Direct calculation of delocalization and resonance energies using truncated LMOs

The small “tails” of energy-localized SCF LMOs have been truncated to give TLMOs which are then symmetrically orthogonalized to obtain OTLMOs with a variational energy E (OTLMO). The “delocalization energy” DE = E (SCF)- E (OTLMO) is found to be reasonable when characteristic LMO hyperconjugation-delocalization corrections, HDCs, and geometry-change corrections, GCCs, are considered. The “resonance energy” is defined to be RE = DE -GCC- HDC i , e.g., for benzene − RE ≅90−23−3(8)=43 kcal mol −1 is estimated for the π-electrons, which is close to earlier estimates. We also estimate RE (CO 2 )= −149 kcal mol −1 , and RE (H 2 CCCH 2 )=−6 kcal mol −1 . Through using isodesmic reactions, errors due to electron correlation and incompleteness of basis sets are hopefully largely eliminated. The HDCs are also reasonable. We treat the delocalization energies of C 6 H 6 , CO 2 , H 2 CCCH 2 , C 2 H 4 , C 2 H 6 , H 2 CO and CH 4 .