Polarization of one-dimensional periodic systems in a static electric field: sawtooth potential treatment revisited

Various periodic piecewise linear potentials for extracting the electronic response of an infinite periodic system to a uniform electrostatic field are examined. It is shown that discontinuous potentials, such as the sawtooth, cannot be used for this purpose. Continuous triangular potentials can be successfully employed to determine both even- and odd-order (hyper)polarizabilities, as demonstrated here for the first time, although the permanent dipole moment of the corresponding long finite chain remains out of reach. Moreover, for typical highly polarizable organic systems, the size of the repeated unit has to be much larger than that of the finite system in order to obtain convergence with respect to system size. All results are illustrated both through extensive model calculations and through ab initio calculations on poly- and oligoacetylenes.