RESUMO
In an attempt to quantify electron delocalization in polyacenes with up to 50 carbon atoms, we have performed self-consistent field calculations in which the π electrons are constrained to occupy highly localized molecular orbitals (HILOs) centered on a maximum of two, six or ten adjacent carbon atoms. We have also performed similar calculations on simple polyacene analogs consisting only of hydrogen atoms and exhibiting electron delocalization in the σ framework. We find that the energetic cost of localizing the π electrons in the polyacenes is roughly 60, 5 or 0.1 kJ/mol per ring atom for the two-, six- and ten-atom HILOs, respectively, and the use of these localized models overestimates the predicted hydrogenation energies of the acenes by roughly 50%, 4% and 0.1%, respectively. We conclude that the chemistry of polyacenes can be modeled well using highly localized descriptions of the π electrons.
RESUMO
A local optimization algorithm for solving the Kohn-Sham equations is presented. It is based on a direct minimization of the energy functional under the equality constraints representing the Grassmann Manifold. The algorithm does not require an eigendecomposition, which may be advantageous in large-scale computations. It is optimized to reduce the number of Kohn-Sham matrix evaluations to one per iteration to be competitive with standard self-consistent field (SCF) approach accelerated by direct inversion of the iterative subspace (DIIS). Numerical experiments include a comparison of the algorithm with DIIS. A high reliability of the algorithm is observed in configurations where SCF iterations fail to converge or find a wrong solution corresponding to a stationary point different from the global minimum. The local optimization algorithm itself does not guarantee that the found minimum is global. However, a randomization of the initial approximation shows a convergence to the right minimum in the vast majority of cases.