxygen vacancies generally create midgap states in transition metal oxides, which are expected to decrease the photoelectrochemical water-splitting efficiency. Recent experiments defy this expectation but leave the mechanism unclear. Focusing on the photoanode WO₃ as a prototypical system, we demonstrate using nonadiabatic molecular dynamics that an oxygen vacancy suppresses nonradiative electron-hole recombination, because the defect acts as an electron reservoir instead of a recombination center. The occupied midgap electrons prefer to be populated a priori compared to the band edge transition because of a larger transition dipole moment, converting to depleted/unoccupied trap states that rapidly accept conduction band electrons and then cause trap-assisted recombination by impeding the bandgap recombination regardless of oxygen vacancy configurations. The reported results provide a fundamental understanding of the "realistic" role of the oxygen vacancies and their influence on charge-phonon dynamics and carrier lifetime. The study generates valuable insights into the design of high-performance transition metal oxide photocatalysts.

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.

The ΔSCF method for non-adiabatic dynamics of systems in the liquid phase

Computational studies of ultrafast photoinduced processes give valuable insights into the photochemical mechanisms of a broad range of compounds. In order to accurately reproduce, interpret, and predict experimental results, which are typically obtained in a condensed phase, it is indispensable to include the condensed phase environment in the computational model. However, most studies are still performed in vacuum due to the high computational cost of state-of-the-art non-adiabatic molecular dynamics (NAMD) simulations. The quantum mechanical/molecular mechanical (QM/MM) solvation method has been a popular model to perform photodynamics in the liquid phase. Nevertheless, the currently used QM/MM embedding techniques cannot sufficiently capture all solute-solvent interactions. In this Perspective, we will discuss the efficient ΔSCF electronic structure method and its applications with respect to the NAMD of solvated compounds, with a particular focus on explicit quantum mechanical solvation. As more research is required for this method to reach its full potential, some challenges and possible directions for future research are presented as well.

Improving Lattice Rigidity and Charge Carrier Lifetime by Engineering Spacer Cation of Ruddlesden-Popper Perovskites: A Time-Domain Ab Initio Study

First-principles quantum dynamics calculations show that charge carrier lifetimes, charge transport, and lattice stability are notably improved when BA (CH₃(CH₂)₃NH₃⁺) in BA₂PbI₄ is replaced with MTEA (CH₃(CH₂)₂SNH₃⁺). By suppressing atomic fluctuations, MTEA enhances the lattice stiffness and inhibits loss of coherence due to the S-S interaction. By delocalizing hole wave functions on the MTEA, particularly on the S atoms, while maintaining the electron wave functions largely unchanged compared to the BA₂PbI₄, MTEA serves to enhance charge transport and NA coupling while narrowing the bandgap by 0.18 eV. Overall, MTEA decreases NA coupling due to slow atomic motions against a large overlap of electron-hole wave functions, which suppresses nonradiative electron-hole recombination and prolongs carrier lifetime twice longer compared with BA₂PbI₄. This simulation presents a rational route to make high performance two-dimensional perovskite solar cells.

Coupled- and Independent-Trajectory Approaches Based on the Exact Factorization Using the PyUNIxMD Package

We present mixed quantum-classical approaches based on the exact factorization framework. The electron-nuclear correlation term in the exact factorization enables us to deal with quantum coherences by accounting for electronic and nuclear nonadiabatic couplings effectively within classical nuclei approximation. We compare coupled- and independent-trajectory approximations with each other to understand algorithms in description of the bifurcation of nuclear wave packets and the correct spatial distribution of electronic wave functions along with nuclear trajectories. Finally, we show numerical results for comparisons of coupled- and independent-trajectory approaches for the photoisomerization of a protonated Schiff base from excited state molecular dynamics (ESMD) simulations with the recently developed Python-based ESMD code, namely, the PyUNIxMD program.

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.

Efficient Computation of Nonadiabatic Coupling Coefficients for Modeling Charge Carrier Recombination in Extended Systems: The Case of Metal-Organic Frameworks

Modeling excited state charge carrier dynamics and recombination in extended systems, such as metal-organic frameworks (MOFs), covalent organic frameworks (COFs), and other hybrid organic-inorganic materials, by surface-hopping approaches is a challenging task due to the high computational cost. In this work, the steps of the simulations and the bottlenecks for such systems are analyzed. In particular, the bottlenecks related to computation of the nonadiabatic coupling coefficients (NACs) are considered. A simple, inexpensive, and portable scheme for computing scalar NACs employing a grid representation of the wave functions is presented and implemented in a Python code. It is tested for the simulation of the electron-hole nonradiative recombination in the MIL-125-NH₂ model system. The proposed approach allows for an on-the-fly estimation of the NACs alongside the simulation of the molecular dynamics trajectory and enables a straightforward interface between the Python libraries for nonadiabatic molecular dynamics and the majority of the existing quantum chemical codes.

Density Functional Theory Half-Electron Self-Energy Correction for Fast and Accurate Nonadiabatic Molecular Dynamics

The nonadiabatic (NA) process is crucial to photochemistry and photophysics and requires an atomistic understanding. However, conventional NA molecular dynamics (MD) for condensed-phase materials on the nanoscale are generally limited to the semilocal exchange-correlation functional, which suffers from the bandgap and thus NA coupling (NAC) problems. We consider TiO₂ and a black phosphorus monolayer as two prototypical systems, perform NA-MD simulations of nonradiative electron-hole recombination, and demonstrate for the first time that density functional theory (DFT) half-electron self-energy correction can reproduce the bandgap, effective masses of carriers, luminescence line widths, NAC, and excited-state lifetimes of the two systems at the hybrid functional level while the computational cost remains at that of the Predew-Burke-Ernzerhof functional. Our study indicates that the DFT-1/2 method can greatly accelerate NA-MD simulations while maintaining the accuracy of the hybrid functional, providing an advantage for studying photoexcitation dynamics for large-scale condensed-phase materials.

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.

The role of alkane chain in primary amine capped CdSe and CdS quantum dots from first-principles

In this study, we performab initiocalculations, using density functional theory, to provide more insights about the role of alkane chain in primary amine capped (CdSe)₃₃and (CdS)₃₃quantum dots (QDs). We passivate the QDs surfaces with seven primary amines of different carbon chain lengths starting from NH₃to hexylamine. The primary amine ligands induce a blue shift in the band gap of the ligated QDs, in agreement with experimental studies, but the alkane chain itself show negligible changes in the band gap. By increasing the chain length the binding energy between ligands and the QDs increases but its rate decreases due to the increase of steric hindrance between the ligands. The role of van der Waals forces in such behavior is found to be notable which is done by performing geometry optimization through adding and neglecting the dispersion correction effects for each system. The results of this study can provide helpful information for ligand selectivity in controlling the size and properties of the QDs using primary amines.

PyUNIxMD: A Python-based excited state molecular dynamics package

Theoretical/computational description of excited state molecular dynamics is nowadays a crucial tool for understanding light-matter interactions in many materials. Here we present an open-source Python-based nonadiabatic molecular dynamics program package, namely PyUNIxMD, to deal with mixed quantum-classical dynamics for correlated electron-nuclear propagation. The PyUNIxMD provides many interfaces for quantum chemical calculation methods with commercial and noncommercial ab initio and semiempirical quantum chemistry programs. In addition, the PyUNIxMD offers many nonadiabatic molecular dynamics algorithms such as fewest-switch surface hopping and its derivatives as well as decoherence-induced surface hopping based on the exact factorization (DISH-XF) and coupled-trajectory mixed quantum-classical dynamics (CTMQC) for general purposes. Detailed structures and flows of PyUNIxMD are explained for the further implementations by developers. We perform a nonadiabatic molecular dynamics simulation for a molecular motor system as a simple demonstration.

Ab initio nonadiabatic molecular dynamics of charge carriers in metal halide perovskites

Photoinduced nonequilibrium processes in nanoscale materials play key roles in photovoltaic and photocatalytic applications. This review summarizes recent theoretical investigations of excited state dynamics in metal halide perovskites (MHPs), carried out using a state-of-the-art methodology combining nonadiabatic molecular dynamics with real-time time-dependent density functional theory. The simulations allow one to study evolution of charge carriers at the ab initio level and in the time-domain, in direct connection with time-resolved spectroscopy experiments. Eliminating the need for the common approximations, such as harmonic phonons, a choice of the reaction coordinate, weak electron-phonon coupling, a particular kinetic mechanism, and perturbative calculation of rate constants, we model full-dimensional quantum dynamics of electrons coupled to semiclassical vibrations. We study realistic aspects of material composition and structure and their influence on various nonequilibrium processes, including nonradiative trapping and relaxation of charge carriers, hot carrier cooling and luminescence, Auger-type charge-charge scattering, multiple excitons generation and recombination, charge and energy transfer between donor and acceptor materials, and charge recombination inside individual materials and across donor/acceptor interfaces. These phenomena are illustrated with representative materials and interfaces. Focus is placed on response to external perturbations, formation of point defects and their passivation, mixed stoichiometries, dopants, grain boundaries, and interfaces of MHPs with charge transport layers, and quantum confinement. In addition to bulk materials, perovskite quantum dots and 2D perovskites with different layer and spacer cation structures, edge passivation, and dielectric screening are discussed. The atomistic insights into excited state dynamics under realistic conditions provide the fundamental understanding needed for design of advanced solar energy and optoelectronic devices.

Concentric Approximation for Fast and Accurate Numerical Evaluation of Nonadiabatic Coupling with Projector Augmented-Wave Pseudopotentials

We develop an efficient and accurate method for numerical evaluation of nonadiabatic (NA) coupling in the Kohn-Sham representation with projector augmented-wave (PAW) pseudopotentials that are commonly used in electronic structure calculations on nanoscale, condensed matter, and molecular systems. Without additional cost, the method provides an order of magnitude improvement in accuracy compared to the current technique, while it is 3-4 orders of magnitude faster than the exact evaluation. Atomic displacements over typical time steps in molecular dynamics (MD) simulations are much smaller than the size of the PAW core region, and therefore, evaluation of the NA in the core is simplified. The accuracy is demonstrated with three condensed matter systems. The method is robust to variation in the MD time step. The accurate NA coupling evaluation also helps in maintaining phase-consistency of the NA coupling and identifying trivial crossings of adiabatic states. The approach stimulates NAMD applications to modeling of modern materials and processes.

Crystal Symmetry and Static Electron Correlation Greatly Accelerate Nonradiative Dynamics in Lead Halide Perovskites

Using a recently developed many-body nonadiabatic molecular dynamics (NA-MD) framework for large condensed matter systems, we study the phonon-driven nonradiative relaxation of excess electronic excitation energy in cubic and tetragonal phases of the lead halide perovskite CsPbI₃. We find that the many-body treatment of the electronic excited states significantly changes the structure of the excited states' coupling, promotes a stronger nonadiabatic coupling of states, and ultimately accelerates the relaxation dynamics relative to the single-particle description of excited states. The acceleration of the nonadiabatic dynamics correlates with the degree of configurational mixing, which is controlled by the crystal symmetry. The higher-symmetry cubic phase of CsPbI₃ exhibits stronger configuration mixing than does the tetragonal phase and subsequently yields faster nonradiative dynamics. Overall, using a many-body treatment of excited states and accounting for decoherence dynamics are important for closing the gap between the computationally derived and experimentally measured nonradiative excitation energy relaxation rates.

Preventing Superoxide Generation on Molecule-Protected CH3NH3PbI3 Perovskite: A Time-Domain Ab Initio Study

Metal halide perovskites are promising materials for photovoltaics and optoelectronics. However, transfer of an electron from perovskite to oxygen leads to the formation of superoxide that significantly decreases the stability and charge carrier lifetime of perovskites, which constitutes major issues for real applications. Using nonadiabatic (NA) molecule dynamics simulations, we demonstrate that the introduction of a perylene diimide (PDI) molecule into the CH₃NH₃PbI₃ system adsorbed with an oxygen molecule creates a midgap state above the trap state generated by the oxygen molecule, and thus the PDI midgap state can rapidly capture the photogenerated electron of perovskite at about 100 ps prior to the O₂-related trap state, which takes about double the time. The route simultaneously avoids the formation of superoxide and enhances the stability of perovskites. The fast electron trapping originates from the strong NA coupling and small energy gap between the PDI midgap state and the CH₃NH₃PbI₃ conduction band minimum. Our simulations suggest that a rational choice an electron-accepting molecule can improve the stability and performance of perovskite solar cells and photoelectric devices.

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

We present a new state tracking algorithm based on a stochastic state reassignment that reflects the quantum mechanical interpretation of the state time-overlaps. We assess the new method with a range of model Hamiltonians and demonstrate that it yields the results generally consistent with the deterministic min-cost algorithm. However, the stochastic state tracking algorithm reduces magnitudes of the state population fluctuations as the quantum system evolves toward its equilibrium. The new algorithm facilitates the thermalization of quantum state populations and suppresses the population revivals and oscillations near the equilibrium in many-state systems. The new stochastic algorithm has a favorable computational scaling, is easy to implement due to its conceptual transparency, and treats various types of state identity changes (trivial or avoided crossings and any intermediate cases) on equal footing.

PySpawn: Software for Nonadiabatic Quantum Molecular Dynamics

The ab initio multiple spawning (AIMS) method enables nonadiabatic quantum molecular dynamics simulations in an arbitrary number of dimensions, with potential energy surfaces provided by electronic structure calculations performed on-the-fly. However, the intricacy of the AIMS algorithm complicates software development, deployment on modern shared computer resources, and postsimulation data analysis. PySpawn is a nonadiabatic molecular dynamics software package that addresses these issues. The program is designed to be easily interfaced with electronic structure software, and an interface to the TeraChem software package is described here. PySpawn introduces a task-based reorganization of the AIMS algorithm, allowing fine-grained restart capability and setting the stage for efficient parallelization in a future release. PySpawn includes a user-friendly and interactive Python analysis module that will enable novice users to painlessly adopt AIMS. As a demonstration of PySpawn's simulation capability and analysis module, we report complete active space self-consistent field-based AIMS simulations of the 1,2-dithienyl-1,2-dicyanoethene molecule, a promising molecular photoswitch.

Hot Electron Cooling in Silicon Nanoclusters via Landau-Zener Nonadiabatic Molecular Dynamics: Size Dependence and Role of Surface Termination

We develop a new express methodology for modeling excited-state dynamics occurring in dense manifolds of electronic states in atomistic systems. The approach leverages a modified Landau-Zener formula, the neglect of a back-reaction approximation, and the highly efficient density functional tight-binding method. We study the hot electron dynamics in a series of H- and F-terminated silicon nanocrystals (NCs) containing up to several hundred atoms. We explain the slower electron cooling dynamics in F-terminated NCs by the larger energy gaps between the adjacent electronic states in these systems as well as their slower fluctuations. We conclude that both the mass and chemical identity of the surface termination groups equally influence the electron dynamics, on average. However, the mass effect becomes dominant for higher-energy excitations. We find that the electron decay dynamics in F-terminated NCs has a greater sensitivity to the mass of the surface ligands than do the H-terminated NCs and explain this observation by the details of the electron-phonon coupling in the systems. We find that in the H-terminated NCs, electronic transitions in the cooling process occur predominantly between the surface states, whereas in F-terminated Si NCs, both surface and NC core states are coupled to the nuclear vibrations. We find that electron energy relaxation is accelerated in larger NCs and attribute this effect to the higher densities of states and smaller energy gaps in these 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.

fromage: A library for the study of molecular crystal excited states at the aggregate scale

The study of photoexcitations in molecular aggregates faces the twofold problem of the increased computational cost associated with excited states and the complexity of the interactions among the constituent monomers. A mechanistic investigation of these processes requires the analysis of the intermolecular interactions, the effect of the environment, and 3D arrangements or crystal packing on the excited states. A considerable number of techniques have been tailored to navigate these obstacles; however, they are usually restricted to in‐house codes and thus require a disproportionate effort to adopt by researchers approaching the field. Herein, we present the FRamewOrk for Molecular AGgregate Excitations (fromage), which implements a collection of such techniques in a Python library complemented with ready‐to‐use scripts. The program structure is presented and the principal features available to the user are described: geometrical analysis, exciton characterization, and a variety of ONIOM schemes. Each is illustrated by examples of diverse organic molecules in condensed phase settings. The program is available at https://github.com/Crespo-Otero-group/fromage.

A molecular perspective on Tully models for nonadiabatic dynamics

We present a series of standardized molecular tests for nonadiabatic dynamics, reminiscent of the one-dimensional Tully models proposed in 1990.

Dependence of electron transfer dynamics on the number of graphene layers in π-stacked 2D materials: insights from ab initio nonadiabatic molecular dynamics

Recent time-resolved transient absorption studies demonstrated that the rate of photoinduced interfacial charge transfer (CT) from Zn-phthalocyanine (ZnPc) to single-layer graphene (SLG) is faster than to double-layer graphene (DLG), in contrast to the expectation from Fermi's golden rule. We present the first time-domain non-adiabatic molecular dynamics (NA-MD) study of the electron injection process from photoexcited ZnPc molecules into SLG and DLG substrates. Our calculations suggest that CT occurs faster in the ZnPc/SLG system than in the ZnPc/DLG system, with 580 fs and 810 fs being the fastest components of the observed CT timescales, respectively. The computed timescales are in close agreement with those reported in the experiment. The computed CT timescales are determined largely by the magnitudes of the non-adiabatic couplings (NAC), which we find to be 4 meV and 2 meV, for the ZnPc/SLG and ZnPc/DLG systems, respectively. The transitions are driven mainly by the ZnPc out-of-plane bending mode at 1100 cm-1 and an overtone of fundamental modes in graphene at 2450 cm-1. We find that dephasing occurs on the timescale of 20 fs and is similar in both systems, so decoherence does not notably change the qualitative trends in the CT timescales. We highlight the importance of proper energy level alignment for capturing the qualitative trends in the CT dynamics observed in experiment. In addition, we illustrate several methodological points that are important for accurately modeling nonadiabatic dynamics in the ZnPc/FLG systems, such as the choice of surface hopping methodology, the use of phase corrections, NAC scaling, and the inclusion of Hubbard terms in the density functional and molecular dynamics calculations.

Non-adiabatic molecular dynamics with ΔSCF excited states

Accurate modelling of nonadiabatic transitions and electron-phonon interactions in extended systems is essential for understanding the charge and energy transfer in photovoltaic and photocatalytic materials. The extensive computational costs of the advanced excited state methods have stimulated the development of many approximations to study the nonadiabatic molecular dynamics (NA-MD) in solid-state and molecular materials. In this work, we present a novel ▵SCF-NA-MD methodology that aims to account for electron-hole interactions and electron-phonon back-reaction critical in modelling photoinduced nuclear dynamics. The excited states dynamics is described using the delta self-consistent field (▵SCF) technique within the density functional formalism and the trajectory surface hopping. The technique is implemented in the open-source Libra-X package freely available on the Internet (https://github.com/Quantum-Dynamics-Hub/Libra-X). This work illustrates the general utility of the developed ▵SCF-NA-MD methodology by characterizing the excited state energies and lifetimes, reorganization energies, photoisomerization quantum yields, and by providing the mechanistic details of reactive processes in a number of organic molecules.

A Simple Phase Correction Makes a Big Difference in Nonadiabatic Molecular Dynamics

The outcomes of nonadiabatic molecular dynamics (NA-MD) calculations are modulated by the parameters entering the time-dependent Schrödinger equation (TD-SE). The adiabatic states are commonly used as the basis in which the TD-SE is integrated. However, the phase inconsistencies of such states along the nuclear trajectories obtained in NA-MD simulations may render the wave function and other relevant properties ill-behaving, adversely affecting the dynamics. This work illustrates the consequence of adiabatic state phase inconsistencies in nonadiabatic Ehrenfest dynamics. A simple phase-correction approach is proposed and is demonstrated to alter the dynamics to make it consistent with the reference calculations done in the phase-consistent diabatic representation.

Charge transfer dynamics at the boron subphthalocyanine chloride/C60 interface: non-adiabatic dynamics study with Libra-X

The Libra-X software for non-adiabatic molecular dynamics is reported. It is used to comprehensively study the charge transfer dynamics at the boron subphtalocyanine chloride (SubPc)/fullerene (C₆₀) interface.

Stochastic and Quasi-Stochastic Hamiltonians for Long-Time Nonadiabatic Molecular Dynamics

In the condensed-matter environments, the vibronic Hamiltonian that describes nonadiabatic dynamics often appears as an erratic entity, and one may assume it can be generated stochastically. This property is utilized to formulate novel stochastic and quasi-stochastic vibronic Hamiltonian methodologies, which open a new route to long-time excited state dynamics in atomistic solid-state systems at negligible computational cost. Using a model mimicking a typical solid-state material in noisy environment, general conclusions regarding the simulation of nonadiabatic dynamics are obtained: (1) including bath is critical to complete excited state relaxation; (2) a totally stochastic modulation of energies and couplings has a net effect of no bath and inhibits relaxation; (3) including a single or several dominant electron-phonon modes may be insufficient to complete the excited state relaxation; (4) only the multiple modes, even those that have negligible weights, can represent both the deterministic modulation of system's Hamiltonian and stochastic effects of bath.