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Using variational methods, we study the existence of stationary solutions to a periodic nonlinear Dirac–Maxwell system. Firstly, we prove the existence of n-periodic solutions to the system for all positive integers n. Then we use the concentration-compactness argument and the periodic approximation method for obtaining soliton-like solutions. We also investigate the existence of periodic ground states and soliton-like ground states, as well as their connection. Besides, results for the regularity of solutions and decay rate of the soliton-like solutions are given.

The mechanism of the adsorption between Au n (n=2,3,4) clusters and ethanol molecules is investigated with the density functional theory. It is found that Au n (n=2,3,4) clusters can adsorb several ethanol molecules to form the Aun-(C2H6O)1-ncompounds. There are many adsorbing conformations when the ethanol molecules are adsorbed by the Au4 cluster. The adsorbing sequence and the corresponding stable configurations are confirmed through the analysis of the adsorption energies and the Mulliken electrical displacement. When the last ethanol molecule is adsorbed,the bonding style changes from the Au—O bond to the Au—H bond. The constructions of the Aun clusters and the ethanol molecule are less changed in the adsorbing process. And the interaction between Aun clusters and ethanol molecules is weak interaction.