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.

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.

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.

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.

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.

Photoemission of the Upconverted Hot Electrons in Mn-Doped CsPbBr3 Nanocrystals.

Hot electrons play a crucial role in enhancing the efficiency of photon-to-current conversion or photocatalytic reactions. In semiconductor nanocrystals, energetic hot electrons capable of photoemission can be generated via the upconversion process involving the dopant-originated intermediate state, currently known only in Mn-doped cadmium chalcogenide quantum dots. Here, we report that Mn-doped CsPbBr3 nanocrystals are an excellent platform for generating hot electrons via upconversion that can benefit from various desirable exciton properties and the structural diversity of metal halide perovskites (MHPs). Two-dimensional Mn-doped CsPbBr3 nanoplatelets are particularly advantageous for hot electron upconversion due to the strong exciton-dopant interaction mediating the upconversion process. Furthermore, nanoplatelets reveal evidence for the hot electron upconversion via long-lived dark excitons in addition to bright excitons that may enhance the upconversion efficiency. This study establishes the feasibility of hot electron upconversion in MHP hosts and demonstrates the potential merits of two-dimensional MHP nanocrystals in the upconversion process.

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.

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.

Magnetic Effect of Dopants on Bright and Dark Excitons in Strongly Confined Mn-Doped CsPbI3 Quantum Dots.

We investigated the magnetic effect of Mn2+ ions on an exciton of Mn-doped CsPbI3 quantum dots (QDs), where we looked for the signatures of an exciton magnetic polaron known to produce a large effective magnetic field in Mn-doped CdSe QDs. In contrast to Mn-doped CdSe QDs that can produce ∼100 T of magnetic field upon photoexcitation, manifested as a large change in the energy and relaxation dynamics of a bright exciton, Mn-doped CsPbI3 QDs exhibited little influence of a magnetic dopant on the behavior of a bright exciton. However, a µs-lived dark exciton in CsPbI3 QDs showed 40% faster decay in the presence of Mn2+, equivalent to the effect of ∼3 T of an external magnetic field. While further study is necessary to fully understand the origin of the large difference in the magneto-optic property of an exciton in two systems, we consider that the difference in antiferromagnetic coupling of the dopants is an important contributing factor.

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.

Nuclear Spin Gyroscope based on the Nitrogen Vacancy Center in Diamond.

A rotation sensor is one of the key elements of inertial navigation systems and compliments most cell phone sensor sets used for various applications. Currently, inexpensive and efficient solutions are mechanoelectronic devices, which nevertheless lack long-term stability. Realization of rotation sensors based on spins of fundamental particles may become a drift-free alternative to such devices. Here, we carry out a proof-of-concept experiment, demonstrating rotation measurements on a rotating setup utilizing nuclear spins of an ensemble of nitrogen vacancy centers as a sensing element with no stationary reference. The measurement is verified by a commercially available microelectromechanical system gyroscope.

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.

Spin-Orbit Coupling Accelerates the Photoinduced Interfacial Electron Transfer in a Fullerene-Based Perovskite Heterojunction.

In this work, we explore the interfacial properties of the C60-Py@MAPbI3 heterojunction of the PbI-terminated MAPbI3(001) surface and pyridine-functionalized C60-Py fullerene derivative through both collinear and noncollinear density functional theory calculations with and without spin-orbit coupling (SOC) effects. C60-Py is bound to the MAPbI3 surface through interfacial Pb-O and Pb-N bonds. Although C60-Py@MAPbI3 is predicted to be the same type II heterojunction at all of the computational levels considered, the SOC effects largely decrease the energy gap of the first conduction bands of C60-Py and MAPbI3, thereby accelerating the interfacial electron transfer. Further dynamics simulations show that the inclusion of the SOC effects induces the transfer of approximately 80% of electrons from MAPbI3 to C60-Py within 1 ps. The work demonstrates that the SOC effects are indispensable for the interfacial properties of C60-Py@MAPbI3 and could also play a non-negligible role in tuning the optoelectronic properties of fullerene-based or similar perovskite 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.

Nonadiabatic Dynamics in Si and CdSe Nanoclusters: Many-Body vs Single-Particle Treatment of Excited States.

In this work, we report a new nonadiabatic molecular dynamics methodology that incorporates many-body (MB) effects in the treatment of electronic excited states in extended atomistic systems via linear-response time-dependent density functional theory (TD-DFT). The nonradiative dynamics of excited states in Si75H64 and Cd33Se33 nanocrystals is studied at the MB (TD-DFT) and single-particle (SP) levels to reveal the role of MB effects. We find that a MB description of the excited states qualitatively changes the structure of coupling between the excited states, leading to larger nonadiabatic couplings and accelerating the dynamics by a factor of 2-4. The dependence of excited state dynamics in these systems on the surface hopping/decoherence methodology and the choice of the dynamical basis is investigated and analyzed. We demonstrated that the use of special "electron-only" or "hole-only" excitation bases may be advantageous over using the full "electron-hole" basis of SP states, making the computed dynamics more consistent with the one obtained at the MB level.

Locomotion of the C60-based nanomachines on graphene surfaces.

We provide a comprehensive computational characterization of surface motion of two types of nanomachines with four C60 "wheels": a flexible chassis Nanocar and a rigid chassis Nanotruck. We study the nanocars' lateral and rotational diffusion as well as the wheels' rolling motion on two kinds of graphene substrates-flexible single-layer graphene which may form surface ripples and an ideally flat graphene monolayer. We find that the graphene surface ripples facilitate the translational diffusion of Nanocar and Nanotruck, but have little effect on their surface rotation or the rolling of their wheels. The latter two types of motion are strongly affected by the structure of the nanomachines instead. Surface diffusion of both nanomachines occurs preferentially via a sliding mechanism whereas the rolling of the "wheels" contributes little. The axial rotation of all "wheels" is uncorrelated.

Random Matrix Theory Analysis of a Temperature-Related Transformation in Statistics of Fano-Feshbach Resonances in Thulium Atoms.

Recently, the transformation from random to chaotic behavior in the statistics of Fano-Feshbach resonances was observed in thulium atoms with rising ensemble temperature. We performed random matrix theory simulations of such spectra and analyzed the resulting statistics in an attempt to understand the mechanism of the transformation. Our simulations show that, when evaluated in terms of the Brody parameter, resonance statistics do not change or change insignificantly when higher temperature resonances are appended to the statistics. In the experiments evaluated, temperature was changed simultaneously with optical dipole trap depth. Thus, simulations included the Stark shift based on the known polarizability of the free atoms and assuming their polarizability remains the same in the bound state. Somewhat surprisingly, we found that, while including the Stark shift does lead to minor statistical changes, it does not change the resonance statistics and, therefore, is not responsible for the experimentally observed statistic transformation. This observation suggests that either our assumption regarding the polarizability of Feshbach molecules is poor or that an additional mechanism changes the statistics and leads to more chaotic statistical behavior.

Size-dependent dark exciton properties in cesium lead halide perovskite quantum dots.

The fine structure of the band edge exciton and the dark exciton photoluminescence (PL) are topics of significant interest in the research of semiconducting metal halide perovskite nanocrystals, with several conflicting reports on the level ordering of the bright and dark states and the accessibility of the emitting dark states. Recently, we observed the intense dark exciton PL in strongly confined CsPbBr3 nanocrystals at cryogenic temperatures, in contrast to weakly confined nanocrystals lacking dark exciton PL, which was explained by the confinement enhanced bright-dark exciton splitting. In this work, we investigated the size-dependence of the dark exciton photoluminescence properties in CsPbBr3 and CsPbI3 quantum dots in the strongly confined regime, showing the clear role of confinement in determining the bright-dark energy splitting (ΔEBD) and the dark exciton lifetime (τD). We observe the increase in both ΔEBD and τD with increasing quantum confinement in CsPbBr3 and CsPbI3 QDs, consistent with the earlier predictions on the size-dependence of ΔEBD and τD. Our results show that quantum confinement plays a crucial role in determining the accessibility to the dark exciton PL and its characteristics in metal halide perovskite nanocrystals.

Accurate Computation of Nonadiabatic Coupling with Projector Augmented-Wave Pseudopotentials.

Synergy of nonadiabatic molecular dynamics with real-time time-dependent density functional theory has led to significant progress in modeling excited-state dynamics in nanoscale and condensed matter systems over the past decade. Nonadiabatic coupling (NAC) is the central quantity in such simulations, and its accurate and efficient evaluation is an enduring challenge in time-dependent Kohn-Sham theory, particularly in conjunction with planewave basis sets and projector augmented-wave (PAW) pseudopotentials because of the complexity of the PAW "all-electron" wave function. We report a method for rigorous evaluation of the NAC with PAW wave functions and demonstrate an efficient approximation to the rigorous NAC that gives comparable accuracy. As a validation, we intensely examine the NAC matrix elements calculated using both pseudo- and all-electron wave functions under the PAW formalism in six representative systems. The approximate NAC obtained with pseudowave functions is close to the exact all-electron NAC, with the largest deviations observed when subshell d-electrons are involved in the transitions. The developed approach provides a rigorous and convenient methodology for the numerical computation of NAC in the Kohn-Sham theory framework.

Intense Dark Exciton Emission from Strongly Quantum-Confined CsPbBr3 Nanocrystals.

Dark exciton as the lowest-energy (ground) exciton state in metal halide perovskite nanocrystals is a subject of much interest. This is because the superior performance of perovskites as the photon source combined with long lifetime of dark exciton can be attractive for many applications of exciton. However, the direct observation of the intense and long-lived dark exciton emission, indicating facile access to dark ground exciton state, has remained elusive. Here, we report the intense photoluminescence from dark exciton with microsecond lifetime in strongly confined CsPbBr3 nanocrystals and reveal the crucial role of confinement in accessing the dark ground exciton state. This study establishes the potential of strongly quantum-confined perovskite nanostructures as the excellent platform to harvest the benefits of extremely long-lived dark exciton.