The method of increments is herein applied to produce accurate singlet triplet gaps, in a variety of challenging polyatomic systems involving main group elements. This strategy computes incremental Full Configuration Interaction (iFCI) energies for the two spin states in a size-extensive n-body expansion. iFCI avoids exponential costs when n is small and thus is dependent on choice of reference function to maintain good accuracy at polynomial cost. The new algorithm presented in this article therefore employs a high-spin perfect pairing reference to capture the major qualities of the singlet and triplet wave functions at n = 0. Systematic studies will show that singlet triplet gap predictions approach 1 kcal/mol accuracy at small n (n <= 3) compared with available experimental and high-level theoretical values.