Abstract
The lowest-energy singlet (S1) and triplet (T1) excited states of organic conjugated chromophores are known to be accurately calculated by modern wavefunction and Time-Dependent Density Functional Theory (TD-DFT) methods, with the accuracy of the latter heavily relying on the exchange-correlation functional employed. However, there are challenging cases for which this cannot be the case, due to the fact that those excited states are not exclusively formed by single excitations and/or are affected by marked correlation effects, and thus TD-DFT might fall short. We will tackle here a set of molecules belonging to the azaphenalene family, for which research recently documented an inversion of the relative energy of S1 and T1 excited states giving rise to a negative energy difference (ΔEST) between them and, thereby, contrary to most of the systems thus far treated by TD-DFT. Since methods going beyond standard TD-DFT are not extensively applied to excited-state calculations and considering how challenging this case is for the molecules investigated, we will prospectively employ here a set of non-standard methods (Multi-Configurational Pair Density Functional Theory or MC-PDFT) and correlation functionals (i.e., Lie–Clementi and Colle–Salvetti) relying not only on the electronic density but also on some modifications considering the intricate electronic structure of these systems.
Highlights
The violation of Hund’s rule in molecules [1], analogously to atoms, is commonly ascribed to an inversion of the excitation energies of the lowest states of spin-singlet (S1) or spin-triplet (T1) multiplicity
Note that the negative sign contradicts the fact that the exchange energy (K) is normally thought to be positive, historically ∆EST ≈ 2K, implying that the lowest singlet excited state lies energetically above the lowest triplet excited state and not the opposite
That exchange energy is known to be of the order of hundreds of meV for common organic chromophores, and this becomes a key parameter for photophysics and related applications [2,3,4]
Summary
The violation of Hund’s rule in molecules [1], analogously to atoms, is commonly ascribed to an inversion of the excitation energies of the lowest states of spin-singlet (S1) or spin-triplet (T1) multiplicity. The energy difference between S1 and T1 excited states, that is ∆EST = E(S1) − E(T1) is positive, contrary to what happens if Hund’s rule is altered (in that case, ∆EST would be negative). Note that the negative sign contradicts the fact that the exchange energy (K) is normally thought to be positive, historically ∆EST ≈ 2K, implying that the lowest singlet excited state lies energetically above the lowest triplet excited state and not the opposite. Fast environmental effects (whenever they are reliably introduced) could lead to negative ∆EST values
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
