Electron correlation and dimerization in trans-polyacetylene: Many-body perturbation theory versus density-functional methods.

Abstract

Structural and energetic aspects of the Peierls-type lattice dimerization were investigated in infinite, one-dimensional, periodic trans-polyacetylene (t-PA) using many-body perturbation theory (MBPT) and density-functional theory (DFT). Cohesive properties and dimerization parameters were obtained first for the classical Coulomb potential in the Hartree approximation and then by gradually turning on exchange and correlation potentials. Besides the nonlocal Hartree-Fock exchange, several other exchange functionals were used incorporating gradient corrections as well. For MBPT, electron correlation was included up to the fourth order of the Mo/ller-Plesset scheme and the behavior of lattice sums for different PT terms was analyzed in detail. The electrostatic part of the infinite lattice sums was computed by the multipole expansion technique. In solving the polymer Kohn-Sham equations, the performance of several different correlation potentials was studied again including different gradient corrections. Atomic basis sets of systematically increasing size, in the range of double-zeta to triple-zeta (TZ) up to TZ (3df,3p2d), were used in all calculations to construct the symmetry-adapted (Bloch-type) polymer wave functions, to fully optimize the structures, and to extrapolate different physical quantities to the limit of a hypothetical infinite basis set. Comparison of the different DFT results with MBPT and with experiments demonstrated the importance of gradient terms both for exchange and correlation. On the other hand, the best DFT functional, using a medium-size atomic basis set, excellently reproduced the cohesive and dimerization energies obtained for infinite t-PA at the MP4/TZ(3d2f,3p2d) level and provided dimerization parameters close to experiment. The experimentally observed lattice spacing of 2.46\ifmmode\pm\else\textpm\fi{}0.01 \AA{} will be correctly predicted both at the MBPT and DFT levels with 2.48 and 2.44 \AA{}, respectively.