Mind the GAP: quantifying the breakdown of the linear vibronic coupling Hamiltonian.

Excited state dynamics play a critical role across a broad range of scientific fields. Importantly, the highly non-equilibrium nature of the states generated by photoexcitation means that excited state simulations should usually include an accurate description of the coupled electronic-nuclear motion, which often requires solving the time-dependent Schrödinger equation (TDSE). One of the biggest challenges for these simulations is the requirement to calculate the PES over which the nuclei evolve. An effective approach for addressing this challenge is to use the approximate linear vibronic coupling (LVC) Hamiltonian, which enables a model potential to be parameterised using relatively few quantum chemistry calculations. However, this approach is only valid provided there are no large amplitude motions in the excited state dynamics. In this paper we introduce and deploy a metric, the global anharmonicity parameter (GAP), which can be used to assess the accuracy of an LVC potential. Following its derivation, we illustrate its utility by applying it to three molecules exhibiting different rigidity in their excited states.

An on-the-fly deep neural network for simulating time-resolved spectroscopy: predicting the ultrafast ring opening dynamics of 1,2-dithiane.

Revolutionary developments in ultrafast light source technology are enabling experimental spectroscopists to probe the structural dynamics of molecules and materials on the femtosecond timescale. The capacity to investigate ultrafast processes afforded by these resources accordingly inspires theoreticians to carry out high-level simulations which facilitate the interpretation of the underlying dynamics probed during these ultrafast experiments. In this Article, we implement a deep neural network (DNN) to convert excited-state molecular dynamics simulations into time-resolved spectroscopic signals. Our DNN is trained on-the-fly from first-principles theoretical data obtained from a set of time-evolving molecular dynamics. The train-test process iterates for each time-step of the dynamics data until the network can predict spectra with sufficient accuracy to replace the computationally intensive quantum chemistry calculations required to produce them, at which point it simulates the time-resolved spectra for longer timescales. The potential of this approach is demonstrated by probing dynamics of the ring opening of 1,2-dithiane using sulphur K-edge X-ray absorption spectroscopy. The benefits of this strategy will be more markedly apparent for simulations of larger systems which will exhibit a more notable computational burden, making this approach applicable to the study of a diverse range of complex chemical dynamics.

Beyond structural insight: a deep neural network for the prediction of Pt L2/3-edge X-ray absorption spectra.

X-ray absorption spectroscopy at the L2/3 edge can be used to obtain detailed information about the local electronic and geometric structure of transition metal complexes. By virtue of the dipole selection rules, the transition metal L2/3 edge usually exhibits two distinct spectral regions: (i) the "white line", which is dominated by bound electronic transitions from metal-centred 2p orbitals into unoccupied orbitals with d character; the intensity and shape of this band consequently reflects the d density of states (d-DOS), which is strongly modulated by mixing with ligand orbitals involved in chemical bonding, and (ii) the post-edge, where oscillations encode the local geometric structure around the X-ray absorption site. In this Article, we extend our recently-developed XANESNET deep neural network (DNN) beyond the K-edge to predict X-ray absorption spectra at the Pt L2/3 edge. We demonstrate that XANESNET is able to predict Pt L2/3 -edge X-ray absorption spectra, including both the parts containing electronic and geometric structural information. The performance of our DNN in practical situations is demonstrated by application to two Pt complexes, and by simulating the transient spectrum of a photoexcited dimeric Pt complex. Our discussion includes an analysis of the feature importance in our DNN which demonstrates the role of key features and assists with interpreting the performance of the network.

Enhancing the analysis of disorder in X-ray absorption spectra: application of deep neural networks to T-jump-X-ray probe experiments.

Many chemical and biological reactions, including ligand exchange processes, require thermal energy for the reactants to overcome a transition barrier and reach the product state. Temperature-jump (T-jump) spectroscopy uses a near-infrared (NIR) pulse to rapidly heat a sample, offering an approach for triggering these processes and directly accessing thermally-activated pathways. However, thermal activation inherently increases the disorder of the system under study and, as a consequence, can make quantitative interpretations of structural changes challenging. In this Article, we optimise a deep neural network (DNN) for the instantaneous prediction of Co K-edge X-ray absorption near-edge structure (XANES) spectra. We apply our DNN to analyse T-jump pump/X-ray probe data pertaining to the ligand exchange processes and solvation dynamics of Co2+ in chlorinated aqueous solution. Our analysis is greatly facilitated by machine learning, as our DNN is able to predict quickly and cost-effectively the XANES spectra of thousands of geometric configurations sampled from ab initio molecular dynamics (MD) using nothing more than the local geometric environment around the X-ray absorption site. We identify directly the structural changes following the T-jump, which are dominated by sample heating and a commensurate increase in the Debye-Waller factor.

Using the Mechanical Bond to Tune the Performance of a Thermally Activated Delayed Fluorescence Emitter*.

We report the characterization of rotaxanes based on a carbazole-benzophenone thermally activated delayed fluorescence luminophore. We find that the mechanical bond leads to an improvement in key photophysical properties of the emitter, notably an increase in photoluminescence quantum yield and a decrease in the energy difference between singlet and triplet states, as well as fine tuning of the emission wavelength, a feat that is difficult to achieve when using covalently bound substituents. Computational simulations, supported by X-ray crystallography, suggest that this tuning of properties occurs due to weak interactions between the axle and the macrocycle that are enforced by the mechanical bond. This work highlights the benefits of using the mechanical bond to refine existing luminophores, providing a new avenue for emitter optimization that can ultimately increase the performance of these molecules.

Understanding and Designing Thermally Activated Delayed Fluorescence Emitters: Beyond the Energy Gap Approximation.

In this article recent progress in the development of molecules exhibiting Thermally Activated Delayed Fluorescence (TADF) is discussed with a particular focus upon their application as emitters in highly efficient organic light emitting diodes (OLEDs). The key aspects controlling the desirable functional properties, e. g. fast intersystem crossing, high radiative rate and unity quantum yield, are introduced with a particular focus upon the competition between the key requirements needed to achieve high performance OLEDs. The design rules required for organic and metal organic materials are discussed, and the correlation between them outlined. Recent progress towards understanding the influence of the interaction between a molecule and its environment are explained as is the role of the mechanism for excited state formation in OLEDs. Finally, all of these aspects are combined to discuss the ability to implement high level design rules for achieving higher quality materials for commercial applications. This article highlights the significant progress that has been made in recent years, but also outlines the significant challenges which persist to achieve a full understanding of the TADF mechanism and improve the stability and performance of these materials.

Spin-Vibronic Mechanism for Intersystem Crossing.

Intersystem crossing (ISC), formally forbidden within nonrelativistic quantum theory, is the mechanism by which a molecule changes its spin state. It plays an important role in the excited state decay dynamics of many molecular systems and not just those containing heavy elements. In the simplest case, ISC is driven by direct spin-orbit coupling between two states of different multiplicities. This coupling is usually assumed to remain unchanged by vibrational motion. It is also often presumed that spin-allowed radiationless transitions, i.e. internal conversion, and the nonadiabatic coupling that drives them, can be considered separately from ISC and spin-orbit coupling owing to the vastly different time scales upon which these processes are assumed to occur. However, these assumptions are too restrictive. Indeed, the strong mixing brought about by the simultaneous presence of nonadiabatic and spin-orbit coupling means that often the spin, electronic, and vibrational dynamics cannot be described independently. Instead of considering a simple ladder of states, as depicted in a Jablonski diagram, one must consider the more complicated spin-vibronic levels. Despite the basic ideas being outlined in the 1960s, it is only with the advent of high-level theory and femtosecond spectroscopy that the importance of the spin-vibronic mechanism for ISC in both fundamental as well as applied research fields has been revealed with significant impact across chemistry, physics, and biology. In this review article, we present the theory and fundamental principles of the spin-vibronic mechanism for ISC. This is followed by empirical rules to estimate the rate of ISC within this regime. The most recent developments in experimental techniques, theoretical methods, and models for the spin-vibronic mechanism are discussed. These concepts are subsequently illustrated with examples, including the ISC mechanisms in transition metal complexes, small organic molecules, and organic chromophores.

The Role of Structural Representation in the Performance of a Deep Neural Network for X-Ray Spectroscopy.

An important consideration when developing a deep neural network (DNN) for the prediction of molecular properties is the representation of the chemical space. Herein we explore the effect of the representation on the performance of our DNN engineered to predict Fe K-edge X-ray absorption near-edge structure (XANES) spectra, and address the question: How important is the choice of representation for the local environment around an arbitrary Fe absorption site? Using two popular representations of chemical space-the Coulomb matrix (CM) and pair-distribution/radial distribution curve (RDC)-we investigate the effect that the choice of representation has on the performance of our DNN. While CM and RDC featurisation are demonstrably robust descriptors, it is possible to obtain a smaller mean squared error (MSE) between the target and estimated XANES spectra when using RDC featurisation, and converge to this state a) faster and b) using fewer data samples. This is advantageous for future extension of our DNN to other X-ray absorption edges, and for reoptimisation of our DNN to reproduce results from higher levels of theory. In the latter case, dataset sizes will be limited more strongly by the resource-intensive nature of the underlying theoretical calculations.

On the geometry dependence of tuned-range separated hybrid functionals.

Molecules and materials that absorb and/or emit light form a central part of our daily lives. Consequently, a description of their excited-state properties plays a crucial role in designing new molecules and materials with enhanced properties. Due to its favorable balance between high computational efficiency and accuracy, time-dependent density functional theory (TDDFT) is often a method of choice for characterizing these properties. However, within standard approximations to the exchange-correlation functional, it remains challenging to achieve a balanced description of all excited states, especially for those exhibiting charge-transfer (CT) characteristics. In this work, we have applied two approaches, namely, the optimal tuning and triplet tuning methods, for a nonempirical definition of range-separated functionals to improve the description of excited states within TDDFT. This is applied to study the CT properties of two thermally activated delayed fluorescence emitters, namely, PTZ-DBTO2 and TAT-3DBTO2 . We demonstrate the connection between the two methods, the performance of each in the presence on multiple excited states of different characters and the geometry dependence of each method especially relevant in the context of developing size-consistent potential energy surfaces. © 2019 Wiley Periodicals, Inc.

Simulation of ultrafast excited-state dynamics and elastic x-ray scattering by quantum wavepacket dynamics.

Simulation of the ultrafast excited-state dynamics and elastic X-ray scattering of the [Fe(bmip)2]2+ [bmip = 2,6-bis(3-methyl-imidazole-1-ylidine)-4-pyridine] complex is presented and analyzed. We employ quantum wavepacket dynamics simulations on a 5-dimensional potential energy surface (PES) calculated by time-dependent density functional theory with 26 coupled diabatic states. The simulations are initiated by explicit inclusion of a time-dependent electromagnetic field. In the case of resonant excitation into singlet metal-to-ligand charge transfer (1MLCT) states, kinetic (exponential) population dynamics are observed with small nuclear motion. In agreement with transient optical absorption spectroscopy experiments, we observe a subpicosecond 1MLCT → 3MLCT intersystem crossing and a subsequent decay into triplet metal-centered (3MC) states on a picosecond time scale. The simulated time-resolved difference scattering signal is dominated by the 3MC component, for which the structural distortions are significant. On the other hand, excitation into 1MC states leads to ballistic (nonexponential) population dynamics with strong nuclear motion. The reason for these ballistic dynamics is that in this case, the excitation occurs into a nonequilibrium region, i.e., far from the minimum of the 1MC PES. This results in wavepacket dynamics along the principal breathing mode, which is clearly visible in both the population dynamics and difference scattering. Finally, the importance of decomposing the difference scattering into components by electronic states is highlighted, information which is not accessible from elastic X-ray scattering experiments.

1,2,4-Triazines in the Synthesis of Bipyridine Bisphenolate ONNO Ligands and Their Highly Luminescent Tetradentate Pt(II) Complexes for Solution-Processable OLEDs.

This article describes a convenient method for the synthesis of ONNO-type tetradentate 6,6'-bis(2-phenoxy)-2,2'-bipyridine (bipyridine bisphenolate, BpyBph) ligands and their platinum(II) complexes. The methodology includes the synthesis of 1,2,4-triazine precursors followed by their transformation to functionalized pyridines by the Boger reaction. Two complementary routes employing 3,3'- and 5,5'-bis-triazines allow a modification of the central pyridine rings in different positions, which was exemplified by the introduction of cyclopentene rings. The new ligands were used to prepare highly luminescent ONNO-type Pt(II) complexes. The position of the cyclopentene rings significantly influences the solubility and photophysical properties of these complexes. Derivatives with closely positioned cyclopentene rings are soluble in organic solvents and proved to be the best candidate for solution-processable organic light-emitting devices (OLEDs), showing efficient single-dopant candlelight electroluminescence.

NO binding kinetics in myoglobin investigated by picosecond Fe K-edge absorption spectroscopy.

Diatomic ligands in hemoproteins and the way they bind to the active center are central to the protein's function. Using picosecond Fe K-edge X-ray absorption spectroscopy, we probe the NO-heme recombination kinetics with direct sensitivity to the Fe-NO binding after 532-nm photoexcitation of nitrosylmyoglobin (MbNO) in physiological solutions. The transients at 70 and 300 ps are identical, but they deviate from the difference between the static spectra of deoxymyoglobin and MbNO, showing the formation of an intermediate species. We propose the latter to be a six-coordinated domed species that is populated on a timescale of ∼ 200 ps by recombination with NO ligands. This work shows the feasibility of ultrafast pump-probe X-ray spectroscopic studies of proteins in physiological media, delivering insight into the electronic and geometric structure of the active center.

Photoaquation Mechanism of Hexacyanoferrate(II) Ions: Ultrafast 2D UV and Transient Visible and IR Spectroscopies.

Ferrous iron(II) hexacyanide in aqueous solutions is known to undergo photoionization and photoaquation reactions depending on the excitation wavelength. To investigate this wavelength dependence, we implemented ultrafast two-dimensional UV transient absorption spectroscopy, covering a range from 280 to 370 nm in both excitation and probing, along with UV pump/visible probe or time-resolved infrared (TRIR) transient absorption spectroscopy and density functional theory (DFT) calculations. As far as photoaquation is concerned, we find that excitation of the molecule leads to ultrafast intramolecular relaxation to the lowest triplet state of the [Fe(CN)6]4- complex, followed by its dissociation into CN- and [Fe(CN)5]3- fragments and partial geminate recombination, all within <0.5 ps. The subsequent time evolution is associated with the [Fe(CN)5]3- fragment going from a triplet square pyramidal geometry, to the lowest triplet trigonal bipyramidal state in 3-4 ps. This is the precursor to aquation, which occurs in ∼20 ps in H2O and D2O solutions, forming the [Fe(CN)5(H2O/D2O)]3- species, although some aquation also occurs during the 3-4 ps time scale. The aquated complex is observed to be stable up to the microsecond time scale. For excitation below 310 nm, the dominant channel is photooxidation with a minor aquation channel. The photoaquation reaction shows no excitation wavelength dependence up to 310 nm, that is, it reflects a Kasha Rule behavior. In contrast, the photooxidation yield increases with decreasing excitation wavelength. The various intermediates that appear in the TRIR experiments are identified with the help of DFT calculations. These results provide a clear example of the energy dependence of various reactive pathways and of the role of spin-states in the reactivity of metal complexes.

Luminescent Gold(III) Thiolates: Supramolecular Interactions Trigger and Control Switchable Photoemissions from Bimolecular Excited States.

A new family of cyclometallated gold(III) thiolato complexes based on pyrazine-centred pincer ligands has been prepared, (C^Npz ^C)AuSR, where C^Npz ^C=2,6-bis(4-But C6 H4 )pyrazine dianion and R=Ph (1), C6 H4 tBu-4 (2), 2-pyridyl (3), 1-naphthyl (1-Np, 4), 2-Np (5), quinolinyl (Quin, 6), 4-methylcoumarinyl (Coum, 7) and 1-adamantyl (8). The complexes were isolated as yellow to red solids in high yields using mild synthetic conditions. The single-crystal X-ray structures revealed that the colour of the deep-red solids is associated with the formation of a particular type of short (3.2-3.3 Å) intermolecular pyrazine⋅⋅⋅pyrazine π-interactions. In some cases, yellow and red crystal polymorphs were formed; only the latter were emissive at room temperature. Combined NMR and UV/Vis techniques showed that the supramolecular π-stacking interactions persist in solution and give rise to intense deep-red photoluminescence. Monomeric molecules show vibronically structured green emissions at low temperature, assigned to ligand-based 3 IL(C^N^C) triplet emissions. By contrast, the unstructured red emissions correlate mainly with a 3 LLCT(SR→{(C^Npz ^C)2 }) charge transfer transition from the thiolate ligand to the π⋅⋅⋅π dimerized pyrazine. Unusually, the π-interactions can be influenced by sample treatment in solution, such that the emissions can switch reversibly from red to green. To our knowledge this is the first report of aggregation-enhanced emission in gold(III) chemistry.

Halogen bonding properties of 4-iodopyrazole and 4-bromopyrazole explored by rotational spectroscopy and ab initio calculations.

The combination of halogen- and hydrogen-bonding capabilities possessed by 4-bromopyrazole and 4-iodopyrazole has led to them being described as "magic bullets" for biochemical structure determination. Laser vaporisation was used to introduce each of these 4-halopyrazoles into an argon gas sample undergoing supersonic expansion prior to the recording of the rotational spectra of these molecules by chirped-pulse Fourier transform microwave spectroscopy. Data were obtained for four isotopologues of 4-bromopyrazole and two isotopologues of 4-iodopyrazole. Isotopic substitutions were achieved at the hydrogens attached to the pyrrolic nitrogen atoms of both 4-halopyrazoles and at the bromine atom of 4-bromopyrazole. The experimentally determined nuclear quadrupole coupling constants, χaa(X) and χbb(X)-χcc(X), of the halogen atoms (where X is the halogen atom) of each molecule are compared with the results of the ab initio calculations and those for a range of other halogen-containing molecules. It is concluded that each of 4-bromopyrazole and 4-iodopyrazole will form halogen bonds that are broadly comparable in strength to those formed by CH3X and CF3X.

Investigating DNA Radiation Damage Using X-Ray Absorption Spectroscopy.

The biological influence of radiation on living matter has been studied for years; however, several questions about the detailed mechanism of radiation damage formation remain largely unanswered. Among all biomolecules exposed to radiation, DNA plays an important role because any damage to its molecular structure can affect the whole cell and may lead to chromosomal rearrangements resulting in genomic instability or cell death. To identify and characterize damage induced in the DNA sugar-phosphate backbone, in this work we performed x-ray absorption spectroscopy at the P K-edge on DNA irradiated with either UVA light or protons. By combining the experimental results with theoretical calculations, we were able to establish the types and relative ratio of lesions produced by both UVA and protons around the phosphorus atoms in DNA.

The Importance of Vibronic Coupling for Efficient Reverse Intersystem Crossing in Thermally Activated Delayed Fluorescence Molecules.

Factors influencing the rate of reverse intersystem crossing (krISC ) in thermally activated delayed fluorescence (TADF) emitters are critical for improving the efficiency and performance of third-generation heavy-metal-free organic light-emitting diodes (OLEDs). However, present understanding of the TADF mechanism does not extend far beyond a thermal equilibrium between the lowest singlet and triplet states and consequently research has focused almost exclusively on the energy gap between these two states. Herein, we use a model spin-vibronic Hamiltonian to reveal the crucial role of non-Born-Oppenheimer effects in determining krISC . We demonstrate that vibronic (nonadiabatic) coupling between the lowest local excitation triplet (3 LE) and lowest charge transfer triplet (3 CT) opens the possibility for significant second-order coupling effects and increases krISC by about four orders of magnitude. Crucially, these simulations reveal the dynamical mechanism for highly efficient TADF and opens design routes that go beyond the Born-Oppenheimer approximation for the future development of high-performing systems.

Local Control Theory in Trajectory Surface Hopping Dynamics Applied to the Excited-State Proton Transfer of 4-Hydroxyacridine.

The application of local control theory combined with nonadiabatic ab initio molecular dynamics to study the photoinduced intramolecular proton transfer reaction in 4-hydroxyacridine was investigated. All calculations were performed within the framework of linear-response time-dependent density functional theory. The computed pulses revealed important information about the underlying excited-state nuclear dynamics highlighting the involvement of collective vibrational modes that would normally be neglected in a study performed on model systems constrained to a subset of the full configuration space. This study emphasizes the strengths of local control theory for the design of pulses that can trigger chemical reactions associated with the population of a given molecular excited state. In addition, analysis of the generated pulses can help to shed new light on the photophysics and photochemistry of complex molecular systems.

Identifying the major intermediate species by combining time-resolved X-ray solution scattering and X-ray absorption spectroscopy.

Identifying the intermediate species along a reaction pathway is a first step towards a complete understanding of the reaction mechanism, but often this task is not trivial. There has been a strong on-going debate: which of the three intermediates, the CHI2 radical, the CHI2-I isomer, and the CHI2(+) ion, is the dominant intermediate species formed in the photolysis of iodoform (CHI3)? Herein, by combining time-resolved X-ray liquidography (TRXL) and time-resolved X-ray absorption spectroscopy (TR-XAS), we present strong evidence that the CHI2 radical is dominantly formed from the photolysis of CHI3 in methanol at 267 nm within the available time resolution of the techniques (∼20 ps for TRXL and ∼100 ps for TR-XAS). The TRXL measurement, conducted using the time-slicing scheme, detected no CHI2-I isomer within our signal-to-noise ratio, indicating that, if formed, the CHI2-I isomer must be a minor intermediate. The TR-XAS transient spectra measured at the iodine L1 and L3 edges support the same conclusion. The present work demonstrates that the application of these two complementary time-resolved X-ray methods to the same system can provide a detailed understanding of the reaction mechanism.

Evidence for a Peierls phase-transition in a three-dimensional multiple charge-density waves solid.

The effect of dimensionality on materials properties has become strikingly evident with the recent discovery of graphene. Charge ordering phenomena can be induced in one dimension by periodic distortions of a material's crystal structure, termed Peierls ordering transition. Charge-density waves can also be induced in solids by strong coulomb repulsion between carriers, and at the extreme limit, Wigner predicted that crystallization itself can be induced in an electrons gas in free space close to the absolute zero of temperature. Similar phenomena are observed also in higher dimensions, but the microscopic description of the corresponding phase transition is often controversial, and remains an open field of research for fundamental physics. Here, we photoinduce the melting of the charge ordering in a complex three-dimensional solid and monitor the consequent charge redistribution by probing the optical response over a broad spectral range with ultrashort laser pulses. Although the photoinduced electronic temperature far exceeds the critical value, the charge-density wave is preserved until the lattice is sufficiently distorted to induce the phase transition. Combining this result with ab initio electronic structure calculations, we identified the Peierls origin of multiple charge-density waves in a three-dimensional system for the first time.