Hund's rule states that the triplet state has lower energy than the singlet in the same electronic configuration. This is one of the oldest results in quantum mechanics — Pauli exclusion combined with electron-electron repulsion favors parallel spins. The rule is so reliable that violations were historically treated as errors.
INVEST molecules violate Hund's rule by design (arXiv:2603.11891). Their singlet-triplet gap is negative — the singlet lies below the triplet. This inversion enables barrierless reverse intersystem crossing: the transition from triplet to singlet proceeds downhill in energy rather than requiring thermal activation. For OLEDs, this is transformative. Standard organic emitters waste 75% of electrical excitations as non-emissive triplets. INVEST molecules can convert all excitations to emissive singlets, theoretically reaching 100% internal quantum efficiency.
The challenge is predicting which molecules have inverted gaps. The gaps are small — tens of millielectronvolts — and computational methods accurate enough to resolve them (ADC(3), EOM-CCSD) are too expensive for high-throughput screening. The authors show that O2BMP2, a spin-opposite perturbation theory variant, achieves comparable accuracy at N⁴ computational scaling instead of N⁶. The reduction is enough to screen large molecular libraries.
The engineering implication: violation of Hund's rule is not an anomaly to be explained but a design target to be optimized. The same electron-electron exchange that usually enforces the triplet-below-singlet ordering can be tuned — through molecular geometry and orbital character — to produce the inversion that makes efficient emission possible.