Nonadiabatic Molecular Dynamics for Thousand Atom Systems: A Tight-Binding Approach toward PYXAID

Influence of Defects on Excited-State Dynamics in Lead Halide Perovskites: Time-Domain ab Initio Studies

This Perspective summarizes recent research into the excited-state dynamics in lead halide perovskites that are of paramount importance for photovoltaic and photocatalytic applications. Nonadiabatic molecular dynamics combined with time-domain ab initio density functional theory allows one to mimic time-resolved spectroscopy experiments at the atomistic level of detail. The focus is placed on realistic aspects of perovskite materials, including point defects, surfaces, grain boundaries, mixed stoichiometries, dopants, and interfaces. The atomistic description of the quantum dynamics of electron and hole trapping and recombination, provided by the time-domain ab initio simulations, generates important insights into the mechanisms of charge and energy losses and guides the development of high-performance perovskite solar cell devices.

Conical Intersections at the Nanoscale: Molecular Ideas for Materials

The ability to predict and describe nonradiative processes in molecules via the identification and characterization of conical intersections is one of the greatest recent successes of theoretical chemistry. Only recently, however, has this concept been extended to materials science, where nonradiative recombination limits the efficiencies of materials for various optoelectronic applications. In this review, we present recent advances in the theoretical study of conical intersections in semiconductor nanomaterials. After briefly introducing conical intersections, we argue that specific defects in materials can induce conical intersections between the ground and first excited electronic states, thus introducing pathways for nonradiative recombination. We present recent developments in theoretical methods, computational tools, and chemical intuition for the prediction of such defect-induced conical intersections. Through examples in various nanomaterials, we illustrate the significance of conical intersections for nanoscience. We also discuss challenges facing research in this area and opportunities for progress.

An efficient approximate algorithm for nonadiabatic molecular dynamics

We propose a modification to the nonadiabatic surface hopping calculation method formulated in a paper by Yu et al. [Phys. Chem. Chem. Phys. 16, 25883 (2014)], which is a multidimensional extension of the Zhu-Nakamura theory with a practical diabatic gradient estimation algorithm. In our modification, their diabatic gradient estimation algorithm, which is based on a simple interpolation of the adiabatic potential energy surfaces, is replaced by an algorithm using the numerical derivatives of the adiabatic gradients. We then apply the algorithm to several models of nonadiabatic dynamics, both analytic and ab initio models, to numerically demonstrate that our method indeed widens the applicability and robustness of their method. We also discuss the validity and limitations of our new nonadiabatic surface hopping method while considering in mind potential applications to excited-state dynamics of biomolecules or unconventional nonadiabatic dynamics such as radiation decay processes in ultraintense X-ray fields.

Non-adiabatic molecular dynamics investigation of the size dependence of the electronic relaxation in polyacenes

Electronic relaxation from the brightest excited state has been investigated for neutral polyacenes ranging in size from naphthalene to heptacene.

Highly efficient surface hopping dynamics using a linear vibronic coupling model

We report an implementation of the linear vibronic coupling (LVC) model within the surface hopping dynamics approach and present utilities for parameterizing this model in a blackbox fashion. This results in an extremely efficient method to obtain qualitative and even semi-quantitative information about the photodynamical behavior of a molecule, and provides a new route toward benchmarking the results of surface hopping computations. The merits and applicability of the method are demonstrated in a number of applications. First, the method is applied to the SO2 molecule showing that it is possible to compute its absorption spectrum beyond the Condon approximation, and that all the main features and timescales of previous on-the-fly dynamics simulations of intersystem crossing are reproduced while reducing the computational effort by three orders of magnitude. The dynamics results are benchmarked against exact wavepacket propagations on the same LVC potentials and against a variation of the electronic structure level. Four additional test cases are presented to exemplify the broader applicability of the model. The photodynamics of the isomeric adenine and 2-aminopurine molecules are studied and it is shown that the LVC model correctly predicts ultrafast decay in the former and an extended excited-state lifetime in the latter. Futhermore, the method correctly predicts ultrafast intersystem crossing in the modified nucleobase 2-thiocytosine and its absence in 5-azacytosine while it fails to describe the ultrafast internal conversion to the ground state in the latter.

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.

Ultrafast, asymmetric charge transfer and slow charge recombination in porphyrin/CNT composites demonstrated by time-domain atomistic simulation

The versatile photochemical properties of porphyrin molecules make them excellent candidates for solar energy applications. Carbon nanotubes (CNTs) exhibit superior charge conductivity and have been combined with porphyrins to achieve efficient and ultrafast charge separation. Experiments show that the charge separated state lives less than 10 ps, which is too short for applications. Using real-time time-dependent tight binding density functional theory (DFTB) combined with non-adiabatic molecular dynamics (NAMD), we model photo-induced charge separation and recombination in two porphyrin/CNT composites. Having achieved excellent agreement with the experiment for the electron transfer from the porphyrins to the CNT, we demonstrate that hole transfer can be achieved upon CNT excitation, although in a less efficient way. By exciting the CNT one can extend light harvesting into lower energies of the solar spectrum and increase solar light conversion efficiency. We also show that the charge separated state can live over 1 ns. The two orders of magnitude difference from the experimental lifetime could arise due to the presence of defects or metallic tubes in the samples. The charge separated state is long-lived because the non-adiabatic electron-phonon coupling is very small, less than 1 meV, and the quantum coherence is short, 15-20 fs. The excited states in the isolated porphyrins and CNT live around 100 ps, in agreement with experiments as well. The porphyrin/CNT interaction occurs through the π-electron systems of the two species. The non-radiative relaxation is promoted by both high and low frequency phonons, with higher frequency phonons playing more important roles in electron relaxation than in hole relaxation. Low frequency phonons contribute significantly to the decay of the charge separated state, because they modulate the relative positions of the porphyrins and the CNT. The time-domain atomistic simulations provide a detailed understanding of the charge separation and recombination mechanisms, and generate valuable guidelines for the optimization of photovoltaic efficiency in modern nanoscale materials.

Detailed balance, internal consistency, and energy conservation in fragment orbital-based surface hopping

We have recently introduced an efficient semi-empirical non-adiabatic molecular dynamics method for the simulation of charge transfer/transport in molecules and molecular materials, denoted fragment orbital-based surface hopping (FOB-SH) [J. Spencer et al., J. Chem. Phys. 145, 064102 (2016)]. In this method, the charge carrier wavefunction is expanded in a set of charge localized, diabatic electronic states and propagated in the time-dependent potential due to classical nuclear motion. Here we derive and implement an exact expression for the non-adiabatic coupling vectors between the adiabatic electronic states in terms of nuclear gradients of the diabatic electronic states. With the non-adiabatic coupling vectors (NACVs) available, we investigate how different flavours of fewest switches surface hopping affect detailed balance, internal consistency, and total energy conservation for electron hole transfer in a molecular dimer with two electronic states. We find that FOB-SH satisfies detailed balance across a wide range of diabatic electronic coupling strengths provided that the velocities are adjusted along the direction of the NACV to satisfy total energy conservation upon a surface hop. This criterion produces the right fraction of energy-forbidden (frustrated) hops, which is essential for correct population of excited states, especially when diabatic couplings are on the order of the thermal energy or larger, as in organic semiconductors and DNA. Furthermore, we find that FOB-SH is internally consistent, that is, the electronic surface population matches the average quantum amplitudes, but only in the limit of small diabatic couplings. For large diabatic couplings, inconsistencies are observed as the decrease in excited state population due to frustrated hops is not matched by a corresponding decrease in quantum amplitudes. The derivation provided here for the NACV should be generally applicable to any electronic structure approach where the electronic Hamiltonian is constructed in a diabatic electronic state basis.

Effect of Aspect Ratio on Multiparticle Auger Recombination in Single-Walled Carbon Nanotubes: Time Domain Atomistic Simulation

Many-particle Auger-type processes are common in nanoscale materials due to a combination of high densities of states that can support multiple excitations and substantial Coulomb coupling between charges enhanced by quantum confinement. Auger decay dynamics in (10,5) semiconductor carbon nanotubes (CNT) with different aspect ratios and particle densities are simulated in time domain using global flux surface hopping, recently developed and implemented within Kohn-Sham tight-binding density functional theory. Despite an increasing density of states, the multiparticle Auger recombination rate decreases in longer CNTs. The atomistic simulation shows that the effect is directly related to the coupling between electronic states, which decreases as the aspect ratio becomes larger. The dependence on tube length is stronger for three-exciton than two-exciton recombination and the calculated time scale ratio approaches the experimental value measured for long CNTs. Phonon-assisted transitions play a particularly important role during Auger recombination. Electron-phonon relaxation is faster than the recombination, and Auger transitions are assisted by phonons over a range of frequencies up to the G-mode. The involvement of phonons strongly enhances the probability of transitions involving asymmetric electron-hole pairs. The time-domain atomistic simulation mimics directly time-resolved optical experiments and provides a detailed, systematic analysis of the phonon-assisted Auger dynamics.

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.

Hydrogen bond dynamics governs the effective photoprotection mechanism of plant phenolic sunscreens

Sinapic acid derivatives are important sunscreen species in natural plants, which could provide protection from solar UV radiation. Using a combination of ultrafast excited state dynamics, together with classical molecular dynamics studies, we demonstrate that there is direct coupling of hydrogen bond motion with excited state photoprotection dynamics as part of the basic mechanism in solution. Beyond the intra-molecular degree of freedom, the inter-molecular motions on all timescales are potentially important for the photochemical or photophysical events, ranging from the ultrafast hydrogen bond motion to solvent rearrangements. This provides not only an enhanced understanding of the anomalous experimental spectroscopic results, but also the key idea in the development of sunscreen agents with improved photo-chemical properties. We suggest that the hydrogen bond dynamics coupled excited state photoprotection mechanism may also be possible in a broad range of bio-related molecules in the condensed phase.

Weak Donor-Acceptor Interaction and Interface Polarization Define Photoexcitation Dynamics in the MoS2/TiO2 Composite: Time-Domain Ab Initio Simulation

To realize the full potential of transition metal dichalcogenides interfaced with bulk semiconductors for solar energy applications, fast photoinduced charge separation, and slow electron-hole recombination are needed. Using a combination of time-domain density functional theory with nonadiabatic molecular dynamics, we demonstrate that the key features of the electron transfer (ET), energy relaxation and electron-hole recombination in a MoS₂-TiO₂ system are governed by the weak van der Waals interfacial interaction and interface polarization. Electric fields formed at the interface allow charge separation to happen already during the photoexcitation process. Those electrons that still reside inside MoS₂, transfer into TiO₂ slowly and by the nonadiabatic mechanism, due to weak donor-acceptor coupling. The ET time depends on excitation energy, because the TiO₂ state density grows with energy, increasing the nonadiabatic transfer rate, and because MoS₂ sulfur atoms start to contribute to the photoexcited state at higher energies, increasing the coupling. The ET is slower than electron-phonon energy relaxation because the donor-acceptor coupling is weak, rationalizing the experimentally observed injection of primarily hot electrons. The weak van der Waals MoS₂-TiO₂ interaction ensures a long-lived charge separated state and a short electron-hole coherence time. The injection is promoted primarily by phonons within the 200-800 cm^-1 range. Higher frequency modes are particularly important for the electron-hole recombinations, because they are able to accept large amounts of electronic energy. The predicted time scales for the forward and backward ET, and energy relaxation can be measured by time-resolved spectroscopies. The reported simulations generate a detailed time-domain atomistic description of the complex interplay of the charge and energy transfer processes at the MoS₂/TiO₂ interface that are of fundamental importance to photovoltaic and photocatalytic applications. The results suggest that even though the photogenerated charge-separated state is long-lived, the slower charge separation, compared to the electron-phonon energy relaxation, can present problems in practical applications.

Pump-Power Dependence of Coherent Acoustic Phonon Frequencies in Colloidal CdSe/CdS Core/Shell Nanoplatelets

Femtosecond optical pump-probe spectroscopy resolves hitherto unobserved coherent acoustic phonons in colloidal CdSe/CdS core/shell nanoplatelets (NPLs). With increasing pump fluence, the frequency of the in-plane acoustic mode increases from 5.2 to 10.7 cm^-1, whereas the frequency of the out-of-plane mode remains at ∼20 cm^-1. Analysis of the oscillation phases suggests that the coherent acoustic phonon generation mechanism transitions from displacive excitation to subpicosecond Auger hole trapping with increasing pump fluence. The measurements yield Huang-Rhys parameters of ∼10^-2 for both acoustic modes. The weak electron-phonon coupling strengths favor the application of NPLs in optoelectronics.

Ultrafast Electronic Energy Transfer in an Orthogonal Molecular Dyad

Understanding electronic energy transfer (EET) is an important ingredient in the development of artificial photosynthetic systems and photovoltaic technologies. Although EET is at the heart of these applications and crucially influences their light-harvesting efficiency, the nature of EET over short distances for covalently bound donor and acceptor units is often not well understood. Here we investigate EET in an orthogonal molecular dyad (BODT4), in which simple models fail to explain the very origin of EET. On the basis of nonadiabatic ab initio molecular dynamics calculations and ultrafast fluorescence experiments, we gain detailed microscopic insights into the ultrafast electrovibrational dynamics following photoexcitation. Our analysis offers molecular-level insights into these processes and reveals that it takes place on time scales ≲100 fs and occurs through an intermediate charge-transfer state.

Microsecond Simulation of Electron Transfer in DNA: Bottom-Up Parametrization of an Efficient Electron Transfer Model Based on Atomistic Details

The transfer of electrons over long distances in complex molecular systems is a phenomenon of significance in both biochemistry and technology. In recent years, we have been developing efficient models to study ET in complex systems, including DNA as a prominent example. Ab initio and model approaches have been combined in an "on-the-fly" calculation of ET parameters, which can be used to propagate nuclear and electronic degrees of freedom simultaneously. These previous efforts have aimed at deriving an efficient nonadiabatic quantum mechanical-molecular mechanical (QM/MM) simulation scheme for ET, making nanosecond simulations of ET in realistic systems possible. This, however, is still insufficient for the treatment of large donor-bridge-acceptor systems, like the ET in DNA, overcoming long adenine bridges. Therefore, we have constructed a theoretical model in a bottom-up manner. All quantum-chemical as well as force-field calculations are substituted by theoretical models of the involved phenomena on a molecular level, including polarization and relaxation of the molecular environment, which are often omitted in other recently developed theoretical models of ET. A nonadiabatic simulation scheme is employed, and no assumptions regarding the ET mechanism are needed. Thus, the predictive power of the simulations is preserved, while pushing the limits of the accessible time scales beyond microseconds. This model-based simulation scheme is applied to ET in various DNA species. Good agreement with the "full" atomistic nonadiabatic QM/MM scheme is observed for the archetypal DNA ET systems, the polyA sequence, as well as the sequences GT_nGGG, containing adenines as bridge sites. Furthermore, ET in larger, more complex DNA sequences is simulated, and the results are discussed.

Sub-Picosecond Auger-Mediated Hole-Trapping Dynamics in Colloidal CdSe/CdS Core/Shell Nanoplatelets

Quasi-two-dimensional colloidal nanoplatelets (NPLs) have recently emerged as a class of semiconductor nanomaterials whose atomically precise monodisperse thicknesses give rise to narrow absorption and emission spectra. However, the sub-picosecond carrier dynamics of NPLs at the band edge remain largely unknown, despite their importance in determining the optoelectronic properties of these materials. Here, we use a combination of femtosecond transient absorption spectroscopy and nonadiabatic molecular dynamics simulations to investigate the early time carrier dynamics of CdSe/CdS core/shell NPLs. Band-selective probing reveals sub-picosecond Auger-mediated trapping of holes with an effective second-order rate constant of 3.5 ± 1.0 cm²/s. Concomitant spectral blue shifts that are indicative of Auger hole heating are found to occur on the same time scale as the sub-picosecond trapping dynamics, whereas spectral red shifts that emerge at low excitation densities furnish an electron-cooling time scale of 0.84 ± 0.09 ps. Finally, nonadiabatic molecular dynamics simulations relate the observed sub-picosecond Auger-mediated hole-trapping dynamics to a shallow trap state that originates from the incomplete passivation of dangling bonds on the NPL surface.

An Efficient, Augmented Surface Hopping Algorithm That Includes Decoherence for Use in Large-Scale Simulations

We propose and implement a highly efficient augmented surface hopping algorithm that (i) can be used for large simulations (with many nuclei and many electronic states) and (ii) includes the effects of decoherence without parametrization. Our protocol is based on three key modifications of the surface hopping methodology: (a) a novel separation of classical and quantum degrees of freedom that treats avoided and trivial crossings efficiently, (b) a multidimensional approximation of the time derivative matrix that avoids explicit construction of the derivative coupling at most time steps, and (c) an efficient approximation for the augmented fewest-switches surface hopping decoherence rate. We will show that this protocol can be several orders of magnitude more efficient than the traditional protocol for large multidimensional problems. Furthermore, the marginal cost for including decoherence effects is now negligible.

Sustainable Nanotechnology: Opportunities and Challenges for Theoretical/Computational Studies

For assistance in the design of the next generation of nanomaterials that are functional and have minimal health and safety concerns, it is imperative to establish causality, rather than correlations, in how properties of nanomaterials determine biological and environmental outcomes. Due to the vast design space available and the complexity of nano/bio interfaces, theoretical and computational studies are expected to play a major role in this context. In this minireview, we highlight opportunities and pressing challenges for theoretical and computational chemistry approaches to explore the relevant physicochemical processes that span broad length and time scales. We focus discussions on a bottom-up framework that relies on the determination of correct intermolecular forces, accurate molecular dynamics, and coarse-graining procedures to systematically bridge the scales, although top-down approaches are also effective at providing insights for many problems such as the effects of nanoparticles on biological membranes.

Recent Progress in Surface Hopping: 2011-2015

Developed 25 years ago, Tully's fewest switches surface hopping (FSSH) has proven to be the most popular approach for simulating quantum-classical dynamics in a broad variety of systems, ranging from the gas phase, to the liquid and solid phases, to biological and nanoscale materials. FSSH is widely adopted as the fundamental platform to introduce modifications as needed. Significant progress has been made recently to enhance the accuracy and efficiency of the surface hopping technique. Various limitations of the standard FSSH-associated with quantum nuclear effects, interference and decoherence, trivial or "unavoided" crossings, superexchange, and representation dependence-have been lifted. These advances are needed to allow one to treat many important phenomena in chemistry, physics, materials, and related disciplines. Examples include charge transport in extended systems such as organic solids, singlet fission in molecular aggregates, Auger-type exciton multiplication, recombination and relaxation in quantum dots and other nanoscale materials, Auger-assisted charge transfer, nonradiative luminescence quenching, and electron-hole recombination. This Perspective summarizes recent advances in the surface hopping formulation of nonadiabatic dynamics and provides an outlook on the future of surface hopping.