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.

A Decentralized Iron Cage: Do Chinese Local Officials Comply with the Central Government?

This paper contributes to the literature in nancial aid and authoritarian institutions.

For a long time, scholars are debating whether nancial aid is able to facilitate

development and governance. Though abundant evidence is provided, the answer is

still inconclusive. On the other hand, scholars investigating China argue that the

leadership uses various institutions to ensure local ocials' compliance. In this paper,

we nd that the nancial aid does not bring a positive impact and the central

government in China does not have enough monitoring capacity to force local o-

cials to comply. We study a redevelopment program established by Chinese central

government after the 2008 Wenchuan earthquake. By adopting a geographic regression

discontinuity combining with a dierence-in-dierences design, we show that

the redevelopment program does not signicantly develop the disaster area. On the

contrary, the evidence implies that the economy in the disaster area is worse after

receiving the aid. The results imply that local ocials do not follow the central government's

regulations and misuse the aid money for other purposes. In the future, we

expect to further investigate through which mechanism do local ocials undermine

the existing institutions.

iii

Numerical detection of the Gardner transition in a mean-field glass former.

Recent theoretical advances predict the existence, deep into the glass phase, of a novel phase transition, the so-called Gardner transition. This transition is associated with the emergence of a complex free energy landscape composed of many marginally stable sub-basins within a glass metabasin. In this study, we explore several methods to detect numerically the Gardner transition in a simple structural glass former, the infinite-range Mari-Kurchan model. The transition point is robustly located from three independent approaches: (i) the divergence of the characteristic relaxation time, (ii) the divergence of the caging susceptibility, and (iii) the abnormal tail in the probability distribution function of cage order parameters. We show that the numerical results are fully consistent with the theoretical expectation. The methods we propose may also be generalized to more realistic numerical models as well as to experimental systems.