The photochemistry of Rydberg-excited cyclobutanone: Photoinduced processes and ground state dynamics.

Owing to ring strain, cyclic ketones exhibit complex excited state dynamics with multiple competing photochemical channels active on the ultrafast timescale. While the excited state dynamics of cyclobutanone after π* ← n excitation into the lowest-energy excited singlet (S1) state has been extensively studied, the dynamics following 3s ← n excitation into the higher-lying singlet Rydberg (S2) state are less well understood. Herein, we employ fully quantum multiconfigurational time-dependent Hartree (MCTDH) simulations using a model Hamiltonian as well as "on-the-fly" trajectory-based surface-hopping dynamics (TSHD) simulations to study the relaxation dynamics of cyclobutanone following 3s ← n excitation and to predict the ultrafast electron diffraction scattering signature of these relaxation dynamics. Our MCTDH and TSHD simulations indicate that relaxation from the initially-populated singlet Rydberg (S2) state occurs on the timescale of a few hundreds of femtoseconds to a picosecond, consistent with the symmetry-forbidden nature of the state-to-state transition involved. There is no obvious involvement of excited triplet states within the timeframe of our simulations (<2 ps). After non-radiative relaxation to the electronic ground state (S0), vibrationally hot cyclobutanone has sufficient internal energy to form multiple fragmented products including C2H4 + CH2CO (C2; 20%) and C3H6 + CO (C3; 2.5%). We discuss the limitations of our MCTDH and TSHD simulations, how these may influence the excited state dynamics we observe, and-ultimately-the predictive power of the simulated experimental observable.

Direct observation of ultrafast exciton localization in an organic semiconductor with soft X-ray transient absorption spectroscopy.

The localization dynamics of excitons in organic semiconductors influence the efficiency of charge transfer and separation in these materials. Here we apply time-resolved X-ray absorption spectroscopy to track photoinduced dynamics of a paradigmatic crystalline conjugated polymer: poly(3-hexylthiophene) (P3HT) commonly used in solar cell devices. The π→π* transition, the first step of solar energy conversion, is pumped with a 15 fs optical pulse and the dynamics are probed by an attosecond soft X-ray pulse at the carbon K-edge. We observe X-ray spectroscopic signatures of the initially hot excitonic state, indicating that it is delocalized over multiple polymer chains. This undergoes a rapid evolution on a sub 50 fs timescale which can be directly associated with cooling and localization to form either a localized exciton or polaron pair.

Accurate, affordable, and generalizable machine learning simulations of transition metal x-ray absorption spectra using the XANESNET deep neural network.

The affordable, accurate, and generalizable prediction of spectroscopic observables plays a key role in the analysis of increasingly complex experiments. In this article, we develop and deploy a deep neural network-XANESNET-for predicting the lineshape of first-row transition metal K-edge x-ray absorption near-edge structure (XANES) spectra. XANESNET predicts the spectral intensities using only information about the local coordination geometry of the transition metal complexes encoded in a feature vector of weighted atom-centered symmetry functions. We address in detail the calibration of the feature vector for the particularities of the problem at hand, and we explore the individual feature importance to reveal the physical insight that XANESNET obtains at the Fe K-edge. XANESNET relies on only a few judiciously selected features-radial information on the first and second coordination shells suffices along with angular information sufficient to separate satisfactorily key coordination geometries. The feature importance is found to reflect the XANES spectral window under consideration and is consistent with the expected underlying physics. We subsequently apply XANESNET at nine first-row transition metal (Ti-Zn) K-edges. It can be optimized in as little as a minute, predicts instantaneously, and provides K-edge XANES spectra with an average accuracy of ∼±2%-4% in which the positions of prominent peaks are matched with a >90% hit rate to sub-eV (∼0.8 eV) error.

Vibrational Coherence Spectroscopy Identifies Ultrafast Branching in an Iron(II) Sensitizer.

The introduction of N-heterocyclic carbene ligands has greatly increased the lifetimes of metal-to-ligand charge transfer states (MLCT) in iron(II) complexes, making them promising candidates for photocatalytic applications. However, the spectrally elusive triplet metal-centered state (3MC) has been suggested to play a decisive role in the relaxation of the MLCT manifold to the ground state, shortening their lifetimes and consequently limiting the application potential. In this work, time-resolved vibrational spectroscopy and quantum chemical calculations are applied to shed light on the 3MCs' involvement in the deactivation of the MLCT manifold of an iron(II) sensitizer. Two distinct symmetric Fe-L breathing vibrations at frequencies below 150 cm-1 are assigned to the 3MC and 3MLCT states by quantum chemical calculations. On the basis of this assignment, an ultrafast branching directly after excitation forms not only the long-lived 3MLCT but also the 3MC as an additional loss channel.

Progress in the Theory of X-ray Spectroscopy: From Quantum Chemistry to Machine Learning and Ultrafast Dynamics.

The development of high-brilliance third- and fourth-generation light sources such as synchrotrons and X-ray free-electron lasers (XFELs), the emergence of laboratory-based X-ray spectrometers, and instrumental and methodological advances in X-ray absorption (XAS) and (non)resonant emission (XES and RXES/RIXS) spectroscopies have had far-reaching effects across the natural sciences. However, new kinds of experiments, and their ever-higher resolution and data acquisition rates, have brought acutely into focus the challenge of accurately, quickly, and cost-effectively analyzing the data; a far-from-trivial task that demands detailed theoretical calculations that are capable of capturing satisfactorily the underlying physics. The past decade has seen significant advances in the theory of core-hole spectroscopies for this purpose, driven by all of the developments above and-crucially-a surge in demand. In this Perspective, we discuss the challenges of calculating core-excited states and spectra, and state-of-the-art developments in electronic structure theory, dynamics, and data-driven/machine-led approaches toward their better description.

A Deep Neural Network for the Rapid Prediction of X-ray Absorption Spectra.

X-ray spectroscopy delivers strong impact across the physical and biological sciences by providing end users with highly detailed information about the electronic and geometric structure of matter. To decode this information in challenging cases, e.g., in operando catalysts, batteries, and temporally evolving systems, advanced theoretical calculations are necessary. The complexity and resource requirements often render these out of reach for end users, and therefore, the data are often not interpreted exhaustively, leaving a wealth of valuable information unexploited. In this paper, we introduce supervised machine learning of X-ray absorption spectra through the development of a deep neural network (DNN) that is able to estimate Fe K-edge X-ray absorption near-edge structure spectra in less than a second with no input beyond geometric information about the local environment of the absorption site. We predict peak positions with sub-eV accuracy and peak intensities with errors over an order of magnitude smaller than the spectral variations that the model is engineered to capture. The performance of the DNN is promising, as illustrated by its application to the structural refinement of tris(bipyridine)iron(II) and nitrosylmyoglobin, but also highlights areas on which future developments should focus.

Ultrafast nonadiabatic dynamics probed by nitrogen K-edge absorption spectroscopy.

The emergence of X-ray free electron lasers (X-FELs) has made it possible to probe structural dynamics on the femtosecond timescale. This extension of experimental capabilities also calls for a simultaneous development in theory to help interpret the underlying structure and dynamics encoded within the experimental observable. In the ultrafast regime this often requires a time-dependent theoretical treatment that describes nuclear dynamics beyond the Born-Oppenheimer approximation. In this work, we perform quantum dynamics simulations based upon time-evolving Gaussian basis functions (GBFs) and simulate the ultrafast X-ray Absorption Near-Edge Structure (XANES) spectra of photoexcited pyrazine including two strongly coupled electronically excited states and four normal mode degrees of freedom. Two methods to simulate the excited state XANES spectra are applied, the first is based upon the multi-configurational second order perturbation theory restricted active space (RASPT2) method and the second uses a combination of the maximum overlap method (MOM) and time-dependent density functional theory (TDDFT). We demonstrate that despite the simplicity of the MOM/TDDFT method, it captures several qualitative features of the RASPT2 simulations at much reduced computational effort. However, features such as the conical intersection are a particular exception as they require a multi-configurational treatment. For the nuclear dynamics, we demonstrate that even a small number of GBFs can provide reasonable description of the spectroscopic observable. This work provides perspectives for computationally efficient approaches important for addressing larger systems.

Understanding the potential for efficient triplet harvesting with hot excitons.

Excited state energy transfer in disordered systems has attracted significant attention owing to the importance of this phenomenon in both artificial and natural systems that operate in electronically excited states. Of particular interest, especially in the context of organic electronics, is the dynamics of triplet excited states. Due to their weak coupling to the singlet manifold they can often act as low energy trapping sites and are therefore detrimental to device performance. Alternatively, by virtue of their long lifetime they can lead to enhanced diffusion lengths important for organic photovoltaics (OPV). Herein, we explore the triplet energy transfer mechanism from dichlorobenzene to thioxanthone in methanol solution. We rationalise previous experimental observations as arising from preferential population transfer into the lowest triplet state rather than the higher lying triplet state that is closer in energy. The reason for this is a delicate balance between the electronic coupling, reorganisation energy and the energy gap involved. The present results provide the understanding to potentially develop a hot exciton mechanism in materials for organic light emitting diodes (OLED) to achieve higher device efficiencies.

Excited State Intramolecular Proton Transfer Dynamics for Triplet Harvesting in Organic Molecules.

Thermally activated delayed fluorescence (TADF) has shown great potential as a mechanism for harvesting low-lying triplet excited states in organic molecules and is therefore of great interest in the context of organic electronics, especially organic light emitting diodes (OLEDs). Herein we study the mechanism for triplet harvesting in triquinolonobenzene (TQB), which instead of relying upon the well-established donor-acceptor (D-A) scheme uses excited-state intramolecular proton transfer (ESIPT). We demonstrate that upon photoexcitation into the lowest singlet excited state the proton is transferred within 20 fs, suggesting it plays little role in triplet harvesting, which occurs on the nano- to microsecond time scale. However, TQB exhibits multiple low-lying triplet states that are strongly coupled along this proton transfer coordinate. The majority of these states favor the structure prior to proton transfer (TQB-TA) and this means that the proton transfer dynamics (3TQB-TA → 1TQB-TB) plays a crucial role in triplet harvesting. This mechanism yields an energy gap in good agreement with that reported experimentally and is consistent with previous photophysical characterization. Finally, a discussion upon extending this understanding into a device context is also presented.

Non-equilibrium x-ray spectroscopy using direct quantum dynamics.

Advances in experimental methodology aligned with technological developments, such as 3rd generation light sources, X-ray Free Electron Lasers, and High Harmonic Generation, have led to a paradigm shift in the capability of X-ray spectroscopy to deliver high temporal and spectral resolution on an extremely broad range of samples in a wide array of different environments. Importantly, the complex nature and high information content of this class of techniques mean that detailed theoretical studies are often essential to provide a firm link between the spectroscopic observables and the underlying molecular structure and dynamics. In this paper, we present approaches for simulating dynamical processes in X-ray spectroscopy based upon on-the-fly quantum dynamics with a Gaussian basis set. We show that it is possible to provide a fully quantum description of X-ray spectra without the need of precomputing highly multidimensional potential energy surfaces. It is applied to study two different dynamical situations, namely, the core-hole lifetime dynamics of the water monomer and the dissociation of C F 4 + recently studied using pump-probe X-ray spectroscopy. Our results compare favourably to previous experiments, while reducing the computational effort, providing the scope to apply them to larger systems.

The intersystem crossing of a cyclic (alkyl)(amino) carbene gold (i) complex.

The intersystem crossing (ISC) mechanism of a cyclic (alkyl)(amino) carbene gold (I) complex (CMA1) is studied using quantum dynamics. A model spin-vibronic Hamiltonian is developed, which includes 10 excited states and two important nuclear degrees of freedom. The quantum dynamics reveals that ISC from S1 → T1 occurs on the tens of picosecond time scale, consistent with recent experiments. It is driven by motion along the torsional degree of freedom of the carbazole (Cz) ligand, which causes orthogonality between the donor and acceptor groups closing the gap between the initial (S1) and final (T1) states. The role of higher triplet states through spin-vibronic interactions is also discussed. Although previous calculations, evaluated in the Condon approximation, yield large ISC rates, our present dynamical treatment, taking into account the large amplitude torsional motion, increases the calculated rate by an order of magnitude improving the agreement with experiments. The model spin-vibronic Hamiltonian developed can also be used to understand the properties of related linear metal carbene compounds, facilitating molecular design.

The theory of thermally activated delayed fluorescence for organic light emitting diodes.

The interest in organic molecules exhibiting thermally activated delayed fluorescence (TADF) has been reinvigorated in recent years owing to their potential to be exploited as emitters in highly efficient purely organic light emitting diodes (OLEDs). However, designing new molecules that exhibit efficient TADF is a non-trivial task because they would appear to require the optimisation of a number of contrasting properties. For example these molecules must exhibit rapid conversion between the singlet and triplet manifolds without the use of heavy elements to enhance spin-orbit coupling. They should also display a large fluorescence rate, but simultaneously a small energy gap between low lying singlet and triplet states. Consequently to achieve systematic material design, a detailed understanding of the fundamental factors influencing the photophysical behaviour of TADF emitters is essential. Towards achieving this goal, theory and computation is playing a crucial role. In this feature article the recent progress in the theory of organic TADF molecules in the context of OLEDs is presented, with a view of achieving a deeper understanding of these molecules and driving systematic material design.

Photophysics of a copper phenanthroline elucidated by trajectory and wavepacket-based quantum dynamics: a synergetic approach.

On-the-fly excited state molecular dynamics is a valuable method for studying non-equilibrium processes in excited states and is beginning to emerge as a mature approach much like its ground state counterparts. In contrast to quantum wavepacket dynamics methods, it negates the need for modelling potential energy surfaces, which usually confine nuclear motion within a reduced number of vibrational modes. In addition, on-the-fly molecular dynamics techniques are easily combined with the atomistic description of the solvents (through the QM/MM approach) making it possible to explicitly address the effect of the environment. Herein, we study the nonadiabatic relaxation of photoexcited [Cu(dmp)2]+ (dmp = 2,9-dimethyl-1,10-phenanthroline) using QM/MM Trajectory Surface Hopping (TSH). We show that the decay of the initially excited singlet state into the lowest singlet (S1) state occurs within 100 fs, in agreement with previous experiments, and is slightly influenced by the solvent. Using a principal component analysis (PCA), we also identify the dominant normal modes activated during the excited state decay, which are then used to design the vibronic Hamiltonian for quantum wavepacket dynamics simulations.

Accelerating direct quantum dynamics using graphical processing units.

Methods using a swarm of Gaussian basis functions to represent the nuclear wavefunction are a very appealing way to solve the time-dependent Schrödinger equation (TDSE) as they avoid the conventional scaling bottleneck of grid-based methods and provide a grid-free trajectory representation of the dynamics understudy. When coupled with direct (on-the-fly) dynamics, these methods offer the ability to simulate quantum dynamics of larger systems in full nuclear configuration space and avoid the requirement of a priori fitting of a potential energy surface. During such simulations, it is often assumed that the limiting factor is the computational cost of the quantum chemistry calculations. To combat this, in the present paper the direct dynamics variational multi-configurational Gaussian (DD-vMCG) method is combined with electronic structure calculations accelerated by Graphical Processing Units (GPUs). For the systems studied, a protonated ammonia dimer and the imidazole dimer, it is shown that the cost of the term responsible for the quantum behaviour of the nuclear dynamics means that the computational time associated with the quantum chemistry quickly becomes a small part of the overall computational time. Using these simulations, an estimated scaling of the vMCG method, with respect to the number of Gaussian basis functions is reported. This can be used to identify when quantum chemistry is the limiting factor and when GPU acceleration will have a significant effect for both ground and excited state simulations.

Nonadiabatic coupling reduces the activation energy in thermally activated delayed fluorescence.

The temperature dependent rate of a thermally activated process is given by the Arrhenius equation. The exponential decrease in the rate with activation energy, which this imposes, strongly promotes processes with small activation barriers. This criterion is one of the most challenging during the design of thermally activated delayed fluorescence (TADF) emitters used in organic light emitting diodes. The small activation energy is usually achieved with donor-acceptor charge transfer complexes. However, this sacrifices the radiative rate and is therefore incommensurate with the high luminescence quantum yields required for applications. Herein we demonstrate that the spin-vibronic mechanism, operative for efficient TADF, overcomes this limitation. Nonadiabatic coupling between the lowest two triplet states give rise to a strong enhancement of the rate of reserve intersystem crossing via a second order mechanism and promotes population transfer between the T1 to T2 states. Consequently the rISC mechanism is actually operative between initial and final state exhibiting an energy gap that is smaller than between the T1 and S1 states. This contributes to the small activation energies for molecules exhibiting a large optical gap, identifies limitations of the present design procedures and provides a basis from which to construct TADF molecules with simultaneous high radiative and rISC rates.

Probing spin-vibronic dynamics using femtosecond X-ray spectroscopy.

Ultrafast pump-probe spectroscopy within the X-ray regime is now possible owing to the development of X-ray Free Electrons Lasers (X-FELs) and is opening new opportunities for the direct probing of femtosecond evolution of the nuclei, the electronic and spin degrees of freedom. In this contribution we use wavepacket dynamics of the photoexcited decay of a new Fe(ii) complex, [Fe(bmip)2]2+ (bmip = 2,6-bis(3-methyl-imidazole-1-ylidine)pyridine), to simulate the experimental observables associated with femtosecond Fe K-edge X-ray Absorption Near-Edge Structure (XANES) and X-ray emission (XES) spectroscopy. We show how the evolution of the nuclear wavepacket is translated into the spectroscopic signal and the sensitivity of these approaches for following excited state dynamics.

Theoretical Rationalization of the Emission Properties of Prototypical Cu(I)-Phenanthroline Complexes.

The excited state properties of transition metal complexes have become a central focus of research owing to a wide range of possible applications that seek to exploit their luminescence properties. Herein, we use density functional theory (DFT), time-dependent DFT (TDDFT), classical and quantum mechanics/molecular mechanics (QM/MM) molecular dynamics (MD) simulations to provide a full understanding on the role of the geometric and electronic structure, spin-orbit coupling, singlet-triplet gap and the solvent environment on the emission properties of nine prototypical copper(I)-phenanthroline complexes. Our calculations reveal clear trends in the electronic properties that are strongly correlated to the luminescence properties, allowing us to rationalize the role of specific structural modifications. The MD simulations show, in agreement with recent experimental observations, that the lifetime shortening of the excited triplet state in donor solvents (acetonitrile) is not due to the formation of an exciplex. Instead, the solute-solvent interaction is transient and arises from solvent structures that are similar to the ones already present in the ground state. These results based on a subset of the prototypical mononuclear Cu(I) complexes shed general insight into these complexes that may be exploited for development of mononuclear Cu(I) complexes for applications as, for example, emitters in third generation OLEDs.

A quantum dynamics study of the ultrafast relaxation in a prototypical Cu(I)-phenanthroline.

The ultrafast nonadiabatic dynamics of a prototypical Cu(I)-phenanthroline complex, [Cu(dmp)2](+) (dmp = 2,9-dimethyl-1,10-phenanthroline), initiated after photoexcitation into the optically bright metal-to-ligand charge-transfer (MLCT) state (S3) is investigated using quantum nuclear dynamics. In agreement with recent experimental conclusions, we find that the system undergoes rapid (∼100 fs) internal conversion from S3 into the S2 and S1 states at or near the Franck-Condon (FC) geometry. This is preceded by a dynamic component with a time constant of ∼400 fs, which corresponds to the flattening of the ligands associated with the pseudo Jahn-Teller distortion. Importantly, our simulations demonstrate that this latter aspect is in competition with subpicosecond intersystem crossing (ISC). The mechanism for ISC is shown to be a dynamic effect, in the sense that it arises from the system traversing the pseudo Jahn-Teller coordinate where the singlet and triplet states become degenerate, leading to efficient crossing. These first-principles quantum dynamics simulations, in conjunction with recent experiments, allow us to clearly resolve the mechanistic details of the ultrafast dynamics within [Cu(dmp)2](+), which have been disputed in the literature.

X-ray spectroscopic study of solvent effects on the ferrous and ferric hexacyanide anions.

We present an Fe Kα resonant inelastic X-ray scattering (RIXS) and X-ray emission (XES) study of ferrous and ferric hexacyanide dissolved in water and ethylene glycol. We observe that transitions below the absorption edge show that the solvent has a distinct effect on the valence electronic structure. In addition, both the RIXS and XES spectra show a stabilization of the 2p levels when dissolved in water. Using molecular dynamics simulations, we propose that this effect arises from the hydrogen-bonding interactions between the complex and nearby solvent molecules. This withdraws electron density from the ligands, stabilizing the complex but also causing a slight increase in π-backbonding.

Photooxidation and photoaquation of iron hexacyanide in aqueous solution: A picosecond X-ray absorption study.

We present a picosecond Fe K-edge absorption study of photoexcited ferrous and ferric hexacyanide in water under 355 and 266 nm excitation. Following 355 nm excitation, the transient spectra for the ferrous and ferric complexes exhibit a red shift of the edge reflecting an increased electron density at the Fe atom. For the former, an enhanced pre-edge transition is also observed. These observations are attributed to the aquated [Fe(CN)5OH2](3-) species, based on quantum chemical calculations which also provide structural parameters. Upon 266 nm excitation of the ferric complex, a transient reminiscent of the aquated species is observed (appearance of a pre-edge feature and red shift of the edge) but it is different from that obtained under 355 nm excitation. This points to a new reaction channel occurring through an intermediate state lying between these two excitation energies. Finally, 266 nm excitation of the ferrous species is dominated by the photooxidation channel with formation of the ferric complex as main photoproduct. However, we observe an additional minor photoproduct, which is identical to the 266 nm generated photoproduct of the ferric species, suggesting that under our experimental conditions, the pump pulse photooxidises the ferrous complex and re-excites the primary ferric photoproduct.