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.

Which Algorithm Best Propagates the Meyer-Miller-Stock-Thoss Mapping Hamiltonian for Non-Adiabatic Dynamics?

A common strategy to simulate mixed quantum-classical dynamics is by propagating classical trajectories with mapping variables, often using the Meyer-Miller-Stock-Thoss (MMST) Hamiltonian or the related spin-mapping approach. When mapping the quantum subsystem, the coupled dynamics reduce to a set of equations of motion to integrate. Several numerical algorithms have been proposed, but a thorough performance comparison appears to be lacking. Here, we compare three time-propagation algorithms for the MMST Hamiltonian: the Momentum Integral (MInt) (J. Chem. Phys., 2018, 148, 102326), the Split-Liouvillian (SL) (Chem. Phys., 2017, 482, 124-134), and the algorithm in J. Chem. Phys., 2012, 136, 084101 that we refer to as the Degenerate Eigenvalue (DE) algorithm due to the approximation required during derivation. We analyze the accuracy of individual trajectories, correlation functions, energy conservation, symplecticity, Liouville's theorem, and the computational cost. We find that the MInt algorithm is the only rigorously symplectic algorithm. However, comparable accuracy at a lower computational cost can be obtained with the SL algorithm. The approximation implicitly made within the DE algorithm conserves energy poorly, even for small timesteps, and thus leads to slightly different results. These results should guide future mapping-variable simulations.

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.

Singlet and triplet to doublet energy transfer: improving organic light-emitting diodes with radicals.

Organic light-emitting diodes (OLEDs) must be engineered to circumvent the efficiency limit imposed by the 3:1 ratio of triplet to singlet exciton formation following electron-hole capture. Here we show the spin nature of luminescent radicals such as TTM-3PCz allows direct energy harvesting from both singlet and triplet excitons through energy transfer, with subsequent rapid and efficient light emission from the doublet excitons. This is demonstrated with a model Thermally-Activated Delayed Fluorescence (TADF) organic semiconductor, 4CzIPN, where reverse intersystem crossing from triplets is characteristically slow (50% emission by 1 µs). The radical:TADF combination shows much faster emission via the doublet channel (80% emission by 100 ns) than the comparable TADF-only system, and sustains higher electroluminescent efficiency with increasing current density than a radical-only device. By unlocking energy transfer channels between singlet, triplet and doublet excitons, further technology opportunities are enabled for optoelectronics using organic radicals.

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.

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.

Intrinsic photogeneration of long-lived charges in a donor-orthogonal acceptor conjugated polymer.

Efficient charge photogeneration in conjugated polymers typically requires the presence of a second component to act as electron acceptor. Here, we report a novel low band-gap conjugated polymer with a donor/orthogonal acceptor motif: poly-2,6-(4,4-dihexadecyl-4H-cyclopenta [2,1-b:3,4-b']dithiophene)-alt-2,6-spiro [cyclopenta[2,1-b:3,4-b']dithiophene-4,9'-fluorene]-2',7'-dicarbonitrile, referred to as PCPDT-sFCN. The role of the orthogonal acceptor is to spatially isolate the LUMO from the HOMO, allowing for negligible exchange energy between electrons in these orbitals and minimising the energy gap between singlet and triplet charge transfer states. We employ ultrafast and microsecond transient absorption spectroscopy to demonstrate that, even in the absence of a separate electron acceptor, PCPDT-sFCN shows efficient charge photogeneration in both pristine solution and film. This efficient charge generation is a result of an isoenergetic singlet/triplet charge transfer state equilibrium acting as a reservoir for charge carrier formation. Furthermore, clear evidence of enhanced triplet populations, which form in less than 1 ps, is observed. Using group theory, we show that this ultrafast triplet formation is due to highly efficient, quantum mechanically allowed intersystem crossing between the bright, initially photoexcited local singlet state and the triplet charge transfer state. Remarkably, the free charges that form via the charge transfer state are extraordinarily long-lived with millisecond lifetimes, possibly due to the stabilisation imparted by the spatial separation of PCPDT-sFCN's donor and orthogonal acceptor motifs. The efficient generation of long-lived charge carriers in a pristine polymer paves the way for single-material applications such as organic photovoltaics and photodetectors.

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.

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.

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.

Vibrationally Assisted Intersystem Crossing in Benchmark Thermally Activated Delayed Fluorescence Molecules.

Electrically injected charge carriers in organic light-emitting devices (OLEDs) undergo recombination events to form singlet and triplet states in a 1:3 ratio, representing a fundamental hurdle for achieving high quantum efficiency. Dopants based on thermally activated delayed fluorescence (TADF) have emerged as promising candidates for addressing the spin statistics issue in OLEDs. In these materials, reverse singlet-triplet intersystem crossing (rISC) becomes efficient, thereby activating luminescence pathways for weakly emissive triplet states. However, despite a growing consensus that torsional vibrations facilitate spin-orbit-coupling- (SOC-) driven ISC in these molecules, there is a shortage of experimental evidence. We use transient electron spin resonance and theory to show unambiguously that SOC interactions drive spin conversion and that ISC is a dynamic process gated by conformational fluctuations for benchmark carbazolyl-dicyanobenzene TADF emitters.

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.

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.

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.

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.

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.