Efficient radical-based light-emitting diodes with doublet emission.

Organic light-emitting diodes (OLEDs)1-5, quantum-dot-based LEDs6-10, perovskite-based LEDs11-13 and micro-LEDs14,15 have been championed to fabricate lightweight and flexible units for next-generation displays and active lighting. Although there are already some high-end commercial products based on OLEDs, costs must decrease whilst maintaining high operational efficiencies for the technology to realise wider impact.  Here we demonstrate efficient action of radical-based OLEDs16, whose emission originates from a spin doublet, rather than a singlet or triplet exciton. While the emission process is still spin-allowed in these OLEDs, the efficiency limitations imposed by triplet excitons are circumvented for doublets. Using a luminescent radical emitter, we demonstrate an OLED with maximum external quantum efficiency of 27 per cent at a wavelength of 710 nanometres-the highest reported value for deep-red and infrared LEDs. For a standard closed-shell organic semiconductor, holes and electrons occupy the highest occupied and lowest unoccupied molecular orbitals (HOMOs and LUMOs), respectively, and recombine to form singlet or triplet excitons. Radical emitters have a singly occupied molecular orbital (SOMO) in the ground state, giving an overall spin-1/2 doublet. If-as expected on energetic grounds-both electrons and holes occupy this SOMO level, recombination returns the system to the ground state, giving no light emission. However, in our very efficient OLEDs, we achieve selective hole injection into the HOMO and electron injection to the SOMO to form the fluorescent doublet excited state with near-unity internal quantum efficiency.

ExROPPP: Fast, accurate, and spin-pure calculation of the electronically excited states of organic hydrocarbon radicals.

Recent years have seen an explosion of interest in organic radicals due to their promise for highly efficient organic light-emitting diodes and molecular qubits. However, accurately and inexpensively computing their electronic structure has been challenging, especially for excited states, due to the spin-contamination problem. Furthermore, while alternacy or "pseudoparity" rules have guided the interpretation and prediction of the excited states of closed-shell hydrocarbons since the 1950s, similar general rules for hydrocarbon radicals have not to our knowledge been found yet. In this article, we present solutions to both of these challenges. First, we combine the extended configuration interaction singles method with Pariser-Parr-Pople (PPP) theory to obtain a method that we call ExROPPP (Extended Restricted Open-shell PPP) theory. We find that ExROPPP computes spin-pure excited states of hydrocarbon radicals with comparable accuracy to experiment as high-level general multi-configurational quasi-degenerate perturbation theory calculations but at a computational cost that is at least two orders of magnitude lower. We then use ExROPPP to derive widely applicable rules for the spectra of alternant hydrocarbon radicals, which are completely consistent with our computed results. These findings pave the way for highly accurate and efficient computation and prediction of the excited states of organic radicals.

Inverse molecular design from first principles: Tailoring organic chromophore spectra for optoelectronic applications.

The discovery of molecules with tailored optoelectronic properties, such as specific frequency and intensity of absorption or emission, is a major challenge in creating next-generation organic light-emitting diodes (OLEDs) and photovoltaics. This raises the following question: How can we predict a potential chemical structure from these properties? Approaches that attempt to tackle this inverse design problem include virtual screening, active machine learning, and genetic algorithms. However, these approaches rely on a molecular database or many electronic structure calculations, and significant computational savings could be achieved if there was prior knowledge of (i) whether the optoelectronic properties of a parent molecule could easily be improved and (ii) what morphing operations on a parent molecule could improve these properties. In this Perspective, we address both of these challenges from first principles. We first adapt the Thomas-Reiche-Kuhn sum rule to organic chromophores and show how this indicates how easily the absorption and emission of a molecule can be improved. We then show how by combining electronic structure theory and intensity borrowing perturbation theory we can predict whether or not the proposed morphing operations will achieve the desired spectral alteration, and thereby derive widely applicable design rules. We go on to provide proof-of-concept illustrations of this approach to optimizing the visible absorption of acenes and the emission of radical OLEDs. We believe that this approach can be integrated into genetic algorithms by biasing morphing operations in favor of those that are likely to be successful, leading to faster molecular discovery and greener chemistry.

Electronic energies from coupled fermionic "Zombie" states' imaginary time evolution.

Zombie states are a recently introduced formalism to describe coupled coherent fermionic states that address the fermionic sign problem in a computationally tractable manner. Previously, it has been shown that Zombie states with fractional occupations of spin orbitals obeyed the correct fermionic creation and annihilation algebra and presented results for real-time evolution [D. V. Shalashilin, J. Chem. Phys. 148, 194109 (2018)]. In this work, we extend and build on this formalism by developing efficient algorithms for evaluating the Hamiltonian and other operators between Zombie states and address their normalization. We also show how imaginary time propagation can be used to find the ground state of a system. We also present a biasing method, for setting up a basis set of random Zombie states, that allows much smaller basis sizes to be used while still accurately describing the electronic structure Hamiltonian and its ground state and describe a technique of wave function "cleaning" that removes the contributions of configurations with the wrong number of electrons, improving the accuracy further. We also show how low-lying excited states can be calculated efficiently using a Gram-Schmidt orthogonalization procedure. The proposed algorithm of imaginary time propagation on biased random grids of Zombie states may present an alternative to the existing quantum Monte Carlo methods.

Understanding the luminescent nature of organic radicals for efficient doublet emitters and pure-red light-emitting diodes.

The doublet-spin nature of radical emitters is advantageous for applications in organic light-emitting diodes, as it avoids the formation of triplet excitons that limit the electroluminescence efficiency of non-radical emitters. However, radicals generally show low optical absorption and photoluminescence yields. Here we explain the poor optical properties of radicals based on alternant hydrocarbons, and establish design rules to increase the absorption and luminescence yields for donor-acceptor-type radicals. We show that non-alternant systems are necessary to lift the degeneracy of the lowest energy orbital excitations; moreover, intensity borrowing from an intense high-lying transition by the low-energy charge-transfer excitation enhances the oscillator strength of the emitter. We apply these rules to design tris(2,4,6-trichlorophenyl)methyl-pyridoindolyl derivatives with a high photoluminescence quantum yield (>90%). Organic light-emitting diodes based on these molecules showed a pure-red emission with an over 12% external quantum efficiency. These insights may be beneficial for the rational design and discovery of highly luminescent doublet emitters.

Systematic improvement of molecular excited state calculations by inclusion of nuclear quantum motion: A mode-resolved picture and the effect of molecular size.

The energies of molecular excited states arise as solutions to the electronic Schrödinger equation and are often compared to experiment. At the same time, nuclear quantum motion is known to be important and to induce a redshift of excited state energies. However, it is thus far unclear whether incorporating nuclear quantum motion in molecular excited state calculations leads to a systematic improvement of their predictive accuracy, making further investigation necessary. Here, we present such an investigation by employing two first-principles methods for capturing the effect of quantum fluctuations on excited state energies, which we apply to the Thiel set of organic molecules. We show that accounting for zero-point motion leads to much improved agreement with experiment, compared to "static" calculations that only account for electronic effects, and the magnitude of the redshift can become as large as 1.36 eV. Moreover, we show that the effect of nuclear quantum motion on excited state energies largely depends on the molecular size, with smaller molecules exhibiting larger redshifts. Our methodology also makes it possible to analyze the contribution of individual vibrational normal modes to the redshift of excited state energies, and in several molecules, we identify a limited number of modes dominating this effect. Overall, our study provides a foundation for systematically quantifying the shift of excited state energies due to nuclear quantum motion and for understanding this effect at a microscopic level.

Switching between Coherent and Incoherent Singlet Fission via Solvent-Induced Symmetry Breaking.

Singlet fission in organic semiconductors causes a singlet exciton to decay into a pair of triplet excitons and holds potential for increasing the efficiency of photovoltaic devices. In this combined experimental and theoretical study, we reveal that a covalent dimer of the organic semiconductor tetracene undergoes activated singlet fission by qualitatively different mechanisms depending on the solvent environment. We show that intramolecular vibrations are an integral part of this mechanism, giving rise to mixing between charge transfer and triplet pair excitations. Either coherent or incoherent singlet fission can occur, depending on the transient solvent-induced energetic proximity between the states, giving rise to complex variation of the singlet fission mechanism and time scale in the different environments. Our results suggest a more general principle for controlling the efficiency of photochemical reactions by utilizing transient interactions to tune the energetics of reactant and product states and switch between incoherent and coherent dynamics.

Anticipating Acene-Based Chromophore Spectra with Molecular Orbital Arguments.

Recent synthetic studies on the organic molecules tetracene and pentacene have found certain dimers and oligomers to exhibit an intense absorption in the visible region of the spectrum that is not present in the monomer or many previously studied dimers. In this article we combine experimental synthesis with electronic structure theory and spectral computation to show that this absorption arises from an otherwise dark charge-transfer excitation "borrowing intensity" from an intense UV excitation. Further, by characterizing the role of relevant monomer molecular orbitals, we arrive at a design principle that allows us to predict the presence or absence of an additional absorption based on the bonding geometry of the dimer. We find this rule correctly explains the spectra of a wide range of acene derivatives and solves an unexplained structure-spectrum phenomenon first observed over 70 years ago. These results pave the way for the design of highly absorbent chromophores with applications ranging from photovoltaics to liquid crystals.

Nonadiabatic semiclassical dynamics in the mixed quantum-classical initial value representation.

We extend the Mixed Quantum-Classical Initial Value Representation (MQC-IVR), a semiclassical method for computing real-time correlation functions, to electronically nonadiabatic systems using the Meyer-Miller-Stock-Thoss (MMST) Hamiltonian in order to treat electronic and nuclear degrees of freedom (dofs) within a consistent dynamic framework. We introduce an efficient symplectic integration scheme, the MInt algorithm, for numerical time evolution of the phase space variables and monodromy matrix under the non-separable MMST Hamiltonian. We then calculate the probability of transmission through a curve crossing in model two-level systems and show that MQC-IVR reproduces quantum-limit semiclassical results in good agreement with exact quantum methods in one limit, and in the other limit yields results that are in keeping with classical limit semiclassical methods like linearized IVR. Finally, exploiting the ability of the MQC-IVR to quantize different dofs to different extents, we present a detailed study of the extents to which quantizing the nuclear and electronic dofs improves numerical convergence properties without significant loss of accuracy.

Tuning Singlet Fission in π-Bridge-π Chromophores.

We have designed a series of pentacene dimers separated by homoconjugated or nonconjugated bridges that exhibit fast and efficient intramolecular singlet exciton fission (iSF). These materials are distinctive among reported iSF compounds because they exist in the unexplored regime of close spatial proximity but weak electronic coupling between the singlet exciton and triplet pair states. Using transient absorption spectroscopy to investigate photophysics in these molecules, we find that homoconjugated dimers display desirable excited-state dynamics, with significantly reduced recombination rates as compared to conjugated dimers with similar singlet fission rates. In addition, unlike conjugated dimers, the time constants for singlet fission are relatively insensitive to the interplanar angle between chromophores, since rotation about σ bonds negligibly affects the orbital overlap within the π-bonding network. In the nonconjugated dimer, where the iSF occurs with a time constant >10 ns, comparable to the fluorescence lifetime, we used electron spin resonance spectroscopy to unequivocally establish the formation of triplet-triplet multiexcitons and uncoupled triplet excitons through singlet fission. Together, these studies enable us to articulate the role of the conjugation motif in iSF.

A mapping variable ring polymer molecular dynamics study of condensed phase proton-coupled electron transfer.

We investigate the mechanisms of condensed phase proton-coupled electron transfer (PCET) using Mapping-Variable Ring Polymer Molecular Dynamics (MV-RPMD), a recently developed method that employs an ensemble of classical trajectories to simulate nonadiabatic excited state dynamics. Here, we construct a series of system-bath model Hamiltonians for the PCET, where four localized electron-proton states are coupled to a thermal bath via a single solvent mode, and we employ MV-RPMD to simulate state population dynamics. Specifically, for each model, we identify the dominant PCET mechanism, and by comparing against rate theory calculations, we verify that our simulations correctly distinguish between concerted PCET, where the electron and proton transfer together, and sequential PCET, where either the electron or the proton transfers first. This work represents a first application of MV-RPMD to multi-level condensed phase systems; we introduce a modified MV-RPMD expression that is derived using a symmetric rather than asymmetric Trotter discretization scheme and an initialization protocol that uses a recently derived population estimator to constrain trajectories to a dividing surface. We also demonstrate that, as expected, the PCET mechanisms predicted by our simulations are robust to an arbitrary choice of the initial dividing surface.

Deriving the exact nonadiabatic quantum propagator in the mapping variable representation.

We derive an exact quantum propagator for nonadiabatic dynamics in multi-state systems using the mapping variable representation, where classical-like Cartesian variables are used to represent both continuous nuclear degrees of freedom and discrete electronic states. The resulting Liouvillian is a Moyal series that, when suitably approximated, can allow for the use of classical dynamics to efficiently model large systems. We demonstrate that different truncations of the exact Liouvillian lead to existing approximate semiclassical and mixed quantum-classical methods and we derive an associated error term for each method. Furthermore, by combining the imaginary-time path-integral representation of the Boltzmann operator with the exact Liouvillian, we obtain an analytic expression for thermal quantum real-time correlation functions. These results provide a rigorous theoretical foundation for the development of accurate and efficient classical-like dynamics to compute observables such as electron transfer reaction rates in complex quantized systems.

Competing quantum effects in the free energy profiles and diffusion rates of hydrogen and deuterium molecules through clathrate hydrates.

Clathrate hydrates hold considerable promise as safe and economical materials for hydrogen storage. Here we present a quantum mechanical study of H2 and D2 diffusion through a hexagonal face shared by two large cages of clathrate hydrates over a wide range of temperatures. Path integral molecular dynamics simulations are used to compute the free-energy profiles for the diffusion of H2 and D2 as a function of temperature. Ring polymer molecular dynamics rate theory, incorporating both exact quantum statistics and approximate quantum dynamical effects, is utilized in the calculations of the H2 and D2 diffusion rates in a broad temperature interval. We find that the shape of the quantum free-energy profiles and their height relative to the classical free energy barriers at a given temperature, as well as the rate of diffusion, are strongly affected by competing quantum effects: above 25 K, zero-point energy (ZPE) perpendicular to the reaction path for diffusion between cavities decreases the quantum rate compared to the classical rate, whereas at lower temperatures tunneling outcompetes the ZPE and as a result the quantum rate is greater than the classical rate.

An alternative derivation of ring-polymer molecular dynamics transition-state theory.

In a previous article [T. J. H. Hele and S. C. Althorpe, J. Chem. Phys. 138, 084108 (2013)], we showed that the t → 0+ limit of ring-polymer molecular dynamics (RPMD) rate-theory is also the t → 0+ limit of a new type of quantum flux-side time-correlation function, in which the dividing surfaces are invariant to imaginary-time translation; in other words, that RPMD transition-state theory (RMPD-TST) is a t → 0+ quantum transition-state theory (QTST). Recently, Jang and Voth [J. Chem. Phys. 144, 084110 (2016)] rederived this quantum t → 0+ limit and claimed that it gives instead the centroid-density approximation. Here we show that the t → 0+ limit derived by Jang and Voth is in fact RPMD-TST.

Should thermostatted ring polymer molecular dynamics be used to calculate thermal reaction rates?

We apply Thermostatted Ring Polymer Molecular Dynamics (TRPMD), a recently proposed approximate quantum dynamics method, to the computation of thermal reaction rates. Its short-time transition-state theory limit is identical to rigorous quantum transition-state theory, and we find that its long-time limit is independent of the location of the dividing surface. TRPMD rate theory is then applied to one-dimensional model systems, the atom-diatom bimolecular reactions H + H2, D + MuH, and F + H2, and the prototypical polyatomic reaction H + CH4. Above the crossover temperature, the TRPMD rate is virtually invariant to the strength of the friction applied to the internal ring-polymer normal modes, and beneath the crossover temperature the TRPMD rate generally decreases with increasing friction, in agreement with the predictions of Kramers theory. We therefore find that TRPMD is approximately equal to, or less accurate than, ring polymer molecular dynamics for symmetric reactions, and for certain asymmetric systems and friction parameters closer to the quantum result, providing a basis for further assessment of the accuracy of this method.

Boltzmann-conserving classical dynamics in quantum time-correlation functions: "Matsubara dynamics".

We show that a single change in the derivation of the linearized semiclassical-initial value representation (LSC-IVR or "classical Wigner approximation") results in a classical dynamics which conserves the quantum Boltzmann distribution. We rederive the (standard) LSC-IVR approach by writing the (exact) quantum time-correlation function in terms of the normal modes of a free ring-polymer (i.e., a discrete imaginary-time Feynman path), taking the limit that the number of polymer beads N → ∞, such that the lowest normal-mode frequencies take their "Matsubara" values. The change we propose is to truncate the quantum Liouvillian, not explicitly in powers of h(2) at h(0) (which gives back the standard LSC-IVR approximation), but in the normal-mode derivatives corresponding to the lowest Matsubara frequencies. The resulting "Matsubara" dynamics is inherently classical (since all terms O(h(2)) disappear from the Matsubara Liouvillian in the limit N → ∞) and conserves the quantum Boltzmann distribution because the Matsubara Hamiltonian is symmetric with respect to imaginary-time translation. Numerical tests show that the Matsubara approximation to the quantum time-correlation function converges with respect to the number of modes and gives better agreement than LSC-IVR with the exact quantum result. Matsubara dynamics is too computationally expensive to be applied to complex systems, but its further approximation may lead to practical methods.

Communication: Relation of centroid molecular dynamics and ring-polymer molecular dynamics to exact quantum dynamics.

We recently obtained a quantum-Boltzmann-conserving classical dynamics by making a single change to the derivation of the "Classical Wigner" approximation. Here, we show that the further approximation of this "Matsubara dynamics" gives rise to two popular heuristic methods for treating quantum Boltzmann time-correlation functions: centroid molecular dynamics (CMD) and ring-polymer molecular dynamics (RPMD). We show that CMD is a mean-field approximation to Matsubara dynamics, obtained by discarding (classical) fluctuations around the centroid, and that RPMD is the result of discarding a term in the Matsubara Liouvillian which shifts the frequencies of these fluctuations. These findings are consistent with previous numerical results and give explicit formulae for the terms that CMD and RPMD leave out.

Derivation of a true (t → 0+) quantum transition-state theory. I. Uniqueness and equivalence to ring-polymer molecular dynamics transition-state-theory.

Surprisingly, there exists a quantum flux-side time-correlation function which has a non-zero t → 0+ limit and thus yields a rigorous quantum generalization of classical transition-state theory (TST). In this Part I of two articles, we introduce the new time-correlation function and derive its t → 0+ limit. The new ingredient is a generalized Kubo transform which allows the flux and side dividing surfaces to be the same function of path-integral space. Choosing this function to be a single point gives a t → 0+ limit which is identical to an expression introduced on heuristic grounds by Wigner in 1932; however, this expression does not give positive-definite quantum statistics, causing it to fail while still in the shallow-tunnelling regime. Positive-definite quantum statistics is obtained only if the dividing surface is invariant to imaginary-time translation, in which case the t → 0+ limit is identical to ring-polymer molecular dynamics (RPMD) TST. The RPMD-TST rate is not a strict upper bound to the exact quantum rate, but is a good approximation to one if real-time coherence effects are small. Part II will show that the RPMD-TST rate is equal to the exact quantum rate in the absence of recrossing.

Derivation of a true (t → 0+) quantum transition-state theory. II. Recovery of the exact quantum rate in the absence of recrossing.

In Paper I [T. J. H. Hele and S. C. Althorpe, J. Chem. Phys. 138, 084108 (2013)] we derived a quantum transition-state theory (TST) by taking the t → 0+ limit of a new form of quantum flux-side time-correlation function containing a ring-polymer dividing surface. This t → 0+ limit appears to be unique in giving positive-definite Boltzmann statistics, and is identical to ring-polymer molecular dynamics (RPMD) TST. Here, we show that quantum TST (i.e., RPMD-TST) is exact if there is no recrossing (by the real-time quantum dynamics) of the ring-polymer dividing surface, nor of any surface orthogonal to it in the space describing fluctuations in the polymer-bead positions along the reaction coordinate. In practice, this means that RPMD-TST gives a good approximation to the exact quantum rate for direct reactions, provided the temperature is not too far below the cross-over to deep tunnelling. We derive these results by comparing the t → ∞ limit of the ring-polymer flux-side time-correlation function with that of a hybrid flux-side time-correlation function (containing a ring-polymer flux operator and a Miller-Schwarz-Tromp side function), and by representing the resulting ring-polymer momentum integrals as hypercubes. Together with Paper I, the results of this article validate a large number of RPMD calculations of reaction rates.

On the uniqueness of t → 0+ quantum transition-state theory.

It was shown recently that there exists a true quantum transition-state theory (QTST) corresponding to the t → 0+ limit of a (new form of) quantum flux-side time-correlation function. Remarkably, this QTST is identical to ring-polymer molecular dynamics (RPMD) TST. Here, we provide evidence which suggests very strongly that this QTST (≡ RPMD-TST) is unique, in the sense that the t → 0+ limit of any other flux-side time-correlation function gives either non-positive-definite quantum statistics or zero. We introduce a generalized flux-side time-correlation function which includes all other (known) flux-side time-correlation functions as special limiting cases. We find that the only non-zero t → 0+ limit of this function that contains positive-definite quantum statistics is RPMD-TST.