Singlet–Triplet Inversion in Heptazine and in Polymeric Carbon Nitrides

Abstract

According to Hund's rule, the lowest triplet state (T 1 ) is lower in energy than the lowest excited singlet state (S 1 ) in closed-shell molecules. The exchange integral lowers the energy of the triplet state and raises the energy of the singlet state of the same orbital character, leading to a positive singlet−triplet energy gap (Δ ST ). Exceptions are known for biradicals and charge-transfer excited states of large molecules in which the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) are spatially separated, resulting in a small exchange integral. In the present work, we discovered with ADC(2), CC2, EOM-CCSD, and CASPT2 calculations that heptazine (1,3,4,6,7,9,9bheptaazaphenalene or tri-s-triazine) exhibits an inverted S 1 /T 1 energy gap (Δ ST ≈ −0.25 eV). This appears to be the first example of a stable closedshell organic molecule exhibiting S 1 /T 1 inversion at its equilibrium geometry. The origins of this phenomenon are the nearly pure HOMO− LUMO excitation character of the S 1 and T 1 states and the lack of spatial overlap of HOMO and LUMO due to a unique structure of these orbitals of heptazine. The S 1 /T 1 inversion is found to be extremely robust, being affected neither by substitution of heptazine nor by oligomerization of heptazine units. Using time-resolved photoluminescence and transient absorption spectroscopy, we investigated the excited-state dynamics of 2,5,8-tris(4-methoxyphenyl)-1,3,4,6,7,9,9bheptaazaphenalene (TAHz), a chemically stable heptazine derivative, in the presence of external heavy atom sources as well as triplet-quenching oxygen. These spectroscopic data are consistent with TAHz singlet excited state decay in the absence of a low-energy triplet loss channel. The absence of intersystem crossing and an exceptionally low radiative rate result in unusually long S 1 lifetimes (of the order of hundreds of nanoseconds in nonaqueous solvents). These features of the heptazine chromophore have profound implications for organic optoelectronics as well as for water-splitting photocatalysis with heptazinebased polymers (e.g., graphitic carbon nitride) which have yet to be systematically explored and exploited.

Singlet‐Triplet Excited‐State Inversion in Heptazine and Related Molecules: Assessment of TD‐DFT and ab initio Methods

“…Generally speaking, the global accuracy of TD‐DFT is out of question, as well as its excellent trade‐off between accuracy and computational cost for real‐world applications, but these are also examples for which the adiabatic approximation (i. e., frequency‐independent kernels) introduces some limits [30] . This issue is further explored here, hopefully complementing previous studies [20,21] after inspecting first the corresponding theoretical expression in which the TD‐DFT singlet‐triplet gap is based. Additionally, we will try to provide insights, beyond the one‐electron molecular picture, [31] to understand why (highly) correlated methods are able to cope with the underlying electronic structure of these systems, and thus predicting the correct order and energy of excited‐states, contrarily to what happens with TD‐DFT.…”

“…Next, we will summarize the available experimental and theoretical information about these systems. Recent experimental studies on heptazine (actually a substituted heptazine but with substituents attached to the corners weakly affecting its electronic structure and photophysics) clearly evidenced the inversion of S 1 and T 1 states [21] from the observed long lifetime of the S 1 state in presence or in absence of molecular oxygen which is expected to quench triplet excited states. Prompt and delayed fluorescence has been also demonstrated on several heptazine derivatives [53] .…”

“…Actually, it was also experimentally found a very short lifetime of the T 1 state of 2T‐4N, [55] compatible with a radiationless intersystem crossing and thus isoenergetic energy levels. From a theoretical point of view, previous estimates of at different sophisticated theoretical levels such as RAS‐SF, ADC(2), and EOM‐CCSD predicted values between −0.10 and −0.16 eV for 2T‐N, [20,56] while ADC(2), CC2, EOM‐CCSD, and CASPT2 methods predicted energies between −0.18 and −0.28 eV for 2T‐7N [21] …”

“…Particularly interesting from both an experimental and theoretical point of view, e. g. in the search of more efficient photophysical applications, is the location of the lowest singlet and triplet excited‐state energy levels of triangular shape molecules. Recent interesting works have shown a violation of Hund's multiplicity rule in N‐doped triangulenes, namely cyclazine and heptazine, with the lowest triplet excited‐state ( T 1 ) found higher in energy than the lowest singlet excited‐state ( S 1 ) contrarily to almost all known closed‐shell organic molecules [20,21] . Violation of Hund's rule has been studied before, mostly for establishing the correct spin multiplicity of the ground‐state, [22,23] and it can occur for π ‐conjugated hydrocarbons with a bipartite lattice.…”

“…Concerning the methods choice, Time‐Dependent Density‐Functional Theory (TD‐DFT) [26–29] has been shown unable before to provide for these molecules the correct order of the states, independently of the exchange‐correlation functional selected [20,21] . Generally speaking, the global accuracy of TD‐DFT is out of question, as well as its excellent trade‐off between accuracy and computational cost for real‐world applications, but these are also examples for which the adiabatic approximation (i. e., frequency‐independent kernels) introduces some limits [30] .…”