Understanding the Control of Singlet-Triplet Splitting for Organic Exciton Manipulating: A Combined Theoretical and Experimental Approach

Developing organic optoelectronic materials with desired photophysical properties has always been at the forefront of organic electronics. The variation of singlet-triplet splitting (ΔEST) can provide useful means in modulating organic excitons for diversified photophysical phenomena, but controlling ΔEST in a desired manner within a large tuning scope remains a daunting challenge. Here, we demonstrate a convenient and quantitative approach to relate ΔEST to the frontier orbital overlap and separation distance via a set of newly developed parameters using natural transition orbital analysis to consider whole pictures of electron transitions for both the lowest singlet (S1) and triplet (T1) excited states. These critical parameters revealed that both separated S1 and T1 states leads to ultralow ΔEST; separated S1 and overlapped T1 states results in small ΔEST; and both overlapped S1 and T1 states induces large ΔEST. Importantly, we realized a widely-tuned ΔEST in a range from ultralow (0.0003 eV) to extra-large (1.47 eV) via a subtle symmetric control of triazine molecules, based on time-dependent density functional theory calculations combined with experimental explorations. These findings provide keen insights into ΔEST control for feasible excited state tuning, offering valuable guidelines for the construction of molecules with desired optoelectronic properties.

The residue was washed using acetone for 3 times to afford a white powder. Yield: 1.70 g: (90%).

Photophysical property measurements
UV/Vis absorption spectra were recorded on a PerkinEImer UV/Vis Spectrometer Lambda 35.
Fluorescence spectra were obtained using a PerkinEImer LS 55 Fluorescence Spectrometer. The phosphorescence spectra of the compound (in chloroform) were measured using an Edinburgh LFS920 fluorescence spectrophotometer at 77 K with a 5 ms delay time after excitation using a microsecond flash lamp.
The experimental ES1 of the compound was determined from the crossing point of the normalized absorption and emission spectra in chloroform at room temperature. 3 The experimental ET1 of the compound is determined from the highest energy vibronic component of its phosphorescence spectrum at S4

The singlet-triplet splitting (ΔEST)
In principle, the molecular energy at the lowest singlet (ES1) or triplet (ET1) excited states is decided by the sum of the orbital energy (E), electron repulsion energy (K) and electron exchange energy (J) of the two unpaired electrons on the frontier orbitals (φH and φL). The electrons at the same molecular orbital have the same E, K and J, however, the spin paired electrons have a positive J while the spin unpaired electrons have a negative J. 5 As described in equations (S1)-(S3), the exchange energy J is the most decisive factor for the singlet-triplet energy splitting of ΔEST.
From equation (S4), J is determined by spatial separation (r1-r2) and overlap integral of φH and φL, i.e., spatial wave function separation of frontier orbitals. 6 Thus a small ΔEST can be expected when there is a small overlap or a large separation between HOMO and LUMO, and a large overlap or a small separation will lead to a large ΔEST. 7 Their relations were demonstrated in Scheme S2.

The calculation of overlap extent
Using the overlap integral function embedded in Multiwfn, 8 More details about the orbital overlap calculations can be found in Multiwfn manual. 9

The calculation of the molecular orbital separation distance
Adopting the function outputting statistic data of the points in specific spatial and value range, the barycenter (rtot) of the absolute value of the molecular orbital can be computed as in equation (S8).
where f is the data value, r denotes coordinate vector, k runs over all grid points including positive and negative points respectively. Thus, the barycenter of HOMO and LUMO (rH and rL respectively) are And the mean distance between HOMO and LUMO is Supposing that the separation distance between HOMO and LUMO (r1-r2) is varying in a small range around (<rH/L>), equation (S5) can be simplified using equation (S11) to get equation (S12).

Natural transition orbital (NTO) analysis
Natural transition orbitals (NTOs), obtained via the singular value decomposition of the 1-particle transition density matrix (T), can offer a compact orbital representation for the electronic transition density Here, U and V are square unitary transformation matrices of dimensions Nocc. × Nocc. and Nvirt. × Nvirt., respectively, and 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, weighted with the appropriate eigenvalue λi. Hence, a NTO analysis is very convenient in providing a better description of an excited state with fewer orbital pairs than the ones given on the basis of frontier molecular orbitals. 11 Consequently, according to equation (S7), the overlap extent of the highest occupied NTO (HONTO) (φH') and the lowest unoccupied NTO (LUNTO) (φL') at S1 or T1 states described by NTO analysis can be calculated in equations (S15)~(S16), respectively. And according to equations (S9) and (S10), the barycenters of HONTO and LUNTO at S1 or T1 states can be expressed in equations (S17)~(S20), respectively Thus, the mean distances between HONTO and LUNTO at S1 or T1 states are The values of IS, IT, <rS>, and <rT> have considered the whole picture of the electron interactions of the corresponding excited states, providing more information and physical insights of the excited states than IH/L and <rH/L>.
All in all, in principle, the ΔEST can be expressed in equation (S5) and can be simplified to equation (S13). From equation (S5) and (S13), the ΔEST is dependent on the frontier orbital overlap extent and separation distance at S0 state. The higher overlap of HOMO and LUMO and smaller spatial separation (r1-r2) lead to higher ΔEST.