Promoting Singlet/triplet Exciton Transformation in Organic Optoelectronic Molecules: Role of Excited State Transition Configuration

Exciton transformation, a non-radiative process in changing the spin multiplicity of an exciton usually between singlet and triplet forms, has received much attention recently due to its crucial effects in manipulating optoelectronic properties for various applications. However, current understanding of exciton transformation mechanism does not extend far beyond a thermal equilibrium of two states with different multiplicity and it is a significant challenge to probe what exactly control the transformation between the highly active excited states. Here, based on the recent developments of three types of purely organic molecules capable of efficient spin-flipping, we perform ab initio structure/energy optimization and similarity/overlap extent analysis to theoretically explore the critical factors in controlling the transformation process of the excited states. The results suggest that the states having close energy levels and similar exciton characteristics with same transition configurations and high heteroatom participation are prone to facilitating exciton transformation. A basic guideline towards the molecular design of purely organic materials with facile exciton transformation ability is also proposed. Our discovery highlights systematically the critical importance of vertical transition configuration of excited states in promoting the singlet/triplet exciton transformation, making a key step forward in excited state tuning of purely organic optoelectronic materials.


Computational Details
The density functional theory (DFT) 1 and time-dependent density functional theory (TD-DFT) 2 calculations were performed to investigate the singlet/triplet exciton transformation using Gaussian 09 package. 3 The Becker's three-parameter exchange functional along with the Lee Yang Parr's correlation functional (B3LYP) that can well predict the geometric structures of organic molecules, 4 was adopted to optimize the ground state (S0) geometries of all molecules in conjunction with the 6-31G(d) basis set. The optimized structures were further characterized by harmonic vibrational frequency analysis to confirm that real local minima without any imaginary frequency was reached at the same computational level. TD-DFT calculations by the B3LYP (20% HF), 5 PBE0 (25% HF), 6 BMK (42% HF), 7 M06-2X (56% HF), 8 and M06-HF (100% HF) 9 functionals with 6-31G(d) basis set were performed based on the optimized ground-state geometries to investigate the vertical excited energies and the singlet-triplet energy splitting (ΔEST) ( Table S1). The vertical excitation energies of the studied molecules were also evaluated using the range separated hybrid exchange functional of ωB97XD, 10 which consists in a mix of short range density functional exchange with long range Hartree-Fock exchange (22% HF at short range and 100% at long range).
To get further insights into the nature of the excited states, NTOs analysis was performed based on TD-DFT results to offer a compact orbital representation for the electronic transition density matrix. 11 In addition, using the overlap integral function embedded in Multiwfn, 12 the overlap integrals of IH/L, IS and IT between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO), the highest occupied NTO (HONTO) and the lowest unoccupied NTO (LUNTO) at the singlet excited states (Sn) and triplet excited states (Tn) of investigated molecules can be calculated respectively. Excited state similarity was evaluated through the contribution percentage difference between the singlet and triplet excited states in HONTO (sH) and LUNTO (sL).
Spin-orbit coupling (SOC) matrix elements between the singlet and triplet excited states are calculated with quadratic response function methods using the S3 Dalton program. 13 The SOCs of DPhCzT were performed at the optimized geometry of the first singlet excited state (S1) using B3LYP functional and cc-pVTZ basis set.
To identify proportion of (n, π * ) configuration (αn%) of the excited states, Mulliken population analysis (MPA) was performed to calculate the n orbital components with the aid of Multiwfn package. 14 As exemplified in DPhCzT, the lone-pair electrons of N atom in carbazole are localized on pz, while that of three N atoms in triazine are on px and py, since all the N atoms of DPhCzT are sp 2 hybridized. The single-center px,y ↔ pz transition can promote the SOC for efficient exciton transformation. Therefore, the n orbital components were calculated as the sum of pz of N atom in carbazole and px and py of N atoms in triazine. Based on the optimized geometries of S1 and T4 excited states at PBE0/6-31G(d) level, the S1 of DPhCzT was found to have a high component of 1 (n, π*) with n orbital proportion (αn%) of 14.3%, while the T4 is mainly 3 (π, π*) with αn% of 0.0%.

The singlet-triplet splitting (ΔEST)
Theoretically, the singlet-triplet energy splitting ΔEST is controlled by the electron-exchange energy, which is the twice of the exchange integral (J) 15 in value as described in equation (S1), resulting from the repulsion interaction of the two unpaired electrons (with electric charge of e) on the HOMO (φH) and LUMO (φL) orbitals as shown in equation (S2).
From equation (S2), J is determined by spatial separation (r1-r2) and overlap integral of φH and φL, i.e., spatial wave function separation of frontier orbitals. 16 In principle, a small overlap or a large separation between HOMO and LUMO will lead to a small ΔEST and vice versa. 17

The calculation of overlap integral
Using the overlap integral function embedded in Multiwfn, 12 More details about the overlap integral can be found in Multiwfn manual. 18

Natural transition orbital (NTO) analysis
Natural transition orbitals (NTOs) can offer a compact orbital representation for the electronic transition density matrix (T), which is diagonal with a dimension of and Nvirt. × Nvirt., respectively; U † denotes the conjugate transpose of matrix U; λi represents the singular value of matrix T; δij is the Kronecker delta. Notably, all one electron properties associated with the transition can be interpreted in a transparent way as a sum over the occupied natural transition orbitals, each orbital being paired with a single unoccupied orbital and weighted with the appropriate eigenvalue λi.
Hence, the NTO analysis can provide a compact description of an excited state with fewer orbital pairs than the ones given on the basis of frontier molecular orbitals. 11 Similarly to equation (S4), the overlap integral of the highest occupied NTO (HONTO) (φH') and the lowest unoccupied NTO (LUNTO) (φL') at Sn or Tn states described by NTO analysis can be calculated in equations (S8) and (S9), respectively.

Excited state similarity (s)
Following the previously developed calculation method of charge transfer amount, 19 excited state similarity in HONTO (sH) and LUNTO (sL) between the S5 singlet and triplet excited states can be calculated according to equation (S10): where iai=1 and ibi=1. The index i is the number of atoms in the molecule; ai and bi are the contribution percentages of different atoms in the frontier NTO of the corresponding singlet and triplet excited states, respectively. This orbital composition analysis was done by using Multiwfn. 12 ai-bi denotes the contribution percentage difference of an atom (i) in the HONTO (or LUNTO) between the singlet and triplet excited states.   Table S1. Calculated vertical excitation energies (ESn and ETn, in eV) and S1-T1 splitting (ΔEST 11 , in eV) of the excited singlet and triplet states using various functionals at 6-31G(d) basis set of DMAC-DPS, Spiro-CN, TAP-NZP, and DPhCzT in comparison with their experimental results (Exp.).        Table S7. TD-DFT calculated singlet (Sn) and triplet (Tn) excited state transition configurations of DCzPhP. The matched excited states that have the close excitation energy (|ΔEST| < 0.37 eV, highlighted in blue) and contain the same orbital transition components of S1 were highlighted in red.  Φf and ΦT are photoluminescent quantum yields of fluorescence and phosphorescence, respectively; τf is the lifetime of fluorescence; kf, kISC, and kIC are the rate constants of fluorescence, intersystem crossing, and internal conversion, respectively.