Internal conversion of singlet and triplet states employing numerical DFT/MRCI derivative couplings: Implementation, tests, and application to xanthone

Internal conversion induced by external electric and magnetic fields

We have developed a new methodology for calculating contributions to the rate constants (kIC) of internal conversion that are induced by external electric (kIC-E) or magnetic (kIC-M) fields. The influence of the external electric and magnetic fields on the kIC was estimated for seven representative molecules. We show that the kIC-E contribution calculated at a field strength of 1011 V m-1 is generally as large as the kIC rate constant in the absence of the external field. For indocyanine green, azaoxa[8]circulene, and pyromitene 567, the kIC-E contribution is as large as kIC already at a field strength of 109 V m-1. Such electric-field strengths occur for example in plasmonic studies and in strong laser-field experiments. The induced effect on the kIC rate constant should be accounted for in calculations of photophysical properties of molecules involved in such experiments. The induced effect of an external magnetic field on kIC can be neglected in experiments on Earth because the magnetic contribution becomes significant only at very strong magnetic fields of 104-105 T that cannot be achieved on Earth. However, the magnetic effect on the rate constant of internal conversion can be important in astrophysical studies, where extremely strong magnetic fields occur near neutron stars and white dwarfs.

Exciton Dynamics of a Diketo-Pyrrolopyrrole Core for All Low-Lying Electronic Excited States Using Density Functional Theory-Based Methods

Ab initio treatments of interexcited state internal conversion (IC) are more often than not missing from exciton dynamic descriptions, because of their inherent complexity. Here, we define "interexcited state IC" as a same-spin nonradiative transition between states i and j, where i ≠ j ≠ 0. Competing directly with multiexciton processes such as singlet fission or triplet photoupconversion, inclusion of this mechanism in the narrative of molecular photophysics would allow for strategic synthesis of chromophores for more efficient photon-harvesting applications. Herein, we present a robust formalism which can model these rates using density functional theory (DFT)-based methods within the Franck-Condon and Herzberg-Teller regime. Using an unsubstituted diketo-pyrrolopyrrole (DPP) core as a case study, we illustrate the exciton dynamics along the first four excited states for both singlet and triplet manifolds, showing ultrafast same-spin transfer mechanisms due to all excited states, excluding the first triplet level, being in close energetic proximity (within 0.8 eV of each other). The resulting electron same-spin rates outcompete the electron spin-flipping intersystem crossing (ISC) rates, with excitons firmly obeying Kasha's rule as they cascade down from the high-lying excited states toward the lower states. Furthermore, we calculated that only the first singlet excited state displayed a reasonable probability of triplet exciton generation, of ∼40%, with a near-zero chance of the exciton reverting to the singlet manifold once the electron-hole pair are of parallel spin.

Vibronic effects accelerate the intersystem crossing processes of the through-space charge transfer states in the triptycene bridged acridine–triazine donor–acceptor molecule TpAT-tFFO

Quantum chemical studies employing combined density functional and multireference configuration interaction methods suggest five excited electronic states to be involved in the prompt and delayed fluorescence emission of TpAT-tFFO. Three of them, a pair of singlet and triplet charge transfer (CT) states (S₁ and T₁) and a locally excited (LE) triplet state (T₃), can be associated with the (Me → N) conformer, the other two CT-type states (S₂ and T₂) form the lowest excited singlet and triplet states of the (Me → Ph) conformer. The two conformers, which differ in essence by the shearing angle of the face-to-face aligned donor and acceptor moieties, are easily interconverted in the electronic ground state whereas the reorganization energy is substantial in the excited singlet state, thus explaining the two experimentally observed time constants of prompt fluorescence emission. Forward and reverse intersystem crossing between the singlet and triplet CT states is mediated by vibronic spin–orbit interactions involving the LE T₃ state. Low-frequency vibrational modes altering the distance and alignment of the donor and acceptor π-systems tune the S₁ and T₃ states (likewise S₂ and T₃) into and out of resonance. The enhancement of intersystem crossing due to the interplay of vibronic and spin–orbit coupling is considered a general feature of organic through-space charge-transfer thermally activated delayed fluorescence emitters.

DFT/MRCI quantum chemical studies suggest five excited electronic states to be involved in the prompt and delayed fluorescence emission of TpAT-tFFO.

Ultrafast Intersystem Crossing in Xanthone from Wavepacket Dynamics

Most aromatic ketones containing first-row elements undergo unexpectedly fast intersystem crossing in a few tens of picoseconds and a quantum yield close to unity. Among them, xanthone (9H-xanthen-9-one) possesses one of the fastest singlet-triplet rates of only ∼1.5 ps. The exact mechanism of this unusually fast transition is still under debate. Here, we perform wavepacket dynamics of the photochemistry of xanthone in the gas phase and in polar solvents. We show that xanthone follows El-Sayed's rule for intersystem crossing. From the second singlet excited state, the mechanism is sequential: (i) an internal conversion between singlets ¹ππ* → ¹nπ* (85 fs), (ii) an intersystem crossing ¹nπ* → ³ππ* (2.0 ps), and (iii) an internal conversion between triplets ³ππ* → ³nπ* (602 fs). Each transfer finds its origin in a barrierless access to electronic state intersections. These intersections are close to minimum energy structures, allowing for efficient transitions from the initial singlet state to the triplets.

Removing the Deadwood from DFT/MRCI Wave Functions: The p-DFT/MRCI Method

The combined density functional theory and multireference configuration interaction (DFT/MRCI) method is a powerful tool for the calculation of excited electronic states of large molecules. There exists, however, a large amount of superfluous configurations in a typical DFT/MRCI wave function. We show that this deadwood may be effectively removed using a simple configuration pruning algorithm based on second-order Epstein-Nesbet perturbation theory. The resulting method, which we denote p-DFT/MRCI, is shown to result in orders of magnitude saving in computational timings, while retaining the accuracy of the original DFT/MRCI method.

Large Inverted Singlet-Triplet Energy Gaps Are Not Always Favorable for Triplet Harvesting: Vibronic Coupling Drives the (Reverse) Intersystem Crossing in Heptazine Derivatives

Heptazine derivatives are promising dopants for electroluminescent devices. Recent studies raised the question whether heptazines exhibit a small regular or an inverted singlet-triplet (IST) gap. It was argued that the S₁ ← T₁ reverse intersystem crossing (RISC) is a downhill process in IST emitters and therefore does not require thermal activation, thus enabling efficient harvesting of triplet excitons. Rate constants were not determined in these studies. Modeling the excited-state properties of heptazine proves challenging because fluorescence and intersystem crossing (ISC) are symmetry-forbidden in first order. In this work, we present a comprehensive theoretical study of the photophysics of heptazine and its derivative HAP-3MF. The calculations of electronic excitation energies and vibronic coupling matrix elements have been conducted at the density functional theory/multireference configuration interaction (DFT/MRCI) level of theory. We have employed a finite difference approach to determine nonadiabatic couplings and derivatives of spin-orbit coupling and electric dipole transition matrix elements with respect to normal coordinate displacements. Kinetic constants for fluorescence, phosphorescence, internal conversion (IC), ISC, and RISC have been computed in the framework of a static approach. Radiative S₁ ↔ S₀ transitions borrow intensity mainly from optically bright E' π → π* states, while S₁ ↔ T₁ (R)ISC is mediated by E″ states of n → π* character. Test calculations show that IST gaps as large as those reported in the literature are counterproductive and slow down the S₁ ← T₁ RISC process. Using the adiabatic DFT/MRCI singlet-triplet splitting of -0.02 eV, we find vibronically enhanced ISC and RISC to be fast in the heptazine core compound. Nevertheless, its photo- and electroluminescence quantum yields are predicted to be very low because S₁ → S₀ IC efficiently quenches the luminescence. In contrast, fluorescence, IC, ISC, and RISC proceed at similar time scales in HAP-3MF.

Modeling radiative and non-radiative pathways at both the Franck-Condon and Herzberg-Teller approximation level

Here, we present a concise model that can predict the photoluminescent properties of a given compound from first principles, both within and beyond the Franck-Condon approximation. The formalism required to compute fluorescence, Internal Conversion (IC), and Inter-System Crossing (ISC) is discussed. The IC mechanism, in particular, is a difficult pathway to compute due to difficulties associated with the computation of required bosonic configurations and non-adiabatic coupling elements. Here, we offer a discussion and breakdown on how to model these pathways at the Density Functional Theory (DFT) level with respect to its computational implementation, strengths, and current limitations. The model is then used to compute the photoluminescent quantum yield (PLQY) of a number of small but important compounds: anthracene, tetracene, pentacene, diketo-pyrrolo-pyrrole (DPP), and Perylene Diimide (PDI) within a polarizable continuum model. Rate constants for fluorescence, IC, and ISC compare well for the most part with respect to experiment, despite triplet energies being overestimated to a degree. The resulting PLQYs are promising with respect to the level of theory being DFT. While we obtained a positive result for PDI within the Franck-Condon limit, the other systems require a second order correction. Recomputing quantum yields with Herzberg-Teller terms yields PLQYs of 0.19, 0.08, 0.04, 0.70, and 0.99 for anthracene, tetracene, pentacene, DPP, and PDI, respectively. Based on these results, we are confident that the presented methodology is sound with respect to the level of quantum chemistry and presents an important stepping stone in the search for a tool to predict the properties of larger coupled systems.