Problematic Energy Differences between Cumulenes and Poly-ynes: Does This Point to a Systematic Improvement of Density Functional Theory?

Abstract

Relative energetics of the C 3 H 4 (allene ( 1 ) and propyne ( 2 )), C 5 H 4 (penta-1,2,3,4-tetraene ( 3 ) and penta-1,3-diyne ( 4 )), and C 7 H 4 (hepta-1,2,3,4,5,6-hexaene ( 5 ) and hepta-1,3,5-triyne ( 6 )) cumulene and poly-yne structures were systematically examined using DFT (B3LYP, BLYP, and BP86), MP2, and CCSD(T) theories. The isomer energy separations, Δ E, were studied with three schemes: standard optimizations and energy determinations (CCSD(T)/cc-pVXZ//MP2/cc-pVTZ), heats of formation predictions via isodesmic and homodesmotic reactions (CCSD(T)/cc-pVTZ//MP2/cc-pVTZ), and BHLYP functional analysis fitted to experimental data. For the C 3 H 4 isomers, Δ E was determined to be −1.4 and −1.4 kcal/mol for the first two schemes, with the BHLYP functional analysis being fit to the experimental Δ E of −1.4 ± 0.5 kcal/mol. The three schemes yield Δ E values of −8.8, −10.1, and −11.7 kcal/mol, respectively, for the C 5 H 4 isomers 3 and 4 . The C 7 H 4 isomers 5 and 6 are separated by −14.3, −16.3, and −19.7 kcal/mol when the three schemes are applied. The theoretical heats of formations, Δ H f, for 1 and 2 are 45.5 (47.4 ± 0.3) and 44.1 kcal/mol (46.0 ± 0.2) at the CCSD(T)/cc-pVTZ//MP2/cc-pVTZ level, respectively (experimental values in parentheses). At the same level of theory, 3 − 6 give Δ H f 's of 111.1, 101.1, 171.6, and 155.4 kcal/mol, respectively. Results from BXLYP (X being a variable to describe the amount of HF exchange included) and energy decomposition analyses in conjunction with previous studies lead to the conclusions that gradient-corrected functionals are not properly constructed to handle delocalized cumulenes and that they tend to overstabilize them.