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.

A Computational-Experimental Approach to Unravel the Excited State Landscape in Heavy-Atom Free BODIPY-Related Dyes.

We performed a time-gated laser-spectroscopy study in a set of heavy-atom free single BODIPY fluorophores, supported by accurate, excited-state computational simulations of the key low-lying excited states in these chromophores. Despite the strong fluorescence of these emitters, we observed a significant fraction of time-delayed (microseconds scale) emission associated with processes that involved passage through the triplet manifold. The accuracy of the predictions of the energy arrangement and electronic nature of the low-lying singlet and triplet excited states meant that an unambiguous assignment of the main deactivation pathways, including thermally activated delayed fluorescence and/or room temperature phosphorescence, was possible. The observation of triplet state formation indicates a breakthrough in the "classic" interpretation of the photophysical properties of the renowned BODIPY and its derivatives.

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.

Competition between the heavy atom effect and vibronic coupling in donor-bridge-acceptor organometallics.

The excited state properties and intersystem crossing dynamics of a series of donor-bridge-acceptor carbene metal-amides based upon the coinage metals Cu, Ag, Au, are investigated using quantum dynamics simulations and supported by photophysical characterisation. The simulated intersystem rates are consistent with experimental observations making it possible to provide a detailed interpretation of the excited state dynamics which ultimately control their functional properties. It is demonstrated that for all complexes there is a competition between the direct intersystem crossing occurring between the 1CT and 3CT states and indirect pathways which couple to an intermediate locally excited ππ* triplet state (3LE) on either the donor or acceptor ligands. The energy of the 3LE states decreases as the size of the metal decreases meaning that the indirect pathway plays an increasingly important role for the lighter metals. Importantly whenever the direct pathway is efficient, the presence of indirect pathways is detrimental to the overall rate of ISC as they provide a slower alternative pathway. Our results provide a detailed insight into the mechanism of intersystem crossing in these complexes and will greatly facilitate the design of new higher performing molecules.

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.

Spin-vibronic quantum dynamics for ultrafast excited-state processes.

Ultrafast intersystem crossing (ISC) processes coupled to nuclear relaxation and solvation dynamics play a central role in the photophysics and photochemistry of a wide range of transition metal complexes. These phenomena occurring within a few hundred femtoseconds are investigated experimentally by ultrafast picosecond and femtosecond transient absorption or luminescence spectroscopies, and optical laser pump-X-ray probe techniques using picosecond and femtosecond X-ray pulses. The interpretation of ultrafast structural changes, time-resolved spectra, quantum yields, and time scales of elementary processes or transient lifetimes needs robust theoretical tools combining state-of-the-art quantum chemistry and developments in quantum dynamics for solving the electronic and nuclear problems. Multimode molecular dynamics beyond the Born-Oppenheimer approximation has been successfully applied to many small polyatomic systems. Its application to large molecules containing a transition metal atom is still a challenge because of the nuclear dimensionality of the problem, the high density of electronic excited states, and the spin-orbit coupling effects. Rhenium(I) α-diimine carbonyl complexes, [Re(L)(CO)3(N,N)](n+) are thermally and photochemically robust and highly flexible synthetically. Structural variations of the N,N and L ligands affect the spectroscopy, the photophysics, and the photochemistry of these chromophores easily incorporated into a complex environment. Visible light absorption opens the route to a wide range of applications such as sensors, probes, or emissive labels for imaging biomolecules. Halide complexes [Re(X)(CO)3(bpy)] (X = Cl, Br, or I; bpy = 2,2'-bipyridine) exhibit complex electronic structure and large spin-orbit effects that do not correlate with the heavy atom effects. Indeed, the (1)MLCT → (3)MLCT intersystem crossing (ISC) kinetics is slower than in [Ru(bpy)3](2+) or [Fe(bpy)3](2+) despite the presence of a third-row transition metal. Counterintuitively, singlet excited-state lifetime increases on going from Cl (85 fs) to Br (128 fs) and to I (152 fs). Moreover, correlation between the Re-X stretching mode and the rate of ISC is observed. In this Account, we emphasize on the role of spin-vibronic coupling on the mechanism of ultrafast ISC put in evidence in [Re(Br)(CO)3(bpy)]. For this purpose, we have developed a model Hamiltonian for solving an 11 electronic excited states multimode problem including vibronic and SO coupling within the linear vibronic coupling (LVC) approximation and the assumption of harmonic potentials. The presence of a central metal atom coupled to rigid ligands, such as α-diimine, ensures nuclear motion of small amplitudes and a priori justifies the use of the LVC model. The simulation of the ultrafast dynamics by wavepacket propagations using the multiconfiguration time-dependent Hartree (MCTDH) method is based on density functional theory (DFT), and its time-dependent extension to excited states (TD-DFT) electronic structure data. We believe that the interplay between time-resolved experiments and these pioneering simulations covering the first picoseconds and including spin-vibronic coupling will promote a number of quantum dynamical studies that will contribute to a better understanding of ultrafast processes in a wide range of organic and inorganic chromophores easily incorporated in biosystems or supramolecular devices for specific functions.

Structural Properties and UV-Visible Absorption Spectroscopy of Retinal-pyridyl-CN Re(I) Carbonyl Bipyridine Complex: A Theoretical Study.

The structural, electronic, and optical properties of the all-trans and five cis conformers of [Re(CO)3(bpy)(ret-pyr-CN)](+) (bpy = 2,2'-bipyridine; ret-pyr-CN = pyridyl-CN-3,7-dimethyl-9-(2,6,6-trimethylcyclohex-2-n)-none-(2,4,6,8-tetraen) were studied in solvent by means of density functional theory (DFT) and time-dependent DFT. The isolated retinal-like chromophore ret-pyr-CN was investigated as well for comparison. By coordination to the complex the two lowest intraligand (IL) states localized on the retinal group are slightly red-shifted from 627 to 690 nm and from 415 to 450 nm, respectively. Several isomerization pathways are open upon irradiation of the Re(I) complex by visible light (400-450 nm), especially to two cis conformers corresponding to the isomerization of the two double bonds of the retinal-like ligand close to the pyridyl group linked to the Re(I) fragment. The metal-to-ligand charge transfer states localized either on the retinal group or on the bpy ligand should play a minor role in the isomerization process itself but could improve its efficiency via ultra-fast intersystem crossing.

Spin-Vibronic Intersystem Crossing and Molecular Packing Effects in Heavy Atom Free Organic Phosphor.

We present a detailed investigation into the excited state properties of a planar D3h symmetric azatriangulenetrione, HTANGO, which has received significant interest due to its high solid-state phosphorescence quantum yield and therefore potential as an organic room temperature phosphorescent (ORTP) dye. Using a model linear vibronic coupling Hamiltonian in combination with quantum dynamics simulations, we observe that intersystem crossing (ISC) in HTANGO occurs with a rate of ∼1010 s-1, comparable to benzophenone, an archetypal molecule for fast ISC in heavy metal free molecules. Our simulations demonstrate that the mechanism for fast ISC is associated with the high density of excited triplet states which lie in close proximity to the lowest singlet states, offering multiple channels into the triplet manifold facilitating rapid population transfer. Finally, to rationalize the solid-state emission properties, we use quantum chemistry to investigate the excited state surfaces of the HTANGO dimer, highlighting the influence and importance of the rotational alignment between the two HTANGO molecules in the solid state and how this contributes to high phosphorescence quantum yield.

Tracking nuclear motion in single-molecule magnets using femtosecond X-ray absorption spectroscopy.

The development of new data storage solutions is crucial for emerging digital technologies. Recently, all-optical magnetic switching has been achieved in dielectrics, proving to be faster than traditional methods. Despite this, single-molecule magnets (SMMs), which are an important class of magnetic materials due to their nanometre size, remain underexplored for ultrafast photomagnetic switching. Herein, we report femtosecond time-resolved K-edge X-ray absorption spectroscopy (TR-XAS) on a Mn(III)-based trinuclear SMM. Exploiting the elemental specificity of XAS, we directly track nuclear dynamics around the metal ions and show that the ultrafast dynamics upon excitation of a crystal-field transition are dominated by a magnetically active Jahn-Teller mode. Our results, supported by simulations, reveal minute bond length changes from 0.01 to 0.05 Å demonstrating the sensitivity of the method. These geometrical changes are discussed in terms of magneto-structural relationships and consequently our results illustrate the importance of TR-XAS for the emerging area of ultrafast molecular magnetism.

Photoinduced Jahn-Teller switch in Mn(III) terpyridine complexes.

Ultrafast transient absorption spectra were recorded for [Mn(terpy)X3], where X = Cl, F, and N3, to explore photoinduced switching from axial to equatorial Jahn-Teller (JT) distortion. Strong oscillations were observed in the transients, corresponding to a wavepacket on the excited-state potential energy surface with oscillation frequency around 115 cm-1 for all three complexes. Multireference quantum chemistry calculations indicate that the reaction coordinate is a pincer-like motion of the terpyridine ligand arising from bond length changes in the excited state due to the JT switch. We observed long dephasing times of the wavepacket, with times of 620 fs for [Mn(terpy)Cl3], 450 fs for [Mn(terpy)F3], and 370 fs for [Mn(terpy)(N3)3]. The dephasing time of these coherences decreases with an increasing number of vibrational modes at lower energy than the mode dominating the reaction coordinate, suggesting they act as an effective bath to dissipate the excess energy obtained from photoexcitation.

Excited-State Lifetime Modulation by Twisted and Tilted Molecular Design in Carbene-Metal-Amide Photoemitters.

Carbene-metal-amides (CMAs) are an emerging class of photoemitters based on a linear donor-linker-acceptor arrangement. They exhibit high flexibility about the carbene-metal and metal-amide bonds, leading to a conformational freedom which has a strong influence on their photophysical properties. Herein we report CMA complexes with (1) nearly coplanar, (2) twisted, (3) tilted, and (4) tilt-twisted orientations between donor and acceptor ligands and illustrate the influence of preferred ground-state conformations on both the luminescence quantum yields and excited-state lifetimes. The performance is found to be optimum for structures with partially twisted and/or tilted conformations, resulting in radiative rates exceeding 1 × 106 s-1. Although the metal atoms make only small contributions to HOMOs and LUMOs, they provide sufficient spin-orbit coupling between the low-lying excited states to reduce the excited-state lifetimes down to 500 ns. At the same time, high photoluminescence quantum yields are maintained for a strongly tilted emitter in a host matrix. Proof-of-concept organic light-emitting diodes (OLEDs) based on these new emitter designs were fabricated, with a maximum external quantum efficiency (EQE) of 19.1% with low device roll-off efficiency. Transient electroluminescence studies indicate that molecular design concepts for new CMA emitters can be successfully translated into the OLED device.

On the factors influencing the chiroptical response of conjugated polymer thin films.

We study the influence of the physical and chemical structure on the chiroptical response of fluorene-based polymeric systems, namely poly(9,9-dioctylfluorene) (PFO) and the donor-acceptor type copolymer poly(9,9-dioctylfluorene-alt-benzothiadiazole) (F8BT). We reveal the significance of electric-magnetic coupling, at both short (molecular-level) and intermediate (delocalised over multiple polymer chains) length scales, on the magnitude of the dissymmetry. These findings provide a framework for the design of new materials with an enhanced chiroptical response.

Hydrostatic Pressure-Induced Spectral Variation of Reichardt's Dye: A Polarity/Pressure Dual Indicator.

The famous solvatochromic Reichardt's dye was applied to quantify hydrostatic pressure in media. The UV/vis spectra of the dye in various organic solvents are shifted bathochromically or hypsochromically at the shorter- or longer-wavelength band, respectively, upon hydrostatic pressurization. The E T value, determined by an absorption maximum, in ethyl acetate increases from 38.5 kcal mol-1 at 0.1 MPa to 39.2 kcal mol-1 at 300 MPa, which is mostly equal to the one in chloroform at 0.1 MPa. These spectroscopic origins were supported by the time-dependent density functional theory (TD-DFT) calculations. The concept and approach proposed in this paper, i.e., a dual indicator, should attract the attention of a broad spectrum in multidisciplinary science.

Vibrational coherences in manganese single-molecule magnets after ultrafast photoexcitation.

Magnetic recording using femtosecond laser pulses has recently been achieved in some dielectric media, showing potential for ultrafast data storage applications. Single-molecule magnets (SMMs) are metal complexes with two degenerate magnetic ground states and are promising for increasing storage density, but remain unexplored using ultrafast techniques. Here we have explored the dynamics occurring after photoexcitation of a trinuclear µ3-oxo-bridged Mn(III)-based SMM, whose magnetic anisotropy is closely related to the Jahn-Teller distortion. Ultrafast transient absorption spectroscopy in solution reveals oscillations superimposed on the decay traces due to a vibrational wavepacket. Based on complementary measurements and calculations on the monomer Mn(acac)3, we conclude that the wavepacket motion in the trinuclear SMM is constrained along the Jahn-Teller axis due to the µ3-oxo and µ-oxime bridges. Our results provide new possibilities for optical control of the magnetization in SMMs on femtosecond timescales and open up new molecular-design challenges to control the wavepacket motion in the excited state of polynuclear transition-metal complexes.

Triazatruxene: A Rigid Central Donor Unit for a D-A3 Thermally Activated Delayed Fluorescence Material Exhibiting Sub-Microsecond Reverse Intersystem Crossing and Unity Quantum Yield via Multiple Singlet-Triplet State Pairs.

By inverting the common structural motif of thermally activated delayed fluorescence materials to a rigid donor core and multiple peripheral acceptors, reverse intersystem crossing (rISC) rates are demonstrated in an organic material that enables utilization of triplet excited states at faster rates than Ir-based phosphorescent materials. A combination of the inverted structure and multiple donor-acceptor interactions yields up to 30 vibronically coupled singlet and triplet states within 0.2 eV that are involved in rISC. This gives a significant enhancement to the rISC rate, leading to delayed fluorescence decay times as low as 103.9 ns. This new material also has an emission quantum yield ≈1 and a very small singlet-triplet gap. This work shows that it is possible to achieve both high photoluminescence quantum yield and fast rISC in the same molecule. Green organic light-emitting diode devices with external quantum efficiency >30% are demonstrated at 76 cd m-2.

Exploring the Mechanism of Ultrafast Intersystem Crossing in Rhenium(I) Carbonyl Bipyridine Halide Complexes: Key Vibrational Modes and Spin-Vibronic Quantum Dynamics.

The mechanism of ultrafast intersystem crossing in rhenium(I) carbonyl bipyridine halide complexes Re(X)(CO)3(bpy) (X = Cl, Br, I) is studied by exploring the structural deformations when going from Franck-Condon (FC) to critical geometries in the low-lying singlet and triplet excited states and by selecting the key vibrational modes. The luminescent decay observed in [Re(Br)(CO)3(bpy)] is investigated by means of wavepacket propagations based on the multiconfiguration time-dependent Hartree (MCTDH) method. The dominant coordinates underlying the nonradiative decay process are extracted from minima, minimum energy seam of crossing (MESX) and minimum energy conical intersection (MECI) geometries obtained by the seam model function (SMF)/single-component artificial force induced reaction (SC-AFIR) approach. By choosing the normal modes used in MCTDH from the MECI and MESX geometries, not only the degenerate energy points but also the low-energy-gap regions are included. For this purpose a careful vibrational analysis is performed at each critical geometry and analyzed under the light of the pertinent nonadiabatic coupling terms obtained from the linear vibronic coupling (LVC) model augmented by spin-orbit coupling (SOC) in the electronic diabatic representation.

Quantum chemical interpretation of ultrafast luminescence decay and intersystem crossings in rhenium(I) carbonyl bipyridine complexes.

Ultrafast luminescence decay and intersystem crossing processes through the seven low-lying singlet and triplet excited states of [Re (X)(CO)3(bpy)] (X = Cl, Br, I; bpy = 2,2'-bipyridine) are interpreted on the basis of time-dependent density functional theory (TD-DFT) electronic structure calculations performed in acetonitrile and including spin-orbit coupling (SOC) effects within the zeroth-order approximation. It is shown that the red shift of the lowest part of the spectra by SOC increases from X = Cl (0.06 eV) to X = Br (0.09 eV) and X = I (0.18 eV) due to the participation of the triplet sublevels to the absorption. The six lowest "spin-orbit" states remain largely triplet in character and the maximum of absorption is not drastically affected by SOC. While the energy of the excited states is affected by SOC, the character of these states is not significantly modified: SOC mixes states of the same nature, namely metal-to-ligand-charge-transfer/halide-to-ligand-charge-transfer (MLCT/XLCT). This mixing can be large, however, as illustrated by the S1/T2 (a(1)A″/a(3)A') mixing that amounts to about 50:50 within the series Cl > Br > I. On the basis of the optimized structures of the six lowest excited states an interpretation of the emission signals detected by ultrafast luminescence spectroscopy is proposed. It is shown that whereas the experimental Stokes shift of 6000 cm(-1) observed for the three complexes is well reproduced without SOC correction for the Cl and Br complexes, SOC effects have to be taken into account for the iodide complex. The early signal of ultrafast luminescence detected immediately after absorption at 400 nm to the S2 state, covering the 500-550 nm energy domain and characterized by a decay τ1 = 85 fs (X = Cl) and 128 fs (X = Br), is attributed to S2 calculated at 505 and 522 nm, respectively, and to some extend to T3 by SOC. The intermediate band observed at longer time-scale between 550 and 600 nm with emissive decay time τ2 = 340 fs (X = Cl) and 470 fs (X = Br) can be assigned to T2 calculated at 558 and 571 nm, respectively. The S1 state could also participate to this band by SOC. In both complexes the long-lived emission at 600-610 nm is attributed to the lowest T1 state calculated at 596 and 592 nm for the chloride and bromide complexes, respectively, and shifted to ∼610 nm by SOC. Important SOC effects characterize the luminescence decay of [Re (I)(CO)3(bpy)], the mechanism of which differs significantly of the one proposed for the two other complexes. The A' spin-orbit sublevel of T3 state calculated at 512 nm with an oscillator strength of 0.17 × 10(-1) participates to the first signal characterized by a rapid decay (τ1 = 152 fs) with a maximum at 525 nm. The intermediate band covering the 550-600 nm region with a decay time τ2 = 1180 fs is assigned to the "spin-orbit" S1 state calculated at 595 nm. The S2 absorbing state calculated at 577 nm could contribute to these two signals. According to the spin-orbit sublevels calculated for T1 and T2, both states contribute to the long-lived emission detected at 600-610 nm, T1 with two sublevels A' of significant oscillator strengths of ∼10(-1) being the main contributor. In order to follow the evolution of the excited states energy and SOC as a function of the Re-X stretching normal mode their potentials have been calculated without and with SOC as a function of the mass and frequency weighted Re-X stretching mode displacement from the Franck-Condon geometries. Exploratory wavepacket propagations show that SOC alone cannot account for the whole ISC process. Vibronic effects should play an important role in the ultrafast luminescence decay observed experimentally.

Directionality of Double-Bond Photoisomerization Dynamics Induced by a Single Stereogenic Center.

In light-driven single-molecule rotary motors, the photoisomerization of a double bond converts light energy into the rotation of a moiety (the rotor) with respect to another (the stator). However, at the level of a molecular population, an effective rotary motion can only be achieved if a large majority of the rotors rotate in the same, specific direction. Here we present a quantitative investigation of the directionality (clockwise vs counterclockwise) induced by a single stereogenic center placed in allylic position with respect to the reactive double bond of a model of the biomimetic indanylidene-pyrrolinium framework. By computing ensembles of nonadiabatic trajectories at 300 K, we predict that the photoisomerization is >70% unidirectional for the Z → E and E → Z conversions. Most importantly, we show that such directionality, resulting from the asymmetry of the excited state force field, can still be observed in the presence of a small (ca. 2°) pretwist or helicity of the reactive double bond. This questions the validity of the conjecture that a significant double-bond pretwist (e.g., >10°) in the ground state equilibrium structure of synthetic or natural rotary motors would be required for unidirectional motion.