The quantum Rabi model can be solved exactly by the Bargmann transformation from real coordinate to complex variable recently [Phys. Rev. Lett. 107, 100401 (2011)]. By the extended coherent states, we recover this solution in an alternative simpler and perhaps more physical way without uses of any extra conditions, like Bargmann conditions. In the same framework, the twophoton Rabi model are solved exactly by extended squeeze states. Transcendental functions have been derived with the similar form as those in one-photon model. Both extended coherent states and squeeze states are essentially Fock states in the space of the corresponding Bogoliubov operators. The present approach could be easily extended to study the exact solvability or integrability of various spin-boson systems with multi-level, even multi-mode.

The structures of Fe 2 O 3 nanoparticles with different sizes were investigated using Fe K-edge X-ray absorption near-edge structure (XANES) and the FEFF calculations, as well as surface modification with enediol ligands. The studies not only revealed the existence of under-coordinated Fe sites in the nanoparticles but also confirmed that these under-coordinated sites were located on the surface. Upon binding of enediol ligands, surface sites were restructured to octahedral sites. In particular, the nature of the surface defects and their correlation with the unique properties of the nanoparticles were discussed. Model calculations were conducted for Fe m O n (m g 1, n g 4) clusters of various sizes centered at Fe sites with octahedral (O h ), distorted octahedral (C 3V ) and tetrahedral (T d ) coordination geometry using FEFF8.10 programs. The main features of the calculated spectra agree with the experimental results and were correlated to the density of states, the Fe coordination geometry, and the long-range order of the lattice.

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Utilization of nonprecious transition metals for high alcohols synthesis is of a great importance in heterogeneous catalysis. We synthesized successfully cobalt metal-carbide (Co− Co 2 C) catalysts, which present remarkable activity and selectivity for high alpha-alcohols via the Fischer−Tropsch reaction. The formation of the stable cobalt carbide and the Co−Co 2 C interface are found to be essential for the observed reactivity. Density functional theory calculations show that Co 2 C is highly efficient for CO nondissociative adsorption, behaving as noble-metal-like, whereas the Co metal is highly active for CO dissociative adsorption and the subsequent carbon-chain growth. The interface between the cobalt metal and its carbide phase, as well as the dual sites available at the interface for facile CO insertion to hydrocarbon, could be used to rationalize the design of the nonprecious transition metal catalysts for the oxygenates in syngas conversion.