Electron pairing: from metastable electron pair to bipolaron

Starting from the shell structure in atoms and the significant correlation within electron pairs, we distinguish the exchange-correlation effects between two electrons of opposite spins occupying the same orbital from the average correlation among many electrons in a crystal. In the periodic potential of the crystal with lattice constant larger than the effective Bohr radius of the valence electrons, these correlated electron pairs can form a metastable energy band above the corresponding single-electron band separated by an energy gap. In order to determine if these metastable electron pairs can be stabilized, we calculate the many-electron exchange-correlation renormalization and the polaron correction to the two-band system with single electrons and electron pairs. We find that the electron-phonon interaction is essential to counterbalance the Coulomb repulsion and to stabilize the electron pairs. The interplay of the electron-electron and electron-phonon interactions, manifested in the exchange-correlation energies, polaron effects, and screening, is responsible for the formation of electron pairs (bipolarons) that are located on the Fermi surface of the single-electron band.Comment: 17 pages, 6 figures, Journal of Physics Communications 201

1-[5-(2-Chloro­phen­yl)-5-hy­droxy-3-methyl-4,5-dihydro-1H-pyrazol-1-yl]­ethanone

The title compound, C12H13ClN2O2, crystallizes with two independent but very similar mol­ecules (A and B) in the asymmetric unit. The pyrazole ring in each mol­ecule has an envelope conformation. The dihedral angle between the pyrazole ring mean plane and the benzene ring is 86.07 (14)° in A and 85.99 (14)° in B. In the crystal, the A and B mol­ecules are linked via a pair of O—H⋯O hydrogen bonds, forming dimers. These dimers are further linked via C—H⋯O inter­actions to form –A–B–A–B– chains propagating along the c-axis direction

Solvable dilation model of PT\cal PT-symmetric systems

The dilation method is a practical way to experimentally simulate non-Hermitian, especially $\cal PT$-symmetric quantum systems. However, the time-dependent dilation problem cannot be explicitly solved in general. In this paper, we present a simple yet non-trivial exactly solvable dilation problem with two dimensional time-dependent $\cal PT$-symmetric Hamiltonian. Our system is initially set in the unbroken $\cal PT$-symmetric phase and later goes across the so-called exceptional point and enters the broken $\cal PT$-symmetric phase. For this system, the dilated Hamiltonian and the evolution of $\cal PT$-symmetric system are analytically worked out. Our result clearly showed that the exceptional points do not have much physical relevance in a \textit{time-dependent} system.Comment: 9 pages, 4 figures, close to the published versio

Methyl 2-amino-3,4,5,6-tetra­fluoro­benzoate

In the title compound, C8H5F4NO2, synthesized by esterification of 2,3,4,5-tetra­fluoro­anthranilic acid with methanol, an intra­molecular amine N—H⋯Ocarbon­yl hydrogen bond is present, while inter­molecular N—H⋯O hydrogen bonds produce chains in the crystal, which extend along the b-axis direction