Nonadiabatic derivative couplings through multiple Franck-Condon modes dictate the energy gap law for near and short-wave infrared dye molecules

Abstract

Near infrared (NIR, 700 - 1,000 nm) and short-wave infrared (SWIR, 1,000 - 2,000 nm) dye molecules exhibit significant nonradiative decay rates from the first singlet excited state to the ground state. While these trends can be empirically explained by a simple energy gap law, detailed mechanisms of the nearly universal behavior have remained unsettled for many cases. Theoretical and experimental results for two representative NIR/SWIR dye molecules reported here clarify the key mechanism for the observed energy gap law behavior. It is shown that the first derivative nonadiabatic coupling terms serve as major coupling pathways for nonadiabatic decay processes from the first excited singlet state to the ground state for these NIR and SWIR dye molecules and that vibrational modes other than the highest frequency ones also make significant contributions to the rate. This assessment is corroborated by further theoretical comparison with possible alternative mechanisms of intersystem crossing to triplet states and also by comparison with experimental data for deuterated molecules.

Figures (37)

• Figure 1: Comparison of the two organic dye molecules Flav5 (upper panel) and Flav7 (lower panel). For the latter, X represent positions of hydrogen atoms being deuterated and Y represents those for which 30% of hydrogen atoms are deuterated. Flav7 with all hydrogen atoms in the aryl rings deuterated are also considered.
• Figure 2: Comparison of the structures of Flav5 (left column) and Flav7 (right column) dye molecules. The top row provides chemical structures indicating different sections with different labels. The middle row shows optimized structures for the ${\rm S}_0$ state, and the bottom row those for the ${\rm S}_1$ state.
• Figure 3: A schematic of adiabatic potential energy surfaces for ${\rm S_0}$ (lower blue line) and ${\rm S_1}$ (upper red line) electronic states, which are in general anharmonic, and relevant energies. $\lambda_{10}$ is the reorganization energy in the ${\rm S}_1$ state from the minimum energy structure of ${\rm S}_0$ to the optimized structure of ${\rm S_1}$, and $\lambda_{01}$ is the reorganization energy in the ${\rm S}_0$ state from the minimum energy structure of ${\rm S}_1$ to the optimized structure of ${\rm S_0}$. Note that $\tilde{E}_0=E_0-\lambda_{01}$ and $\tilde{E}_1=E_1-\lambda_{10}$. Reorganization energies within the harmonic approximation, $\lambda_{h,10}$ and $\lambda_{h,01}$ are also shown (see text for more detailed explanation).
• Figure 4: Absorption ($S_0 \rightarrow S_1$) and emission ($S_1 \rightarrow S_0$) lineshapes for Flav5 (upper) and Flav7 (lower). Experimental lineshapes in solution phase are compared with theoretical lineshapes of isolated molecules, which were shifted to match the corresponding maxima of experimental spectra. For the absorption, the shifts were $1.423\ {\rm eV}$ for Flav5 and $1.191\ {\rm eV}$ for Flav7. For the emission, the shifts were $1.405\ {\rm eV}$ for Flav5 and $1.185\ {\rm eV}$ for Flav7. We also normalized heights with respect to those of their maxima.
• Figure 5: Nonadiabatic couplings projected on to each normal mode for the Flav5 (upper panel) and Flav7 (lower panel). Black lines represent results for original molecules and red lines represent those for fully deuterated ones.