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We employ the Laplace-transformed second-order Moller-Plesset perturbation theory for periodic systems in its atomic orbital basis formulation to determine the geometric structure and band gap of interacting polyacetylene chains. We have studied single, double, and triple chains, and also two-dimensional crystals. We estimate from first principles the equilibrium interchain distance and setting angle, along with binding energy between trans-polyacetylene chains due to dispersion interactions. The dependence of the correlation corrected quasiparticle band gap on the intrachain and interchain geometric parameters is studied, obtaining that the gap of the compound structures is substantially reduced with respect to the single chain polymer.

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We obtain exact solutions of the Klein-Gordon and Pauli Schrödinger equations for a two-dimensional hydrogen-like atom in the presence of a constant magnetic field. Analytic solutions for the energy spectrum are obtained for particular values of the magnetic field strength. The results are compared to those obtained in the non-relativistic and spinless case. We obtain that the relativistic spectrum does not present s states.

In the present article we study the energy levels of a 2D hydrogenic atom when a constant magnetic field is applied. We compute the energy spectrum with the help of a generalization of the mesh point technique recently proposed by Schwartz. We also estimate, via a variational method, the upper energy bound for small and large values of the external magnetic field. We show that the results obtained by O Mustafa (1993 J. Phys.: Condens. Matter 5 1327) have to be modified in the weak-magnetic-field regime.