One implication of Hund's first rule for molecules is that the first excited triplet is, for most molecules, more stable than the first excited singlet. Only few structural motifs are known to violate it. Recently, the potential of such molecules has been appreciated as their inverted singlet-triplet gaps enable both favorable triplet exciton harvesting and low triplet exciton population to be utilized in both efficient and long-lived light-emitting diodes. Here, we report bottom-up design of organic molecules with inverted singlet-triplet gaps via the ring-bonds-substitutions (RiBS) rule set we introduce. It relies on simple rules based on orbital interactions in alternant hydrocarbons to both minimize the exchange integral between the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) and maximize dynamic spin polarization. Using RiBS, we find many molecules violating Hund's first rule in their first excited states, greatly expanding the chemical space of potential inverted singlet-triplet gap (INVEST) emitters.