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

Abstract

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.

On the origin of the inverted singlet–triplet gap of the 5th generation light-emitting molecules

“…However, increasing the active space to 14 electrons in 14 orbitals (14,14) yielded an inverted singlet-triplet gap for all six molecules. Considering the dynamic correlation at the CASPT2 level on top of the (12,9) CASSCF calculations also led to the exhibition of the INVEST property in all the studied molecules. CASPT2 calculation with a (14,14) reference on molecule 1 yielded almost the same singlet-triplet gap as obtained in the (12,9) CASPT2 calculation suggesting that the energy gaps obtained in the CASPT2 (9,12) calculations are accurate.…”

“…Calculations at the CASSCF level using an active space with 12 electrons in 9 orbitals (12,9) showed that molecules 1, 2, and 3 are INVEST molecules, whereas 4, 5, and 6 are not. However, increasing the active space to 14 electrons in 14 orbitals (14,14) yielded an inverted singlet-triplet gap for all six molecules.…”

Establishing design strategies for emissive materials with an inverted singlet–triplet energy gap (INVEST): a computational perspective on how symmetry rules the interplay between triplet harvesting and light emission

“…The RISC rate from T 2 to S 1 computed without accounting for vibronic effects (HT-like or reverse internal conversion from T 1 to T n ) leads to a range of values compatible with that measured experimentally for MR-TADF emitters (see Table 3). However, recently, Marian et al 62 highlighted the critical role played by the Herzberg–Teller mechanism in promoting a non-vanishing SOC for mediating an efficient S 1 –T 1 interconversion in heptazine and its derivative, leading to an increase in RISC rate resulting from symmetry lowering. Furthermore, a similar mechanism is also expected to enhance the S 1 –T n spin interconversion.…”

Origin of the Failure of Density Functional Theories in Predicting Inverted Singlet–Triplet Gaps

“… 14 Dinkelbach et al studied the effect of negative singlet–triplet gap and vibronic coupling in heptazine derivatives using the DFT/multireference configuration interaction (DFT/MRCI) approach. 23 Sancho-Garcia and co-workers suggested that small chemical modifications of the triangle derivatives can produce good candidates for inverted singlet–triplet gap using several single reference correlated methods like spin-component scaled second-order coupled cluster (SCS-CC2), 24 second-order ADC [ADC(2)], 25 and multireference methods like complete active space self-consistent field (CASSCF) and N-electron valence second-order perturbation theory (NEVPT2). 26 − 28 Domain-based local pair natural orbital (DLPNO) similarity transformed EOM-CCSD (STEOM-CCSD) 29 have accurately predicated inverted singlet–triplet gaps as well.…”