Intersystem crossing rate dependent dual emission and phosphorescence from cyclometalated platinum complexes: a second order cumulant expansion based approach

Abstract

Rates of intersystem crossing (kISC) of two platinum(ii) complexes containing acetylacetonate (acac) and extended cyclometalated ppy (Hppy = 2-phenylpyridine) (1) and thpy (Hthpy = 2-(2' thienyl)pyridine) (2) ligands are calculated using the Condon approximation to the Golden Rule and employing the second-order cumulant expansion method. The emission wavelengths obtained at the RI-CC2 level for the lowest excited singlet (S1) and triplet (T1) states of the two complexes are well in agreement with the experimental results. Our analysis based on kISC evinces that the major pathway involved with the phosphorescence process in complex 1 arises from the S1 → T2 intersystem crossing while the S1 → T1 intersystem crossing is the key step towards the commencement of dual emission in complex 2. Furthermore, it is found that the different pathways are mostly guided by two factors namely, the energy gap and the spin-orbit interaction between the concerned states. Interestingly, the calculated kISC for complex 1 is found to be 107 times larger than that of complex 2, which suggests a rapid depletion of the S1 state population vis-à-vis radiative emission only by phosphorescence from the internally converted lowest excited triplet state while for complex 2, the relatively lower kISC is attributed to the dual emission from this complex.

Behind the scenes of spin-forbidden decay pathways in transition metal complexes

“…107 As a consequence, p-SOC method is now widely used to compute the SOC matrix elements of large transition metal complexes. [108][109][110] However, this approach should in principle be always used in combination with specially designed ZORA basis, as one might otherwise get significant errors.…”

“…The singlet to triplet transition under study must have a large metal contribution in order to have a substantial amount of SOC. 109,120 For instance, the S 1 | ĤSO |T 1 and S 1 | ĤSO |T 2 values for (acetylacetonato)-bis(1-methyl-2-phenylimidazol)iridium(III) (aka N966) complex is 93 and 513 cm −1 , respectively. 108 This stark difference is reasonable as only the latter matrix element involves charge transfer from the 5d orbital of iridium to the acetylacetonato group.…”

“…Metal-to-ligand charge-transfer states involve excitations from the heavy-atom center, leading to stronger SOC and thereby enhanced phospho-rescence quantum yield. 15,109,128 The second term in Eq. 6 is important for purely organic molecules.…”

Strong Duschinsky Mixing Induced Breakdown of Kasha’s Rule in an Organic Phosphor

“…We have calculated the rate of ISCs (k ISCs ) explicitly using the Condon approximation to the Fermi Golden rule within the framework of the time-dependent second-order cumulant expansion approach that includes Duschinsky mixing effect. 17 Furthermore, the vibronic contribution of the two triplet states (T 1 and T 2 ) and the corresponding phosphorescence lifetimes (τ) 18 for the two states are also computed.…”

“…The simplified expression for k ISC is given as 1is obtained by separating the real and imaginary part of the cumulants. 17,25,26 The first term provides the square of the SOC matrix elements for the S 1 →T n transition (<T 1 |H SOC |S 1 > = 25 cm -1 and <T 2 |H SOC |S 1 > = 29 cm -1 ), whereas the second term consists of the real time-independent (κ R,TI ) part, the real time-dependent (κ R,TD ) part and the imaginary (κ Im ) part of the cumulant expansion, which inturn contains the Duschinsky rotation matrix (J) and the displacement vector (D) connecting the normal modes of triplet (Q T ) and singlet (Q S ) states. The SOC matrix elements are calculated using the zero-order regular approximation (ZORA) as implemented in ADF 2016.…”