  A systematic method for determining correlated wavefunctions of extended
systems in the ground and excited states is presented. It allows to fully
exploit the power of quantum-chemical programs designed for correlation
calculations of finite molecules. Using localized Hartree-Fock (HF) orbitals
(both occupied and virtual ones), an effective Hamiltonian which can easily be
transferred from finite to infinite systems is built up. Correlation
corrections to the matrix elements of the effective Hamiltonian are derived
from clusters. To treat correlation effects, multireference configuration
interaction (MRCI) calculations with singly and doubly excited configurations
(SD) are performed. This way one is able to generate both valence and
conduction bands where all correlation effects in the excited states as well as
in the ground state of the system are taken into account. An appropriate
size-extensivity correction to the MRCI(SD) correlation energies is developed
which takes into account the open-shell character of the excited states. This
approach is applicable to a wide range of polymers and crystals. In the present
work trans-polyacetylene is chosen as a test system. The corresponding band
structure is obtained with the correlation of all electrons in the system being
included on a high level of sophistication. The account of correlation effects
leads to substantial shifts of the "center-of-mass" positions of the bands
(valence bands are shifted upwards and conduction bands downwards) and a
flattening of all bands compared to the corresponding HF band structure.
Further an extention of the above approach to excitons (optical excitations) in
crystals is developed which allows to use standard quantum-chemical methods to
describe the electron-hole pairs and to finally obtain excitonic bands.
