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.

Ventricular conduction and long-term heart failure outcomes and mortality in African Americans: insights from the Jackson Heart Study.

BACKGROUND: QRS prolongation is associated with adverse outcomes in mostly white populations, but its clinical significance is not well established for other groups. We investigated the association between QRS duration and mortality in African Americans. METHODS AND RESULTS: We analyzed data from 5146 African Americans in the Jackson Heart Study stratified by QRS duration on baseline 12-lead ECG. We defined QRS prolongation as QRS≥100 ms. We assessed the association between QRS duration and all-cause mortality using Cox proportional hazards models and reported the cumulative incidence of heart failure hospitalization. We identified factors associated with the development of QRS prolongation in patients with normal baseline QRS. At baseline, 30% (n=1528) of participants had QRS prolongation. The cumulative incidences of mortality and heart failure hospitalization were greater with versus without baseline QRS prolongation: 12.6% (95% confidence interval [CI], 11.0-14.4) versus 7.1% (95% CI, 6.3-8.0) and 8.2% (95% CI, 6.9-9.7) versus 4.4% (95% CI, 3.7-5.1), respectively. After risk adjustment, QRS prolongation was associated with increased mortality (hazard ratio, 1.27; 95% CI, 1.03-1.56; P=0.02). There was a linear relationship between QRS duration and mortality (hazard ratio per 10 ms increase, 1.06; 95% CI, 1.01-1.12). Older age, male sex, prior myocardial infarction, lower ejection fraction, left ventricular hypertrophy, and left ventricular dilatation were associated with the development of QRS prolongation. CONCLUSIONS: QRS prolongation in African Americans was associated with increased mortality and heart failure hospitalization. Factors associated with developing QRS prolongation included age, male sex, prior myocardial infarction, and left ventricular structural abnormalities.