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.

Memory and coping with stress: the relationship between cognitive-emotional distinctiveness, memory valence, and distress.

Cognitive-emotional distinctiveness (CED), the extent to which an individual separates emotions from an event in the cognitive representation of the event, was explored in four studies. CED was measured using a modified multidimensional scaling procedure. The first study found that lower levels of CED in memories of the September 11 terrorist attacks predicted greater frequency of intrusive thoughts about the attacks. The second study revealed that CED levels are higher in negative events, in comparison to positive events and that low CED levels in emotionally intense negative events are associated with a pattern of greater event-related distress. The third study replicated the findings from the previous study when examining CED levels in participants' memories of the 2004 Presidential election. The fourth study revealed that low CED in emotionally intense negative events is associated with worse mental health. We argue that CED is an adaptive and healthy coping feature of stressful memories.