In this paper, methods of correlation corrections for 1D and 2D periodic systems as well as for 1D nonperiodic polymers are reviewed. These procedures include not only the correlation correction of the total energy per unit cell, but also the recalculation (using the generalized electronic polaron model) of the band structures themselves in the periodic case, as well as the density of states (DOS) in nonperiodic chains. In both cases the inverse Dyson equation was used in an iterative way in the MP/2 and MP/3 level. The programming of the same procedure for the coupled cluster method is in progress. In a number of examples (ground state properties of (SN)X, the gap of alternating trans-polyacetylene, the exciton spectrum of diacetylene, polyglycine and polyalanine, of a cytosine stack, the bulk modules of polyethylene, the hopping conductivity of insulin), we have obtained quite good agreement with experiment, if a good basis set ab initio calculation was supplemented of the correlation correction at the bands or DOS curves, respectively. In the second part of the paper a new method is developed to take into account the simulataneous effect of a static and a periodic time-dependent electric field on the one-electron wave functions and on the total electronic energy of a periodic polymer. The method uses a variational technique (coupled Hartree–Fock equations) instead of perturbation theory for the time-dependent one-electron wave functions. The proper treatment of the potential caused by the field, which in this way does not destroy the periodicity of the polymer, as well as the inclusion of correlation at the MP/2 level of the t-and ω-dependent quasienergy per unit cell is part of the method. Finally, it is shown how one obtains in the usual way the different polarizabilities, second- and third-order hyperpolarizability tensor elements with the help of the derivatives of the quasienergies according to the different field (both static and time-dependent) components. © 1993 John Wiley & Sons, Inc.