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

Theoretical Study on the Electrocatalytic CO2 Reduction Mechanism of Single-Atom Co Complexed Carbon-Based (Co-Nχ@C) Catalysts Supported on Carbon Nanotubes

Electrocatalytic CO2 reduction serves as an effective strategy to tackle energy crises and mitigate greenhouse gas effects. The development of efficient and cost-effective electrocatalysts has been a research hotspot in the field. In this study, we designed four Co-doped single-atom catalysts (Co-Nχ@C) using carbon nanotubes as carriers, these catalysts included tri- and dicoordinated N-doped carbon nanoribbons, as well as tri- and dicoordinated N-doped graphene, respectively denoted as H3(H2)-Co/CNT and 3(2)-Co/CNT. The stable configurations of these Co-Nχ@C catalysts were optimized using the PBE+D3 method. Additionally, we explored the reaction mechanisms of these catalysts for the electrocatalytic reduction of CO2 into four C1 products, including CO, HCOOH, CH3OH and CH4, in detail. Upon comparing the limiting potentials (UL) across the Co-Nχ@C catalysts, the activity sequence for the electrocatalytic reduction of CO2 was H2-Co/CNT > 3-Co/CNT > H3-Co/CNT > 2-Co/CNT. Meanwhile, our investigation of the hydrogen evolution reaction (HER) with four catalysts elucidated the influence of acidic conditions on the electrocatalytic CO2 reduction process. Specifically, controlling the acidity of the solution was crucial when using the H3-Co/CNT and H2-Co/CNT catalysts, while the 3-Co/CNT and 2-Co/CNT catalysts were almost unaffected by the solution's acidity. We hope that our research will provide a theoretical foundation for designing more effective CO2 reduction electrocatalysts.

Computational and experimental assessment of efficient dye adsorption method from aqueous effluents by halloysite and palygorskite clay minerals

The removal of dyes from effluents of textile industries represents a technological challenge, due to their significant environmental impact. The application of halloysite (Hal) and palygorskite (Pal) clay minerals as adsorbents for the removal of Congo red (CR) and methylene blue (MB) was evaluated in this work. The materials were applied both in natural and acid-treated forms, and characterized by XRD, XPS, SEM-EDS, FTIR, and N2 adsorption-desorption isotherm techniques to identify their properties and main active sites. The adsorbents showed potential to remove CR (> 98%) and MB (> 85%) within 180 min, using 0.3 g adsorbent and initial dye concentration of 250 mg L-1. Semi-empirical quantum mechanical calculations (SQM) confirmed the interaction mechanism between dyes and the adsorbents via chemisorption (- 69.0 kcal mol-1 < Eads <  - 28.8 kcal mol-1), which was further observed experimentally due to the high fit of adsorption data to pseudo-second order kinetic model (R2 > 0.99) and Langmuir isotherm (R2 > 0.98). The use of Pal and Hal to remove dyes was proven to be economically and environmentally viable for industrial application.

Decoherence ensures convergence of non-adiabatic molecular dynamics with number of states

Non-adiabatic (NA) molecular dynamics (MD) is a powerful approach for studying far-from-equilibrium quantum dynamics in photophysical and photochemical systems. Most NA-MD methods are developed and tested with few-state models, and their validity with complex systems involving many states is not well studied. By modeling intraband equilibration and interband recombination of charge carriers in MoS2, we investigate the convergence of three popular NA-MD algorithms, fewest switches surface hopping (FSSH), global flux surface hopping (GFSH), and decoherence induced surface hopping (DISH) with the number of states. Only the standard DISH algorithm converges with the number of states and produces Boltzmann equilibrium. Unitary propagation of the wave function in FSSH and GFSH violates the Boltzmann distribution, leads to internal inconsistency between time-dependent Schrödinger equation state populations and trajectory counts, and produces non-convergent results. Introducing decoherence in FSSH and GFSH by collapsing the wave function fixes these problems. The simplified version of DISH that omits projecting out the occupied state and is applicable to few-state systems also causes problems when the number of states is increased. We discuss the algorithmic application of wave function collapse and Boltzmann detailed balance and provide detailed FSSH, GFSH, and DISH flow charts. The use of convergent NA-MD methods is highly important for modeling complicated quantum processes involving multiple states. Our findings provide the basis for investigating quantum dynamics in realistic complex systems.

Energy-Conserving Surface Hopping for Auger Processes

Auger-type processes are ubiquitous in nanoscale materials because quantum confinement enhances Coulomb interactions, and there exist large densities of states. Modeling Auger processes requires the modification of nonadiabatic (NA) molecular dynamics algorithms to include transitions caused by both NA and Coulomb couplings. The system is split into quantum and classical subsystems, e.g., electrons and vibrations, and as a result, energy conservation becomes nontrivial. In surface hopping, an electronic transition induced by NA coupling is accompanied by a classical velocity readjustment to ensure conservation of the total quantum-classical energy. A different treatment is needed for Auger transitions driven by Coulomb interactions. We develop a nonadiabatic molecular dynamics methodology that meticulously differentiates the energy redistribution accompanying hops induced by the NA coupling and the Coulomb interaction and correctly conserves the total energy at each transition. If the transition is driven by a Coulomb interaction, the hop energy is redistributed within the quantum electronic subsystem only. If the transition is NA, the energy is redistributed between the quantum and classical subsystems. Properly maintaining energy conservation for both types of transitions is crucial to generate a correct order of events, obtain accurate transition times, maintain a proper statistical distribution of state populations, and reach thermodynamic equilibrium. We test the method with biexciton annihilation and Auger-assisted hot electron relaxation in a CdSe quantum dot. The sequence of Auger and phonon-driven processes and the calculated time scales are in excellent agreement with the experimental results. The developed approach can be coupled with any surface-hopping method and provides a crucial practical advance to study charge-carrier dynamics in the nanoscale and condensed matter systems.

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.

Selective Adsorption of Sr(II) from Aqueous Solution by Na3FePO4CO3: Experimental and DFT Studies

The efficient segregation of radioactive nuclides from low-level radioactive liquid waste (LLRW) is paramount for nuclear emergency protocols and waste minimization. Here, we synthesized Na3FePO4CO3 (NFPC) via a one-pot hydrothermal method and applied it for the first time to the selective separation of Sr2+ from simulated LLRW. Static adsorption experimental results indicated that the distribution coefficient Kd remained above 5000 mL·g-1, even when the concentration of interfering ions was more than 40 times that of Sr2+. Furthermore, the removal efficiency of Sr2+ showed no significant change within the pH range of 4 to 9. The adsorption of Sr2+ fitted the pseudo-second-order kinetic model and the Langmuir isotherm model, with an equilibrium time of 36 min and a maximum adsorption capacity of 99.6 mg·g-1. Notably, the adsorption capacity was observed to increment marginally with an elevation in temperature. Characterization analyses and density functional theory (DFT) calculations elucidated the adsorption mechanism, demonstrating that Sr2+ initially engaged in an ion exchange reaction with Na+. Subsequently, Sr2+ coordinated with four oxygen atoms on the NFPC (100) facet, establishing a robust Sr-O bond via orbital hybridization.

Ultrafast hydrogen production in boron/oxygen-codoped graphitic carbon nitride revealed by nonadiabatic dynamics simulations

Graphitic carbon nitride (g-C3N4 or GCN) shows promise in photocatalytic water splitting, despite facing the challenge of rapid electron-hole recombination. In this study, we investigated the influence of boron/oxygen codoping on the photocatalytic performance of GCN systems for hydrogen generation. First-principles calculations and nonadiabatic molecular dynamics (NAMD) simulations were employed to reveal that the recombination time of photogenerated carriers could be increased by 16% to 64% in the codoped systems compared to the pristine GCN. The time-dependent density functional theory (TDDFT) scheme was utilized to select energy windows and initiate dynamics in cluster models of B/O co-doped heptazine with water molecules. Notably, we observed efficient direct photodissociation of hydrogen atoms from water molecules within 60 fs and proton hops within the hydrogen-bonded network within 80 fs in the co-doped system, diverging from the previously proposed mechanism for pristine heptazine in NAMD simulations. This discovery underscores the significant role of faster proton-coupled electron transfer (PCET) reactions and rapid radiationless relaxation in achieving high photocatalytic efficiency in water splitting. Our work enhances the understanding of the internal mechanism of highly efficient photocatalysts for water splitting and provides a new design strategy for doped GCN.

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.

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.

Interlayer Charge Transport in 2D Lead Halide Perovskites from First Principles

We report on the implementation of a versatile projection-operator diabatization approach to calculate electronic coupling integrals in layered periodic systems. The approach is applied to model charge transport across the saturated organic spacers in two-dimensional (2D) lead halide perovskites. The calculations yield out-of-plane charge transfer rates that decay exponentially with the increasing length of the alkyl chain, range from a few nanoseconds to milliseconds, and are supportive of a hopping mechanism. Most importantly, we show that the charge carriers strongly couple to distortions of the Pb-I framework and that accounting for the associated nonlocal dynamic disorder increases the thermally averaged interlayer rates by a few orders of magnitude compared to the frozen-ion 0 K-optimized structure. Our formalism provides the first comprehensive insight into the role of the organic spacer cation on vertical transport in 2D lead halide perovskites and can be readily extended to functional π-conjugated spacers, where we expect the improved energy alignment with the inorganic layout to speed up the charge transfer between the semiconducting layers.

Surface hopping modeling of charge and energy transfer in active environments

An active environment is any atomic or molecular system changing a chromophore's nonadiabatic dynamics compared to the isolated molecule. The action of the environment on the chromophore occurs by changing the potential energy landscape and triggering new energy and charge flows unavailable in the vacuum. Surface hopping is a mixed quantum-classical approach whose extreme flexibility has made it the primary platform for implementing novel methodologies to investigate the nonadiabatic dynamics of a chromophore in active environments. This Perspective paper surveys the latest developments in the field, focusing on charge and energy transfer processes.