Accelerating wavepacket propagation with machine learning.

In this work, we discuss the use of a recently introduced machine learning (ML) technique known as Fourier neural operators (FNO) as an efficient alternative to the traditional solution of the time-dependent Schrödinger equation (TDSE). FNOs are ML models which are employed in the approximated solution of partial differential equations. For a wavepacket propagating in an anharmonic potential and for a tunneling system, we show that the FNO approach can accurately and faithfully model wavepacket propagation via the density. Additionally, we demonstrate that FNOs can be a suitable replacement for traditional TDSE solvers in cases where the results of the quantum dynamical simulation are required repeatedly such as in the case of parameter optimization problems (e.g., control). The speed-up from the FNO method allows for its combination with the Markov-chain Monte Carlo approach in applications that involve solving inverse problems such as optimal and coherent laser control of the outcome of dynamical processes.

Photo-excited charge transfer from adamantane to electronic bound states in water.

Aqueous nanodiamonds illuminated by UV light produce free solvated electrons, which may drive high-energy reduction reactions in water. However, the influence of water conformations on the excited-state electron-transfer mechanism are still under debate. In this work, we offer a theoretical study of charge-transfer states in adamantane-water structures obtained by linear-response time-dependent density-functional theory. Small water clusters with broken hydrogen bonds are found to efficiently bind the electron from adamantane. A distinction is made with respect to the nature of the water clusters: some bind the electron in a water cavity, others along a strong permanent total dipole. These two types of bound states are more strongly binding, the higher their electron affinity and their positive electrostatic potential, the latter being dominated by the energy of the lowest unoccupied molecular orbital of the isolated water clusters. Structural sampling in a thermal equilibrium at room temperature via molecular dynamics snapshots confirms under which conditions the underlying waters clusters can occur and verifies that broken hydrogen bonds in the water network close to adamantane can create traps for the solvated electron.

Ground and excited state charge transfer at aqueous nanodiamonds.

Nanodiamonds (NDs) are unique carbonaceous materials with exceptionally high stability, hardness, and notable electronic properties. Their applications in photocatalysis, biomedicine, and energy materials are usually carried out in aqueous environments, where they interact with aqueous adsorbates. Especially, electron density may rearrange from the diamond material toward oxidative adsorbates such as oxygen, which is known as charge transfer doping. In this article, we quantify the charge transfer doping for NDs with inhomogeneous surface coverings (hydroxyl, fluorine, and amorphous carbon), as well as NDs doped with heteroatoms (B, Si, N) using hybrid density functional theory (DFT) calculations. The transfer doping magnitude is largely determined by the NDs' highest occupied molecular orbital energies, which can in turn be modified by the surface covering and doping. However, local modifications of the ND structures do not have any local effects on the magnitude of the charge transfer. We furthermore analyze the impact of aqueous adsorbates on the excited states of an aqueous ND in the context of photocatalysis via time-dependent DFT. Here, we find that the excited electrons are biased to move in the direction of the respective oxidative adsorbate. Surprisingly, we find that also unreactive species such as nitrous oxide may attract the excited electrons, which is probably due to the positive partial charge that is induced by the local N 2 O solvation geometry.

Integrating Explainability into Graph Neural Network Models for the Prediction of X-ray Absorption Spectra.

The use of sophisticated machine learning (ML) models, such as graph neural networks (GNNs), to predict complex molecular properties or all kinds of spectra has grown rapidly. However, ensuring the interpretability of these models' predictions remains a challenge. For example, a rigorous understanding of the predicted X-ray absorption spectrum (XAS) generated by such ML models requires an in-depth investigation of the respective black-box ML model used. Here, this is done for different GNNs based on a comprehensive, custom-generated XAS data set for small organic molecules. We show that a thorough analysis of the different ML models with respect to the local and global environments considered in each ML model is essential for the selection of an appropriate ML model that allows a robust XAS prediction. Moreover, we employ feature attribution to determine the respective contributions of various atoms in the molecules to the peaks observed in the XAS spectrum. By comparing this peak assignment to the core and virtual orbitals from the quantum chemical calculations underlying our data set, we demonstrate that it is possible to relate the atomic contributions via these orbitals to the XAS spectrum.

Machine Learning Frontier Orbital Energies of Nanodiamonds.

Nanodiamonds have a wide range of applications including catalysis, sensing, tribology, and biomedicine. To leverage nanodiamond design via machine learning, we introduce the new data set ND5k, consisting of 5089 diamondoid and nanodiamond structures and their frontier orbital energies. ND5k structures are optimized via tight-binding density functional theory (DFTB) and their frontier orbital energies are computed using density functional theory (DFT) with the PBE0 hybrid functional. From this data set we derive a qualitative design suggestion for nanodiamonds in photocatalysis. We also compare recent machine learning models for predicting frontier orbital energies for similar structures as they have been trained on (interpolation on ND5k), and we test their abilities to extrapolate predictions to larger structures. For both the interpolation and extrapolation task, we find the best performance using the equivariant message passing neural network PaiNN. The second best results are achieved with a message passing neural network using a tailored set of atomic descriptors proposed here.

How Regiochemistry Influences Aggregation Behavior and Charge Transport in Conjugated Organosulfur Polymer Cathodes for Lithium-Sulfur Batteries.

For lithium-sulfur (Li-S) batteries to become competitive, they require high stability and energy density. Organosulfur polymer-based cathodes have recently shown promising performance due to their ability to overcome common limitations of Li-S batteries, such as the insulating nature of sulfur. In this study, we use a multiscale modeling approach to explore the influence of the regiochemistry of a conjugated poly(4-(thiophene-3-yl)benzenethiol) (PTBT) polymer on its aggregation behavior and charge transport. Classical molecular dynamics simulations of the self-assembly of polymer chains with different regioregularity show that a head-to-tail/head-to-tail regularity can form a well-ordered crystalline phase of planar chains allowing for fast charge transport. Our X-ray diffraction measurements, in conjunction with our predicted crystal structure, confirm the presence of crystalline phases in the electropolymerized PTBT polymer. We quantitatively describe the charge transport in the crystalline phase in a band-like regime. Our results give detailed insights into the interplay between microstructural and electrical properties of conjugated polymer cathode materials, highlighting the effect of polymer chain regioregularity on its charge transport properties.

Three-Electron Dynamics of the Interparticle Coulombic Decay in Doubly Excited Clusters with One-Dimensional Continuum Confinement.

A detailed analysis of the electronic structure and decay dynamics in a symmetric system with three electrons in three linearly aligned binding sites representing quantum dots (QDs) is given. The two outer A QDs are two-level potentials and can act as (virtual) photon emitters, whereas the central B QD can be ionized from its one level into a continuum confined on the QD axis upon absorbing virtual photons in the inter-Coulombic decay (ICD) process. Two scenarios in such an ABA array are explored. One ICD process is from a singly excited resonance state, whose decay releasing one virtual photon we find superimposed with resonance energy transfer among both A QDs. Moreover, the decay-process manifold for a doubly excited (DE) resonance is explored, in which collective ICD among all three sites and excited ICD among the outer QDs engage. Rates for all processes are found to be extremely low, although ICD rates with two neighbors are predicted to double compared to ICD among two sites only. The slowing is caused by Coulomb barriers imposed from ground or excited state electrons in the A sites. Outliers occur on the one hand at short distances, where the charge transfer among QDs mixes the possible decay pathways. On the other hand, we discovered a shape resonance-enhanced DE-ICD pathway, in which an excited and localized B* shape resonance state forms, which is able to decay quickly into the final ICD continuum.

Quantum-Compute Algorithm for Exact Laser-Driven Electron Dynamics in Molecules.

In this work, we investigate the capability of known quantum computing algorithms for fault-tolerant quantum computing to simulate the laser-driven electron dynamics of excitation and ionization processes in small molecules such as lithium hydride, which can be benchmarked against the most accurate time-dependent full configuration interaction (TD-FCI) calculations. The conventional TD-FCI wave packet propagation is reproduced using the Jordan-Wigner transformation for wave function and operators and the Trotter product formula for expressing the propagator. In addition, the time-dependent dipole moment, as an example of a time-dependent expectation value, is calculated using the Hadamard test. To include non-Hermitian operators in the ionization dynamics, a similar approach to the quantum imaginary time evolution (QITE) algorithm is employed to translate the propagator, including a complex absorption potential, into quantum gates. The computations are executed on a quantum computer simulator. By construction, all quantum computer algorithms, except for the QITE algorithm used only for ionization but not for excitation dynamics, would scale polynomially on a quantum computer with fully entangled qubits. In contrast, TD-FCI scales exponentially. Hence, quantum computation holds promises for substantial progress in the understanding of electron dynamics of excitation processes in increasingly large molecular systems, as has already been witnessed in electronic structure theory.

Early dynamics of the emission of solvated electrons from nanodiamonds in water.

Solvated electrons are among the most reductive species in an aqueous environment. Diamond materials have been proposed as a promising source of solvated electrons, but the underlying emission process in water remains elusive so far. Here, we show spectroscopic evidence for the emission of solvated electrons from detonation nanodiamonds upon excitation with both deep ultraviolet (225 nm) and visible (400 nm) light using ultrafast transient absorption. The crucial role of surface termination in the emission process is evidenced by comparing hydrogenated, hydroxylated and carboxylated nanodiamonds. In particular, a transient response that we attribute to solvated electrons is observed on hydrogenated nanodiamonds upon visible light excitation, while it shows a sub-ps recombination due to trap states when excited with deep ultraviolet light. The essential role of surface reconstructions on the nanodiamonds in these processes is proposed based on density functional theory calculations. These results open new perspectives for solar-driven emission of solvated electrons in an aqueous phase using nanodiamonds.

Graph Neural Networks for Learning Molecular Excitation Spectra.

Machine learning (ML) approaches have demonstrated the ability to predict molecular spectra at a fraction of the computational cost of traditional theoretical chemistry methods while maintaining high accuracy. Graph neural networks (GNNs) are particularly promising in this regard, but different types of GNNs have not yet been systematically compared. In this work, we benchmark and analyze five different GNNs for the prediction of excitation spectra from the QM9 dataset of organic molecules. We compare the GNN performance in the obvious runtime measurements, prediction accuracy, and analysis of outliers in the test set. Moreover, through TMAP clustering and statistical analysis, we are able to highlight clear hotspots of high prediction errors as well as optimal spectra prediction for molecules with certain functional groups. This in-depth benchmarking and subsequent analysis protocol lays down a recipe for comparing different ML methods and evaluating dataset quality.

Constructing Binder- and Carbon Additive-Free Organosulfur Cathodes Based on Conducting Thiol-Polymers through Electropolymerization for Lithium-Sulfur Batteries.

Herein, the concept of constructing binder- and carbon additive-free organosulfur cathode was proved based on thiol-containing conducting polymer poly(4-(thiophene-3-yl) benzenethiol) (PTBT). The PTBT featured the polythiophene-structure main chain as a highly conducting framework and the benzenethiol side chain to copolymerize with sulfur and form a crosslinked organosulfur polymer (namely S/PTBT). Meanwhile, it could be in-situ deposited on the current collector by electro-polymerization, making it a binder-free and free-standing cathode for Li-S batteries. The S/PTBT cathode exhibited a reversible capacity of around 870 mAh g-1 at 0.1 C and improved cycling performance compared to the physically mixed cathode (namely S&PTBT). This multifunction cathode eliminated the influence of the additives (carbon/binder), making it suitable to be applied as a model electrode for operando analysis. Operando X-ray imaging revealed the remarkable effect in the suppression of polysulfides shuttle via introducing covalent bonds, paving the way for the study of the intrinsic mechanisms in Li-S batteries.

Effects of oxidative adsorbates and cluster formation on the electronic structure of nanodiamonds.

Nanodiamonds (NDs) are modern high-potential materials relevant for applications in biomedicine, photocatalysis, and various other fields. Their electronic surface properties, especially in the liquid phase, are key to their function in the applications, but we show that they are sensitively modified by their interactions with the environment. Two important interaction modes are those with oxidative aqueous adsorbates as well as ND self-aggregation towards the formation of ND clusters. For planar diamond surfaces it is known that the electron density migrates from the diamond towards oxidative adsorbates, which is known as transfer doping. Here, we quantify this effect for highly curved NDs of varying sizes (35-147 C atoms) and surface terminations (H, OH, F), focusing on their interactions with the most abundant aqueous oxidative adsorbates (H3 O+ , O2 , O3 ). We prove that the concept of transfer doping stays valid for the case of the high-curvature NDs and can be tuned via the ND's specific properties. Secondly, we investigate the electronic structures of clusters of NDs which are known to form in particular in aqueous dispersions. Upon cluster formation, we find that the optical gaps of the structures are significantly reduced, which explains why different experimental values were obtained for the optical gap of the same structures, and the cluster's LUMO shapes resemble atom-type orbitals, as in the case of isolated spherical NDs. Our findings have implications for ND applications as photocatalysts or electronic devices, where the specific electronic properties are key to the functionality of the ND material.

Role of Dopants on the Local Electronic Structure of Polymeric Carbon Nitride Photocatalysts.

Polymeric carbon nitride (PCN) is a promising class of materials for solar-to-chemical energy conversion. The increase of the photocatalytic activity of PCN is often achieved by the incorporation of heteroatoms, whose impact on the electronic structure of PCN remains poorly explored. This work reveals that the local electronic structure of PCN is strongly altered by doping with sulfur and iron using X-ray absorption spectroscopy (XAS) and resonant inelastic X-ray scattering (RIXS). From XAS at the carbon and nitrogen K-edges, sulfur atoms are found to mostly affect carbon atoms, in contrast to iron doping mostly altering nitrogen sites. In RIXS at the nitrogen K-edge, a vibrational progression, affected by iron doping, is evidenced, which is attributed to a vibronic coupling between excited electrons in nitrogen atoms and C-N stretching modes in PCN heterocycling rings. This work opens new perspectives for the characterization of vibronic coupling in polymeric photocatalysts.

Combined first-principles statistical mechanics approach to sulfur structure in organic cathode hosts for polymer based lithium-sulfur (Li-S) batteries.

Polymer-based batteries that utilize organic electrode materials are considered viable candidates to overcome the common drawbacks of lithium-sulfur (Li-S) batteries. A promising cathode can be developed using a conductive, flexible, and free-standing polymer, poly(4-thiophen-3-yl)benzenethiol) (PTBT), as the sulfur host material. By a vulcanization process, sulfur is embedded into this polymer. Here, we present a combination of electronic structure theory and statistical mechanics to characterize the structure of the initial state of the charged cathode on an atomic level. We perform a stability analysis of differently sulfurized TBT dimers as the basic polymer unit calculated within density-functional theory (DFT) and combine this with a statistical binding model for the binding probability distributions of the vulcanization process. From this, we deduce sulfur chain length ("rank") distributions and calculate the average sulfur rank depending on the sulfur concentration and temperature. This multi-scale approach allows us to bridge the gap between the local description of the covalent bonding process and the derivation of the macroscopic properties of the cathode. Our calculations show that the main reaction of the vulcanization process leads to high-probability states of sulfur chains cross-linking TBT units belonging to different polymer backbones, with a dominant rank around n = 5. In contrast, the connection of adjacent TBT units of the same polymer backbone by a sulfur chain is the side reaction. These results are experimentally supported by Raman spectroscopy.

Atomistic Simulations of Laser-Controlled Exciton Transfer and Stabilization in Symmetric Double Quantum Dots.

The creation, transfer, and stabilization of localized excitations are studied in a donor-acceptor Frenkel exciton model in an atomistic treatment of reduced-size double quantum dots (QDs) of various sizes. The explicit time-dependent dynamics simulations carried out by hybrid time-dependent density functional theory/configuration interaction show that laser-controlled hole trapping in stacked, coupled germanium/silicon quantum dots can be achieved by a UV/IR pump-dump pulse sequence. The first UV excitation creates an exciton localized on the topmost QD and after some coherent transfer time, an IR pulse dumps and localizes an exciton in the bottom QD. While hole trapping is observed in each excitation step, we show that the stability of the localized electron depends on its multiexcitonic character. We present how size and geometry variations of three Ge/Si nanocrystals influence transfer times and thus the efficiency of laser-driven populations of the electron-hole pair states.

Three-electron dynamics of the interparticle Coulombic decay with two-dimensional continuum confinement.

In a pair of self-assembled or gated laterally arranged quantum dots, an electronically excited state can undergo interparticle Coulombic decay. Then, an electron from a neighbor quantum dot is emitted into the electronic continuum along the two available dimensions. This study proves that the process is not only operative among two but also among three quantum dots, where a second electron-emitting dot causes a rate increase by a factor of two according to the predictions from the analytical Wigner-Weisskopf rate equation. The predictions hold over the complete range of conformation angles among the quantum dots and over a large range of distances. Electron dynamics was calculated by multiconfiguration time-dependent Hartree and is, irrespective of the large number of discrete variable representation grid points, feasible after having developed an OpenACC graphic card compilation of the program.

Predicting the performance of the inter-Coulombic electron capture from single-electron quantities.

The probability of the inter-Coulombic electron capture (ICEC) is studied for nanowire-embedded quantum-dot pairs where electron capture in one dot leads to electron emission from the other. Previous studies pointed to an interdependence of several ICEC pathways which can enhance the ICEC reaction probability. To identify favorable criteria for such synergies in a qualitative and quantitative manner, we conducted a considerable amount of simulations scanning multiple geometrical parameters. The focus of the paper is not only to find the geometries which are most favorable to ICEC but most importantly to explain the basic principles of the ICEC probability. We have thus derived a number of energy relations among solely single-electron level energies that explain the mechanisms of the multiple reaction pathways. Among them are direct ICEC, both slowing or accelerating the outgoing electron, as well as resonance-enhanced ICEC which captures into a two-electron resonance state that decays thereafter. These pathways may apply simultaneously for just one single geometric configuration and contribute constructively leading to an enhancement of the reaction probability. Likewise some conditions are found that clearly turn down the ICEC probability to zero. The results based on single-electron relations are so general that they can as well be used to predict the ICEC probability from the electronic structure in arbitrary physical systems such as atoms or molecules.

Quantum size effect affecting environment assisted electron capture in quantum confinements.

Ultrafast inter-Coulombic electron capture (ICEC) has been established as an important energy-transfer process in open paired-quantum-dot systems which can mediate between entrapment of free-moving electrons and release of trapped ones elsewhere by long-range electron-electron interaction within nanowires. Previous studies indicated ICEC enhancement through population and secondary decay of two-center resonance states, the latter known as inter-Coulombic decay (ICD). This study investigates the quantum-size effect of single- and double-electron states in an established model of a quasi-one-dimensional nanowire with two embedded confinement sites, represented by a pair of Gaussian wells. We analyze the ICEC related electron flux density as a function of confinement size and are able to clearly identify two distinct capture channels: a direct long-range electron-electron impulse and a conversion of kinetic energy to electron-electron correlation energy with consecutive ICD. The overlay of both channels makes ICEC extremely likely, while nanowires are a strong candidate for the next miniaturization step of integrated-circuit components.

Effects of temperature and pressure on the optical and vibrational properties of thermoelectric SnSe.

We have conducted a comprehensive investigation of the optical and vibrational properties of the binary semiconductor SnSe as a function of temperature and pressure by means of experimental and ab initio probes. Our high-temperature investigations at ambient pressure have successfully reproduced the progressive enhancement of the free carrier concentration upon approaching the Pnma → Bbmm transition, whereas the pressure-induced Pnma → Bbmm transformation at ambient temperature, accompanied by an electronic semiconductor → semi-metal transition, has been identified for bulk SnSe close to 10 GPa. Modeling of the Raman-active vibrations revealed that three-phonon anharmonic processes dominate the temperature-induced mode frequency evolution. In addition, SnSe was found to exhibit a pressure-induced enhancement of the Born effective charge. Such behavior is quite unique and cannot be rationalized within the proposed effective charge trends of binary materials under pressure.

Theoretical X-ray absorption spectroscopy database analysis for oxidised 2D carbon nanomaterials.

In this work we provide a proof of principle for a theoretical methodology to identify functionalisation patterns in oxidised carbon 2D nanomaterials. The methodology is based on calculating a large number of X-ray absorption spectra of individually excited carbon atoms in different chemical environments using density functional theory. Since each resulting spectrum gives a fingerprint of the local electronic structure surrounding the excited atom, we may relate each spectrum to the functionalisation pattern of that excited atom up to a desired neighbourhood radius. These functionalisation pattern-specific spectra are collected in a database, that allows fast composition of X-ray absorption spectra for arbitrary structures in density functional theory quality. Finally, we present an exemplary application of the database approach to estimate the relative amount of functional groups in two different experimental samples of carbon nanomaterials.