Structural manifestation of the delocalization error of density functional approximations: C(4N+2) rings and C(20) bowl, cage, and ring isomers.

The ground state structure of C(4N+2) rings is believed to exhibit a geometric transition from angle alternation (N < or = 2) to bond alternation (N > 2). All previous density functional theory (DFT) studies on these molecules have failed to reproduce this behavior by predicting either that the transition occurs at too large a ring size, or that the transition leads to a higher symmetry cumulene. Employing the recently proposed perspective of delocalization error within DFT we rationalize this failure of common density functional approximations (DFAs) and present calculations with the rCAM-B3LYP exchange-correlation functional that show an angle-to-bond-alternation transition between C(10) and C(14). The behavior exemplified here manifests itself more generally as the well known tendency of DFAs to bias toward delocalized electron distributions as favored by Huckel aromaticity, of which the C(4N+2) rings provide a quintessential example. Additional examples are the relative energies of the C(20) bowl, cage, and ring isomers; we show that the results from functionals with minimal delocalization error are in good agreement with CCSD(T) results, in contrast to other commonly used DFAs. An unbiased DFT treatment of electron delocalization is a key for reliable prediction of relative stability and hence the structures of complex molecules where many structure stabilization mechanisms exist.

People over forty feel 20% younger than their age: subjective age across the lifespan.

Subjective age--the age people think of themselves asbeing--is measured in a representative Danish sample of 1,470 adults between 20 and 97 years of age through personal, in-home interviews. On the average, adults younger than 25 have older subjective ages, and those older than 25 have younger subjective ages, favoring a lifespan-developmental view over an age-denial view of subjective age. When the discrepancy between subjective and chronological age is calculated as a proportion of chronological age, no increase is seen after age 40; older respondents feel 20% younger than their actual age. Demographic variables (gender, income, and education) account for very little variance in subjective age.

Distribution of important and word-cued autobiographical memories in 20-, 35-, and 70-year-old adults.

For word-cued autobiographical memories, older adults had an increase, or bump, from the ages 10 to 30. All age groups had fewer memories from childhood than from other years and a power-function retention for memories from the most recent 10 years. There were no consistent differences in reaction times and rating scale responses across decades. Concrete words cued older memories, but no property of the cues predicted which memories would come from the bump. The 5 most important memories given by 20- and 35-year-old participants were distributed similarly to their word-cued memories, but those given by 70-year-old participants came mostly from the single 20-to-30 decade. No theory fully accounts for the bump.